%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN393^4.004 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:41:43 AM UTC 2026
% Result : Theorem 48.35s 8.41s
% Output : Refutation 48.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN393^4.004 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n016.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 16:21:04 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.27 Running higher-order theorem proving
% 0.24/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.63/0.45 % (546654)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.63/0.45 % (546665)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.63/0.45 % (546665)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.63/0.45 % (546665)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1785768261:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.63/0.45 % (546659)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2334865673:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.63/0.45 % (546663)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3499480913:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.63/0.45 % (546662)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2034715283:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.63/0.45 % (546664)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2532495877:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.63/0.45 % (546661)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3394831983:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.63/0.45 % (546660)lrs+10_16_si=on:nwc=1.5:random_seed=1401723887:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.63/0.45 % (546661)Instruction limit reached!
% 0.63/0.45 % (546661)------------------------------
% 0.63/0.45 % (546661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.45 % (546661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.45 % (546661)CaDiCaL version: 2.1.3
% 0.63/0.45 % (546661)Termination reason: Instruction limit
% 0.63/0.45 % (546661)Termination phase: Function definition elimination
% 0.63/0.45 % (546661)Time elapsed: 0.003 s
% 0.63/0.45 % (546661)Peak memory usage: 10 MB
% 0.63/0.45 % (546661)Instructions burned: 3 (million)
% 0.63/0.45 % (546660)Instruction limit reached!
% 0.63/0.45 % (546660)------------------------------
% 0.63/0.45 % (546660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.45 % (546660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.45 % (546660)CaDiCaL version: 2.1.3
% 0.63/0.45 % (546660)Termination reason: Instruction limit
% 0.63/0.45 % (546660)Termination phase: Saturation
% 0.63/0.45 % (546660)Time elapsed: 0.015 s
% 0.63/0.45 % (546660)Peak memory usage: 11 MB
% 0.63/0.45 % (546660)Instructions burned: 19 (million)
% 0.63/0.45 % (546663)Instruction limit reached!
% 0.63/0.45 % (546663)------------------------------
% 0.63/0.45 % (546663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.45 % (546663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.45 % (546663)CaDiCaL version: 2.1.3
% 0.63/0.45 % (546663)Termination reason: Instruction limit
% 0.63/0.45 % (546663)Termination phase: Saturation
% 0.63/0.45 % (546663)Time elapsed: 0.024 s
% 0.63/0.45 % (546663)Peak memory usage: 11 MB
% 0.63/0.45 % (546663)Instructions burned: 24 (million)
% 0.63/0.45 % (546673)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=246380099:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.63/0.45 % (546673)Instruction limit reached!
% 0.63/0.45 % (546673)------------------------------
% 0.63/0.45 % (546673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.45 % (546673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.45 % (546673)CaDiCaL version: 2.1.3
% 0.63/0.45 % (546673)Termination reason: Instruction limit
% 0.63/0.45 % (546673)Termination phase: Property scanning
% 0.63/0.45 % (546673)Time elapsed: 0.002 s
% 0.63/0.45 % (546673)Peak memory usage: 10 MB
% 0.63/0.45 % (546673)Instructions burned: 2 (million)
% 0.63/0.45 % (546665)Instruction limit reached!
% 0.63/0.45 % (546665)------------------------------
% 0.63/0.45 % (546665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.51 % (546665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.51 % (546665)CaDiCaL version: 2.1.3
% 1.44/0.51 % (546665)Termination reason: Instruction limit
% 1.44/0.51 % (546665)Termination phase: Saturation
% 1.44/0.51 % (546665)Time elapsed: 0.064 s
% 1.44/0.51 % (546665)Peak memory usage: 13 MB
% 1.44/0.51 % (546665)Instructions burned: 158 (million)
% 1.44/0.51 % (546675)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.44/0.51 % (546674)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2252826811:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.44/0.51 % (546664)Instruction limit reached!
% 1.44/0.51 % (546664)------------------------------
% 1.44/0.51 % (546664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.51 % (546664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.51 % (546664)CaDiCaL version: 2.1.3
% 1.44/0.51 % (546664)Termination reason: Instruction limit
% 1.44/0.51 % (546664)Termination phase: Saturation
% 1.44/0.51 % (546664)Time elapsed: 0.056 s
% 1.44/0.51 % (546664)Peak memory usage: 12 MB
% 1.44/0.51 % (546664)Instructions burned: 75 (million)
% 1.44/0.51 % (546675)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4236810915:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.44/0.51 % (546674)Instruction limit reached!
% 1.44/0.51 % (546674)------------------------------
% 1.44/0.51 % (546674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.51 % (546674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.51 % (546674)CaDiCaL version: 2.1.3
% 1.44/0.51 % (546674)Termination reason: Instruction limit
% 1.44/0.51 % (546674)Termination phase: Property scanning
% 1.44/0.51 % (546674)Time elapsed: 0.005 s
% 1.44/0.51 % (546674)Peak memory usage: 10 MB
% 1.44/0.51 % (546674)Instructions burned: 5 (million)
% 1.44/0.51 % (546675)Instruction limit reached!
% 1.44/0.51 % (546675)------------------------------
% 1.44/0.51 % (546675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.51 % (546675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.51 % (546675)CaDiCaL version: 2.1.3
% 1.44/0.51 % (546675)Termination reason: Instruction limit
% 1.44/0.51 % (546675)Termination phase: Saturation
% 1.44/0.51 % (546675)Time elapsed: 0.006 s
% 1.44/0.51 % (546675)Peak memory usage: 11 MB
% 1.44/0.51 % (546675)Instructions burned: 7 (million)
% 1.44/0.51 % (546659)Instruction limit reached!
% 1.44/0.51 % (546659)------------------------------
% 1.44/0.51 % (546659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.51 % (546659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.51 % (546659)CaDiCaL version: 2.1.3
% 1.44/0.51 % (546659)Termination reason: Instruction limit
% 1.44/0.51 % (546659)Termination phase: Saturation
% 1.44/0.51 % (546659)Time elapsed: 0.065 s
% 1.44/0.51 % (546659)Peak memory usage: 12 MB
% 1.44/0.51 % (546659)Instructions burned: 87 (million)
% 1.44/0.51 % (546677)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4178449664:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.44/0.51 % (546678)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.44/0.51 % (546678)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.44/0.51 % (546678)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3898534319:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.44/0.51 % (546677)Instruction limit reached!
% 1.44/0.51 % (546677)------------------------------
% 1.44/0.51 % (546677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.51 % (546677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.51 % (546677)CaDiCaL version: 2.1.3
% 1.44/0.51 % (546677)Termination reason: Instruction limit
% 1.44/0.51 % (546677)Termination phase: Saturation
% 1.44/0.51 % (546677)Time elapsed: 0.006 s
% 1.44/0.51 % (546677)Peak memory usage: 12 MB
% 1.44/0.56 % (546677)Instructions burned: 13 (million)
% 1.44/0.56 % (546678)Instruction limit reached!
% 1.44/0.56 % (546678)------------------------------
% 1.44/0.56 % (546678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.56 % (546678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.56 % (546678)CaDiCaL version: 2.1.3
% 1.44/0.56 % (546678)Termination reason: Instruction limit
% 1.44/0.56 % (546678)Termination phase: Saturation
% 1.44/0.56 % (546678)Time elapsed: 0.011 s
% 1.44/0.56 % (546678)Peak memory usage: 11 MB
% 1.44/0.56 % (546678)Instructions burned: 30 (million)
% 1.44/0.56 % (546682)lrs+10_1_si=on:cs=on:random_seed=658059584:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.44/0.56 % (546681)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3110497593:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.44/0.56 % (546683)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.44/0.56 % (546687)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3611472967:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.44/0.56 % (546683)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3565311189:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.44/0.56 % (546684)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1663700748:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.44/0.56 % (546682)Instruction limit reached!
% 1.44/0.56 % (546682)------------------------------
% 1.44/0.56 % (546682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.56 % (546682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.56 % (546682)CaDiCaL version: 2.1.3
% 1.44/0.56 % (546682)Termination reason: Instruction limit
% 1.44/0.56 % (546682)Termination phase: Saturation
% 1.44/0.56 % (546682)Time elapsed: 0.008 s
% 1.44/0.56 % (546682)Peak memory usage: 11 MB
% 1.44/0.56 % (546682)Instructions burned: 9 (million)
% 1.44/0.56 % (546688)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2689917382:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.44/0.56 % (546687)Refutation not found, incomplete strategy
% 1.44/0.56 % (546687)------------------------------
% 1.44/0.56 % (546687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.56 % (546687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.56 % (546687)CaDiCaL version: 2.1.3
% 1.44/0.56 % (546687)Termination reason: Refutation not found, incomplete strategy
% 1.44/0.56 % (546687)Time elapsed: 0.004 s
% 1.44/0.56 % (546687)Peak memory usage: 12 MB
% 1.44/0.56 % (546687)Instructions burned: 6 (million)
% 1.44/0.56 % (546683)Instruction limit reached!
% 1.44/0.56 % (546683)------------------------------
% 1.44/0.56 % (546683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.56 % (546683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.56 % (546683)CaDiCaL version: 2.1.3
% 1.44/0.56 % (546683)Termination reason: Instruction limit
% 1.44/0.56 % (546683)Termination phase: Property scanning
% 1.44/0.56 % (546683)Time elapsed: 0.002 s
% 1.44/0.56 % (546683)Peak memory usage: 10 MB
% 1.44/0.56 % (546683)Instructions burned: 2 (million)
% 1.44/0.56 % (546687)------------------------------
% 1.44/0.56 % (546687)------------------------------
% 1.44/0.56 % (546684)Refutation not found, incomplete strategy
% 1.44/0.56 % (546684)------------------------------
% 1.44/0.56 % (546684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.56 % (546684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.56 % (546684)CaDiCaL version: 2.1.3
% 1.44/0.56 % (546684)Termination reason: Refutation not found, incomplete strategy
% 1.44/0.56 % (546684)Time elapsed: 0.004 s
% 1.44/0.56 % (546684)Peak memory usage: 12 MB
% 1.44/0.56 % (546684)Instructions burned: 3 (million)
% 1.44/0.56 % (546684)------------------------------
% 1.44/0.56 % (546684)------------------------------
% 1.44/0.56 % (546688)Instruction limit reached!
% 1.44/0.56 % (546688)------------------------------
% 2.09/0.62 % (546688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.62 % (546688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.62 % (546688)CaDiCaL version: 2.1.3
% 2.09/0.62 % (546688)Termination reason: Instruction limit
% 2.09/0.62 % (546688)Termination phase: Saturation
% 2.09/0.62 % (546688)Time elapsed: 0.013 s
% 2.09/0.62 % (546688)Peak memory usage: 12 MB
% 2.09/0.62 % (546688)Instructions burned: 26 (million)
% 2.09/0.62 % (546695)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=919839251:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.09/0.62 % (546696)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1780706117:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.09/0.62 % (546697)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=4138375865:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.09/0.62 % (546698)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3254404287:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 2.09/0.62 % (546698)Instruction limit reached!
% 2.09/0.62 % (546698)------------------------------
% 2.09/0.62 % (546698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.62 % (546698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.62 % (546698)CaDiCaL version: 2.1.3
% 2.09/0.62 % (546698)Termination reason: Instruction limit
% 2.09/0.62 % (546698)Termination phase: SInE selection
% 2.09/0.62 % (546698)Time elapsed: 0.002 s
% 2.09/0.62 % (546698)Peak memory usage: 10 MB
% 2.09/0.62 % (546698)Instructions burned: 2 (million)
% 2.09/0.62 % (546699)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1792476814:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 2.09/0.62 % (546695)Instruction limit reached!
% 2.09/0.62 % (546695)------------------------------
% 2.09/0.62 % (546695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.62 % (546695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.62 % (546695)CaDiCaL version: 2.1.3
% 2.09/0.62 % (546695)Termination reason: Instruction limit
% 2.09/0.62 % (546695)Termination phase: Saturation
% 2.09/0.62 % (546695)Time elapsed: 0.011 s
% 2.09/0.62 % (546695)Peak memory usage: 11 MB
% 2.09/0.62 % (546695)Instructions burned: 14 (million)
% 2.09/0.62 % (546697)Instruction limit reached!
% 2.09/0.62 % (546697)------------------------------
% 2.09/0.62 % (546697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.62 % (546697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.62 % (546697)CaDiCaL version: 2.1.3
% 2.09/0.62 % (546697)Termination reason: Instruction limit
% 2.09/0.62 % (546697)Termination phase: Saturation
% 2.09/0.62 % (546697)Time elapsed: 0.011 s
% 2.09/0.62 % (546697)Peak memory usage: 12 MB
% 2.09/0.62 % (546697)Instructions burned: 15 (million)
% 2.09/0.62 % (546699)Instruction limit reached!
% 2.09/0.62 % (546699)------------------------------
% 2.09/0.62 % (546699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.62 % (546699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.62 % (546699)CaDiCaL version: 2.1.3
% 2.09/0.62 % (546699)Termination reason: Instruction limit
% 2.09/0.62 % (546699)Termination phase: Saturation
% 2.09/0.62 % (546699)Time elapsed: 0.010 s
% 2.09/0.62 % (546699)Peak memory usage: 11 MB
% 2.09/0.62 % (546699)Instructions burned: 26 (million)
% 2.09/0.62 % (546681)Instruction limit reached!
% 2.09/0.62 % (546681)------------------------------
% 2.09/0.62 % (546681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.62 % (546681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.62 % (546681)CaDiCaL version: 2.1.3
% 2.09/0.62 % (546681)Termination reason: Instruction limit
% 2.09/0.62 % (546681)Termination phase: Saturation
% 2.09/0.62 % (546681)Time elapsed: 0.063 s
% 2.09/0.62 % (546681)Peak memory usage: 13 MB
% 2.09/0.62 % (546681)Instructions burned: 86 (million)
% 2.09/0.62 % (546708)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.09/0.62 % (546708)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=2249958147:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.32/0.69 % (546707)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.32/0.69 % (546707)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.32/0.69 % (546705)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2475479564:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.32/0.69 % (546706)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3968659173:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.32/0.69 % (546708)Instruction limit reached!
% 2.32/0.69 % (546708)------------------------------
% 2.32/0.69 % (546708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.69 % (546708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.69 % (546708)CaDiCaL version: 2.1.3
% 2.32/0.69 % (546708)Termination reason: Instruction limit
% 2.32/0.69 % (546708)Termination phase: Saturation
% 2.32/0.69 % (546708)Time elapsed: 0.004 s
% 2.32/0.69 % (546708)Peak memory usage: 11 MB
% 2.32/0.69 % (546708)Instructions burned: 9 (million)
% 2.32/0.69 % (546707)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=554336576:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.32/0.69 % (546709)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1789605225:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.32/0.69 % (546707)Instruction limit reached!
% 2.32/0.69 % (546707)------------------------------
% 2.32/0.69 % (546707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.69 % (546707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.69 % (546707)CaDiCaL version: 2.1.3
% 2.32/0.69 % (546707)Termination reason: Instruction limit
% 2.32/0.69 % (546707)Termination phase: Saturation
% 2.32/0.69 % (546707)Time elapsed: 0.011 s
% 2.32/0.69 % (546707)Peak memory usage: 11 MB
% 2.32/0.69 % (546707)Instructions burned: 15 (million)
% 2.32/0.69 % (546705)Instruction limit reached!
% 2.32/0.69 % (546705)------------------------------
% 2.32/0.69 % (546705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.69 % (546705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.69 % (546705)CaDiCaL version: 2.1.3
% 2.32/0.69 % (546705)Termination reason: Instruction limit
% 2.32/0.69 % (546705)Termination phase: Saturation
% 2.32/0.69 % (546705)Time elapsed: 0.017 s
% 2.32/0.69 % (546705)Peak memory usage: 11 MB
% 2.32/0.69 % (546705)Instructions burned: 23 (million)
% 2.32/0.69 % (546713)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1878595953:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.32/0.69 % (546713)Instruction limit reached!
% 2.32/0.69 % (546713)------------------------------
% 2.32/0.69 % (546713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.69 % (546713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.69 % (546713)CaDiCaL version: 2.1.3
% 2.32/0.69 % (546713)Termination reason: Instruction limit
% 2.32/0.69 % (546713)Termination phase: Saturation
% 2.32/0.69 % (546713)Time elapsed: 0.004 s
% 2.32/0.69 % (546713)Peak memory usage: 12 MB
% 2.32/0.69 % (546713)Instructions burned: 9 (million)
% 2.32/0.69 % (546716)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1242490682:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.32/0.69 % (546709)Instruction limit reached!
% 2.32/0.69 % (546709)------------------------------
% 2.32/0.69 % (546709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.69 % (546709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.69 % (546709)CaDiCaL version: 2.1.3
% 2.32/0.69 % (546709)Termination reason: Instruction limit
% 2.32/0.69 % (546709)Termination phase: Saturation
% 2.73/0.76 % (546709)Time elapsed: 0.029 s
% 2.73/0.76 % (546709)Peak memory usage: 12 MB
% 2.73/0.76 % (546709)Instructions burned: 31 (million)
% 2.73/0.76 % (546716)Instruction limit reached!
% 2.73/0.76 % (546716)------------------------------
% 2.73/0.76 % (546716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.73/0.76 % (546716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/0.76 % (546716)CaDiCaL version: 2.1.3
% 2.73/0.76 % (546716)Termination reason: Instruction limit
% 2.73/0.76 % (546716)Termination phase: Saturation
% 2.73/0.76 % (546716)Time elapsed: 0.011 s
% 2.73/0.76 % (546716)Peak memory usage: 12 MB
% 2.73/0.76 % (546716)Instructions burned: 28 (million)
% 2.73/0.76 % (546717)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1759783120:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.73/0.76 % (546719)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=444908528:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.73/0.76 % (546706)Instruction limit reached!
% 2.73/0.76 % (546706)------------------------------
% 2.73/0.76 % (546706)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.73/0.76 % (546706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/0.76 % (546706)CaDiCaL version: 2.1.3
% 2.73/0.76 % (546706)Termination reason: Instruction limit
% 2.73/0.76 % (546706)Termination phase: Saturation
% 2.73/0.76 % (546706)Time elapsed: 0.056 s
% 2.73/0.76 % (546706)Peak memory usage: 12 MB
% 2.73/0.76 % (546706)Instructions burned: 60 (million)
% 2.73/0.76 % (546722)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=816833111:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.73/0.76 % (546722)Refutation not found, incomplete strategy
% 2.73/0.76 % (546722)------------------------------
% 2.73/0.76 % (546722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.73/0.76 % (546722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/0.76 % (546722)CaDiCaL version: 2.1.3
% 2.73/0.76 % (546722)Termination reason: Refutation not found, incomplete strategy
% 2.73/0.76 % (546722)Time elapsed: 0.005 s
% 2.73/0.76 % (546722)Peak memory usage: 13 MB
% 2.73/0.76 % (546722)Instructions burned: 8 (million)
% 2.73/0.76 % (546717)Instruction limit reached!
% 2.73/0.76 % (546717)------------------------------
% 2.73/0.76 % (546717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.73/0.76 % (546717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/0.76 % (546717)CaDiCaL version: 2.1.3
% 2.73/0.76 % (546717)Termination reason: Instruction limit
% 2.73/0.76 % (546717)Termination phase: Saturation
% 2.73/0.76 % (546717)Time elapsed: 0.020 s
% 2.73/0.76 % (546717)Peak memory usage: 12 MB
% 2.73/0.76 % (546717)Instructions burned: 20 (million)
% 2.73/0.76 % (546722)------------------------------
% 2.73/0.76 % (546722)------------------------------
% 2.73/0.76 % (546721)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=767739582:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.73/0.76 % (546728)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1061480582:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.73/0.76 % (546728)Refutation not found, incomplete strategy
% 2.73/0.76 % (546728)------------------------------
% 2.73/0.76 % (546728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.73/0.76 % (546728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/0.76 % (546728)CaDiCaL version: 2.1.3
% 2.73/0.76 % (546728)Termination reason: Refutation not found, incomplete strategy
% 2.73/0.76 % (546728)Time elapsed: 0.002 s
% 2.73/0.76 % (546728)Peak memory usage: 12 MB
% 2.73/0.76 % (546728)Instructions burned: 3 (million)
% 2.73/0.76 % (546728)------------------------------
% 2.73/0.76 % (546728)------------------------------
% 2.73/0.76 % (546725)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1318406079:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.73/0.76 % (546727)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.73/0.76 % (546727)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3371166705:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 3.22/0.89 % (546727)Instruction limit reached!
% 3.22/0.89 % (546727)------------------------------
% 3.22/0.89 % (546727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.22/0.89 % (546727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/0.89 % (546727)CaDiCaL version: 2.1.3
% 3.22/0.89 % (546727)Termination reason: Instruction limit
% 3.22/0.89 % (546727)Termination phase: Saturation
% 3.22/0.89 % (546727)Time elapsed: 0.006 s
% 3.22/0.89 % (546727)Peak memory usage: 11 MB
% 3.22/0.89 % (546727)Instructions burned: 8 (million)
% 3.22/0.89 % (546731)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3914684216:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 3.22/0.89 % (546725)Instruction limit reached!
% 3.22/0.89 % (546725)------------------------------
% 3.22/0.89 % (546725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.22/0.89 % (546725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/0.89 % (546725)CaDiCaL version: 2.1.3
% 3.22/0.89 % (546725)Termination reason: Instruction limit
% 3.22/0.89 % (546725)Termination phase: Saturation
% 3.22/0.89 % (546725)Time elapsed: 0.032 s
% 3.22/0.89 % (546725)Peak memory usage: 11 MB
% 3.22/0.89 % (546725)Instructions burned: 42 (million)
% 3.22/0.89 % (546734)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 3.22/0.89 % (546734)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=118650627:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 3.22/0.89 % (546731)Refutation not found, incomplete strategy
% 3.22/0.89 % (546731)------------------------------
% 3.22/0.89 % (546731)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.22/0.89 % (546731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/0.89 % (546731)CaDiCaL version: 2.1.3
% 3.22/0.89 % (546731)Termination reason: Refutation not found, incomplete strategy
% 3.22/0.89 % (546731)Time elapsed: 0.018 s
% 3.22/0.89 % (546731)Peak memory usage: 13 MB
% 3.22/0.89 % (546731)Instructions burned: 28 (million)
% 3.22/0.89 % (546731)------------------------------
% 3.22/0.89 % (546731)------------------------------
% 3.22/0.89 % (546734)Instruction limit reached!
% 3.22/0.89 % (546734)------------------------------
% 3.22/0.89 % (546734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.22/0.89 % (546734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/0.89 % (546734)CaDiCaL version: 2.1.3
% 3.22/0.89 % (546734)Termination reason: Instruction limit
% 3.22/0.89 % (546734)Termination phase: Property scanning
% 3.22/0.89 % (546734)Time elapsed: 0.005 s
% 3.22/0.89 % (546734)Peak memory usage: 10 MB
% 3.22/0.89 % (546734)Instructions burned: 6 (million)
% 3.22/0.89 % (546736)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1655987142:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 3.22/0.89 % (546738)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=966644267:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 3.22/0.89 % (546738)Instruction limit reached!
% 3.22/0.89 % (546738)------------------------------
% 3.22/0.89 % (546738)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.22/0.89 % (546738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/0.89 % (546738)CaDiCaL version: 2.1.3
% 3.22/0.89 % (546738)Termination reason: Instruction limit
% 3.22/0.89 % (546738)Termination phase: Saturation
% 3.22/0.89 % (546738)Time elapsed: 0.009 s
% 3.22/0.89 % (546738)Peak memory usage: 12 MB
% 3.22/0.89 % (546738)Instructions burned: 20 (million)
% 3.22/0.89 % (546736)Instruction limit reached!
% 3.22/0.89 % (546736)------------------------------
% 3.22/0.89 % (546736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.22/0.89 % (546736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/0.89 % (546736)CaDiCaL version: 2.1.3
% 3.22/0.89 % (546736)Termination reason: Instruction limit
% 3.22/0.89 % (546736)Termination phase: Saturation
% 3.22/0.89 % (546736)Time elapsed: 0.017 s
% 3.58/0.97 % (546736)Peak memory usage: 11 MB
% 3.58/0.97 % (546736)Instructions burned: 22 (million)
% 3.58/0.97 % (546739)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=4015564456:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 3.58/0.97 % (546721)Instruction limit reached!
% 3.58/0.97 % (546721)------------------------------
% 3.58/0.97 % (546721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.97 % (546721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/0.97 % (546721)CaDiCaL version: 2.1.3
% 3.58/0.97 % (546721)Termination reason: Instruction limit
% 3.58/0.97 % (546721)Termination phase: Saturation
% 3.58/0.97 % (546721)Time elapsed: 0.114 s
% 3.58/0.97 % (546721)Peak memory usage: 13 MB
% 3.58/0.97 % (546721)Instructions burned: 144 (million)
% 3.58/0.97 % (546742)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=1661775792:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 3.58/0.97 % (546662)Instruction limit reached!
% 3.58/0.97 % (546662)------------------------------
% 3.58/0.97 % (546662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.97 % (546662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/0.97 % (546662)CaDiCaL version: 2.1.3
% 3.58/0.97 % (546662)Termination reason: Instruction limit
% 3.58/0.97 % (546662)Termination phase: Saturation
% 3.58/0.97 % (546662)Time elapsed: 0.372 s
% 3.58/0.97 % (546662)Peak memory usage: 13 MB
% 3.58/0.97 % (546662)Instructions burned: 634 (million)
% 3.58/0.97 % (546744)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3074686743:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 3.58/0.97 % (546696)Instruction limit reached!
% 3.58/0.97 % (546696)------------------------------
% 3.58/0.97 % (546696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.97 % (546696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/0.97 % (546696)CaDiCaL version: 2.1.3
% 3.58/0.97 % (546696)Termination reason: Instruction limit
% 3.58/0.97 % (546696)Termination phase: Saturation
% 3.58/0.97 % (546696)Time elapsed: 0.259 s
% 3.58/0.97 % (546696)Peak memory usage: 15 MB
% 3.58/0.97 % (546696)Instructions burned: 328 (million)
% 3.58/0.97 % (546747)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=2352695187:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2995 on theBenchmark for (2995ds/21Mi)
% 3.58/0.97 % (546745)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=644697575:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.58/0.97 % (546745)Refutation not found, incomplete strategy
% 3.58/0.97 % (546745)------------------------------
% 3.58/0.97 % (546745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.97 % (546745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/0.97 % (546745)CaDiCaL version: 2.1.3
% 3.58/0.97 % (546745)Termination reason: Refutation not found, incomplete strategy
% 3.58/0.97 % (546745)Time elapsed: 0.005 s
% 3.58/0.97 % (546745)Peak memory usage: 12 MB
% 3.58/0.97 % (546745)Instructions burned: 5 (million)
% 3.58/0.97 % (546745)------------------------------
% 3.58/0.97 % (546745)------------------------------
% 3.58/0.97 % (546747)Instruction limit reached!
% 3.58/0.97 % (546747)------------------------------
% 3.58/0.97 % (546747)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.97 % (546747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/0.97 % (546747)CaDiCaL version: 2.1.3
% 3.58/0.97 % (546747)Termination reason: Instruction limit
% 3.58/0.97 % (546747)Termination phase: Saturation
% 3.58/0.97 % (546747)Time elapsed: 0.010 s
% 3.58/0.97 % (546747)Peak memory usage: 11 MB
% 3.58/0.97 % (546747)Instructions burned: 21 (million)
% 3.58/0.97 % (546744)Instruction limit reached!
% 3.58/0.97 % (546744)------------------------------
% 3.58/0.97 % (546744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.97 % (546744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.07 % (546744)CaDiCaL version: 2.1.3
% 5.27/1.07 % (546744)Termination reason: Instruction limit
% 5.27/1.07 % (546744)Termination phase: Saturation
% 5.27/1.07 % (546744)Time elapsed: 0.033 s
% 5.27/1.07 % (546744)Peak memory usage: 11 MB
% 5.27/1.07 % (546744)Instructions burned: 46 (million)
% 5.27/1.07 % (546749)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 5.27/1.07 % (546752)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=677272382:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 5.27/1.07 % (546749)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=865380147:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/200Mi)
% 5.27/1.07 % (546752)Instruction limit reached!
% 5.27/1.07 % (546752)------------------------------
% 5.27/1.07 % (546752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.07 % (546752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.07 % (546752)CaDiCaL version: 2.1.3
% 5.27/1.07 % (546752)Termination reason: Instruction limit
% 5.27/1.07 % (546752)Termination phase: Saturation
% 5.27/1.07 % (546752)Time elapsed: 0.009 s
% 5.27/1.07 % (546752)Peak memory usage: 12 MB
% 5.27/1.07 % (546752)Instructions burned: 14 (million)
% 5.27/1.07 % (546753)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=2277244066:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 5.27/1.07 % (546754)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=105934208:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 5.27/1.07 % (546757)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3562493104:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 5.27/1.07 % (546757)Instruction limit reached!
% 5.27/1.07 % (546757)------------------------------
% 5.27/1.07 % (546757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.07 % (546757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.07 % (546757)CaDiCaL version: 2.1.3
% 5.27/1.07 % (546757)Termination reason: Instruction limit
% 5.27/1.07 % (546757)Termination phase: Saturation
% 5.27/1.07 % (546757)Time elapsed: 0.016 s
% 5.27/1.07 % (546757)Peak memory usage: 11 MB
% 5.27/1.07 % (546757)Instructions burned: 33 (million)
% 5.27/1.07 % (546753)Instruction limit reached!
% 5.27/1.07 % (546753)------------------------------
% 5.27/1.07 % (546753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.07 % (546753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.07 % (546753)CaDiCaL version: 2.1.3
% 5.27/1.07 % (546753)Termination reason: Instruction limit
% 5.27/1.07 % (546753)Termination phase: Saturation
% 5.27/1.07 % (546753)Time elapsed: 0.049 s
% 5.27/1.07 % (546753)Peak memory usage: 12 MB
% 5.27/1.07 % (546753)Instructions burned: 67 (million)
% 5.27/1.07 % (546754)Instruction limit reached!
% 5.27/1.07 % (546754)------------------------------
% 5.27/1.07 % (546754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.07 % (546754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.07 % (546754)CaDiCaL version: 2.1.3
% 5.27/1.07 % (546754)Termination reason: Instruction limit
% 5.27/1.07 % (546754)Termination phase: Saturation
% 5.27/1.07 % (546754)Time elapsed: 0.036 s
% 5.27/1.07 % (546754)Peak memory usage: 11 MB
% 5.27/1.07 % (546754)Instructions burned: 51 (million)
% 5.27/1.07 % (546761)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=3869210043:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2994 on theBenchmark for (2994ds/137Mi)
% 5.27/1.07 % (546763)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3714458256:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2994 on theBenchmark for (2994ds/67Mi)
% 5.27/1.07 % (546762)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=3015464847:cond=on:i=34:hud=10:nm=10:rtra=on_2994 on theBenchmark for (2994ds/34Mi)
% 5.27/1.07 % (546762)Instruction limit reached!
% 5.27/1.07 % (546762)------------------------------
% 5.27/1.07 % (546762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.05/1.20 % (546762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.20 % (546762)CaDiCaL version: 2.1.3
% 6.05/1.20 % (546762)Termination reason: Instruction limit
% 6.05/1.20 % (546762)Termination phase: Saturation
% 6.05/1.20 % (546762)Time elapsed: 0.028 s
% 6.05/1.20 % (546762)Peak memory usage: 11 MB
% 6.05/1.20 % (546762)Instructions burned: 34 (million)
% 6.05/1.20 % (546763)Instruction limit reached!
% 6.05/1.20 % (546763)------------------------------
% 6.05/1.20 % (546763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.05/1.20 % (546763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.20 % (546763)CaDiCaL version: 2.1.3
% 6.05/1.20 % (546763)Termination reason: Instruction limit
% 6.05/1.20 % (546763)Termination phase: Saturation
% 6.05/1.20 % (546763)Time elapsed: 0.049 s
% 6.05/1.20 % (546763)Peak memory usage: 11 MB
% 6.05/1.20 % (546763)Instructions burned: 67 (million)
% 6.05/1.20 % (546767)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 6.05/1.20 % (546749)Instruction limit reached!
% 6.05/1.20 % (546749)------------------------------
% 6.05/1.20 % (546749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.05/1.20 % (546761)Instruction limit reached!
% 6.05/1.20 % (546761)------------------------------
% 6.05/1.20 % (546761)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.05/1.20 % (546761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.20 % (546749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.20 % (546749)CaDiCaL version: 2.1.3
% 6.05/1.20 % (546761)CaDiCaL version: 2.1.3
% 6.05/1.20 % (546749)Termination reason: Instruction limit
% 6.05/1.20 % (546749)Termination phase: Saturation
% 6.05/1.20 % (546761)Termination reason: Instruction limit
% 6.05/1.20 % (546761)Termination phase: Saturation
% 6.05/1.20 % (546749)Time elapsed: 0.159 s
% 6.05/1.20 % (546761)Time elapsed: 0.091 s
% 6.05/1.20 % (546749)Peak memory usage: 13 MB
% 6.05/1.20 % (546761)Peak memory usage: 12 MB
% 6.05/1.20 % (546761)Instructions burned: 138 (million)
% 6.05/1.20 % (546749)Instructions burned: 201 (million)
% 6.05/1.20 % (546767)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3765747270:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2994 on theBenchmark for (2994ds/180Mi)
% 6.05/1.20 % (546768)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=2343416062:st=2:i=246:sd=3:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/246Mi)
% 6.05/1.20 % (546739)Instruction limit reached!
% 6.05/1.20 % (546739)------------------------------
% 6.05/1.20 % (546739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.05/1.20 % (546739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.20 % (546739)CaDiCaL version: 2.1.3
% 6.05/1.20 % (546739)Termination reason: Instruction limit
% 6.05/1.20 % (546739)Termination phase: Saturation
% 6.05/1.20 % (546739)Time elapsed: 0.245 s
% 6.05/1.20 % (546739)Peak memory usage: 15 MB
% 6.05/1.20 % (546739)Instructions burned: 317 (million)
% 6.05/1.20 % (546768)Refutation not found, incomplete strategy
% 6.05/1.20 % (546768)------------------------------
% 6.05/1.20 % (546768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.05/1.20 % (546768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.20 % (546768)CaDiCaL version: 2.1.3
% 6.05/1.20 % (546768)Termination reason: Refutation not found, incomplete strategy
% 6.05/1.20 % (546768)Time elapsed: 0.011 s
% 6.05/1.20 % (546768)Peak memory usage: 13 MB
% 6.05/1.20 % (546768)Instructions burned: 21 (million)
% 6.05/1.20 % (546768)------------------------------
% 6.05/1.20 % (546768)------------------------------
% 6.05/1.20 % (546769)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=1228732866:cond=on:i=96:bd=all:rtra=on_2993 on theBenchmark for (2993ds/96Mi)
% 6.05/1.20 % (546770)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=3153060890:i=427:sd=1:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/427Mi)
% 6.05/1.20 % (546774)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=3239377026:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/515Mi)
% 6.05/1.20 % (546770)Refutation not found, incomplete strategy
% 6.05/1.20 % (546770)------------------------------
% 6.05/1.20 % (546770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.67/1.47 % (546770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.47 % (546770)CaDiCaL version: 2.1.3
% 6.67/1.47 % (546770)Termination reason: Refutation not found, incomplete strategy
% 6.67/1.47 % (546770)Time elapsed: 0.004 s
% 6.67/1.47 % (546770)Peak memory usage: 12 MB
% 6.67/1.47 % (546770)Instructions burned: 3 (million)
% 6.67/1.47 % (546770)------------------------------
% 6.67/1.47 % (546770)------------------------------
% 6.67/1.47 % (546773)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3933880656:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/874Mi)
% 6.67/1.47 % (546774)Refutation not found, incomplete strategy
% 6.67/1.47 % (546774)------------------------------
% 6.67/1.47 % (546774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.67/1.47 % (546774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.47 % (546774)CaDiCaL version: 2.1.3
% 6.67/1.47 % (546774)Termination reason: Refutation not found, incomplete strategy
% 6.67/1.47 % (546774)Time elapsed: 0.019 s
% 6.67/1.47 % (546774)Peak memory usage: 13 MB
% 6.67/1.47 % (546774)Instructions burned: 38 (million)
% 6.67/1.47 % (546774)------------------------------
% 6.67/1.47 % (546774)------------------------------
% 6.67/1.47 % (546778)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=2929852224:st=1.5:i=130:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/130Mi)
% 6.67/1.47 % (546780)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3794681926:i=44:ep=R:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/44Mi)
% 6.67/1.47 % (546769)Instruction limit reached!
% 6.67/1.47 % (546769)------------------------------
% 6.67/1.47 % (546769)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.67/1.47 % (546769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.47 % (546769)CaDiCaL version: 2.1.3
% 6.67/1.47 % (546769)Termination reason: Instruction limit
% 6.67/1.47 % (546769)Termination phase: Saturation
% 6.67/1.47 % (546769)Time elapsed: 0.071 s
% 6.67/1.47 % (546769)Peak memory usage: 12 MB
% 6.67/1.47 % (546769)Instructions burned: 97 (million)
% 6.67/1.47 % (546780)Instruction limit reached!
% 6.67/1.47 % (546780)------------------------------
% 6.67/1.47 % (546780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.67/1.47 % (546780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.47 % (546780)CaDiCaL version: 2.1.3
% 6.67/1.47 % (546780)Termination reason: Instruction limit
% 6.67/1.47 % (546780)Termination phase: Saturation
% 6.67/1.47 % (546780)Time elapsed: 0.031 s
% 6.67/1.47 % (546780)Peak memory usage: 11 MB
% 6.67/1.47 % (546780)Instructions burned: 44 (million)
% 6.67/1.47 % (546778)Refutation not found, incomplete strategy
% 6.67/1.47 % (546778)------------------------------
% 6.67/1.47 % (546778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.67/1.47 % (546778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.47 % (546778)CaDiCaL version: 2.1.3
% 6.67/1.47 % (546778)Termination reason: Refutation not found, incomplete strategy
% 6.67/1.47 % (546778)Time elapsed: 0.060 s
% 6.67/1.47 % (546778)Peak memory usage: 14 MB
% 6.67/1.47 % (546778)Instructions burned: 79 (million)
% 6.67/1.47 % (546767)Instruction limit reached!
% 6.67/1.47 % (546767)------------------------------
% 6.67/1.47 % (546767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.67/1.47 % (546767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.47 % (546767)CaDiCaL version: 2.1.3
% 6.67/1.47 % (546767)Termination reason: Instruction limit
% 6.67/1.47 % (546767)Termination phase: Saturation
% 6.67/1.47 % (546767)Time elapsed: 0.135 s
% 6.67/1.47 % (546767)Peak memory usage: 13 MB
% 6.67/1.47 % (546767)Instructions burned: 181 (million)
% 6.67/1.47 % (546778)------------------------------
% 6.67/1.47 % (546778)------------------------------
% 6.67/1.47 % (546783)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=1424745555:s2a=on:i=571:nm=16:rtra=on_2992 on theBenchmark for (2992ds/571Mi)
% 6.67/1.47 % (546783)Refutation not found, incomplete strategy
% 6.67/1.47 % (546783)------------------------------
% 6.67/1.47 % (546783)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.67/1.47 % (546783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.65 % (546783)CaDiCaL version: 2.1.3
% 8.37/1.65 % (546783)Termination reason: Refutation not found, incomplete strategy
% 8.37/1.65 % (546783)Time elapsed: 0.006 s
% 8.37/1.65 % (546783)Peak memory usage: 12 MB
% 8.37/1.65 % (546783)Instructions burned: 5 (million)
% 8.37/1.65 % (546783)------------------------------
% 8.37/1.65 % (546783)------------------------------
% 8.37/1.65 % (546784)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=2072480890:i=450:rtra=on:ixr=off:ntd=on_2992 on theBenchmark for (2992ds/450Mi)
% 8.37/1.65 % (546742)Instruction limit reached!
% 8.37/1.65 % (546742)------------------------------
% 8.37/1.65 % (546742)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.37/1.65 % (546742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.65 % (546742)CaDiCaL version: 2.1.3
% 8.37/1.65 % (546742)Termination reason: Instruction limit
% 8.37/1.65 % (546742)Termination phase: Saturation
% 8.37/1.65 % (546742)Time elapsed: 0.371 s
% 8.37/1.65 % (546742)Peak memory usage: 15 MB
% 8.37/1.65 % (546742)Instructions burned: 853 (million)
% 8.37/1.65 % (546787)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=499129166:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2992 on theBenchmark for (2992ds/65Mi)
% 8.37/1.65 % (546789)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=2683514500:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2992 on theBenchmark for (2992ds/105Mi)
% 8.37/1.65 % (546786)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=2992989384:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2992 on theBenchmark for (2992ds/95Mi)
% 8.37/1.65 % (546790)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=2626676973:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2992 on theBenchmark for (2992ds/5755Mi)
% 8.37/1.65 % (546787)Instruction limit reached!
% 8.37/1.65 % (546787)------------------------------
% 8.37/1.65 % (546787)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.37/1.65 % (546787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.65 % (546787)CaDiCaL version: 2.1.3
% 8.37/1.65 % (546787)Termination reason: Instruction limit
% 8.37/1.65 % (546787)Termination phase: Saturation
% 8.37/1.65 % (546787)Time elapsed: 0.047 s
% 8.37/1.65 % (546787)Peak memory usage: 13 MB
% 8.37/1.65 % (546787)Instructions burned: 65 (million)
% 8.37/1.65 % (546789)Instruction limit reached!
% 8.37/1.65 % (546789)------------------------------
% 8.37/1.65 % (546789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.37/1.65 % (546789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.65 % (546789)CaDiCaL version: 2.1.3
% 8.37/1.65 % (546789)Termination reason: Instruction limit
% 8.37/1.65 % (546789)Termination phase: Saturation
% 8.37/1.65 % (546789)Time elapsed: 0.050 s
% 8.37/1.65 % (546789)Peak memory usage: 13 MB
% 8.37/1.65 % (546789)Instructions burned: 105 (million)
% 8.37/1.65 % (546795)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=2467237136:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/375Mi)
% 8.37/1.65 % (546786)Instruction limit reached!
% 8.37/1.65 % (546786)------------------------------
% 8.37/1.65 % (546786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.37/1.65 % (546786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.65 % (546786)CaDiCaL version: 2.1.3
% 8.37/1.65 % (546786)Termination reason: Instruction limit
% 8.37/1.65 % (546786)Termination phase: Saturation
% 8.37/1.65 % (546786)Time elapsed: 0.071 s
% 8.37/1.65 % (546786)Peak memory usage: 12 MB
% 8.37/1.65 % (546786)Instructions burned: 95 (million)
% 8.37/1.65 % (546796)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3395338828:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2991 on theBenchmark for (2991ds/495Mi)
% 8.37/1.65 % (546798)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=194524919:cond=on:i=34:hud=10:nm=10:rtra=on_2991 on theBenchmark for (2991ds/34Mi)
% 8.75/1.78 % (546798)Instruction limit reached!
% 8.75/1.78 % (546798)------------------------------
% 8.75/1.78 % (546798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.75/1.78 % (546798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/1.78 % (546798)CaDiCaL version: 2.1.3
% 8.75/1.78 % (546798)Termination reason: Instruction limit
% 8.75/1.78 % (546798)Termination phase: Saturation
% 8.75/1.78 % (546798)Time elapsed: 0.025 s
% 8.75/1.78 % (546798)Peak memory usage: 11 MB
% 8.75/1.78 % (546798)Instructions burned: 35 (million)
% 8.75/1.78 % (546802)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=3494475345:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2990 on theBenchmark for (2990ds/91Mi)
% 8.75/1.78 % (546802)Instruction limit reached!
% 8.75/1.78 % (546802)------------------------------
% 8.75/1.78 % (546802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.75/1.78 % (546802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/1.78 % (546802)CaDiCaL version: 2.1.3
% 8.75/1.78 % (546802)Termination reason: Instruction limit
% 8.75/1.78 % (546802)Termination phase: Saturation
% 8.75/1.78 % (546802)Time elapsed: 0.054 s
% 8.75/1.78 % (546802)Peak memory usage: 13 MB
% 8.75/1.78 % (546802)Instructions burned: 92 (million)
% 8.75/1.78 % (546807)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=3284906527:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2989 on theBenchmark for (2989ds/66Mi)
% 8.75/1.78 % (546807)Refutation not found, incomplete strategy
% 8.75/1.78 % (546807)------------------------------
% 8.75/1.78 % (546807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.75/1.78 % (546807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/1.78 % (546807)CaDiCaL version: 2.1.3
% 8.75/1.78 % (546807)Termination reason: Refutation not found, incomplete strategy
% 8.75/1.78 % (546807)Time elapsed: 0.002 s
% 8.75/1.78 % (546807)Peak memory usage: 12 MB
% 8.75/1.78 % (546807)Instructions burned: 3 (million)
% 8.75/1.78 % (546807)------------------------------
% 8.75/1.78 % (546807)------------------------------
% 8.75/1.78 % (546809)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1629898877:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2989 on theBenchmark for (2989ds/22Mi)
% 8.75/1.78 % (546809)Instruction limit reached!
% 8.75/1.78 % (546809)------------------------------
% 8.75/1.78 % (546809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.75/1.78 % (546809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/1.78 % (546809)CaDiCaL version: 2.1.3
% 8.75/1.78 % (546809)Termination reason: Instruction limit
% 8.75/1.78 % (546809)Termination phase: Saturation
% 8.75/1.78 % (546809)Time elapsed: 0.010 s
% 8.75/1.78 % (546809)Peak memory usage: 12 MB
% 8.75/1.78 % (546809)Instructions burned: 23 (million)
% 8.75/1.78 % (546811)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=1525184700:i=338:bd=all:ins=4:rtra=on_2989 on theBenchmark for (2989ds/338Mi)
% 8.75/1.78 % (546784)Instruction limit reached!
% 8.75/1.78 % (546784)------------------------------
% 8.75/1.78 % (546784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.75/1.79 % (546784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/1.79 % (546784)CaDiCaL version: 2.1.3
% 8.75/1.79 % (546784)Termination reason: Instruction limit
% 8.75/1.79 % (546784)Termination phase: Saturation
% 8.75/1.79 % (546784)Time elapsed: 0.353 s
% 8.75/1.79 % (546784)Peak memory usage: 16 MB
% 8.75/1.79 % (546784)Instructions burned: 450 (million)
% 8.75/1.79 % (546813)lrs+10_1_sil=128000:si=on:urr=on:random_seed=4011982453:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2988 on theBenchmark for (2988ds/28Mi)
% 8.75/1.79 % (546795)Instruction limit reached!
% 8.75/1.79 % (546795)------------------------------
% 8.75/1.79 % (546795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.75/1.79 % (546795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/1.79 % (546795)CaDiCaL version: 2.1.3
% 8.75/1.79 % (546795)Termination reason: Instruction limit
% 8.75/1.79 % (546795)Termination phase: Saturation
% 8.75/1.79 % (546795)Time elapsed: 0.301 s
% 8.75/1.79 % (546795)Peak memory usage: 13 MB
% 8.75/1.79 % (546795)Instructions burned: 375 (million)
% 9.40/1.90 % (546813)Instruction limit reached!
% 9.40/1.90 % (546813)------------------------------
% 9.40/1.90 % (546813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.40/1.90 % (546813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/1.90 % (546813)CaDiCaL version: 2.1.3
% 9.40/1.90 % (546813)Termination reason: Instruction limit
% 9.40/1.90 % (546813)Termination phase: Saturation
% 9.40/1.90 % (546813)Time elapsed: 0.021 s
% 9.40/1.90 % (546813)Peak memory usage: 11 MB
% 9.40/1.90 % (546813)Instructions burned: 29 (million)
% 9.40/1.90 % (546815)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 9.40/1.90 % (546815)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=2698906013:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2988 on theBenchmark for (2988ds/137Mi)
% 9.40/1.90 % (546816)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=890400491:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2988 on theBenchmark for (2988ds/340Mi)
% 9.40/1.90 % (546719)Instruction limit reached!
% 9.40/1.90 % (546719)------------------------------
% 9.40/1.90 % (546719)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.40/1.90 % (546719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/1.90 % (546719)CaDiCaL version: 2.1.3
% 9.40/1.90 % (546719)Termination reason: Instruction limit
% 9.40/1.90 % (546719)Termination phase: Saturation
% 9.40/1.90 % (546719)Time elapsed: 0.978 s
% 9.40/1.90 % (546719)Peak memory usage: 16 MB
% 9.40/1.90 % (546719)Instructions burned: 1241 (million)
% 9.40/1.90 % (546819)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=984731352:i=227:sd=1:bd=all:rtra=on:ss=axioms_2987 on theBenchmark for (2987ds/227Mi)
% 9.40/1.90 % (546819)Refutation not found, incomplete strategy
% 9.40/1.90 % (546819)------------------------------
% 9.40/1.90 % (546819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.40/1.90 % (546819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/1.90 % (546819)CaDiCaL version: 2.1.3
% 9.40/1.90 % (546819)Termination reason: Refutation not found, incomplete strategy
% 9.40/1.90 % (546819)Time elapsed: 0.003 s
% 9.40/1.90 % (546819)Peak memory usage: 12 MB
% 9.40/1.90 % (546819)Instructions burned: 3 (million)
% 9.40/1.90 % (546819)------------------------------
% 9.40/1.90 % (546819)------------------------------
% 9.40/1.90 % (546796)Instruction limit reached!
% 9.40/1.90 % (546796)------------------------------
% 9.40/1.90 % (546796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.40/1.90 % (546796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/1.90 % (546796)CaDiCaL version: 2.1.3
% 9.40/1.90 % (546796)Termination reason: Instruction limit
% 9.40/1.90 % (546796)Termination phase: Saturation
% 9.40/1.90 % (546796)Time elapsed: 0.395 s
% 9.40/1.90 % (546796)Peak memory usage: 17 MB
% 9.40/1.90 % (546796)Instructions burned: 496 (million)
% 9.40/1.90 % (546821)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 9.40/1.90 % (546815)Instruction limit reached!
% 9.40/1.90 % (546815)------------------------------
% 9.40/1.90 % (546815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.40/1.90 % (546815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/1.90 % (546815)CaDiCaL version: 2.1.3
% 9.40/1.90 % (546815)Termination reason: Instruction limit
% 9.40/1.90 % (546815)Termination phase: Saturation
% 9.40/1.90 % (546815)Time elapsed: 0.100 s
% 9.40/1.90 % (546815)Peak memory usage: 13 MB
% 9.40/1.90 % (546815)Instructions burned: 138 (million)
% 9.40/1.90 % (546821)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=3356459065:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/373Mi)
% 9.40/1.90 % (546822)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=3626437704:i=116:ep=RSTC:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/116Mi)
% 9.40/1.90 % (546823)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=2209756717:i=575:rtra=on_2987 on theBenchmark for (2987ds/575Mi)
% 9.40/1.90 % (546811)Instruction limit reached!
% 13.14/2.27 % (546811)------------------------------
% 13.14/2.27 % (546811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.14/2.27 % (546811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.14/2.27 % (546811)CaDiCaL version: 2.1.3
% 13.14/2.27 % (546811)Termination reason: Instruction limit
% 13.14/2.27 % (546811)Termination phase: Saturation
% 13.14/2.27 % (546811)Time elapsed: 0.272 s
% 13.14/2.27 % (546811)Peak memory usage: 15 MB
% 13.14/2.27 % (546811)Instructions burned: 339 (million)
% 13.14/2.27 % (546773)Instruction limit reached!
% 13.14/2.27 % (546773)------------------------------
% 13.14/2.27 % (546773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.14/2.27 % (546773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.14/2.27 % (546773)CaDiCaL version: 2.1.3
% 13.14/2.27 % (546773)Termination reason: Instruction limit
% 13.14/2.27 % (546773)Termination phase: Saturation
% 13.14/2.27 % (546773)Time elapsed: 0.700 s
% 13.14/2.27 % (546773)Peak memory usage: 21 MB
% 13.14/2.27 % (546773)Instructions burned: 875 (million)
% 13.14/2.27 % (546827)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=3391045063:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2986 on theBenchmark for (2986ds/270Mi)
% 13.14/2.27 % (546822)Instruction limit reached!
% 13.14/2.27 % (546822)------------------------------
% 13.14/2.27 % (546822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.14/2.27 % (546822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.14/2.27 % (546822)CaDiCaL version: 2.1.3
% 13.14/2.27 % (546822)Termination reason: Instruction limit
% 13.14/2.27 % (546822)Termination phase: Saturation
% 13.14/2.27 % (546822)Time elapsed: 0.089 s
% 13.14/2.27 % (546822)Peak memory usage: 12 MB
% 13.14/2.27 % (546822)Instructions burned: 116 (million)
% 13.14/2.27 % (546828)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=553794035:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2986 on theBenchmark for (2986ds/9840Mi)
% 13.14/2.27 % (546830)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=2209196240:i=421:rtra=on:ss=axioms_2985 on theBenchmark for (2985ds/421Mi)
% 13.14/2.27 % (546830)Refutation not found, incomplete strategy
% 13.14/2.27 % (546830)------------------------------
% 13.14/2.27 % (546830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.14/2.27 % (546830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.14/2.27 % (546830)CaDiCaL version: 2.1.3
% 13.14/2.27 % (546830)Termination reason: Refutation not found, incomplete strategy
% 13.14/2.27 % (546830)Time elapsed: 0.004 s
% 13.14/2.27 % (546830)Peak memory usage: 12 MB
% 13.14/2.27 % (546830)Instructions burned: 3 (million)
% 13.14/2.27 % (546830)------------------------------
% 13.14/2.27 % (546830)------------------------------
% 13.14/2.27 % (546816)Instruction limit reached!
% 13.14/2.27 % (546816)------------------------------
% 13.14/2.27 % (546816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.14/2.27 % (546816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.14/2.27 % (546816)CaDiCaL version: 2.1.3
% 13.14/2.27 % (546816)Termination reason: Instruction limit
% 13.14/2.27 % (546816)Termination phase: Saturation
% 13.14/2.27 % (546816)Time elapsed: 0.239 s
% 13.14/2.27 % (546816)Peak memory usage: 13 MB
% 13.14/2.27 % (546816)Instructions burned: 341 (million)
% 13.14/2.27 % (546833)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 13.14/2.27 % (546833)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=388407565:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2985 on theBenchmark for (2985ds/270Mi)
% 13.14/2.27 % (546821)Instruction limit reached!
% 13.14/2.27 % (546821)------------------------------
% 13.14/2.27 % (546821)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.14/2.27 % (546821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.14/2.27 % (546821)CaDiCaL version: 2.1.3
% 13.14/2.27 % (546821)Termination reason: Instruction limit
% 16.38/2.75 % (546821)Termination phase: Saturation
% 16.38/2.75 % (546821)Time elapsed: 0.187 s
% 16.38/2.75 % (546821)Peak memory usage: 14 MB
% 16.38/2.75 % (546821)Instructions burned: 375 (million)
% 16.38/2.75 % (546834)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2947457703:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2985 on theBenchmark for (2985ds/31Mi)
% 16.38/2.75 % (546836)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 16.38/2.75 % (546836)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 16.38/2.75 % (546834)Instruction limit reached!
% 16.38/2.75 % (546834)------------------------------
% 16.38/2.75 % (546834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.38/2.75 % (546834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.38/2.75 % (546834)CaDiCaL version: 2.1.3
% 16.38/2.75 % (546834)Termination reason: Instruction limit
% 16.38/2.75 % (546834)Termination phase: Saturation
% 16.38/2.75 % (546834)Time elapsed: 0.022 s
% 16.38/2.75 % (546834)Peak memory usage: 11 MB
% 16.38/2.75 % (546834)Instructions burned: 31 (million)
% 16.38/2.75 % (546836)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1623668884:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2985 on theBenchmark for (2985ds/1440Mi)
% 16.38/2.75 % (546833)Refutation not found, incomplete strategy
% 16.38/2.75 % (546833)------------------------------
% 16.38/2.75 % (546833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.38/2.75 % (546833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.38/2.75 % (546833)CaDiCaL version: 2.1.3
% 16.38/2.75 % (546833)Termination reason: Refutation not found, incomplete strategy
% 16.38/2.75 % (546833)Time elapsed: 0.040 s
% 16.38/2.75 % (546833)Peak memory usage: 12 MB
% 16.38/2.75 % (546833)Instructions burned: 54 (million)
% 16.38/2.75 % (546833)------------------------------
% 16.38/2.75 % (546833)------------------------------
% 16.38/2.75 % (546840)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=1214707415:i=111:add=on:fgj=on:rtra=on:fdi=1024_2984 on theBenchmark for (2984ds/111Mi)
% 16.38/2.75 % (546838)dis+10_2_sil=128000:si=on:random_seed=3254131712:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2984 on theBenchmark for (2984ds/339Mi)
% 16.38/2.75 % (546838)Refutation not found, incomplete strategy
% 16.38/2.75 % (546838)------------------------------
% 16.38/2.75 % (546838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.38/2.75 % (546838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.38/2.75 % (546838)CaDiCaL version: 2.1.3
% 16.38/2.75 % (546838)Termination reason: Refutation not found, incomplete strategy
% 16.38/2.75 % (546838)Time elapsed: 0.004 s
% 16.38/2.75 % (546838)Peak memory usage: 12 MB
% 16.38/2.75 % (546838)Instructions burned: 3 (million)
% 16.38/2.75 % (546838)------------------------------
% 16.38/2.75 % (546838)------------------------------
% 16.38/2.75 % (546843)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=1743634073:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2984 on theBenchmark for (2984ds/122Mi)
% 16.38/2.75 % (546827)Instruction limit reached!
% 16.38/2.75 % (546827)------------------------------
% 16.38/2.75 % (546827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.38/2.75 % (546827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.38/2.75 % (546827)CaDiCaL version: 2.1.3
% 16.38/2.75 % (546827)Termination reason: Instruction limit
% 16.38/2.75 % (546827)Termination phase: Saturation
% 16.38/2.75 % (546827)Time elapsed: 0.199 s
% 16.38/2.75 % (546827)Peak memory usage: 13 MB
% 16.38/2.75 % (546827)Instructions burned: 270 (million)
% 16.38/2.75 % (546840)Instruction limit reached!
% 16.38/2.75 % (546840)------------------------------
% 16.38/2.75 % (546840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.38/2.75 % (546840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.38/2.75 % (546840)CaDiCaL version: 2.1.3
% 16.38/2.75 % (546840)Termination reason: Instruction limit
% 16.38/2.75 % (546840)Termination phase: Saturation
% 18.12/2.98 % (546840)Time elapsed: 0.051 s
% 18.12/2.98 % (546840)Peak memory usage: 12 MB
% 18.12/2.98 % (546840)Instructions burned: 111 (million)
% 18.12/2.98 % (546843)Refutation not found, incomplete strategy
% 18.12/2.98 % (546843)------------------------------
% 18.12/2.98 % (546843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.12/2.98 % (546843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.12/2.98 % (546843)CaDiCaL version: 2.1.3
% 18.12/2.98 % (546843)Termination reason: Refutation not found, incomplete strategy
% 18.12/2.98 % (546843)Time elapsed: 0.022 s
% 18.12/2.98 % (546843)Peak memory usage: 13 MB
% 18.12/2.98 % (546843)Instructions burned: 28 (million)
% 18.12/2.98 % (546843)------------------------------
% 18.12/2.98 % (546843)------------------------------
% 18.12/2.98 % (546846)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1483088856:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2984 on theBenchmark for (2984ds/232Mi)
% 18.12/2.98 % (546845)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=2786276620:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2984 on theBenchmark for (2984ds/136Mi)
% 18.12/2.98 % (546847)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=1758587442:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2983 on theBenchmark for (2983ds/1254Mi)
% 18.12/2.98 % (546845)Instruction limit reached!
% 18.12/2.98 % (546845)------------------------------
% 18.12/2.98 % (546845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.12/2.98 % (546845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.12/2.98 % (546845)CaDiCaL version: 2.1.3
% 18.12/2.98 % (546845)Termination reason: Instruction limit
% 18.12/2.98 % (546845)Termination phase: Saturation
% 18.12/2.98 % (546845)Time elapsed: 0.113 s
% 18.12/2.98 % (546845)Peak memory usage: 13 MB
% 18.12/2.98 % (546845)Instructions burned: 136 (million)
% 18.12/2.98 % (546851)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 18.12/2.98 % (546851)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=419831849:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2982 on theBenchmark for (2982ds/281Mi)
% 18.12/2.98 % (546823)Instruction limit reached!
% 18.12/2.98 % (546823)------------------------------
% 18.12/2.98 % (546823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.12/2.98 % (546823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.12/2.98 % (546823)CaDiCaL version: 2.1.3
% 18.12/2.98 % (546823)Termination reason: Instruction limit
% 18.12/2.98 % (546823)Termination phase: Saturation
% 18.12/2.98 % (546823)Time elapsed: 0.456 s
% 18.12/2.98 % (546823)Peak memory usage: 17 MB
% 18.12/2.98 % (546823)Instructions burned: 576 (million)
% 18.12/2.98 % (546853)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3992457207:i=619:add=on:rtra=on_2982 on theBenchmark for (2982ds/619Mi)
% 18.12/2.98 % (546846)Instruction limit reached!
% 18.12/2.98 % (546846)------------------------------
% 18.12/2.98 % (546846)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.12/2.98 % (546846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.12/2.98 % (546846)CaDiCaL version: 2.1.3
% 18.12/2.98 % (546846)Termination reason: Instruction limit
% 18.12/2.98 % (546846)Termination phase: Saturation
% 18.12/2.98 % (546846)Time elapsed: 0.196 s
% 18.12/2.98 % (546846)Peak memory usage: 13 MB
% 18.12/2.98 % (546846)Instructions burned: 232 (million)
% 18.12/2.98 % (546855)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1937135013:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2981 on theBenchmark for (2981ds/865Mi)
% 18.12/2.98 % (546851)Instruction limit reached!
% 18.12/2.98 % (546851)------------------------------
% 18.12/2.98 % (546851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.12/2.98 % (546851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.12/2.98 % (546851)CaDiCaL version: 2.1.3
% 18.12/2.98 % (546851)Termination reason: Instruction limit
% 18.12/2.98 % (546851)Termination phase: Saturation
% 18.12/2.98 % (546851)Time elapsed: 0.202 s
% 20.18/3.23 % (546851)Peak memory usage: 12 MB
% 20.18/3.23 % (546851)Instructions burned: 281 (million)
% 20.18/3.23 % (546857)lrs+10_1_sil=128000:si=on:urr=on:random_seed=149187243:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2980 on theBenchmark for (2980ds/212Mi)
% 20.18/3.23 % (546857)Instruction limit reached!
% 20.18/3.23 % (546857)------------------------------
% 20.18/3.23 % (546857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.18/3.23 % (546857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.18/3.23 % (546857)CaDiCaL version: 2.1.3
% 20.18/3.23 % (546857)Termination reason: Instruction limit
% 20.18/3.23 % (546857)Termination phase: Saturation
% 20.18/3.23 % (546857)Time elapsed: 0.160 s
% 20.18/3.23 % (546857)Peak memory usage: 13 MB
% 20.18/3.23 % (546857)Instructions burned: 212 (million)
% 20.18/3.23 % (546861)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=2836063687:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2978 on theBenchmark for (2978ds/130Mi)
% 20.18/3.23 % (546861)Refutation not found, incomplete strategy
% 20.18/3.23 % (546861)------------------------------
% 20.18/3.23 % (546861)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.18/3.23 % (546861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.18/3.23 % (546861)CaDiCaL version: 2.1.3
% 20.18/3.23 % (546861)Termination reason: Refutation not found, incomplete strategy
% 20.18/3.23 % (546861)Time elapsed: 0.006 s
% 20.18/3.23 % (546861)Peak memory usage: 12 MB
% 20.18/3.23 % (546861)Instructions burned: 8 (million)
% 20.18/3.23 % (546861)------------------------------
% 20.18/3.23 % (546861)------------------------------
% 20.18/3.23 % (546863)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=958485362:st=1.5:i=346:rtra=on:ss=axioms_2978 on theBenchmark for (2978ds/346Mi)
% 20.18/3.23 % (546863)Refutation not found, incomplete strategy
% 20.18/3.23 % (546863)------------------------------
% 20.18/3.23 % (546863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.18/3.23 % (546863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.18/3.23 % (546863)CaDiCaL version: 2.1.3
% 20.18/3.23 % (546863)Termination reason: Refutation not found, incomplete strategy
% 20.18/3.23 % (546863)Time elapsed: 0.060 s
% 20.18/3.23 % (546863)Peak memory usage: 13 MB
% 20.18/3.23 % (546863)Instructions burned: 80 (million)
% 20.18/3.23 % (546863)------------------------------
% 20.18/3.23 % (546863)------------------------------
% 20.18/3.23 % (546853)Instruction limit reached!
% 20.18/3.23 % (546853)------------------------------
% 20.18/3.23 % (546853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.18/3.23 % (546853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.18/3.23 % (546853)CaDiCaL version: 2.1.3
% 20.18/3.23 % (546853)Termination reason: Instruction limit
% 20.18/3.23 % (546853)Termination phase: Saturation
% 20.18/3.23 % (546853)Time elapsed: 0.485 s
% 20.18/3.23 % (546853)Peak memory usage: 14 MB
% 20.18/3.23 % (546853)Instructions burned: 621 (million)
% 20.18/3.23 % (546865)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=3047410466:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2977 on theBenchmark for (2977ds/152Mi)
% 20.18/3.23 % (546866)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=661417251:i=75:ep=R:rtra=on:ntd=on_2977 on theBenchmark for (2977ds/75Mi)
% 20.18/3.24 % (546866)Instruction limit reached!
% 20.18/3.24 % (546866)------------------------------
% 20.18/3.24 % (546866)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.18/3.24 % (546866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.18/3.24 % (546866)CaDiCaL version: 2.1.3
% 20.18/3.24 % (546866)Termination reason: Instruction limit
% 20.18/3.24 % (546866)Termination phase: Saturation
% 20.18/3.24 % (546866)Time elapsed: 0.056 s
% 20.18/3.24 % (546866)Peak memory usage: 12 MB
% 20.18/3.24 % (546866)Instructions burned: 76 (million)
% 20.18/3.24 % (546869)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=1642872238:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2976 on theBenchmark for (2976ds/387Mi)
% 20.18/3.24 % (546865)Instruction limit reached!
% 20.18/3.24 % (546865)------------------------------
% 20.18/3.24 % (546865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.18/3.24 % (546865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.18/3.24 % (546865)CaDiCaL version: 2.1.3
% 22.57/3.64 % (546865)Termination reason: Instruction limit
% 22.57/3.64 % (546865)Termination phase: Saturation
% 22.57/3.64 % (546865)Time elapsed: 0.118 s
% 22.57/3.64 % (546865)Peak memory usage: 13 MB
% 22.57/3.64 % (546865)Instructions burned: 153 (million)
% 22.57/3.64 % (546871)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=98890360:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2975 on theBenchmark for (2975ds/148Mi)
% 22.57/3.64 % (546847)Instruction limit reached!
% 22.57/3.64 % (546847)------------------------------
% 22.57/3.64 % (546847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.57/3.64 % (546847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.57/3.64 % (546847)CaDiCaL version: 2.1.3
% 22.57/3.64 % (546847)Termination reason: Instruction limit
% 22.57/3.64 % (546847)Termination phase: Saturation
% 22.57/3.64 % (546847)Time elapsed: 0.870 s
% 22.57/3.64 % (546847)Peak memory usage: 16 MB
% 22.57/3.64 % (546847)Instructions burned: 1254 (million)
% 22.57/3.64 % (546876)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=3952568808:i=161:piset=and:rtra=on:ntd=on_2975 on theBenchmark for (2975ds/161Mi)
% 22.57/3.64 % (546855)Instruction limit reached!
% 22.57/3.64 % (546855)------------------------------
% 22.57/3.64 % (546855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.57/3.64 % (546855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.57/3.64 % (546855)CaDiCaL version: 2.1.3
% 22.57/3.64 % (546855)Termination reason: Instruction limit
% 22.57/3.64 % (546855)Termination phase: Saturation
% 22.57/3.64 % (546855)Time elapsed: 0.703 s
% 22.57/3.64 % (546855)Peak memory usage: 17 MB
% 22.57/3.64 % (546855)Instructions burned: 866 (million)
% 22.57/3.64 % (546880)lrs+10_1_sil=128000:si=on:random_seed=135479348:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2974 on theBenchmark for (2974ds/888Mi)
% 22.57/3.64 % (546871)Instruction limit reached!
% 22.57/3.64 % (546871)------------------------------
% 22.57/3.64 % (546871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.57/3.64 % (546871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.57/3.64 % (546871)CaDiCaL version: 2.1.3
% 22.57/3.64 % (546871)Termination reason: Instruction limit
% 22.57/3.64 % (546871)Termination phase: Saturation
% 22.57/3.64 % (546871)Time elapsed: 0.107 s
% 22.57/3.64 % (546871)Peak memory usage: 13 MB
% 22.57/3.64 % (546871)Instructions burned: 149 (million)
% 22.57/3.64 % (546884)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=2764505751:i=136:add=on:ins=4:rtra=on:sup=off_2974 on theBenchmark for (2974ds/136Mi)
% 22.57/3.64 % (546884)Refutation not found, incomplete strategy
% 22.57/3.64 % (546884)------------------------------
% 22.57/3.64 % (546884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.57/3.64 % (546884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.57/3.64 % (546884)CaDiCaL version: 2.1.3
% 22.57/3.64 % (546884)Termination reason: Refutation not found, incomplete strategy
% 22.57/3.64 % (546884)Time elapsed: 0.039 s
% 22.57/3.64 % (546884)Peak memory usage: 12 MB
% 22.57/3.64 % (546884)Instructions burned: 52 (million)
% 22.57/3.64 % (546884)------------------------------
% 22.57/3.64 % (546884)------------------------------
% 22.57/3.64 % (546836)Instruction limit reached!
% 22.57/3.64 % (546836)------------------------------
% 22.57/3.64 % (546836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.57/3.64 % (546836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.57/3.64 % (546836)CaDiCaL version: 2.1.3
% 22.57/3.64 % (546836)Termination reason: Instruction limit
% 22.57/3.64 % (546836)Termination phase: Saturation
% 22.57/3.64 % (546836)Time elapsed: 1.139 s
% 22.57/3.64 % (546836)Peak memory usage: 26 MB
% 22.57/3.64 % (546836)Instructions burned: 1440 (million)
% 22.57/3.64 % (546876)Instruction limit reached!
% 22.57/3.64 % (546876)------------------------------
% 22.57/3.64 % (546876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.57/3.64 % (546876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.57/3.64 % (546876)CaDiCaL version: 2.1.3
% 22.57/3.64 % (546876)Termination reason: Instruction limit
% 22.57/3.64 % (546876)Termination phase: Saturation
% 22.57/3.64 % (546876)Time elapsed: 0.123 s
% 22.57/3.64 % (546876)Peak memory usage: 12 MB
% 22.57/3.64 % (546876)Instructions burned: 161 (million)
% 22.57/3.64 % (546887)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=1518449412:i=88:s2at=3:nm=2:rtra=on:rawr=on_2973 on theBenchmark for (2973ds/88Mi)
% 23.80/3.87 % (546888)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2193004523:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2973 on theBenchmark for (2973ds/93Mi)
% 23.80/3.87 % (546889)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=865561753:i=2186:rtra=on:ixr=off_2973 on theBenchmark for (2973ds/2186Mi)
% 23.80/3.87 % (546869)Instruction limit reached!
% 23.80/3.87 % (546869)------------------------------
% 23.80/3.87 % (546869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.80/3.87 % (546869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.80/3.87 % (546869)CaDiCaL version: 2.1.3
% 23.80/3.87 % (546869)Termination reason: Instruction limit
% 23.80/3.87 % (546869)Termination phase: Saturation
% 23.80/3.87 % (546869)Time elapsed: 0.286 s
% 23.80/3.87 % (546869)Peak memory usage: 13 MB
% 23.80/3.87 % (546869)Instructions burned: 388 (million)
% 23.80/3.87 % (546888)Instruction limit reached!
% 23.80/3.87 % (546888)------------------------------
% 23.80/3.87 % (546888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.80/3.87 % (546888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.80/3.87 % (546888)CaDiCaL version: 2.1.3
% 23.80/3.87 % (546888)Termination reason: Instruction limit
% 23.80/3.87 % (546888)Termination phase: Saturation
% 23.80/3.87 % (546888)Time elapsed: 0.062 s
% 23.80/3.87 % (546888)Peak memory usage: 12 MB
% 23.80/3.87 % (546888)Instructions burned: 93 (million)
% 23.80/3.87 % (546887)Instruction limit reached!
% 23.80/3.87 % (546887)------------------------------
% 23.80/3.87 % (546887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.80/3.87 % (546887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.80/3.87 % (546887)CaDiCaL version: 2.1.3
% 23.80/3.87 % (546887)Termination reason: Instruction limit
% 23.80/3.87 % (546887)Termination phase: Saturation
% 23.80/3.87 % (546887)Time elapsed: 0.066 s
% 23.80/3.87 % (546887)Peak memory usage: 12 MB
% 23.80/3.87 % (546887)Instructions burned: 88 (million)
% 23.80/3.87 % (546893)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2736522042:s2a=on:i=240:rtra=on:ntd=on_2972 on theBenchmark for (2972ds/240Mi)
% 23.80/3.87 % (546894)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=1472737198:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2972 on theBenchmark for (2972ds/805Mi)
% 23.80/3.87 % (546896)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 23.80/3.87 % (546896)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=2139939890:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2972 on theBenchmark for (2972ds/391Mi)
% 23.80/3.87 % (546896)Refutation not found, incomplete strategy
% 23.80/3.87 % (546896)------------------------------
% 23.80/3.87 % (546896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.80/3.87 % (546896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.80/3.87 % (546896)CaDiCaL version: 2.1.3
% 23.80/3.87 % (546896)Termination reason: Refutation not found, incomplete strategy
% 23.80/3.87 % (546896)Time elapsed: 0.049 s
% 23.80/3.87 % (546896)Peak memory usage: 13 MB
% 23.80/3.87 % (546896)Instructions burned: 65 (million)
% 23.80/3.87 % (546896)------------------------------
% 23.80/3.87 % (546896)------------------------------
% 23.80/3.87 % (546899)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=2764413249:i=355:av=off:fsr=off:rtra=on:ixr=off_2971 on theBenchmark for (2971ds/355Mi)
% 23.80/3.87 % (546893)Instruction limit reached!
% 23.80/3.87 % (546893)------------------------------
% 23.80/3.87 % (546893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.80/3.87 % (546893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.80/3.87 % (546893)CaDiCaL version: 2.1.3
% 23.80/3.87 % (546893)Termination reason: Instruction limit
% 23.80/3.87 % (546893)Termination phase: Saturation
% 23.80/3.87 % (546893)Time elapsed: 0.188 s
% 23.80/3.87 % (546893)Peak memory usage: 14 MB
% 24.64/3.95 % (546893)Instructions burned: 240 (million)
% 24.64/3.95 % (546901)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=2621018890:lrd=on:i=314:sd=1:rtra=on:ss=axioms_2970 on theBenchmark for (2970ds/314Mi)
% 24.64/3.95 % (546901)Refutation not found, incomplete strategy
% 24.64/3.95 % (546901)------------------------------
% 24.64/3.95 % (546901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.64/3.95 % (546901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.64/3.95 % (546901)CaDiCaL version: 2.1.3
% 24.64/3.95 % (546901)Termination reason: Refutation not found, incomplete strategy
% 24.64/3.95 % (546901)Time elapsed: 0.003 s
% 24.64/3.95 % (546901)Peak memory usage: 12 MB
% 24.64/3.95 % (546901)Instructions burned: 4 (million)
% 24.64/3.95 % (546901)------------------------------
% 24.64/3.95 % (546901)------------------------------
% 24.64/3.95 % (546903)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=2341089537:s2a=on:i=251:fsr=off:rtra=on_2970 on theBenchmark for (2970ds/251Mi)
% 24.64/3.95 % (546899)Instruction limit reached!
% 24.64/3.95 % (546899)------------------------------
% 24.64/3.95 % (546899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.64/3.95 % (546899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.64/3.95 % (546899)CaDiCaL version: 2.1.3
% 24.64/3.95 % (546899)Termination reason: Instruction limit
% 24.64/3.95 % (546899)Termination phase: Saturation
% 24.64/3.95 % (546899)Time elapsed: 0.277 s
% 24.64/3.95 % (546899)Peak memory usage: 14 MB
% 24.64/3.95 % (546899)Instructions burned: 355 (million)
% 24.64/3.95 % (546905)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=4223351839:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2470:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2968 on theBenchmark for (2968ds/2470Mi)
% 24.64/3.95 % (546903)Instruction limit reached!
% 24.64/3.95 % (546903)------------------------------
% 24.64/3.95 % (546903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.64/3.95 % (546903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.64/3.95 % (546903)CaDiCaL version: 2.1.3
% 24.64/3.95 % (546903)Termination reason: Instruction limit
% 24.64/3.95 % (546903)Termination phase: Saturation
% 24.64/3.95 % (546903)Time elapsed: 0.187 s
% 24.64/3.95 % (546903)Peak memory usage: 12 MB
% 24.64/3.95 % (546903)Instructions burned: 252 (million)
% 24.64/3.95 % (546907)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=238128857:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_2968 on theBenchmark for (2968ds/673Mi)
% 24.64/3.95 % (546790)Instruction limit reached!
% 24.64/3.95 % (546790)------------------------------
% 24.64/3.95 % (546790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.64/3.95 % (546790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.64/3.95 % (546790)CaDiCaL version: 2.1.3
% 24.64/3.95 % (546790)Termination reason: Instruction limit
% 24.64/3.95 % (546790)Termination phase: Saturation
% 24.64/3.95 % (546790)Time elapsed: 2.467 s
% 24.64/3.95 % (546790)Peak memory usage: 38 MB
% 24.64/3.95 % (546790)Instructions burned: 5757 (million)
% 24.64/3.95 % (546880)Instruction limit reached!
% 24.64/3.95 % (546880)------------------------------
% 24.64/3.95 % (546880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.64/3.95 % (546880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.64/3.95 % (546880)CaDiCaL version: 2.1.3
% 24.64/3.95 % (546880)Termination reason: Instruction limit
% 24.64/3.95 % (546880)Termination phase: Saturation
% 24.64/3.95 % (546880)Time elapsed: 0.709 s
% 24.64/3.95 % (546880)Peak memory usage: 22 MB
% 24.64/3.95 % (546880)Instructions burned: 889 (million)
% 24.64/3.95 % (546909)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=1043953122:i=116:ep=RSTC:rtra=on:ntd=on_2967 on theBenchmark for (2967ds/116Mi)
% 24.64/3.95 % (546910)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2486613427:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2967 on theBenchmark for (2967ds/270Mi)
% 24.64/3.95 % (546909)Instruction limit reached!
% 24.64/3.95 % (546909)------------------------------
% 24.64/3.95 % (546909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.79/4.35 % (546909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.79/4.35 % (546909)CaDiCaL version: 2.1.3
% 27.79/4.35 % (546909)Termination reason: Instruction limit
% 27.79/4.35 % (546909)Termination phase: Saturation
% 27.79/4.35 % (546909)Time elapsed: 0.047 s
% 27.79/4.35 % (546909)Peak memory usage: 12 MB
% 27.79/4.35 % (546909)Instructions burned: 120 (million)
% 27.79/4.35 % (546894)Instruction limit reached!
% 27.79/4.35 % (546894)------------------------------
% 27.79/4.35 % (546894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.79/4.35 % (546894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.79/4.35 % (546894)CaDiCaL version: 2.1.3
% 27.79/4.35 % (546894)Termination reason: Instruction limit
% 27.79/4.35 % (546894)Termination phase: Saturation
% 27.79/4.35 % (546894)Time elapsed: 0.602 s
% 27.79/4.35 % (546894)Peak memory usage: 20 MB
% 27.79/4.35 % (546894)Instructions burned: 806 (million)
% 27.79/4.35 % (546913)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=798205871:hsq=on:hsqr=16,1:s2a=on:i=30:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2966 on theBenchmark for (2966ds/30Mi)
% 27.79/4.35 % (546915)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 27.79/4.35 % (546913)Instruction limit reached!
% 27.79/4.35 % (546913)------------------------------
% 27.79/4.35 % (546913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.79/4.35 % (546913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.79/4.35 % (546913)CaDiCaL version: 2.1.3
% 27.79/4.35 % (546913)Termination reason: Instruction limit
% 27.79/4.35 % (546913)Termination phase: Saturation
% 27.79/4.35 % (546913)Time elapsed: 0.029 s
% 27.79/4.35 % (546913)Peak memory usage: 12 MB
% 27.79/4.35 % (546913)Instructions burned: 30 (million)
% 27.79/4.35 % (546915)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=2517147789:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2966 on theBenchmark for (2966ds/39Mi)
% 27.79/4.35 % (546916)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2248796807:i=365:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2966 on theBenchmark for (2966ds/365Mi)
% 27.79/4.35 % (546915)Instruction limit reached!
% 27.79/4.35 % (546915)------------------------------
% 27.79/4.35 % (546915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.79/4.35 % (546915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.79/4.35 % (546915)CaDiCaL version: 2.1.3
% 27.79/4.35 % (546915)Termination reason: Instruction limit
% 27.79/4.35 % (546915)Termination phase: Saturation
% 27.79/4.35 % (546915)Time elapsed: 0.028 s
% 27.79/4.35 % (546915)Peak memory usage: 11 MB
% 27.79/4.35 % (546915)Instructions burned: 40 (million)
% 27.79/4.35 % (546920)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=482955760:i=158:av=off:rtra=on_2965 on theBenchmark for (2965ds/158Mi)
% 27.79/4.35 % (546910)Instruction limit reached!
% 27.79/4.35 % (546910)------------------------------
% 27.79/4.35 % (546910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.79/4.35 % (546910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.79/4.35 % (546910)CaDiCaL version: 2.1.3
% 27.79/4.35 % (546910)Termination reason: Instruction limit
% 27.79/4.35 % (546910)Termination phase: Saturation
% 27.79/4.35 % (546910)Time elapsed: 0.203 s
% 27.79/4.35 % (546910)Peak memory usage: 13 MB
% 27.79/4.35 % (546910)Instructions burned: 271 (million)
% 27.79/4.35 % (546923)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 27.79/4.35 % (546923)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=2157084213:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2964 on theBenchmark for (2964ds/252Mi)
% 27.79/4.35 % (546923)Refutation not found, incomplete strategy
% 27.79/4.35 % (546923)------------------------------
% 27.79/4.35 % (546923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.79/4.35 % (546923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.24/4.51 % (546923)CaDiCaL version: 2.1.3
% 29.24/4.51 % (546923)Termination reason: Refutation not found, incomplete strategy
% 29.24/4.51 % (546923)Time elapsed: 0.025 s
% 29.24/4.51 % (546923)Peak memory usage: 12 MB
% 29.24/4.51 % (546923)Instructions burned: 54 (million)
% 29.24/4.51 % (546916)Instruction limit reached!
% 29.24/4.51 % (546916)------------------------------
% 29.24/4.51 % (546916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.24/4.51 % (546916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.24/4.51 % (546916)CaDiCaL version: 2.1.3
% 29.24/4.51 % (546916)Termination reason: Instruction limit
% 29.24/4.51 % (546916)Termination phase: Saturation
% 29.24/4.51 % (546916)Time elapsed: 0.150 s
% 29.24/4.51 % (546916)Peak memory usage: 15 MB
% 29.24/4.51 % (546916)Instructions burned: 367 (million)
% 29.24/4.51 % (546923)------------------------------
% 29.24/4.51 % (546923)------------------------------
% 29.24/4.51 % (546920)Instruction limit reached!
% 29.24/4.51 % (546920)------------------------------
% 29.24/4.51 % (546920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.24/4.51 % (546920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.24/4.51 % (546920)CaDiCaL version: 2.1.3
% 29.24/4.51 % (546920)Termination reason: Instruction limit
% 29.24/4.51 % (546920)Termination phase: Saturation
% 29.24/4.51 % (546920)Time elapsed: 0.125 s
% 29.24/4.51 % (546920)Peak memory usage: 12 MB
% 29.24/4.51 % (546920)Instructions burned: 158 (million)
% 29.24/4.51 % (546925)lrs+10_1_cnfonf=off:si=on:sos=on:uwa=off:random_seed=2335023027:i=213:rtra=on:ss=axioms_2964 on theBenchmark for (2964ds/213Mi)
% 29.24/4.51 % (546925)Refutation not found, incomplete strategy
% 29.24/4.51 % (546925)------------------------------
% 29.24/4.51 % (546925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.24/4.51 % (546925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.24/4.51 % (546925)CaDiCaL version: 2.1.3
% 29.24/4.51 % (546925)Termination reason: Refutation not found, incomplete strategy
% 29.24/4.51 % (546925)Time elapsed: 0.002 s
% 29.24/4.51 % (546925)Peak memory usage: 12 MB
% 29.24/4.51 % (546925)Instructions burned: 3 (million)
% 29.24/4.51 % (546925)------------------------------
% 29.24/4.51 % (546925)------------------------------
% 29.24/4.51 % (546926)dis+1010_28_sil=128000:tgt=full:plsq=on:plsqc=1:cnfonf=off:si=on:plsqr=128,1:uwa=off:slsqc=2:sac=on:slsq=on:random_seed=1357217750:st=3:i=160:s2at=3:bd=preordered:nm=16:rtra=on:ss=axioms:ntd=on_2964 on theBenchmark for (2964ds/160Mi)
% 29.24/4.51 % (546927)lrs+1010_2:3_sil=128000:cnfonf=off:e2e=on:si=on:sp=unary_first:uwa=off:br=off:lftc=80:random_seed=1540646416:hsq=on:hsqr=16,1:i=763:kws=inv_frequency:piset=and:bd=all:rtra=on:ntd=on_2964 on theBenchmark for (2964ds/763Mi)
% 29.24/4.51 % (546929)WARNING Broken Constraint: if ho_split_queue_layered_arrangement(off) has been set then ho_split_queue(off) is equal to on
% 29.24/4.51 % (546929)ott+1010_40_sil=128000:tgt=full:plsq=on:plsqc=5:si=on:sos=all:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2039353309:i=237:hsql=off:fgj=on:piset=all_but_not_eq:bd=preordered:av=off:rtra=on:ss=axioms:sgt=4:rawr=on_2964 on theBenchmark for (2964ds/237Mi)
% 29.24/4.51 % (546927)Refutation not found, incomplete strategy
% 29.24/4.51 % (546927)------------------------------
% 29.24/4.51 % (546927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.24/4.51 % (546927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.24/4.51 % (546927)CaDiCaL version: 2.1.3
% 29.24/4.51 % (546927)Termination reason: Refutation not found, incomplete strategy
% 29.24/4.51 % (546927)Time elapsed: 0.025 s
% 29.24/4.51 % (546927)Peak memory usage: 12 MB
% 29.24/4.51 % (546927)Instructions burned: 51 (million)
% 29.24/4.51 % (546927)------------------------------
% 29.24/4.51 % (546927)------------------------------
% 29.24/4.51 % (546926)Refutation not found, incomplete strategy
% 29.24/4.51 % (546926)------------------------------
% 29.24/4.51 % (546926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.24/4.51 % (546926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.24/4.51 % (546926)CaDiCaL version: 2.1.3
% 29.24/4.51 % (546926)Termination reason: Refutation not found, incomplete strategy
% 29.24/4.51 % (546926)Time elapsed: 0.040 s
% 29.24/4.51 % (546926)Peak memory usage: 12 MB
% 29.24/4.51 % (546926)Instructions burned: 56 (million)
% 29.24/4.51 % (546926)------------------------------
% 29.24/4.51 % (546926)------------------------------
% 29.73/4.66 % (546933)dis+1002_1_drc=ordering:cnfonf=lazy_not_gen_be_off:si=on:lma=off:cbe=off:uwa=off:random_seed=2713309509:s2a=on:i=386:rtra=on:ntd=on_2963 on theBenchmark for (2963ds/386Mi)
% 29.73/4.66 % (546907)Instruction limit reached!
% 29.73/4.66 % (546907)------------------------------
% 29.73/4.66 % (546907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.73/4.66 % (546907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.73/4.66 % (546907)CaDiCaL version: 2.1.3
% 29.73/4.66 % (546907)Termination reason: Instruction limit
% 29.73/4.66 % (546907)Termination phase: Saturation
% 29.73/4.66 % (546907)Time elapsed: 0.466 s
% 29.73/4.66 % (546907)Peak memory usage: 17 MB
% 29.73/4.66 % (546907)Instructions burned: 673 (million)
% 29.73/4.66 % (546934)dis+10_128_to=lpo:sil=128000:si=on:spb=intro:uwa=off:random_seed=2892135411:i=300:piset=and:nm=32:rtra=on_2963 on theBenchmark for (2963ds/300Mi)
% 29.73/4.66 % (546936)dis+1010_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:urr=on:random_seed=2965762485:st=5:s2a=on:i=567:sd=2:rtra=on:ss=axioms_2963 on theBenchmark for (2963ds/567Mi)
% 29.73/4.66 % (546929)Instruction limit reached!
% 29.73/4.66 % (546929)------------------------------
% 29.73/4.66 % (546929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.73/4.66 % (546929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.73/4.66 % (546929)CaDiCaL version: 2.1.3
% 29.73/4.66 % (546929)Termination reason: Instruction limit
% 29.73/4.66 % (546929)Termination phase: Saturation
% 29.73/4.66 % (546929)Time elapsed: 0.098 s
% 29.73/4.66 % (546929)Peak memory usage: 14 MB
% 29.73/4.66 % (546929)Instructions burned: 237 (million)
% 29.73/4.66 % (546939)lrs+1010_1_si=on:uwa=one_side_interpreted:random_seed=3258796460:s2a=on:i=379:sd=1:rtra=on:ss=axioms:sgt=128_2962 on theBenchmark for (2962ds/379Mi)
% 29.73/4.66 % (546933)Instruction limit reached!
% 29.73/4.66 % (546933)------------------------------
% 29.73/4.66 % (546933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.73/4.66 % (546933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.73/4.66 % (546933)CaDiCaL version: 2.1.3
% 29.73/4.66 % (546933)Termination reason: Instruction limit
% 29.73/4.66 % (546933)Termination phase: Saturation
% 29.73/4.66 % (546933)Time elapsed: 0.168 s
% 29.73/4.66 % (546933)Peak memory usage: 13 MB
% 29.73/4.66 % (546933)Instructions burned: 388 (million)
% 29.73/4.66 % (546941)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=2558550096:s2a=on:i=429:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2961 on theBenchmark for (2961ds/429Mi)
% 29.73/4.66 % (546934)Instruction limit reached!
% 29.73/4.66 % (546934)------------------------------
% 29.73/4.66 % (546934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.73/4.66 % (546934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.73/4.66 % (546934)CaDiCaL version: 2.1.3
% 29.73/4.66 % (546934)Termination reason: Instruction limit
% 29.73/4.66 % (546934)Termination phase: Saturation
% 29.73/4.66 % (546934)Time elapsed: 0.233 s
% 29.73/4.66 % (546934)Peak memory usage: 14 MB
% 29.73/4.66 % (546934)Instructions burned: 300 (million)
% 29.73/4.66 % (546943)ott+10_1_to=lpo:sil=128000:e2e=on:si=on:sos=on:uwa=off:sac=on:random_seed=3550255721:i=478:bd=all:rtra=on_2960 on theBenchmark for (2960ds/478Mi)
% 29.73/4.66 % (546941)Instruction limit reached!
% 29.73/4.66 % (546941)------------------------------
% 29.73/4.66 % (546941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.73/4.66 % (546941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.73/4.66 % (546941)CaDiCaL version: 2.1.3
% 29.73/4.66 % (546941)Termination reason: Instruction limit
% 29.73/4.66 % (546941)Termination phase: Saturation
% 29.73/4.66 % (546941)Time elapsed: 0.179 s
% 29.73/4.66 % (546941)Peak memory usage: 15 MB
% 29.73/4.66 % (546941)Instructions burned: 430 (million)
% 29.73/4.66 % (546945)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3723843641:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2959 on theBenchmark for (2959ds/445Mi)
% 29.73/4.66 % (546939)Instruction limit reached!
% 29.73/4.66 % (546939)------------------------------
% 29.73/4.66 % (546939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.73/4.66 % (546939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.73/4.66 % (546939)CaDiCaL version: 2.1.3
% 29.73/4.66 % (546939)Termination reason: Instruction limit
% 31.57/4.91 % (546939)Termination phase: Saturation
% 31.57/4.91 % (546939)Time elapsed: 0.307 s
% 31.57/4.91 % (546939)Peak memory usage: 16 MB
% 31.57/4.91 % (546939)Instructions burned: 379 (million)
% 31.57/4.91 % (546947)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=2021847765:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2959 on theBenchmark for (2959ds/71Mi)
% 31.57/4.91 % (546947)Instruction limit reached!
% 31.57/4.91 % (546947)------------------------------
% 31.57/4.91 % (546947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.57/4.91 % (546947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.57/4.91 % (546947)CaDiCaL version: 2.1.3
% 31.57/4.91 % (546947)Termination reason: Instruction limit
% 31.57/4.91 % (546947)Termination phase: Saturation
% 31.57/4.91 % (546947)Time elapsed: 0.031 s
% 31.57/4.91 % (546947)Peak memory usage: 13 MB
% 31.57/4.91 % (546947)Instructions burned: 72 (million)
% 31.57/4.91 % (546949)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=32124457:i=302:sd=2:bd=preordered:rtra=on:ss=axioms_2958 on theBenchmark for (2958ds/302Mi)
% 31.57/4.91 % (546949)Refutation not found, incomplete strategy
% 31.57/4.91 % (546949)------------------------------
% 31.57/4.91 % (546949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.57/4.91 % (546949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.57/4.91 % (546949)CaDiCaL version: 2.1.3
% 31.57/4.91 % (546949)Termination reason: Refutation not found, incomplete strategy
% 31.57/4.91 % (546949)Time elapsed: 0.002 s
% 31.57/4.91 % (546949)Peak memory usage: 12 MB
% 31.57/4.91 % (546949)Instructions burned: 3 (million)
% 31.57/4.91 % (546949)------------------------------
% 31.57/4.91 % (546949)------------------------------
% 31.57/4.91 % (546936)Instruction limit reached!
% 31.57/4.91 % (546936)------------------------------
% 31.57/4.91 % (546936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.57/4.91 % (546936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.57/4.91 % (546936)CaDiCaL version: 2.1.3
% 31.57/4.91 % (546936)Termination reason: Instruction limit
% 31.57/4.91 % (546936)Termination phase: Saturation
% 31.57/4.91 % (546936)Time elapsed: 0.440 s
% 31.57/4.91 % (546936)Peak memory usage: 13 MB
% 31.57/4.91 % (546936)Instructions burned: 568 (million)
% 31.57/4.91 % (546951)lrs+10_1_sil=128000:fde=none:cnfonf=off:si=on:uwa=off:random_seed=484138132:s2a=on:i=4980:sd=2:bd=all:rtra=on:ss=axioms:ntd=on_2958 on theBenchmark for (2958ds/4980Mi)
% 31.57/4.91 % (546952)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 31.57/4.91 % (546952)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 31.57/4.91 % (546952)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1210486964:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2958 on theBenchmark for (2958ds/100Mi)
% 31.57/4.91 % (546951)Refutation not found, incomplete strategy
% 31.57/4.91 % (546951)------------------------------
% 31.57/4.91 % (546951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.57/4.91 % (546951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.57/4.91 % (546951)CaDiCaL version: 2.1.3
% 31.57/4.91 % (546951)Termination reason: Refutation not found, incomplete strategy
% 31.57/4.91 % (546951)Time elapsed: 0.006 s
% 31.57/4.91 % (546951)Peak memory usage: 12 MB
% 31.57/4.91 % (546951)Instructions burned: 5 (million)
% 31.57/4.91 % (546951)------------------------------
% 31.57/4.91 % (546951)------------------------------
% 31.57/4.91 % (546955)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1808167861:i=76:piset=equals:rtra=on:ntd=on_2958 on theBenchmark for (2958ds/76Mi)
% 31.57/4.91 % (546952)Instruction limit reached!
% 31.57/4.91 % (546952)------------------------------
% 31.57/4.91 % (546952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.57/4.91 % (546952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.57/4.91 % (546952)CaDiCaL version: 2.1.3
% 31.57/4.91 % (546952)Termination reason: Instruction limit
% 31.57/4.91 % (546952)Termination phase: Saturation
% 34.63/5.21 % (546952)Time elapsed: 0.038 s
% 34.63/5.21 % (546952)Peak memory usage: 13 MB
% 34.63/5.21 % (546952)Instructions burned: 101 (million)
% 34.63/5.21 % (546957)lrs+10_1_to=lpo:sil=128000:cnfonf=off:si=on:sp=unary_first:sos=all:spb=goal:uwa=off:random_seed=1042214964:i=289:rtra=on_2957 on theBenchmark for (2957ds/289Mi)
% 34.63/5.21 % (546957)Refutation not found, incomplete strategy
% 34.63/5.21 % (546957)------------------------------
% 34.63/5.21 % (546957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.63/5.21 % (546957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.63/5.21 % (546957)CaDiCaL version: 2.1.3
% 34.63/5.21 % (546957)Termination reason: Refutation not found, incomplete strategy
% 34.63/5.21 % (546957)Time elapsed: 0.028 s
% 34.63/5.21 % (546957)Peak memory usage: 13 MB
% 34.63/5.21 % (546957)Instructions burned: 60 (million)
% 34.63/5.21 % (546957)------------------------------
% 34.63/5.21 % (546957)------------------------------
% 34.63/5.21 % (546955)Instruction limit reached!
% 34.63/5.21 % (546955)------------------------------
% 34.63/5.21 % (546955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.63/5.21 % (546955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.63/5.21 % (546955)CaDiCaL version: 2.1.3
% 34.63/5.21 % (546955)Termination reason: Instruction limit
% 34.63/5.21 % (546955)Termination phase: Saturation
% 34.63/5.21 % (546955)Time elapsed: 0.059 s
% 34.63/5.21 % (546955)Peak memory usage: 13 MB
% 34.63/5.21 % (546955)Instructions burned: 76 (million)
% 34.63/5.21 % (546959)lrs+2_64_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_first:bsr=unit_only:cbe=off:uwa=interpreted_only:nwc=0.5:slsqc=5:sac=on:slsq=on:random_seed=3764244722:i=493:s2at=5:kws=frequency:doe=on:rtra=on:er=known_2957 on theBenchmark for (2957ds/493Mi)
% 34.63/5.21 % (546960)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=3899857616:cond=on:i=34:hud=10:nm=10:rtra=on_2957 on theBenchmark for (2957ds/34Mi)
% 34.63/5.21 % (546945)Instruction limit reached!
% 34.63/5.21 % (546945)------------------------------
% 34.63/5.21 % (546945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.63/5.21 % (546945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.63/5.21 % (546945)CaDiCaL version: 2.1.3
% 34.63/5.21 % (546945)Termination reason: Instruction limit
% 34.63/5.21 % (546945)Termination phase: Saturation
% 34.63/5.21 % (546945)Time elapsed: 0.252 s
% 34.63/5.21 % (546945)Peak memory usage: 15 MB
% 34.63/5.21 % (546945)Instructions burned: 446 (million)
% 34.63/5.21 % (546943)Instruction limit reached!
% 34.63/5.21 % (546943)------------------------------
% 34.63/5.21 % (546943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.63/5.21 % (546943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.63/5.21 % (546943)CaDiCaL version: 2.1.3
% 34.63/5.21 % (546943)Termination reason: Instruction limit
% 34.63/5.21 % (546943)Termination phase: Saturation
% 34.63/5.21 % (546943)Time elapsed: 0.375 s
% 34.63/5.21 % (546943)Peak memory usage: 16 MB
% 34.63/5.21 % (546943)Instructions burned: 478 (million)
% 34.63/5.21 % (546960)Instruction limit reached!
% 34.63/5.21 % (546960)------------------------------
% 34.63/5.21 % (546960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.63/5.21 % (546960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.63/5.21 % (546960)CaDiCaL version: 2.1.3
% 34.63/5.21 % (546960)Termination reason: Instruction limit
% 34.63/5.21 % (546960)Termination phase: Saturation
% 34.63/5.21 % (546960)Time elapsed: 0.024 s
% 34.63/5.21 % (546960)Peak memory usage: 11 MB
% 34.63/5.21 % (546960)Instructions burned: 34 (million)
% 34.63/5.21 % (546963)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 34.63/5.21 % (546963)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=468620526:i=372:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2957 on theBenchmark for (2957ds/372Mi)
% 34.63/5.21 % (546964)lrs+1002_1024_sil=128000:tgt=ground:e2e=on:si=on:uwa=interpreted_only:fd=off:nwc=1:random_seed=2170313126:cts=off:avsq=on:i=670:avsqr=1,16:nm=16:rtra=on_2956 on theBenchmark for (2956ds/670Mi)
% 34.63/5.21 % (546965)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1097105983:hsq=on:st=2:i=647:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2956 on theBenchmark for (2956ds/647Mi)
% 35.86/5.57 % (546889)Instruction limit reached!
% 35.86/5.57 % (546889)------------------------------
% 35.86/5.57 % (546889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.86/5.57 % (546889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.86/5.57 % (546889)CaDiCaL version: 2.1.3
% 35.86/5.57 % (546889)Termination reason: Instruction limit
% 35.86/5.57 % (546889)Termination phase: Saturation
% 35.86/5.57 % (546889)Time elapsed: 1.734 s
% 35.86/5.57 % (546889)Peak memory usage: 17 MB
% 35.86/5.57 % (546889)Instructions burned: 2186 (million)
% 35.86/5.57 % (546969)dis+10_128_sil=128000:tgt=full:plsq=on:plsqc=3:cnfonf=off:si=on:sp=arity:spb=goal_then_units:uwa=one_side_interpreted:nwc=1.5:random_seed=1438442456:i=857:add=off:kws=frequency:rtra=on:ntd=on_2955 on theBenchmark for (2955ds/857Mi)
% 35.86/5.57 % (546969)Refutation not found, incomplete strategy
% 35.86/5.57 % (546969)------------------------------
% 35.86/5.57 % (546969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.86/5.57 % (546969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.86/5.57 % (546969)CaDiCaL version: 2.1.3
% 35.86/5.57 % (546969)Termination reason: Refutation not found, incomplete strategy
% 35.86/5.57 % (546969)Time elapsed: 0.029 s
% 35.86/5.57 % (546969)Peak memory usage: 13 MB
% 35.86/5.57 % (546969)Instructions burned: 55 (million)
% 35.86/5.57 % (546969)------------------------------
% 35.86/5.57 % (546969)------------------------------
% 35.86/5.57 % (546959)Instruction limit reached!
% 35.86/5.57 % (546959)------------------------------
% 35.86/5.57 % (546959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.86/5.57 % (546959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.86/5.57 % (546959)CaDiCaL version: 2.1.3
% 35.86/5.57 % (546959)Termination reason: Instruction limit
% 35.86/5.57 % (546959)Termination phase: Saturation
% 35.86/5.57 % (546959)Time elapsed: 0.217 s
% 35.86/5.57 % (546959)Peak memory usage: 13 MB
% 35.86/5.57 % (546959)Instructions burned: 496 (million)
% 35.86/5.57 % (546971)dis+1010_4_anc=all_dependent:to=lpo:sil=128000:fde=unused:cnfonf=conj_eager:si=on:sp=reverse_frequency:lma=off:spb=intro:cbe=off:uwa=off:random_seed=446218694:i=693:add=off:fsr=off:rtra=on:fe=abstraction:ntd=on_2955 on theBenchmark for (2955ds/693Mi)
% 35.86/5.57 % (546972)dis+10_7_sil=128000:cnfonf=lazy_gen:si=on:sos=on:random_seed=2012402329:i=285:hud=10:bd=all:rtra=on:ss=axioms_2955 on theBenchmark for (2955ds/285Mi)
% 35.86/5.57 % (546972)Refutation not found, incomplete strategy
% 35.86/5.57 % (546972)------------------------------
% 35.86/5.57 % (546972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.86/5.57 % (546972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.86/5.57 % (546972)CaDiCaL version: 2.1.3
% 35.86/5.57 % (546972)Termination reason: Refutation not found, incomplete strategy
% 35.86/5.57 % (546972)Time elapsed: 0.005 s
% 35.86/5.57 % (546972)Peak memory usage: 12 MB
% 35.86/5.57 % (546972)Instructions burned: 4 (million)
% 35.86/5.57 % (546972)------------------------------
% 35.86/5.57 % (546972)------------------------------
% 35.86/5.57 % (546975)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 35.86/5.57 % (546975)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=3641106836:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2954 on theBenchmark for (2954ds/52Mi)
% 35.86/5.57 % (546975)Instruction limit reached!
% 35.86/5.57 % (546975)------------------------------
% 35.86/5.57 % (546975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.86/5.57 % (546975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.86/5.57 % (546975)CaDiCaL version: 2.1.3
% 35.86/5.57 % (546975)Termination reason: Instruction limit
% 35.86/5.57 % (546975)Termination phase: Saturation
% 35.86/5.57 % (546975)Time elapsed: 0.037 s
% 35.86/5.57 % (546975)Peak memory usage: 11 MB
% 35.86/5.57 % (546975)Instructions burned: 53 (million)
% 35.86/5.57 % (546963)Instruction limit reached!
% 35.86/5.57 % (546963)------------------------------
% 35.86/5.57 % (546963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.86/5.57 % (546963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.18/5.97 % (546963)CaDiCaL version: 2.1.3
% 38.18/5.97 % (546963)Termination reason: Instruction limit
% 38.18/5.97 % (546963)Termination phase: Saturation
% 38.18/5.97 % (546963)Time elapsed: 0.278 s
% 38.18/5.97 % (546963)Peak memory usage: 12 MB
% 38.18/5.97 % (546963)Instructions burned: 375 (million)
% 38.18/5.97 % (546977)dis+10_1_si=on:random_seed=4150741051:i=407:sd=4:rtra=on:ss=axioms:sgt=20_2953 on theBenchmark for (2953ds/407Mi)
% 38.18/5.97 % (546978)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1213534894:i=2240:bs=unit_only:ins=25:rtra=on:ntd=on_2953 on theBenchmark for (2953ds/2240Mi)
% 38.18/5.97 % (546971)Instruction limit reached!
% 38.18/5.97 % (546971)------------------------------
% 38.18/5.97 % (546971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 38.18/5.97 % (546971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.18/5.97 % (546971)CaDiCaL version: 2.1.3
% 38.18/5.97 % (546971)Termination reason: Instruction limit
% 38.18/5.97 % (546971)Termination phase: Saturation
% 38.18/5.97 % (546971)Time elapsed: 0.291 s
% 38.18/5.97 % (546971)Peak memory usage: 15 MB
% 38.18/5.97 % (546971)Instructions burned: 694 (million)
% 38.18/5.97 % (546981)lrs+10_1_sil=128000:e2e=on:si=on:uwa=interpreted_only:random_seed=2370271963:st=2:i=336:sd=1:rtra=on:ss=axioms:ntd=on_2952 on theBenchmark for (2952ds/336Mi)
% 38.18/5.97 % (546981)Refutation not found, incomplete strategy
% 38.18/5.97 % (546981)------------------------------
% 38.18/5.97 % (546981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 38.18/5.97 % (546981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.18/5.97 % (546981)CaDiCaL version: 2.1.3
% 38.18/5.97 % (546981)Termination reason: Refutation not found, incomplete strategy
% 38.18/5.97 % (546981)Time elapsed: 0.004 s
% 38.18/5.97 % (546981)Peak memory usage: 12 MB
% 38.18/5.97 % (546981)Instructions burned: 7 (million)
% 38.18/5.97 % (546981)------------------------------
% 38.18/5.97 % (546981)------------------------------
% 38.18/5.97 % (546983)lrs+10_1_to=lpo:sil=128000:fde=none:cnfonf=off:si=on:sp=unary_first:urr=on:uwa=one_side_constant:random_seed=3356825513:s2a=on:i=1142:s2at=3:bd=all:rtra=on_2951 on theBenchmark for (2951ds/1142Mi)
% 38.18/5.97 % (546983)Refutation not found, incomplete strategy
% 38.18/5.97 % (546983)------------------------------
% 38.18/5.97 % (546983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 38.18/5.97 % (546983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.18/5.97 % (546983)CaDiCaL version: 2.1.3
% 38.18/5.97 % (546983)Termination reason: Refutation not found, incomplete strategy
% 38.18/5.97 % (546983)Time elapsed: 0.016 s
% 38.18/5.97 % (546983)Peak memory usage: 12 MB
% 38.18/5.97 % (546983)Instructions burned: 27 (million)
% 38.18/5.97 % (546983)------------------------------
% 38.18/5.97 % (546983)------------------------------
% 38.18/5.97 % (546965)Instruction limit reached!
% 38.18/5.97 % (546965)------------------------------
% 38.18/5.97 % (546965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 38.18/5.97 % (546965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.18/5.97 % (546965)CaDiCaL version: 2.1.3
% 38.18/5.97 % (546965)Termination reason: Instruction limit
% 38.18/5.97 % (546965)Termination phase: Saturation
% 38.18/5.97 % (546965)Time elapsed: 0.523 s
% 38.18/5.97 % (546965)Peak memory usage: 14 MB
% 38.18/5.97 % (546965)Instructions burned: 648 (million)
% 38.18/5.97 % (546985)dis+1002_1_sil=128000:si=on:uwa=off:random_seed=3526501872:st=3:i=376:sd=4:rtra=on:ss=axioms:ntd=on_2951 on theBenchmark for (2951ds/376Mi)
% 38.18/5.97 % (546964)Instruction limit reached!
% 38.18/5.97 % (546964)------------------------------
% 38.18/5.97 % (546964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 38.18/5.97 % (546964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.18/5.97 % (546964)CaDiCaL version: 2.1.3
% 38.18/5.97 % (546964)Termination reason: Instruction limit
% 38.18/5.97 % (546964)Termination phase: Saturation
% 38.18/5.97 % (546964)Time elapsed: 0.535 s
% 38.18/5.97 % (546964)Peak memory usage: 19 MB
% 38.18/5.97 % (546964)Instructions burned: 670 (million)
% 38.18/5.97 % (546988)WARNING Broken Constraint: if avatar_split_queue_cutoffs(4) has been set then avatar_split_queue(off) is equal to on
% 38.18/5.97 % (546988)lrs+10_1_to=kbo:si=on:sp=const_frequency:sos=on:spb=non_intro:uwa=hol:avsqc=4:random_seed=2121840084:st=3:uwa_fpi=on:i=959:fgj=on:piset=pi_sigma:hud=5:nm=16:rtra=on:fe=abstraction:ss=axioms:ixr=off:ntd=on_2951 on theBenchmark for (2951ds/959Mi)
% 41.24/6.15 % (546986)dis+1002_4:1_anc=none:sil=128000:sas=cadical:si=on:sp=weighted_frequency:sos=on:uwa=one_side_interpreted:random_seed=2590865433:i=766:bd=all:rtra=on_2951 on theBenchmark for (2951ds/766Mi)
% 41.24/6.15 % (546977)Instruction limit reached!
% 41.24/6.15 % (546977)------------------------------
% 41.24/6.15 % (546977)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.24/6.15 % (546977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.24/6.15 % (546977)CaDiCaL version: 2.1.3
% 41.24/6.15 % (546977)Termination reason: Instruction limit
% 41.24/6.15 % (546977)Termination phase: Saturation
% 41.24/6.15 % (546977)Time elapsed: 0.304 s
% 41.24/6.15 % (546977)Peak memory usage: 16 MB
% 41.24/6.15 % (546977)Instructions burned: 407 (million)
% 41.24/6.15 % (546991)dis+1010_1024_sil=128000:plsq=on:plsqc=1:e2e=on:si=on:lma=off:plsqr=64,1:uwa=interpreted_only:fd=off:random_seed=176395694:i=6359:add=on:kws=inv_frequency:aac=none:rtra=on:c=on:er=filter:ntd=on_2950 on theBenchmark for (2950ds/6359Mi)
% 41.24/6.15 % (546905)Instruction limit reached!
% 41.24/6.15 % (546905)------------------------------
% 41.24/6.15 % (546905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.24/6.15 % (546905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.24/6.15 % (546905)CaDiCaL version: 2.1.3
% 41.24/6.15 % (546905)Termination reason: Instruction limit
% 41.24/6.15 % (546905)Termination phase: Saturation
% 41.24/6.15 % (546905)Time elapsed: 1.904 s
% 41.24/6.15 % (546905)Peak memory usage: 17 MB
% 41.24/6.15 % (546905)Instructions burned: 2470 (million)
% 41.24/6.15 % (546993)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1980363935:st=4:i=35:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2949 on theBenchmark for (2949ds/35Mi)
% 41.24/6.15 % (546985)Instruction limit reached!
% 41.24/6.15 % (546985)------------------------------
% 41.24/6.15 % (546985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.24/6.15 % (546985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.24/6.15 % (546985)CaDiCaL version: 2.1.3
% 41.24/6.15 % (546985)Termination reason: Instruction limit
% 41.24/6.15 % (546985)Termination phase: Saturation
% 41.24/6.15 % (546985)Time elapsed: 0.226 s
% 41.24/6.15 % (546985)Peak memory usage: 15 MB
% 41.24/6.15 % (546985)Instructions burned: 377 (million)
% 41.24/6.15 % (546993)Instruction limit reached!
% 41.24/6.15 % (546993)------------------------------
% 41.24/6.15 % (546993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.24/6.15 % (546993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.24/6.15 % (546993)CaDiCaL version: 2.1.3
% 41.24/6.15 % (546993)Termination reason: Instruction limit
% 41.24/6.15 % (546993)Termination phase: Saturation
% 41.24/6.15 % (546993)Time elapsed: 0.017 s
% 41.24/6.15 % (546993)Peak memory usage: 11 MB
% 41.24/6.15 % (546993)Instructions burned: 35 (million)
% 41.24/6.15 % (546996)dis+21_1_sil=128000:tgt=full:fde=none:e2e=on:si=on:urr=on:uwa=interpreted_only:s2agt=32:sac=on:random_seed=2206631208:s2a=on:i=876:s2at=6:nm=2:rtra=on_2948 on theBenchmark for (2948ds/876Mi)
% 41.24/6.15 % (546995)dis+10_1_sfv=off:sil=128000:cnfonf=lazy_gen:si=on:uwa=off:nwc=1:chr=on:random_seed=3868487388:hsq=on:hsqr=1,8:i=53:hsql=off:bd=all:rtra=on:ixr=off_2948 on theBenchmark for (2948ds/53Mi)
% 41.24/6.15 % (546995)Instruction limit reached!
% 41.24/6.15 % (546995)------------------------------
% 41.24/6.15 % (546995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.24/6.15 % (546995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.24/6.15 % (546995)CaDiCaL version: 2.1.3
% 41.24/6.15 % (546995)Termination reason: Instruction limit
% 41.24/6.15 % (546995)Termination phase: Saturation
% 41.24/6.15 % (546995)Time elapsed: 0.041 s
% 41.24/6.15 % (546995)Peak memory usage: 12 MB
% 41.24/6.15 % (546995)Instructions burned: 53 (million)
% 41.24/6.15 % (546999)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3692561313:i=57:ep=R:rtra=on:ntd=on_2948 on theBenchmark for (2948ds/57Mi)
% 41.24/6.15 % (546999)Instruction limit reached!
% 41.24/6.15 % (546999)------------------------------
% 41.24/6.15 % (546999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.90/6.31 % (546999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.90/6.31 % (546999)CaDiCaL version: 2.1.3
% 41.90/6.31 % (546999)Termination reason: Instruction limit
% 41.90/6.31 % (546999)Termination phase: Saturation
% 41.90/6.31 % (546999)Time elapsed: 0.043 s
% 41.90/6.31 % (546999)Peak memory usage: 12 MB
% 41.90/6.31 % (546999)Instructions burned: 58 (million)
% 41.90/6.31 % (547001)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 41.90/6.31 % (547001)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=945912809:i=306:bd=all:rtra=on_2947 on theBenchmark for (2947ds/306Mi)
% 41.90/6.31 % (546988)Instruction limit reached!
% 41.90/6.31 % (546988)------------------------------
% 41.90/6.31 % (546988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.90/6.31 % (546988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.90/6.31 % (546988)CaDiCaL version: 2.1.3
% 41.90/6.31 % (546988)Termination reason: Instruction limit
% 41.90/6.31 % (546988)Termination phase: Saturation
% 41.90/6.31 % (546988)Time elapsed: 0.396 s
% 41.90/6.31 % (546988)Peak memory usage: 21 MB
% 41.90/6.31 % (546988)Instructions burned: 961 (million)
% 41.90/6.31 % (547003)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=3532010591:i=262:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_2946 on theBenchmark for (2946ds/262Mi)
% 41.90/6.31 % (547003)Instruction limit reached!
% 41.90/6.31 % (547003)------------------------------
% 41.90/6.31 % (547003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.90/6.31 % (547003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.90/6.31 % (547003)CaDiCaL version: 2.1.3
% 41.90/6.31 % (547003)Termination reason: Instruction limit
% 41.90/6.31 % (547003)Termination phase: Saturation
% 41.90/6.31 % (547003)Time elapsed: 0.101 s
% 41.90/6.31 % (547003)Peak memory usage: 13 MB
% 41.90/6.31 % (547003)Instructions burned: 263 (million)
% 41.90/6.31 % (547005)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on
% 41.90/6.31 % (547005)ott+1002_16_sil=128000:si=on:random_seed=2463955749:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_2945 on theBenchmark for (2945ds/409Mi)
% 41.90/6.31 % (547001)Instruction limit reached!
% 41.90/6.31 % (547001)------------------------------
% 41.90/6.31 % (547001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.90/6.31 % (547001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.90/6.31 % (547001)CaDiCaL version: 2.1.3
% 41.90/6.31 % (547001)Termination reason: Instruction limit
% 41.90/6.31 % (547001)Termination phase: Saturation
% 41.90/6.31 % (547001)Time elapsed: 0.212 s
% 41.90/6.31 % (547001)Peak memory usage: 14 MB
% 41.90/6.31 % (547001)Instructions burned: 307 (million)
% 41.90/6.31 % (546986)Instruction limit reached!
% 41.90/6.31 % (546986)------------------------------
% 41.90/6.31 % (546986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.90/6.31 % (546986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.90/6.31 % (546986)CaDiCaL version: 2.1.3
% 41.90/6.31 % (546986)Termination reason: Instruction limit
% 41.90/6.31 % (546986)Termination phase: Saturation
% 41.90/6.31 % (546986)Time elapsed: 0.611 s
% 41.90/6.31 % (546986)Peak memory usage: 20 MB
% 41.90/6.31 % (546986)Instructions burned: 766 (million)
% 41.90/6.31 % (547007)dis+10_1_sil=128000:plsq=on:si=on:plsqr=32,1:uwa=off:random_seed=65330187:s2a=on:i=381:rtra=on_2944 on theBenchmark for (2944ds/381Mi)
% 41.90/6.31 % (547008)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1427321468:cond=on:i=324:rtra=on:ntd=on_2944 on theBenchmark for (2944ds/324Mi)
% 41.90/6.31 % (547005)Instruction limit reached!
% 41.90/6.31 % (547005)------------------------------
% 41.90/6.31 % (547005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.90/6.31 % (547005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.90/6.31 % (547005)CaDiCaL version: 2.1.3
% 41.90/6.31 % (547005)Termination reason: Instruction limit
% 41.90/6.31 % (547005)Termination phase: Saturation
% 41.90/6.31 % (547005)Time elapsed: 0.177 s
% 41.90/6.31 % (547005)Peak memory usage: 15 MB
% 41.90/6.31 % (547005)Instructions burned: 410 (million)
% 41.90/6.31 % (547011)lrs+10_1_sil=128000:fde=none:si=on:sos=on:spb=goal_then_units:urr=on:random_seed=820903252:i=240:kws=inv_precedence:rtra=on_2943 on theBenchmark for (2943ds/240Mi)
% 43.55/6.64 % (547011)Refutation not found, incomplete strategy
% 43.55/6.64 % (547011)------------------------------
% 43.55/6.64 % (547011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.55/6.64 % (547011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.55/6.64 % (547011)CaDiCaL version: 2.1.3
% 43.55/6.64 % (547011)Termination reason: Refutation not found, incomplete strategy
% 43.55/6.64 % (547011)Time elapsed: 0.008 s
% 43.55/6.64 % (547011)Peak memory usage: 12 MB
% 43.55/6.64 % (547011)Instructions burned: 6 (million)
% 43.55/6.64 % (547011)------------------------------
% 43.55/6.64 % (547011)------------------------------
% 43.55/6.64 % (547013)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 43.55/6.64 % (547013)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3461994816:cts=off:uwa_fpi=on:i=124:av=off:fsr=off:rtra=on:ntd=on_2943 on theBenchmark for (2943ds/124Mi)
% 43.55/6.64 % (547007)Instruction limit reached!
% 43.55/6.64 % (547007)------------------------------
% 43.55/6.64 % (547007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.55/6.64 % (547007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.55/6.64 % (547007)CaDiCaL version: 2.1.3
% 43.55/6.64 % (547007)Termination reason: Instruction limit
% 43.55/6.64 % (547007)Termination phase: Saturation
% 43.55/6.64 % (547007)Time elapsed: 0.203 s
% 43.55/6.64 % (547007)Peak memory usage: 15 MB
% 43.55/6.64 % (547007)Instructions burned: 381 (million)
% 43.55/6.64 % (547015)lrs+1010_2_to=lpo:cnfonf=off:e2e=on:si=on:random_seed=222821100:uwa_fpi=on:i=223:bd=all:rtra=on:fe=abstraction:ntd=on_2942 on theBenchmark for (2942ds/223Mi)
% 43.55/6.64 % (547013)Instruction limit reached!
% 43.55/6.64 % (547013)------------------------------
% 43.55/6.64 % (547013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.55/6.64 % (547013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.55/6.64 % (547013)CaDiCaL version: 2.1.3
% 43.55/6.64 % (547013)Termination reason: Instruction limit
% 43.55/6.64 % (547013)Termination phase: Saturation
% 43.55/6.64 % (547013)Time elapsed: 0.049 s
% 43.55/6.64 % (547013)Peak memory usage: 12 MB
% 43.55/6.64 % (547013)Instructions burned: 124 (million)
% 43.55/6.64 % (547017)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1003456214:s2a=on:i=282:kws=inv_frequency:bd=all:rtra=on_2942 on theBenchmark for (2942ds/282Mi)
% 43.55/6.64 % (547015)Refutation not found, incomplete strategy
% 43.55/6.64 % (547015)------------------------------
% 43.55/6.64 % (547015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.55/6.64 % (547015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.55/6.64 % (547015)CaDiCaL version: 2.1.3
% 43.55/6.64 % (547015)Termination reason: Refutation not found, incomplete strategy
% 43.55/6.64 % (547015)Time elapsed: 0.041 s
% 43.55/6.64 % (547015)Peak memory usage: 13 MB
% 43.55/6.64 % (547015)Instructions burned: 51 (million)
% 43.55/6.64 % (547015)------------------------------
% 43.55/6.64 % (547015)------------------------------
% 43.55/6.64 % (547008)Instruction limit reached!
% 43.55/6.64 % (547008)------------------------------
% 43.55/6.64 % (547008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.55/6.64 % (547008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.55/6.65 % (547008)CaDiCaL version: 2.1.3
% 43.55/6.65 % (547008)Termination reason: Instruction limit
% 43.55/6.65 % (547008)Termination phase: Saturation
% 43.55/6.65 % (547008)Time elapsed: 0.276 s
% 43.55/6.65 % (547008)Peak memory usage: 13 MB
% 43.55/6.65 % (547008)Instructions burned: 324 (million)
% 43.55/6.65 % (547019)lrs+10_1_sil=128000:tgt=ground:cnfonf=conj_eager:si=on:random_seed=1926809037:s2a=on:i=464:kws=frequency:bd=all:rtra=on:ss=axioms_2941 on theBenchmark for (2941ds/464Mi)
% 43.55/6.65 % (547019)Refutation not found, incomplete strategy
% 43.55/6.65 % (547019)------------------------------
% 43.55/6.65 % (547019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.55/6.65 % (547019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.55/6.65 % (547019)CaDiCaL version: 2.1.3
% 43.55/6.65 % (547019)Termination reason: Refutation not found, incomplete strategy
% 43.55/6.65 % (547019)Time elapsed: 0.006 s
% 43.55/6.65 % (547019)Peak memory usage: 13 MB
% 43.55/6.65 % (547019)Instructions burned: 5 (million)
% 43.55/6.65 % (546996)Instruction limit reached!
% 43.55/6.65 % (546996)------------------------------
% 44.50/6.91 % (546996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.50/6.91 % (546996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.50/6.91 % (546996)CaDiCaL version: 2.1.3
% 44.50/6.91 % (546996)Termination reason: Instruction limit
% 44.50/6.91 % (546996)Termination phase: Saturation
% 44.50/6.91 % (547019)------------------------------
% 44.50/6.91 % (547019)------------------------------
% 44.50/6.91 % (546996)Time elapsed: 0.706 s
% 44.50/6.91 % (546996)Peak memory usage: 14 MB
% 44.50/6.91 % (546996)Instructions burned: 876 (million)
% 44.50/6.91 % (547020)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=1819900428:i=88:s2at=3:nm=2:rtra=on:rawr=on_2941 on theBenchmark for (2941ds/88Mi)
% 44.50/6.91 % (547022)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=1854564236:s2a=on:cond=on:i=280:add=on:bd=preordered:rtra=on:er=filter_2941 on theBenchmark for (2941ds/280Mi)
% 44.50/6.91 % (547024)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 44.50/6.91 % (547024)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=2130345436:i=4386:hud=10:nm=16:av=off:rtra=on:ntd=on_2941 on theBenchmark for (2941ds/4386Mi)
% 44.50/6.91 % (547020)Instruction limit reached!
% 44.50/6.91 % (547020)------------------------------
% 44.50/6.91 % (547020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.50/6.91 % (547020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.50/6.91 % (547020)CaDiCaL version: 2.1.3
% 44.50/6.91 % (547020)Termination reason: Instruction limit
% 44.50/6.91 % (547020)Termination phase: Saturation
% 44.50/6.91 % (547020)Time elapsed: 0.034 s
% 44.50/6.91 % (547020)Peak memory usage: 12 MB
% 44.50/6.91 % (547020)Instructions burned: 89 (million)
% 44.50/6.91 % (547027)WARNING Broken Constraint: if lookahaed_delay(10) has been set then selection(21) is not lookahead selection
% 44.50/6.91 % (547027)WARNING Broken Constraint: if mono_ep(off) has been set then equality_proxy(off) is not equal to off
% 44.50/6.91 % (547027)ott+21_3:13_sil=128000:cnfonf=off:sas=cadical:si=on:sp=arity:lma=off:lsd=10:uwa=one_side_interpreted:mep=off:chr=on:random_seed=749223784:hsq=on:st=2:i=483:sd=1:hsql=off:rtra=on:fe=abstraction:fdi=32:ss=axioms:sgt=20:ntd=on_2941 on theBenchmark for (2941ds/483Mi)
% 44.50/6.91 % (547027)Refutation not found, incomplete strategy
% 44.50/6.91 % (547027)------------------------------
% 44.50/6.91 % (547027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.50/6.91 % (547027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.50/6.91 % (547027)CaDiCaL version: 2.1.3
% 44.50/6.91 % (547027)Termination reason: Refutation not found, incomplete strategy
% 44.50/6.91 % (547027)Time elapsed: 0.021 s
% 44.50/6.91 % (547027)Peak memory usage: 13 MB
% 44.50/6.91 % (547027)Instructions burned: 53 (million)
% 44.50/6.91 % (547027)------------------------------
% 44.50/6.91 % (547027)------------------------------
% 44.50/6.91 % (547029)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=3899095856:i=73:rtra=on_2940 on theBenchmark for (2940ds/73Mi)
% 44.50/6.91 % (547029)Instruction limit reached!
% 44.50/6.91 % (547029)------------------------------
% 44.50/6.91 % (547029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.50/6.91 % (547029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.50/6.91 % (547029)CaDiCaL version: 2.1.3
% 44.50/6.91 % (547029)Termination reason: Instruction limit
% 44.50/6.91 % (547029)Termination phase: Saturation
% 44.50/6.91 % (547029)Time elapsed: 0.035 s
% 44.50/6.91 % (547029)Peak memory usage: 12 MB
% 44.50/6.91 % (547029)Instructions burned: 74 (million)
% 44.50/6.91 % (547017)Instruction limit reached!
% 44.50/6.91 % (547017)------------------------------
% 44.50/6.91 % (547017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.50/6.91 % (547017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.50/6.91 % (547017)CaDiCaL version: 2.1.3
% 44.50/6.91 % (547017)Termination reason: Instruction limit
% 44.50/6.91 % (547017)Termination phase: Saturation
% 44.50/6.91 % (547017)Time elapsed: 0.214 s
% 44.50/6.91 % (547017)Peak memory usage: 13 MB
% 44.50/6.91 % (547017)Instructions burned: 282 (million)
% 49.26/7.35 % (547032)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2931158337:cts=off:i=176:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2940 on theBenchmark for (2940ds/176Mi)
% 49.26/7.35 % (547034)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 49.26/7.35 % (547034)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=3990241185:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2939 on theBenchmark for (2939ds/39Mi)
% 49.26/7.35 % (547034)Instruction limit reached!
% 49.26/7.35 % (547034)------------------------------
% 49.26/7.35 % (547034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 49.26/7.35 % (547034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 49.26/7.35 % (547034)CaDiCaL version: 2.1.3
% 49.26/7.35 % (547034)Termination reason: Instruction limit
% 49.26/7.35 % (547034)Termination phase: Saturation
% 49.26/7.35 % (547034)Time elapsed: 0.017 s
% 49.26/7.35 % (547034)Peak memory usage: 11 MB
% 49.26/7.35 % (547034)Instructions burned: 41 (million)
% 49.26/7.35 % (547039)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1622017581:i=708:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2939 on theBenchmark for (2939ds/708Mi)
% 49.26/7.35 % (547022)Instruction limit reached!
% 49.26/7.35 % (547022)------------------------------
% 49.26/7.35 % (547022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 49.26/7.35 % (547022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 49.26/7.35 % (547022)CaDiCaL version: 2.1.3
% 49.26/7.35 % (547022)Termination reason: Instruction limit
% 49.26/7.35 % (547022)Termination phase: Saturation
% 49.26/7.35 % (547022)Time elapsed: 0.196 s
% 49.26/7.35 % (547022)Peak memory usage: 12 MB
% 49.26/7.35 % (547022)Instructions burned: 281 (million)
% 49.26/7.35 % (547043)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 49.26/7.35 % (547043)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=2821570344:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2939 on theBenchmark for (2939ds/252Mi)
% 49.26/7.35 % (547043)Refutation not found, incomplete strategy
% 49.26/7.35 % (547043)------------------------------
% 49.26/7.35 % (547043)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 49.26/7.35 % (547043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 49.26/7.35 % (547043)CaDiCaL version: 2.1.3
% 49.26/7.35 % (547043)Termination reason: Refutation not found, incomplete strategy
% 49.26/7.35 % (547043)Time elapsed: 0.039 s
% 49.26/7.35 % (547043)Peak memory usage: 12 MB
% 49.26/7.35 % (547043)Instructions burned: 54 (million)
% 49.26/7.35 % (547043)------------------------------
% 49.26/7.35 % (547043)------------------------------
% 49.26/7.35 % (547032)Instruction limit reached!
% 49.26/7.35 % (547032)------------------------------
% 49.26/7.35 % (547032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 49.26/7.35 % (547032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 49.26/7.35 % (547032)CaDiCaL version: 2.1.3
% 49.26/7.35 % (547032)Termination reason: Instruction limit
% 49.26/7.35 % (547032)Termination phase: Saturation
% 49.26/7.35 % (547032)Time elapsed: 0.133 s
% 49.26/7.35 % (547032)Peak memory usage: 13 MB
% 49.26/7.35 % (547032)Instructions burned: 177 (million)
% 49.26/7.35 % (547045)dis+10_4_sil=128000:tgt=full:fde=unused:cnfonf=lazy_not_gen:sas=cadical:si=on:uwa=off:sac=on:random_seed=3168294601:i=823:fsr=off:rtra=on_2938 on theBenchmark for (2938ds/823Mi)
% 49.26/7.35 % (547046)WARNING Broken Constraint: lrs_first_time_check(100) is less than 100
% 49.26/7.35 % (547046)lrs+1010_7_anc=all_dependent:sil=128000:cnfonf=lazy_not_gen:si=on:urr=on:rp=on:sac=on:lftc=100:random_seed=2844001899:lrd=on:st=3:i=16202:add=on:sd=3:kws=frequency:rtra=on:ss=axioms_2938 on theBenchmark for (2938ds/16202Mi)
% 49.26/7.35 % (546978)Instruction limit reached!
% 49.26/7.35 % (546978)------------------------------
% 49.26/7.35 % (546978)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 49.26/7.35 % (546978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 49.26/7.35 % (546978)CaDiCaL version: 2.1.3
% 51.96/7.99 % (546978)Termination reason: Instruction limit
% 51.96/7.99 % (546978)Termination phase: Saturation
% 51.96/7.99 % (546978)Time elapsed: 1.698 s
% 51.96/7.99 % (546978)Peak memory usage: 17 MB
% 51.96/7.99 % (546978)Instructions burned: 2240 (million)
% 51.96/7.99 % (546828)Instruction limit reached!
% 51.96/7.99 % (546828)------------------------------
% 51.96/7.99 % (546828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.96/7.99 % (546828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.96/7.99 % (546828)CaDiCaL version: 2.1.3
% 51.96/7.99 % (546828)Termination reason: Instruction limit
% 51.96/7.99 % (546828)Termination phase: Saturation
% 51.96/7.99 % (546828)Time elapsed: 4.935 s
% 51.96/7.99 % (546828)Peak memory usage: 13 MB
% 51.96/7.99 % (546828)Instructions burned: 9841 (million)
% 51.96/7.99 % (547050)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(2) has been set then positive_literal_split_queue(off) is equal to on
% 51.96/7.99 % (547050)WARNING Broken Constraint: if ho_split_queue_lambda_weight(0) has been set then ho_split_queue(off) is equal to on
% 51.96/7.99 % (547050)dis+1010_1_anc=none:sil=128000:plsqc=2:sas=cadical:si=on:hsqlw=0:uwa=one_side_interpreted:sac=on:random_seed=356730157:i=177:add=on:bd=preordered:rtra=on:rawr=on_2936 on theBenchmark for (2936ds/177Mi)
% 51.96/7.99 % (547049)dis+10_1_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:uwa=off:random_seed=1546508750:s2a=on:i=300:s2at=10:bd=all:rtra=on:ntd=on_2936 on theBenchmark for (2936ds/300Mi)
% 51.96/7.99 % (547050)Instruction limit reached!
% 51.96/7.99 % (547050)------------------------------
% 51.96/7.99 % (547050)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.96/7.99 % (547050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.96/7.99 % (547050)CaDiCaL version: 2.1.3
% 51.96/7.99 % (547050)Termination reason: Instruction limit
% 51.96/7.99 % (547050)Termination phase: Saturation
% 51.96/7.99 % (547050)Time elapsed: 0.072 s
% 51.96/7.99 % (547050)Peak memory usage: 13 MB
% 51.96/7.99 % (547050)Instructions burned: 179 (million)
% 51.96/7.99 % (547053)lrs+10_1_cnfonf=conj_eager:si=on:random_seed=1336917569:st=1.5:s2a=on:i=715:rtra=on:ss=axioms_2935 on theBenchmark for (2935ds/715Mi)
% 51.96/7.99 % (547039)Instruction limit reached!
% 51.96/7.99 % (547039)------------------------------
% 51.96/7.99 % (547039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.96/7.99 % (547039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.96/7.99 % (547039)CaDiCaL version: 2.1.3
% 51.96/7.99 % (547039)Termination reason: Instruction limit
% 51.96/7.99 % (547039)Termination phase: Saturation
% 51.96/7.99 % (547039)Time elapsed: 0.402 s
% 51.96/7.99 % (547039)Peak memory usage: 19 MB
% 51.96/7.99 % (547039)Instructions burned: 708 (million)
% 51.96/7.99 % (547055)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(3) has been set then positive_literal_split_queue(off) is equal to on
% 51.96/7.99 % (547055)WARNING Broken Constraint: if positive_literal_split_queue_ratios(19,3) has been set then positive_literal_split_queue(off) is equal to on
% 51.96/7.99 % (547055)dis+11_1_sil=128000:plsqc=3:cnfonf=lazy_gen:si=on:sp=const_max:lma=off:plsqr=19,3:lcm=predicate:uwa=off:fd=preordered:nwc=1:random_seed=2288653601:i=230:add=on:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2935 on theBenchmark for (2935ds/230Mi)
% 51.96/7.99 % (547055)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 51.96/7.99 % (547049)Instruction limit reached!
% 51.96/7.99 % (547049)------------------------------
% 51.96/7.99 % (547049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.96/7.99 % (547049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.96/7.99 % (547049)CaDiCaL version: 2.1.3
% 51.96/7.99 % (547049)Termination reason: Instruction limit
% 51.96/7.99 % (547049)Termination phase: Saturation
% 51.96/7.99 % (547049)Time elapsed: 0.224 s
% 51.96/7.99 % (547049)Peak memory usage: 13 MB
% 51.96/7.99 % (547049)Instructions burned: 301 (million)
% 51.96/7.99 % (547055)Instruction limit reached!
% 51.96/7.99 % (547055)------------------------------
% 51.96/7.99 % (547055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.96/7.99 % (547055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.96/7.99 % (547055)CaDiCaL version: 2.1.3
% 51.96/7.99 % (547055)Termination reason: Instruction limit
% 51.96/7.99 % (547055)Termination phase: Saturation
% 48.35/8.41 % (547055)Time elapsed: 0.114 s
% 48.35/8.41 % (547055)Peak memory usage: 13 MB
% 48.35/8.41 % (547055)Instructions burned: 232 (million)
% 48.35/8.41 % (547058)WARNING Broken Constraint: if lrs_retroactive_deletes(on) has been set then saturation_algorithm(otter) is equal to lrs
% 48.35/8.41 % (547058)ott+2_2:1_sil=128000:tgt=full:drc=off:si=on:lma=off:urr=on:cbe=off:uwa=interpreted_only:random_seed=2262506628:lrd=on:i=841:nm=0:rtra=on_2933 on theBenchmark for (2933ds/841Mi)
% 48.35/8.41 % (547057)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=2192004631:s2a=on:i=606:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2934 on theBenchmark for (2934ds/606Mi)
% 48.35/8.41 % (547045)Instruction limit reached!
% 48.35/8.41 % (547045)------------------------------
% 48.35/8.41 % (547045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/8.41 % (547045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/8.41 % (547045)CaDiCaL version: 2.1.3
% 48.35/8.41 % (547045)Termination reason: Instruction limit
% 48.35/8.41 % (547045)Termination phase: Saturation
% 48.35/8.41 % (547045)Time elapsed: 0.657 s
% 48.35/8.41 % (547045)Peak memory usage: 14 MB
% 48.35/8.41 % (547045)Instructions burned: 823 (million)
% 48.35/8.41 % (547061)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4047328138:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2931 on theBenchmark for (2931ds/445Mi)
% 48.35/8.41 % (547053)Instruction limit reached!
% 48.35/8.41 % (547053)------------------------------
% 48.35/8.41 % (547053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/8.41 % (547053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/8.41 % (547053)CaDiCaL version: 2.1.3
% 48.35/8.41 % (547053)Termination reason: Instruction limit
% 48.35/8.41 % (547053)Termination phase: Saturation
% 48.35/8.41 % (547053)Time elapsed: 0.461 s
% 48.35/8.41 % (547053)Peak memory usage: 13 MB
% 48.35/8.41 % (547053)Instructions burned: 715 (million)
% 48.35/8.41 % (547063)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=3707437414:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2930 on theBenchmark for (2930ds/71Mi)
% 48.35/8.41 % (547063)Instruction limit reached!
% 48.35/8.41 % (547063)------------------------------
% 48.35/8.41 % (547063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/8.41 % (547063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/8.41 % (547063)CaDiCaL version: 2.1.3
% 48.35/8.41 % (547063)Termination reason: Instruction limit
% 48.35/8.41 % (547063)Termination phase: Saturation
% 48.35/8.41 % (547063)Time elapsed: 0.035 s
% 48.35/8.41 % (547063)Peak memory usage: 13 MB
% 48.35/8.41 % (547063)Instructions burned: 72 (million)
% 48.35/8.41 % (547065)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 48.35/8.41 % (547065)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 48.35/8.41 % (547065)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3349862152:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2930 on theBenchmark for (2930ds/100Mi)
% 48.35/8.41 % (547058)Instruction limit reached!
% 48.35/8.41 % (547058)------------------------------
% 48.35/8.41 % (547058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/8.41 % (547058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/8.41 % (547058)CaDiCaL version: 2.1.3
% 48.35/8.41 % (547058)Termination reason: Instruction limit
% 48.35/8.41 % (547058)Termination phase: Saturation
% 48.35/8.41 % (547058)Time elapsed: 0.380 s
% 48.35/8.41 % (547058)Peak memory usage: 20 MB
% 48.35/8.41 % (547058)Instructions burned: 842 (million)
% 48.35/8.41 % (547067)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(3) has been set then sine_level_split_queue(off) is equal to on
% 48.35/8.41 % (547067)lrs+2_128_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=const_max:sos=on:plsqr=32,1:spb=goal:uwa=interpreted_only:slsqc=3:random_seed=4048318982:i=1352:add=on:aac=none:rtra=on_2929 on theBenchmark for (2929ds/1352Mi)
% 48.35/8.41 % (547065)Instruction limit reached!
% 48.35/8.41 % (547065)------------------------------
% 48.35/8.41 % (547065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/8.41 % (547065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/8.41 % (547065)CaDiCaL version: 2.1.3
% 48.35/8.41 % (547065)Termination reason: Instruction limit
% 48.35/8.41 % (547065)Termination phase: Saturation
% 48.35/8.41 % (547065)Time elapsed: 0.045 s
% 48.35/8.41 % (547065)Peak memory usage: 13 MB
% 48.35/8.41 % (547065)Instructions burned: 101 (million)
% 48.35/8.41 % (547069)lrs-1002_4:1_sfv=off:to=lpo:plsq=on:prc=on:e2e=on:si=on:hsqlw=5:ser=on:spb=goal:acc=on:uwa=off:foolp=on:s2agt=16:slsqc=1:slsq=on:random_seed=3499517657:hsq=on:hsqr=16,1:s2a=on:i=646:nm=16:rtra=on:gtg=exists_top:proc=on_2929 on theBenchmark for (2929ds/646Mi)
% 48.35/8.41 % (547057)Instruction limit reached!
% 48.35/8.41 % (547057)------------------------------
% 48.35/8.41 % (547057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/8.41 % (547057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/8.41 % (547057)CaDiCaL version: 2.1.3
% 48.35/8.41 % (547057)Termination reason: Instruction limit
% 48.35/8.41 % (547057)Termination phase: Saturation
% 48.35/8.41 % (547057)Time elapsed: 0.489 s
% 48.35/8.41 % (547057)Peak memory usage: 19 MB
% 48.35/8.41 % (547057)Instructions burned: 607 (million)
% 48.35/8.41 % (547071)lrs+10_1_sil=128000:si=on:uwa=all:random_seed=3196682228:i=1924:sd=2:kws=precedence:bd=all:rtra=on:ss=axioms:sgt=16_2928 on theBenchmark for (2928ds/1924Mi)
% 48.35/8.41 % (547061)Instruction limit reached!
% 48.35/8.41 % (547061)------------------------------
% 48.35/8.41 % (547061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/8.41 % (547061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/8.41 % (547061)CaDiCaL version: 2.1.3
% 48.35/8.41 % (547061)Termination reason: Instruction limit
% 48.35/8.41 % (547061)Termination phase: Saturation
% 48.35/8.41 % (547061)Time elapsed: 0.336 s
% 48.35/8.41 % (547061)Peak memory usage: 15 MB
% 48.35/8.41 % (547061)Instructions burned: 445 (million)
% 48.35/8.41 % (547074)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3947534032:hsq=on:i=984:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2928 on theBenchmark for (2928ds/984Mi)
% 48.35/8.41 % (547069)Instruction limit reached!
% 48.35/8.41 % (547069)------------------------------
% 48.35/8.41 % (547069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/8.41 % (547069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/8.41 % (547069)CaDiCaL version: 2.1.3
% 48.35/8.41 % (547069)Termination reason: Instruction limit
% 48.35/8.41 % (547069)Termination phase: Saturation
% 48.35/8.41 % (547069)Time elapsed: 0.286 s
% 48.35/8.41 % (547069)Peak memory usage: 19 MB
% 48.35/8.41 % (547069)Instructions burned: 648 (million)
% 48.35/8.41 % (547077)dis+10_128_sil=128000:drc=ordering:fde=unused:si=on:lma=off:uwa=interpreted_only:avsqc=4:random_seed=3498488706:avsq=on:i=592:add=off:kws=inv_frequency:bd=preordered:rtra=on_2926 on theBenchmark for (2926ds/592Mi)
% 48.35/8.41 % (547077)Instruction limit reached!
% 48.35/8.41 % (547077)------------------------------
% 48.35/8.41 % (547077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/8.41 % (547077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/8.41 % (547077)CaDiCaL version: 2.1.3
% 48.35/8.41 % (547077)Termination reason: Instruction limit
% 48.35/8.41 % (547077)Termination phase: Saturation
% 48.35/8.41 % (547077)Time elapsed: 0.254 s
% 48.35/8.41 % (547077)Peak memory usage: 13 MB
% 48.35/8.41 % (547077)Instructions burned: 594 (million)
% 48.35/8.41 % (547079)dis+1010_7_si=on:uwa=off:nwc=1.2:random_seed=377887062:st=2.5:i=872:sd=4:fsr=off:rtra=on:ss=axioms:c=on:ntd=on_2923 on theBenchmark for (2923ds/872Mi)
% 48.35/8.41 % (547079)Refutation not found, incomplete strategy
% 48.35/8.41 % (547079)------------------------------
% 48.35/8.41 % (547079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/8.41 % (547079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/8.41 % (547079)CaDiCaL version: 2.1.3
% 48.35/8.41 % (547079)Termination reason: Refutation not found, incomplete strategy
% 48.35/8.41 % (547079)Time elapsed: 0.012 s
% 48.35/8.41 % (547079)Peak memory usage: 12 MB
% 48.35/8.41 % (547079)Instructions burned: 25 (million)
% 48.35/8.41 % (547079)------------------------------
% 48.35/8.41 % (547079)------------------------------
% 48.35/8.41 % (547081)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 48.35/8.41 % (547081)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2929509061:i=999:add=on:rtra=on_2923 on theBenchmark for (2923ds/999Mi)
% 48.35/8.41 % (547067) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-546654-547067"...
% 48.35/8.41 % (547074)Instruction limit reached!
% 48.35/8.41 % (547074)------------------------------
% 48.35/8.41 % (547074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/8.41 % (547074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/8.41 % (547074)CaDiCaL version: 2.1.3
% 48.35/8.41 % (547074)Termination reason: Instruction limit
% 48.35/8.41 % (547074)Termination phase: Saturation
% 48.35/8.41 % (547074)Time elapsed: 0.788 s
% 48.35/8.41 % (547074)Peak memory usage: 22 MB
% 48.35/8.41 % (547074)Instructions burned: 985 (million)
% 48.35/8.41 % (547083)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 48.35/8.41 % (547083)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=2981747410:i=244:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2919 on theBenchmark for (2919ds/244Mi)
% 48.35/8.41 % (547067)...printing done.
% 48.35/8.41 % (547081)Instruction limit reached!
% 48.35/8.41 % (547081)------------------------------
% 48.35/8.41 % (547081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/8.41 % (547081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/8.41 % (547081)CaDiCaL version: 2.1.3
% 48.35/8.41 % (547081)Termination reason: Instruction limit
% 48.35/8.41 % (547081)Termination phase: Saturation
% 48.35/8.41 % (547081)Time elapsed: 0.404 s
% 48.35/8.41 % (547081)Peak memory usage: 13 MB
% 48.35/8.41 % (547081)Instructions burned: 1001 (million)
% 48.35/8.41 % (547067)Refutation found. Thanks to Tanya!
% 48.35/8.41 % SZS status Theorem for theBenchmark
% 48.35/8.41 % SZS output start Proof for theBenchmark
% 48.35/8.41 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 48.35/8.41 thf(func_def_0, type, irel: ($i > $i > $o)).
% 48.35/8.41 thf(func_def_2, type, mnot: (($i > $o) > $i > $o)).
% 48.35/8.41 thf(func_def_3, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 48.35/8.41 thf(func_def_4, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 48.35/8.41 thf(func_def_5, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 48.35/8.41 thf(func_def_6, type, mbox_s4: (($i > $o) > $i > $o)).
% 48.35/8.41 thf(func_def_7, type, iatom: (($i > $o) > $i > $o)).
% 48.35/8.41 thf(func_def_8, type, inot: (($i > $o) > $i > $o)).
% 48.35/8.41 thf(func_def_9, type, itrue: ($i > $o)).
% 48.35/8.41 thf(func_def_10, type, ifalse: ($i > $o)).
% 48.35/8.41 thf(func_def_11, type, iand: (($i > $o) > ($i > $o) > $i > $o)).
% 48.35/8.41 thf(func_def_12, type, ior: (($i > $o) > ($i > $o) > $i > $o)).
% 48.35/8.41 thf(func_def_13, type, iimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 48.35/8.41 thf(func_def_14, type, iimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 48.35/8.41 thf(func_def_15, type, iequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 48.35/8.41 thf(func_def_16, type, ixor: (($i > $o) > ($i > $o) > $i > $o)).
% 48.35/8.41 thf(func_def_17, type, ivalid: (($i > $o) > $o)).
% 48.35/8.41 thf(func_def_18, type, isatisfiable: (($i > $o) > $o)).
% 48.35/8.41 thf(func_def_19, type, icountersatisfiable: (($i > $o) > $o)).
% 48.35/8.41 thf(func_def_20, type, iinvalid: (($i > $o) > $o)).
% 48.35/8.41 thf(func_def_21, type, a1: ($i > $o)).
% 48.35/8.41 thf(func_def_22, type, a2: ($i > $o)).
% 48.35/8.41 thf(func_def_23, type, a3: ($i > $o)).
% 48.35/8.41 thf(func_def_24, type, a4: ($i > $o)).
% 48.35/8.41 thf(func_def_25, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 48.35/8.41 thf(func_def_26, type, vNOT: ($o > $o)).
% 48.35/8.41 thf(func_def_27, type, db1: !>[X0: $tType]:(X0)).
% 48.35/8.41 thf(func_def_28, type, db0: !>[X0: $tType]:(X0)).
% 48.35/8.41 thf(func_def_29, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 48.35/8.41 thf(func_def_32, type, vAND: ($o > $o > $o)).
% 48.35/8.41 thf(func_def_33, type, db2: !>[X0: $tType]:(X0)).
% 48.35/8.41 thf(func_def_34, type, vOR: ($o > $o > $o)).
% 48.35/8.41 thf(func_def_35, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 48.35/8.41 thf(func_def_36, type, vIMP: ($o > $o > $o)).
% 48.35/8.41 thf(f3,axiom,(
% 48.35/8.41 ((^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))) = mnot)),
% 48.35/8.41 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mnot)).
% 48.35/8.41 thf(f4,axiom,(
% 48.35/8.41 ((^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 48.35/8.41 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mor)).
% 48.35/8.41 thf(f5,axiom,(
% 48.35/8.41 (mand = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) & (X1 @ X2))))),
% 48.35/8.41 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mand)).
% 48.35/8.41 thf(f6,axiom,(
% 48.35/8.41 ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mnot @ X0) @ X1))) = mimplies)),
% 48.35/8.41 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mimplies)).
% 48.35/8.41 thf(f7,axiom,(
% 48.35/8.41 (mbox_s4 = (^[X0 : ($i > $o), X1 : $i] : (! [X2 : $i] : ((irel @ X1 @ X2) => (X0 @ X2)))))),
% 48.35/8.41 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mbox_s4)).
% 48.35/8.41 thf(f8,axiom,(
% 48.35/8.41 (iatom = (^[X0 : ($i > $o)] : (X0)))),
% 48.35/8.41 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iatom)).
% 48.35/8.41 thf(f12,axiom,(
% 48.35/8.41 (iand = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mand @ X0 @ X1))))),
% 48.35/8.41 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iand)).
% 48.35/8.41 thf(f14,axiom,(
% 48.35/8.41 ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))) = iimplies)),
% 48.35/8.41 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iimplies)).
% 48.35/8.41 thf(f16,axiom,(
% 48.35/8.41 ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((iand @ (iimplies @ X0 @ X1) @ (iimplies @ X1 @ X0)))) = iequiv)),
% 48.35/8.41 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iequiv)).
% 48.35/8.41 thf(f18,axiom,(
% 48.35/8.41 ((^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))) = ivalid)),
% 48.35/8.41 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ivalid)).
% 48.35/8.41 thf(f22,conjecture,(
% 48.35/8.41 (ivalid @ (iequiv @ (iequiv @ (iequiv @ (iequiv @ (iatom @ a1) @ (iatom @ a2)) @ (iatom @ a3)) @ (iatom @ a4)) @ (iequiv @ (iatom @ a4) @ (iequiv @ (iatom @ a3) @ (iequiv @ (iatom @ a2) @ (iatom @ a1))))))),
% 48.35/8.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 48.35/8.41 thf(f23,negated_conjecture,(
% 48.35/8.41 ~(ivalid @ (iequiv @ (iequiv @ (iequiv @ (iequiv @ (iatom @ a1) @ (iatom @ a2)) @ (iatom @ a3)) @ (iatom @ a4)) @ (iequiv @ (iatom @ a4) @ (iequiv @ (iatom @ a3) @ (iequiv @ (iatom @ a2) @ (iatom @ a1))))))),
% 48.35/8.41 inference(negated_conjecture,[status(cth)],[f22])).
% 48.35/8.41 thf(f27,plain,(
% 48.35/8.41 ~(ivalid @ (iequiv @ (iequiv @ (iequiv @ (iequiv @ (iatom @ a1) @ (iatom @ a2)) @ (iatom @ a3)) @ (iatom @ a4)) @ (iequiv @ (iatom @ a4) @ (iequiv @ (iatom @ a3) @ (iequiv @ (iatom @ a2) @ (iatom @ a1))))))),
% 48.35/8.41 inference(rectify,[],[f23])).
% 48.35/8.41 thf(f28,plain,(
% 48.35/8.41 ($true = ((~ (ivalid @ (iequiv @ (iequiv @ (iequiv @ (iequiv @ (iatom @ a1) @ (iatom @ a2)) @ (iatom @ a3)) @ (iatom @ a4)) @ (iequiv @ (iatom @ a4) @ (iequiv @ (iatom @ a3) @ (iequiv @ (iatom @ a2) @ (iatom @ a1)))))))))),
% 48.35/8.41 inference(fool_elimination,[],[f27])).
% 48.35/8.41 thf(f29,plain,(
% 48.35/8.41 (mand = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) & (X1 @ X2))))),
% 48.35/8.41 inference(rectify,[],[f5])).
% 48.35/8.41 thf(f30,plain,(
% 48.35/8.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 48.35/8.41 inference(fool_elimination,[],[f29])).
% 48.35/8.41 thf(f31,plain,(
% 48.35/8.41 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 48.35/8.41 inference(fool_elimination,[],[f8])).
% 48.35/8.41 thf(f33,plain,(
% 48.35/8.41 ((^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 48.35/8.41 inference(rectify,[],[f4])).
% 48.35/8.41 thf(f34,plain,(
% 48.35/8.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 48.35/8.41 inference(fool_elimination,[],[f33])).
% 48.35/8.41 thf(f36,plain,(
% 48.35/8.41 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 48.35/8.41 inference(fool_elimination,[],[f16])).
% 48.35/8.41 thf(f37,plain,(
% 48.35/8.41 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 48.35/8.41 inference(fool_elimination,[],[f14])).
% 48.35/8.41 thf(f38,plain,(
% 48.35/8.41 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ Y0 @ Y1)))))),
% 48.35/8.41 inference(fool_elimination,[],[f12])).
% 48.35/8.41 thf(f40,plain,(
% 48.35/8.41 ((^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))) = mnot)),
% 48.35/8.41 inference(rectify,[],[f3])).
% 48.35/8.41 thf(f41,plain,(
% 48.35/8.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 48.35/8.41 inference(fool_elimination,[],[f40])).
% 48.35/8.41 thf(f44,plain,(
% 48.35/8.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 48.35/8.41 inference(fool_elimination,[],[f6])).
% 48.35/8.41 thf(f50,plain,(
% 48.35/8.41 ((^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))) = ivalid)),
% 48.35/8.41 inference(rectify,[],[f18])).
% 48.35/8.41 thf(f51,plain,(
% 48.35/8.41 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 48.35/8.41 inference(fool_elimination,[],[f50])).
% 48.35/8.41 thf(f55,plain,(
% 48.35/8.41 (mbox_s4 = (^[X0 : ($i > $o), X1 : $i] : (! [X2 : $i] : ((irel @ X1 @ X2) => (X0 @ X2)))))),
% 48.35/8.41 inference(rectify,[],[f7])).
% 48.35/8.41 thf(f56,plain,(
% 48.35/8.41 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 48.35/8.41 inference(fool_elimination,[],[f55])).
% 48.35/8.41 thf(f57,plain,(
% 48.35/8.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 48.35/8.41 inference(cnf_transformation,[],[f41])).
% 48.35/8.41 thf(f58,plain,(
% 48.35/8.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 48.35/8.41 inference(cnf_transformation,[],[f34])).
% 48.35/8.41 thf(f60,plain,(
% 48.35/8.41 ($true = ((~ (ivalid @ (iequiv @ (iequiv @ (iequiv @ (iequiv @ (iatom @ a1) @ (iatom @ a2)) @ (iatom @ a3)) @ (iatom @ a4)) @ (iequiv @ (iatom @ a4) @ (iequiv @ (iatom @ a3) @ (iequiv @ (iatom @ a2) @ (iatom @ a1)))))))))),
% 48.35/8.41 inference(cnf_transformation,[],[f28])).
% 48.35/8.41 thf(f62,plain,(
% 48.35/8.41 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 48.35/8.41 inference(cnf_transformation,[],[f37])).
% 48.35/8.41 thf(f64,plain,(
% 48.35/8.41 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 48.35/8.41 inference(cnf_transformation,[],[f56])).
% 48.35/8.41 thf(f67,plain,(
% 48.35/8.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 48.35/8.41 inference(cnf_transformation,[],[f44])).
% 48.35/8.41 thf(f69,plain,(
% 48.35/8.41 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 48.35/8.41 inference(cnf_transformation,[],[f31])).
% 48.35/8.41 thf(f70,plain,(
% 48.35/8.41 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ Y0 @ Y1)))))),
% 48.35/8.41 inference(cnf_transformation,[],[f38])).
% 48.35/8.41 thf(f73,plain,(
% 48.35/8.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 48.35/8.41 inference(cnf_transformation,[],[f30])).
% 48.35/8.41 thf(f74,plain,(
% 48.35/8.41 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 48.35/8.41 inference(cnf_transformation,[],[f51])).
% 48.35/8.41 thf(f78,plain,(
% 48.35/8.41 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 48.35/8.41 inference(cnf_transformation,[],[f36])).
% 48.35/8.41 thf(f80,definition,(
% 48.35/8.41 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 48.35/8.41 introduced(theory,[fool_exhaustiveness_axiom])).
% 48.35/8.41 thf(f81,plain,(
% 48.35/8.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 48.35/8.41 inference(definition_unfolding,[],[f67,f58,f57])).
% 48.35/8.41 thf(f84,plain,(
% 48.35/8.41 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ Y0 @ Y1)))))),
% 48.35/8.41 inference(definition_unfolding,[],[f70,f73])).
% 48.35/8.41 thf(f86,plain,(
% 48.35/8.41 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))))),
% 48.35/8.41 inference(definition_unfolding,[],[f62,f81,f64,f64])).
% 48.35/8.41 thf(f88,plain,(
% 48.35/8.41 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))))),
% 48.35/8.41 inference(definition_unfolding,[],[f78,f84,f86,f86])).
% 48.35/8.41 thf(f90,plain,(
% 48.35/8.41 (((~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! 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@ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: (Y0)) @ a1) @ ((^[Y0 : $i > $o]: (Y0)) @ a2)) @ ((^[Y0 : $i > $o]: (Y0)) @ a3)) @ ((^[Y0 : $i > $o]: (Y0)) @ a4)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: (Y0)) @ a4) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: (Y0)) @ a3) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: (Y0)) @ a2) @ ((^[Y0 : $i > $o]: (Y0)) @ a1)))))))) = $true)),
% 48.35/8.41 inference(definition_unfolding,[],[f60,f74,f88,f88,f88,f88,f69,f69,f69,f69,f88,f69,f88,f69,f88,f69,f69])).
% 48.35/8.41 thf(f91,plain,(
% 48.35/8.41 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))))))))))))))),
% 48.35/8.41 inference(beta-eta_normalization,[],[f90])).
% 48.35/8.41 thf(f93,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))))))))))))) | (((~ $true)) = $true)),
% 48.35/8.41 inference(constrained_superposition,[],[f91,f80])).
% 48.35/8.41 thf(f94,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))))))))))))) | ($false = $true)),
% 48.35/8.41 inference(boolean_simplification,[],[f93])).
% 48.35/8.41 thf(f95,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))))))))))))))))))),
% 48.35/8.41 inference(trivial_inequality_removal,[],[f94])).
% 48.35/8.41 thf(f96,plain,(
% 48.35/8.41 ($false = (((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))))))))))))))) @ sK0)))),
% 48.35/8.41 inference(sigma_proxy_clausification,[],[f95])).
% 48.35/8.41 thf(f99,plain,(
% 48.35/8.41 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))))))),
% 48.35/8.41 inference(beta-eta_normalization,[],[f96])).
% 48.35/8.41 thf(f101,plain,(
% 48.35/8.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))))) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))))))),
% 48.35/8.41 inference(constrained_superposition,[],[f99,f80])).
% 48.35/8.41 thf(f102,plain,(
% 48.35/8.41 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) & $true))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))))))))))),
% 48.35/8.41 inference(constrained_superposition,[],[f99,f80])).
% 48.35/8.41 thf(f104,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))))))))) | ($false = ((((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | $true))))),
% 48.35/8.41 inference(constrained_superposition,[],[f99,f80])).
% 48.35/8.41 thf(f111,plain,(
% 48.35/8.41 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) & $true))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))))))))))),
% 48.35/8.41 inference(boolean_simplification,[],[f101])).
% 48.35/8.41 thf(f112,plain,(
% 48.35/8.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))))))))))),
% 48.35/8.41 inference(boolean_simplification,[],[f111])).
% 48.35/8.41 thf(f118,plain,(
% 48.35/8.41 ($false = ((((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) & $true))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))))),
% 48.35/8.41 inference(boolean_simplification,[],[f104])).
% 48.35/8.41 thf(f119,plain,(
% 48.35/8.41 ((((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))))))))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))))),
% 48.35/8.41 inference(boolean_simplification,[],[f118])).
% 48.35/8.41 thf(f120,plain,(
% 48.35/8.41 ($false = (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))))),
% 48.35/8.41 inference(boolean_simplification,[],[f119])).
% 48.35/8.41 thf(f121,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))))),
% 48.35/8.41 inference(boolean_simplification,[],[f120])).
% 48.35/8.41 thf(f122,plain,(
% 48.35/8.41 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))))))))))),
% 48.35/8.41 inference(boolean_simplification,[],[f102])).
% 48.35/8.41 thf(f124,definition,(
% 48.35/8.41 spl1_1 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 48.35/8.41 thf(f125,plain,(
% 48.35/8.41 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))))) | ~spl1_1),
% 48.35/8.41 inference(avatar_component_clause,[],[f124])).
% 48.35/8.41 thf(f127,definition,(
% 48.35/8.41 spl1_2 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 48.35/8.41 thf(f128,plain,(
% 48.35/8.41 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))))) | ~spl1_2),
% 48.35/8.41 inference(avatar_component_clause,[],[f127])).
% 48.35/8.41 thf(f131,definition,(
% 48.35/8.41 spl1_3 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 48.35/8.41 thf(f132,plain,(
% 48.35/8.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))))) | ~spl1_3),
% 48.35/8.41 inference(avatar_component_clause,[],[f131])).
% 48.35/8.41 thf(f135,definition,(
% 48.35/8.41 spl1_4 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
% 48.35/8.41 thf(f136,plain,(
% 48.35/8.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))))) | ~spl1_4),
% 48.35/8.41 inference(avatar_component_clause,[],[f135])).
% 48.35/8.41 thf(f137,plain,(
% 48.35/8.41 spl1_1 | spl1_4),
% 48.35/8.41 inference(avatar_split_clause,[],[f112,f135,f124])).
% 48.35/8.41 thf(f139,definition,(
% 48.35/8.41 spl1_5 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition])).
% 48.35/8.41 thf(f140,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))))))))) | ~spl1_5),
% 48.35/8.41 inference(avatar_component_clause,[],[f139])).
% 48.35/8.41 thf(f142,definition,(
% 48.35/8.41 spl1_6 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition])).
% 48.35/8.41 thf(f143,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))))))))) | ~spl1_6),
% 48.35/8.41 inference(avatar_component_clause,[],[f142])).
% 48.35/8.41 thf(f146,plain,(
% 48.35/8.41 spl1_6 | spl1_5),
% 48.35/8.41 inference(avatar_split_clause,[],[f121,f139,f142])).
% 48.35/8.41 thf(f147,plain,(
% 48.35/8.41 spl1_2 | spl1_1),
% 48.35/8.41 inference(avatar_split_clause,[],[f122,f124,f127])).
% 48.35/8.41 thf(f148,plain,(
% 48.35/8.41 ($false = (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))))) | (~spl1_2 | ~spl1_4)),
% 48.35/8.41 inference(forward_demodulation,[],[f128,f136])).
% 48.35/8.41 thf(f149,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))))))))) | (~spl1_2 | ~spl1_4)),
% 48.35/8.41 inference(boolean_simplification,[],[f148])).
% 48.35/8.41 thf(f150,plain,(
% 48.35/8.41 ($false = (((^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))) @ sK2))) | ~spl1_5),
% 48.35/8.41 inference(sigma_proxy_clausification,[],[f140])).
% 48.35/8.41 thf(f152,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))))) | ~spl1_5),
% 48.35/8.41 inference(beta-eta_normalization,[],[f150])).
% 48.35/8.41 thf(f156,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))))) | ~spl1_5),
% 48.35/8.41 inference(constrained_superposition,[],[f152,f80])).
% 48.35/8.41 thf(f157,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) & $true)))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | ~spl1_5),
% 48.35/8.41 inference(constrained_superposition,[],[f152,f80])).
% 48.35/8.41 thf(f159,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | $true))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | ~spl1_5),
% 48.35/8.41 inference(constrained_superposition,[],[f152,f80])).
% 48.35/8.41 thf(f160,plain,(
% 48.35/8.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | ($false = (((irel @ sK0 @ sK2) => (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))))) | ~spl1_5),
% 48.35/8.41 inference(constrained_superposition,[],[f152,f80])).
% 48.35/8.41 thf(f161,plain,(
% 48.35/8.41 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))))) | ($false = (((irel @ sK0 @ sK2) => ($true & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))))) | ~spl1_5),
% 48.35/8.41 inference(constrained_superposition,[],[f152,f80])).
% 48.35/8.41 thf(f165,plain,(
% 48.35/8.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | ($false = (((irel @ sK0 @ sK2) => ($true & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))))) | ~spl1_5),
% 48.35/8.41 inference(boolean_simplification,[],[f160])).
% 48.35/8.41 thf(f166,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | ~spl1_5),
% 48.35/8.41 inference(boolean_simplification,[],[f165])).
% 48.35/8.41 thf(f167,plain,(
% 48.35/8.41 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | ($false = (((irel @ sK0 @ sK2) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))))) | ~spl1_5),
% 48.35/8.41 inference(boolean_simplification,[],[f157])).
% 48.35/8.41 thf(f172,plain,(
% 48.35/8.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))))) | ($false = (((irel @ sK0 @ sK2) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) & $true)))) | ~spl1_5),
% 48.35/8.41 inference(boolean_simplification,[],[f156])).
% 48.35/8.41 thf(f173,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))))) | ~spl1_5),
% 48.35/8.41 inference(boolean_simplification,[],[f172])).
% 48.35/8.41 thf(f174,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) & $true)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | ~spl1_5),
% 48.35/8.41 inference(boolean_simplification,[],[f159])).
% 48.35/8.41 thf(f175,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | ~spl1_5),
% 48.35/8.41 inference(boolean_simplification,[],[f174])).
% 48.35/8.41 thf(f176,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | ~spl1_5),
% 48.35/8.41 inference(boolean_simplification,[],[f175])).
% 48.35/8.41 thf(f177,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | ~spl1_5),
% 48.35/8.41 inference(boolean_simplification,[],[f176])).
% 48.35/8.41 thf(f181,plain,(
% 48.35/8.41 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))))) | ($false = (((irel @ sK0 @ sK2) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))))) | ~spl1_5),
% 48.35/8.41 inference(boolean_simplification,[],[f161])).
% 48.35/8.41 thf(f184,definition,(
% 48.35/8.41 spl1_7 <=> ($false = (((irel @ sK0 @ sK2) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition])).
% 48.35/8.41 thf(f185,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))))) | ~spl1_7),
% 48.35/8.41 inference(avatar_component_clause,[],[f184])).
% 48.35/8.41 thf(f187,definition,(
% 48.35/8.41 spl1_8 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition])).
% 48.35/8.41 thf(f188,plain,(
% 48.35/8.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | ~spl1_8),
% 48.35/8.41 inference(avatar_component_clause,[],[f187])).
% 48.35/8.41 thf(f189,plain,(
% 48.35/8.41 spl1_7 | spl1_8 | ~spl1_5),
% 48.35/8.41 inference(avatar_split_clause,[],[f166,f139,f187,f184])).
% 48.35/8.41 thf(f191,definition,(
% 48.35/8.41 spl1_9 <=> ($false = (((irel @ sK0 @ sK2) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition])).
% 48.35/8.41 thf(f192,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))))) | ~spl1_9),
% 48.35/8.41 inference(avatar_component_clause,[],[f191])).
% 48.35/8.41 thf(f194,definition,(
% 48.35/8.41 spl1_10 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition])).
% 48.35/8.41 thf(f195,plain,(
% 48.35/8.41 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | ~spl1_10),
% 48.35/8.41 inference(avatar_component_clause,[],[f194])).
% 48.35/8.41 thf(f196,plain,(
% 48.35/8.41 spl1_9 | spl1_10 | ~spl1_5),
% 48.35/8.41 inference(avatar_split_clause,[],[f167,f139,f194,f191])).
% 48.35/8.41 thf(f198,definition,(
% 48.35/8.41 spl1_11 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition])).
% 48.35/8.41 thf(f199,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))) | ~spl1_11),
% 48.35/8.41 inference(avatar_component_clause,[],[f198])).
% 48.35/8.41 thf(f205,definition,(
% 48.35/8.41 spl1_13 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition])).
% 48.35/8.41 thf(f206,plain,(
% 48.35/8.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))))) | ~spl1_13),
% 48.35/8.41 inference(avatar_component_clause,[],[f205])).
% 48.35/8.41 thf(f207,plain,(
% 48.35/8.41 spl1_9 | spl1_13 | ~spl1_5),
% 48.35/8.41 inference(avatar_split_clause,[],[f173,f139,f205,f191])).
% 48.35/8.41 thf(f209,definition,(
% 48.35/8.41 spl1_14 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition])).
% 48.35/8.41 thf(f210,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | ~spl1_14),
% 48.35/8.41 inference(avatar_component_clause,[],[f209])).
% 48.35/8.41 thf(f212,definition,(
% 48.35/8.41 spl1_15 <=> ($false = (((irel @ sK0 @ sK2) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_15])],[avatar_definition])).
% 48.35/8.41 thf(f213,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))))) | ~spl1_15),
% 48.35/8.41 inference(avatar_component_clause,[],[f212])).
% 48.35/8.41 thf(f214,plain,(
% 48.35/8.41 spl1_14 | spl1_15 | ~spl1_5),
% 48.35/8.41 inference(avatar_split_clause,[],[f177,f139,f212,f209])).
% 48.35/8.41 thf(f216,definition,(
% 48.35/8.41 spl1_16 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition])).
% 48.35/8.41 thf(f217,plain,(
% 48.35/8.41 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))))) | ~spl1_16),
% 48.35/8.41 inference(avatar_component_clause,[],[f216])).
% 48.35/8.41 thf(f218,plain,(
% 48.35/8.41 spl1_16 | spl1_7 | ~spl1_5),
% 48.35/8.41 inference(avatar_split_clause,[],[f181,f139,f184,f216])).
% 48.35/8.41 thf(f219,plain,(
% 48.35/8.41 spl1_5 | ~spl1_2 | ~spl1_4),
% 48.35/8.41 inference(avatar_split_clause,[],[f149,f135,f127,f139])).
% 48.35/8.41 thf(f220,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))))) | (~spl1_7 | ~spl1_11)),
% 48.35/8.41 inference(forward_demodulation,[],[f185,f199])).
% 48.35/8.41 thf(f221,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))))) | (~spl1_7 | ~spl1_11)),
% 48.35/8.41 inference(boolean_simplification,[],[f220])).
% 48.35/8.41 thf(f222,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => $true))) | (~spl1_7 | ~spl1_11)),
% 48.35/8.41 inference(boolean_simplification,[],[f221])).
% 48.35/8.41 thf(f223,plain,(
% 48.35/8.41 ($false = $true) | (~spl1_7 | ~spl1_11)),
% 48.35/8.41 inference(boolean_simplification,[],[f222])).
% 48.35/8.41 thf(f224,plain,(
% 48.35/8.41 $false | (~spl1_7 | ~spl1_11)),
% 48.35/8.41 inference(trivial_inequality_removal,[],[f223])).
% 48.35/8.41 thf(f225,plain,(
% 48.35/8.41 ~spl1_7 | ~spl1_11),
% 48.35/8.41 inference(avatar_contradiction_clause,[],[f224])).
% 48.35/8.41 thf(f226,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))))) | (~spl1_9 | ~spl1_14)),
% 48.35/8.41 inference(forward_demodulation,[],[f192,f210])).
% 48.35/8.41 thf(f227,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))))) | (~spl1_9 | ~spl1_14)),
% 48.35/8.41 inference(boolean_simplification,[],[f226])).
% 48.35/8.41 thf(f228,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => $true))) | (~spl1_9 | ~spl1_14)),
% 48.35/8.41 inference(boolean_simplification,[],[f227])).
% 48.35/8.41 thf(f229,plain,(
% 48.35/8.41 ($false = $true) | (~spl1_9 | ~spl1_14)),
% 48.35/8.41 inference(boolean_simplification,[],[f228])).
% 48.35/8.41 thf(f230,plain,(
% 48.35/8.41 $false | (~spl1_9 | ~spl1_14)),
% 48.35/8.41 inference(trivial_inequality_removal,[],[f229])).
% 48.35/8.41 thf(f231,plain,(
% 48.35/8.41 ~spl1_9 | ~spl1_14),
% 48.35/8.41 inference(avatar_contradiction_clause,[],[f230])).
% 48.35/8.41 thf(f259,plain,(
% 48.35/8.41 ($false = (((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))) @ sK3))) | ~spl1_14),
% 48.35/8.41 inference(sigma_proxy_clausification,[],[f210])).
% 48.35/8.41 thf(f262,plain,(
% 48.35/8.41 ($false = (((irel @ sK2 @ sK3) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))))) | ~spl1_14),
% 48.35/8.41 inference(beta-eta_normalization,[],[f259])).
% 48.35/8.41 thf(f264,plain,(
% 48.35/8.41 ($true = ((irel @ sK2 @ sK3))) | ~spl1_14),
% 48.35/8.41 inference(imp_proxy_clausification,[],[f262])).
% 48.35/8.41 thf(f265,plain,(
% 48.35/8.41 ($false = (((irel @ sK2 @ sK3) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))))) | ~spl1_14),
% 48.35/8.41 inference(constrained_superposition,[],[f262,f80])).
% 48.35/8.41 thf(f267,plain,(
% 48.35/8.41 ($false = (((irel @ sK2 @ sK3) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $true) & ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))) | ~spl1_14),
% 48.35/8.41 inference(constrained_superposition,[],[f262,f80])).
% 48.35/8.41 thf(f269,plain,(
% 48.35/8.41 ($false = (((irel @ sK2 @ sK3) => (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | ~spl1_14),
% 48.35/8.41 inference(constrained_superposition,[],[f262,f80])).
% 48.35/8.41 thf(f270,plain,(
% 48.35/8.41 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))))) | ($false = (((irel @ sK2 @ sK3) => ($true & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))))) | ~spl1_14),
% 48.35/8.41 inference(constrained_superposition,[],[f262,f80])).
% 48.35/8.41 thf(f271,plain,(
% 48.35/8.41 ((((irel @ sK2 @ sK3) => $true)) = $false) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | ~spl1_14),
% 48.35/8.41 inference(constrained_superposition,[],[f262,f80])).
% 48.35/8.41 thf(f275,plain,(
% 48.35/8.41 ($false = (((irel @ sK2 @ sK3) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))))) | ~spl1_14),
% 48.35/8.41 inference(boolean_simplification,[],[f270])).
% 48.35/8.41 thf(f276,plain,(
% 48.35/8.41 ($false = (((irel @ sK2 @ sK3) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) & $true)))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))))) | ~spl1_14),
% 48.35/8.41 inference(boolean_simplification,[],[f265])).
% 48.35/8.41 thf(f277,plain,(
% 48.35/8.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))))) | ($false = (((irel @ sK2 @ sK3) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))))) | ~spl1_14),
% 48.35/8.41 inference(boolean_simplification,[],[f276])).
% 48.35/8.41 thf(f278,plain,(
% 48.35/8.41 ($false = (((irel @ sK2 @ sK3) => ($true & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | ~spl1_14),
% 48.35/8.41 inference(boolean_simplification,[],[f269])).
% 48.35/8.41 thf(f279,plain,(
% 48.35/8.41 ($false = (((irel @ sK2 @ sK3) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | ~spl1_14),
% 48.35/8.41 inference(boolean_simplification,[],[f278])).
% 48.35/8.41 thf(f285,plain,(
% 48.35/8.41 ($false = $true) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | ~spl1_14),
% 48.35/8.41 inference(boolean_simplification,[],[f271])).
% 48.35/8.41 thf(f286,plain,(
% 48.35/8.41 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | ~spl1_14),
% 48.35/8.41 inference(trivial_inequality_removal,[],[f285])).
% 48.35/8.41 thf(f288,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))) | ($false = (((irel @ sK2 @ sK3) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $true) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))))) | ~spl1_14),
% 48.35/8.41 inference(boolean_simplification,[],[f267])).
% 48.35/8.41 thf(f289,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))) | ((((irel @ sK2 @ sK3) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $true) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) = $false) | ~spl1_14),
% 48.35/8.41 inference(boolean_simplification,[],[f288])).
% 48.35/8.41 thf(f290,plain,(
% 48.35/8.41 ($false = (((irel @ sK2 @ sK3) => ($true & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))) | ~spl1_14),
% 48.35/8.41 inference(boolean_simplification,[],[f289])).
% 48.35/8.41 thf(f291,plain,(
% 48.35/8.41 ($false = (((irel @ sK2 @ sK3) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))) | ~spl1_14),
% 48.35/8.41 inference(boolean_simplification,[],[f290])).
% 48.35/8.41 thf(f293,definition,(
% 48.35/8.41 spl1_17 <=> ($false = (((irel @ sK2 @ sK3) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition])).
% 48.35/8.41 thf(f294,plain,(
% 48.35/8.41 ($false = (((irel @ sK2 @ sK3) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))))) | ~spl1_17),
% 48.35/8.41 inference(avatar_component_clause,[],[f293])).
% 48.35/8.41 thf(f300,definition,(
% 48.35/8.41 spl1_19 <=> ($false = (((irel @ sK2 @ sK3) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_19])],[avatar_definition])).
% 48.35/8.41 thf(f301,plain,(
% 48.35/8.41 ($false = (((irel @ sK2 @ sK3) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | ~spl1_19),
% 48.35/8.41 inference(avatar_component_clause,[],[f300])).
% 48.35/8.41 thf(f303,definition,(
% 48.35/8.41 spl1_20 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_20])],[avatar_definition])).
% 48.35/8.41 thf(f304,plain,(
% 48.35/8.41 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))))) | ~spl1_20),
% 48.35/8.41 inference(avatar_component_clause,[],[f303])).
% 48.35/8.41 thf(f305,plain,(
% 48.35/8.41 spl1_19 | spl1_20 | ~spl1_14),
% 48.35/8.41 inference(avatar_split_clause,[],[f275,f209,f303,f300])).
% 48.35/8.41 thf(f307,definition,(
% 48.35/8.41 spl1_21 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_21])],[avatar_definition])).
% 48.35/8.41 thf(f308,plain,(
% 48.35/8.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))))) | ~spl1_21),
% 48.35/8.41 inference(avatar_component_clause,[],[f307])).
% 48.35/8.41 thf(f309,plain,(
% 48.35/8.41 spl1_21 | spl1_17 | ~spl1_14),
% 48.35/8.41 inference(avatar_split_clause,[],[f277,f209,f293,f307])).
% 48.35/8.41 thf(f311,definition,(
% 48.35/8.41 spl1_22 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_22])],[avatar_definition])).
% 48.35/8.41 thf(f312,plain,(
% 48.35/8.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | ~spl1_22),
% 48.35/8.41 inference(avatar_component_clause,[],[f311])).
% 48.35/8.41 thf(f313,plain,(
% 48.35/8.41 spl1_19 | spl1_22 | ~spl1_14),
% 48.35/8.41 inference(avatar_split_clause,[],[f279,f209,f311,f300])).
% 48.35/8.41 thf(f318,definition,(
% 48.35/8.41 spl1_24 <=> ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_24])],[avatar_definition])).
% 48.35/8.41 thf(f319,plain,(
% 48.35/8.41 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | ~spl1_24),
% 48.35/8.41 inference(avatar_component_clause,[],[f318])).
% 48.35/8.41 thf(f323,plain,(
% 48.35/8.41 spl1_24 | ~spl1_14),
% 48.35/8.41 inference(avatar_split_clause,[],[f286,f209,f318])).
% 48.35/8.41 thf(f324,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))) | ($false = (($true => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | ~spl1_14),
% 48.35/8.41 inference(forward_demodulation,[],[f291,f264])).
% 48.35/8.41 thf(f325,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))) | ~spl1_14),
% 48.35/8.41 inference(boolean_simplification,[],[f324])).
% 48.35/8.41 thf(f327,definition,(
% 48.35/8.41 spl1_25 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_25])],[avatar_definition])).
% 48.35/8.41 thf(f328,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))) | ~spl1_25),
% 48.35/8.41 inference(avatar_component_clause,[],[f327])).
% 48.35/8.41 thf(f330,definition,(
% 48.35/8.41 spl1_26 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))),
% 48.35/8.41 introduced(definition,[new_symbols(definition,[spl1_26])],[avatar_definition])).
% 48.35/8.41 thf(f331,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | ~spl1_26),
% 48.35/8.41 inference(avatar_component_clause,[],[f330])).
% 48.35/8.41 thf(f333,plain,(
% 48.35/8.41 spl1_26 | spl1_25 | ~spl1_14),
% 48.35/8.41 inference(avatar_split_clause,[],[f325,f209,f327,f330])).
% 48.35/8.41 thf(f354,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK2) => $true))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))) | ~spl1_15),
% 48.35/8.41 inference(constrained_superposition,[],[f213,f80])).
% 48.35/8.41 thf(f359,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))) | ($false = $true) | ~spl1_15),
% 48.35/8.41 inference(boolean_simplification,[],[f354])).
% 48.35/8.41 thf(f360,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))) | ~spl1_15),
% 48.35/8.41 inference(trivial_inequality_removal,[],[f359])).
% 48.35/8.41 thf(f363,plain,(
% 48.35/8.41 spl1_11 | ~spl1_15),
% 48.35/8.41 inference(avatar_split_clause,[],[f360,f212,f198])).
% 48.35/8.41 thf(f376,plain,(
% 48.35/8.41 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | $false))) | (~spl1_1 | ~spl1_6)),
% 48.35/8.41 inference(forward_demodulation,[],[f125,f143])).
% 48.35/8.41 thf(f377,plain,(
% 48.35/8.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))))) | (~spl1_1 | ~spl1_6)),
% 48.35/8.41 inference(boolean_simplification,[],[f376])).
% 48.35/8.41 thf(f378,plain,(
% 48.35/8.41 spl1_3 | ~spl1_1 | ~spl1_6),
% 48.35/8.41 inference(avatar_split_clause,[],[f377,f142,f124,f131])).
% 48.35/8.41 thf(f419,plain,(
% 48.35/8.41 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | $true))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | ~spl1_10),
% 48.35/8.41 inference(constrained_superposition,[],[f195,f80])).
% 48.35/8.41 thf(f423,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | ($false = $true) | ~spl1_10),
% 48.35/8.41 inference(boolean_simplification,[],[f419])).
% 48.35/8.41 thf(f424,plain,(
% 48.35/8.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | ~spl1_10),
% 48.35/8.41 inference(trivial_inequality_removal,[],[f423])).
% 48.35/8.41 thf(f430,plain,(
% 48.35/8.41 spl1_14 | ~spl1_10),
% 48.35/8.41 inference(avatar_split_clause,[],[f424,f194,f209])).
% 48.35/8.41 thf(f474,plain,(
% 48.35/8.41 ($false = (((^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))) @ sK5))) | ~spl1_6),
% 48.35/8.41 inference(sigma_proxy_clausification,[],[f143])).
% 48.35/8.41 thf(f476,plain,(
% 48.35/8.41 ($false = (((irel @ sK0 @ sK5) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))))))) | ~spl1_6),
% 48.35/8.41 inference(beta-eta_normalization,[],[f474])).
% 48.35/8.41 thf(f478,plain,(
% 48.35/8.41 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0)))))))) | ~spl1_6),
% 48.35/8.41 inference(imp_proxy_clausification,[],[f476])).
% 48.35/8.41 thf(f479,plain,(
% 48.35/8.41 ($true = ((irel @ sK0 @ sK5))) | ~spl1_6),
% 48.35/8.41 inference(imp_proxy_clausification,[],[f476])).
% 48.35/8.41 thf(f483,plain,(
% 48.35/8.41 ((((irel @ sK0 @ sK5) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | $true)))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0)))))) | ~spl1_6),
% 48.35/8.42 inference(constrained_superposition,[],[f476,f80])).
% 48.35/8.42 thf(f484,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))))) | ($false = (((irel @ sK0 @ sK5) => (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))))))) | ~spl1_6),
% 48.35/8.42 inference(constrained_superposition,[],[f476,f80])).
% 48.35/8.42 thf(f494,plain,(
% 48.35/8.42 ($false = (((irel @ sK0 @ sK5) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & $true)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0)))))) | ~spl1_6),
% 48.35/8.42 inference(boolean_simplification,[],[f483])).
% 48.35/8.42 thf(f495,plain,(
% 48.35/8.42 ($false = (((irel @ sK0 @ sK5) => ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0)))))) | ~spl1_6),
% 48.35/8.42 inference(boolean_simplification,[],[f494])).
% 48.35/8.42 thf(f496,plain,(
% 48.35/8.42 ($false = (((irel @ sK0 @ sK5) => ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0)))))) | ~spl1_6),
% 48.35/8.42 inference(boolean_simplification,[],[f495])).
% 48.35/8.42 thf(f497,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0)))))) | ($false = (((irel @ sK0 @ sK5) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))))) | ~spl1_6),
% 48.35/8.42 inference(boolean_simplification,[],[f496])).
% 48.35/8.42 thf(f501,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))))) | ($false = (((irel @ sK0 @ sK5) => ($true & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))))))) | ~spl1_6),
% 48.35/8.42 inference(boolean_simplification,[],[f484])).
% 48.35/8.42 thf(f502,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))))) | ($false = (((irel @ sK0 @ sK5) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0)))))))) | ~spl1_6),
% 48.35/8.42 inference(boolean_simplification,[],[f501])).
% 48.35/8.42 thf(f511,definition,(
% 48.35/8.42 spl1_29 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_29])],[avatar_definition])).
% 48.35/8.42 thf(f512,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) | ~spl1_29),
% 48.35/8.42 inference(avatar_component_clause,[],[f511])).
% 48.35/8.42 thf(f515,definition,(
% 48.35/8.42 spl1_30 <=> ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_30])],[avatar_definition])).
% 48.35/8.42 thf(f516,plain,(
% 48.35/8.42 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0)))))))) | ~spl1_30),
% 48.35/8.42 inference(avatar_component_clause,[],[f515])).
% 48.35/8.42 thf(f522,definition,(
% 48.35/8.42 spl1_32 <=> ($false = (((irel @ sK0 @ sK5) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_32])],[avatar_definition])).
% 48.35/8.42 thf(f523,plain,(
% 48.35/8.42 ($false = (((irel @ sK0 @ sK5) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))))) | ~spl1_32),
% 48.35/8.42 inference(avatar_component_clause,[],[f522])).
% 48.35/8.42 thf(f525,definition,(
% 48.35/8.42 spl1_33 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_33])],[avatar_definition])).
% 48.35/8.42 thf(f526,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0)))))) | ~spl1_33),
% 48.35/8.42 inference(avatar_component_clause,[],[f525])).
% 48.35/8.42 thf(f527,plain,(
% 48.35/8.42 spl1_32 | spl1_33 | ~spl1_6),
% 48.35/8.42 inference(avatar_split_clause,[],[f497,f142,f525,f522])).
% 48.35/8.42 thf(f528,plain,(
% 48.35/8.42 spl1_30 | ~spl1_6),
% 48.35/8.42 inference(avatar_split_clause,[],[f478,f142,f515])).
% 48.35/8.42 thf(f531,plain,(
% 48.35/8.42 ($false = (($true => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0)))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))))) | ~spl1_6),
% 48.35/8.42 inference(forward_demodulation,[],[f502,f479])).
% 48.35/8.42 thf(f532,plain,(
% 48.35/8.42 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))))) | ~spl1_6),
% 48.35/8.42 inference(boolean_simplification,[],[f531])).
% 48.35/8.42 thf(f541,definition,(
% 48.35/8.42 spl1_35 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_35])],[avatar_definition])).
% 48.35/8.42 thf(f542,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))))) | ~spl1_35),
% 48.35/8.42 inference(avatar_component_clause,[],[f541])).
% 48.35/8.42 thf(f545,definition,(
% 48.35/8.42 spl1_36 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0)))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_36])],[avatar_definition])).
% 48.35/8.42 thf(f546,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))))) | ~spl1_36),
% 48.35/8.42 inference(avatar_component_clause,[],[f545])).
% 48.35/8.42 thf(f548,definition,(
% 48.35/8.42 spl1_37 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0)))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_37])],[avatar_definition])).
% 48.35/8.42 thf(f549,plain,(
% 48.35/8.42 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))))) | ~spl1_37),
% 48.35/8.42 inference(avatar_component_clause,[],[f548])).
% 48.35/8.42 thf(f550,plain,(
% 48.35/8.42 spl1_36 | spl1_37 | ~spl1_6),
% 48.35/8.42 inference(avatar_split_clause,[],[f532,f142,f548,f545])).
% 48.35/8.42 thf(f600,plain,(
% 48.35/8.42 ($false = ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | $false)))) | (~spl1_30 | ~spl1_33)),
% 48.35/8.42 inference(forward_demodulation,[],[f516,f526])).
% 48.35/8.42 thf(f601,plain,(
% 48.35/8.42 ($false = ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))))) | (~spl1_30 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f600])).
% 48.35/8.42 thf(f602,plain,(
% 48.35/8.42 ($false = ((($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))))) | (~spl1_30 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f601])).
% 48.35/8.42 thf(f603,plain,(
% 48.35/8.42 ($false = (($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))))) | (~spl1_30 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f602])).
% 48.35/8.42 thf(f604,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))))) | (~spl1_30 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f603])).
% 48.35/8.42 thf(f610,plain,(
% 48.35/8.42 ($false = (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))))) | (~spl1_29 | ~spl1_37)),
% 48.35/8.42 inference(forward_demodulation,[],[f549,f512])).
% 48.35/8.42 thf(f611,plain,(
% 48.35/8.42 ($false = (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))))) | (~spl1_29 | ~spl1_37)),
% 48.35/8.42 inference(boolean_simplification,[],[f610])).
% 48.35/8.42 thf(f612,plain,(
% 48.35/8.42 ($false = $true) | (~spl1_29 | ~spl1_37)),
% 48.35/8.42 inference(boolean_simplification,[],[f611])).
% 48.35/8.42 thf(f613,plain,(
% 48.35/8.42 $false | (~spl1_29 | ~spl1_37)),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f612])).
% 48.35/8.42 thf(f614,plain,(
% 48.35/8.42 ~spl1_29 | ~spl1_37),
% 48.35/8.42 inference(avatar_contradiction_clause,[],[f613])).
% 48.35/8.42 thf(f631,plain,(
% 48.35/8.42 spl1_35 | ~spl1_30 | ~spl1_33),
% 48.35/8.42 inference(avatar_split_clause,[],[f604,f525,f515,f541])).
% 48.35/8.42 thf(f737,plain,(
% 48.35/8.42 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))) = $true) | ~spl1_36),
% 48.35/8.42 inference(not_proxy_clausification,[],[f546])).
% 48.35/8.42 thf(f761,plain,(
% 48.35/8.42 ($false = (((^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))) @ sK7))) | ~spl1_29),
% 48.35/8.42 inference(sigma_proxy_clausification,[],[f512])).
% 48.35/8.42 thf(f763,plain,(
% 48.35/8.42 ($false = (((irel @ sK5 @ sK7) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))))))) | ~spl1_29),
% 48.35/8.42 inference(beta-eta_normalization,[],[f761])).
% 48.35/8.42 thf(f766,plain,(
% 48.35/8.42 ($true = ((irel @ sK5 @ sK7))) | ~spl1_29),
% 48.35/8.42 inference(imp_proxy_clausification,[],[f763])).
% 48.35/8.42 thf(f767,plain,(
% 48.35/8.42 ($false = (((irel @ sK5 @ sK7) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | ~spl1_29),
% 48.35/8.42 inference(constrained_superposition,[],[f763,f80])).
% 48.35/8.42 thf(f770,plain,(
% 48.35/8.42 ($false = (((irel @ sK5 @ sK7) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $true))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0)))))) | ~spl1_29),
% 48.35/8.42 inference(constrained_superposition,[],[f763,f80])).
% 48.35/8.42 thf(f771,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))))) | ($false = (((irel @ sK5 @ sK7) => (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))))))) | ~spl1_29),
% 48.35/8.42 inference(constrained_superposition,[],[f763,f80])).
% 48.35/8.42 thf(f780,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | ($false = (((irel @ sK5 @ sK7) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & $true)))) | ~spl1_29),
% 48.35/8.42 inference(boolean_simplification,[],[f767])).
% 48.35/8.42 thf(f781,plain,(
% 48.35/8.42 ($false = (((irel @ sK5 @ sK7) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | ~spl1_29),
% 48.35/8.42 inference(boolean_simplification,[],[f780])).
% 48.35/8.42 thf(f782,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0)))))) | ($false = (((irel @ sK5 @ sK7) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & $true)))) | ~spl1_29),
% 48.35/8.42 inference(boolean_simplification,[],[f770])).
% 48.35/8.42 thf(f783,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0)))))) | ($false = (((irel @ sK5 @ sK7) => ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))))) | ~spl1_29),
% 48.35/8.42 inference(boolean_simplification,[],[f782])).
% 48.35/8.42 thf(f784,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0)))))) | ($false = (((irel @ sK5 @ sK7) => ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))))) | ~spl1_29),
% 48.35/8.42 inference(boolean_simplification,[],[f783])).
% 48.35/8.42 thf(f785,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0)))))) | ($false = (((irel @ sK5 @ sK7) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | ~spl1_29),
% 48.35/8.42 inference(boolean_simplification,[],[f784])).
% 48.35/8.42 thf(f787,plain,(
% 48.35/8.42 ($false = (((irel @ sK5 @ sK7) => ($true & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))))) | ~spl1_29),
% 48.35/8.42 inference(boolean_simplification,[],[f771])).
% 48.35/8.42 thf(f788,plain,(
% 48.35/8.42 ($false = (((irel @ sK5 @ sK7) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0)))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))))) | ~spl1_29),
% 48.35/8.42 inference(boolean_simplification,[],[f787])).
% 48.35/8.42 thf(f798,definition,(
% 48.35/8.42 spl1_49 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_49])],[avatar_definition])).
% 48.35/8.42 thf(f799,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ~spl1_49),
% 48.35/8.42 inference(avatar_component_clause,[],[f798])).
% 48.35/8.42 thf(f802,definition,(
% 48.35/8.42 spl1_50 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_50])],[avatar_definition])).
% 48.35/8.42 thf(f803,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | ~spl1_50),
% 48.35/8.42 inference(avatar_component_clause,[],[f802])).
% 48.35/8.42 thf(f805,definition,(
% 48.35/8.42 spl1_51 <=> ($false = (((irel @ sK5 @ sK7) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_51])],[avatar_definition])).
% 48.35/8.42 thf(f806,plain,(
% 48.35/8.42 ($false = (((irel @ sK5 @ sK7) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))))) | ~spl1_51),
% 48.35/8.42 inference(avatar_component_clause,[],[f805])).
% 48.35/8.42 thf(f807,plain,(
% 48.35/8.42 spl1_50 | spl1_51 | ~spl1_29),
% 48.35/8.42 inference(avatar_split_clause,[],[f781,f511,f805,f802])).
% 48.35/8.42 thf(f809,definition,(
% 48.35/8.42 spl1_52 <=> ($false = (((irel @ sK5 @ sK7) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_52])],[avatar_definition])).
% 48.35/8.42 thf(f810,plain,(
% 48.35/8.42 ($false = (((irel @ sK5 @ sK7) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | ~spl1_52),
% 48.35/8.42 inference(avatar_component_clause,[],[f809])).
% 48.35/8.42 thf(f812,definition,(
% 48.35/8.42 spl1_53 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_53])],[avatar_definition])).
% 48.35/8.42 thf(f813,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0)))))) | ~spl1_53),
% 48.35/8.42 inference(avatar_component_clause,[],[f812])).
% 48.35/8.42 thf(f814,plain,(
% 48.35/8.42 spl1_52 | spl1_53 | ~spl1_29),
% 48.35/8.42 inference(avatar_split_clause,[],[f785,f511,f812,f809])).
% 48.35/8.42 thf(f817,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))))) | ($false = (($true => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0)))))))) | ~spl1_29),
% 48.35/8.42 inference(forward_demodulation,[],[f788,f766])).
% 48.35/8.42 thf(f818,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))))) | ~spl1_29),
% 48.35/8.42 inference(boolean_simplification,[],[f817])).
% 48.35/8.42 thf(f825,definition,(
% 48.35/8.42 spl1_55 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0)))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_55])],[avatar_definition])).
% 48.35/8.42 thf(f826,plain,(
% 48.35/8.42 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))))) | ~spl1_55),
% 48.35/8.42 inference(avatar_component_clause,[],[f825])).
% 48.35/8.42 thf(f829,definition,(
% 48.35/8.42 spl1_56 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0)))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_56])],[avatar_definition])).
% 48.35/8.42 thf(f830,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))))) | ~spl1_56),
% 48.35/8.42 inference(avatar_component_clause,[],[f829])).
% 48.35/8.42 thf(f831,plain,(
% 48.35/8.42 spl1_55 | spl1_56 | ~spl1_29),
% 48.35/8.42 inference(avatar_split_clause,[],[f818,f511,f829,f825])).
% 48.35/8.42 thf(f841,plain,(
% 48.35/8.42 ($false = (((^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ sK8))) | ~spl1_49),
% 48.35/8.42 inference(sigma_proxy_clausification,[],[f799])).
% 48.35/8.42 thf(f843,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK8) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))))))) | ~spl1_49),
% 48.35/8.42 inference(beta-eta_normalization,[],[f841])).
% 48.35/8.42 thf(f846,plain,(
% 48.35/8.42 ($true = ((irel @ sK7 @ sK8))) | ~spl1_49),
% 48.35/8.42 inference(imp_proxy_clausification,[],[f843])).
% 48.35/8.42 thf(f847,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK8) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))))) | ~spl1_49),
% 48.35/8.42 inference(constrained_superposition,[],[f843,f80])).
% 48.35/8.42 thf(f849,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))) | ($false = (((irel @ sK7 @ sK8) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | $true) & ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))))))) | ~spl1_49),
% 48.35/8.42 inference(constrained_superposition,[],[f843,f80])).
% 48.35/8.42 thf(f850,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK8) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))) | $true))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0)))))) | ~spl1_49),
% 48.35/8.42 inference(constrained_superposition,[],[f843,f80])).
% 48.35/8.42 thf(f856,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))))) | ($false = (((irel @ sK7 @ sK8) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))) & $true)))) | ~spl1_49),
% 48.35/8.42 inference(boolean_simplification,[],[f847])).
% 48.35/8.42 thf(f857,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK8) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))))) | ~spl1_49),
% 48.35/8.42 inference(boolean_simplification,[],[f856])).
% 48.35/8.42 thf(f860,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK8) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | $true) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))) | ~spl1_49),
% 48.35/8.42 inference(boolean_simplification,[],[f849])).
% 48.35/8.42 thf(f861,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK8) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | $true) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))) | ~spl1_49),
% 48.35/8.42 inference(boolean_simplification,[],[f860])).
% 48.35/8.42 thf(f862,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK8) => ($true & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))) | ~spl1_49),
% 48.35/8.42 inference(boolean_simplification,[],[f861])).
% 48.35/8.42 thf(f863,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK8) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))) | ~spl1_49),
% 48.35/8.42 inference(boolean_simplification,[],[f862])).
% 48.35/8.42 thf(f868,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK8) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))) & $true)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0)))))) | ~spl1_49),
% 48.35/8.42 inference(boolean_simplification,[],[f850])).
% 48.35/8.42 thf(f869,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0)))))) | ($false = (((irel @ sK7 @ sK8) => ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))))) | ~spl1_49),
% 48.35/8.42 inference(boolean_simplification,[],[f868])).
% 48.35/8.42 thf(f870,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0)))))) | ($false = (((irel @ sK7 @ sK8) => ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))))) | ~spl1_49),
% 48.35/8.42 inference(boolean_simplification,[],[f869])).
% 48.35/8.42 thf(f871,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0)))))) | ($false = (((irel @ sK7 @ sK8) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))))) | ~spl1_49),
% 48.35/8.42 inference(boolean_simplification,[],[f870])).
% 48.35/8.42 thf(f875,definition,(
% 48.35/8.42 spl1_57 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_57])],[avatar_definition])).
% 48.35/8.42 thf(f876,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))))) | ~spl1_57),
% 48.35/8.42 inference(avatar_component_clause,[],[f875])).
% 48.35/8.42 thf(f878,definition,(
% 48.35/8.42 spl1_58 <=> ($false = (((irel @ sK7 @ sK8) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_58])],[avatar_definition])).
% 48.35/8.42 thf(f879,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK8) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))))) | ~spl1_58),
% 48.35/8.42 inference(avatar_component_clause,[],[f878])).
% 48.35/8.42 thf(f880,plain,(
% 48.35/8.42 spl1_57 | spl1_58 | ~spl1_49),
% 48.35/8.42 inference(avatar_split_clause,[],[f857,f798,f878,f875])).
% 48.35/8.42 thf(f882,definition,(
% 48.35/8.42 spl1_59 <=> ($false = (((irel @ sK7 @ sK8) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0)))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_59])],[avatar_definition])).
% 48.35/8.42 thf(f883,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK8) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))))) | ~spl1_59),
% 48.35/8.42 inference(avatar_component_clause,[],[f882])).
% 48.35/8.42 thf(f885,definition,(
% 48.35/8.42 spl1_60 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_60])],[avatar_definition])).
% 48.35/8.42 thf(f886,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))) | ~spl1_60),
% 48.35/8.42 inference(avatar_component_clause,[],[f885])).
% 48.35/8.42 thf(f887,plain,(
% 48.35/8.42 spl1_59 | spl1_60 | ~spl1_49),
% 48.35/8.42 inference(avatar_split_clause,[],[f863,f798,f885,f882])).
% 48.35/8.42 thf(f894,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0)))))) | ($false = (($true => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))))) | ~spl1_49),
% 48.35/8.42 inference(forward_demodulation,[],[f871,f846])).
% 48.35/8.42 thf(f895,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0)))))) | ~spl1_49),
% 48.35/8.42 inference(boolean_simplification,[],[f894])).
% 48.35/8.42 thf(f900,definition,(
% 48.35/8.42 spl1_62 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0)))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_62])],[avatar_definition])).
% 48.35/8.42 thf(f901,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))))) | ~spl1_62),
% 48.35/8.42 inference(avatar_component_clause,[],[f900])).
% 48.35/8.42 thf(f909,definition,(
% 48.35/8.42 spl1_64 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_64])],[avatar_definition])).
% 48.35/8.42 thf(f910,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0)))))) | ~spl1_64),
% 48.35/8.42 inference(avatar_component_clause,[],[f909])).
% 48.35/8.42 thf(f911,plain,(
% 48.35/8.42 spl1_60 | spl1_64 | ~spl1_49),
% 48.35/8.42 inference(avatar_split_clause,[],[f895,f798,f909,f885])).
% 48.35/8.42 thf(f943,plain,(
% 48.35/8.42 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))) = $true) | ~spl1_57),
% 48.35/8.42 inference(not_proxy_clausification,[],[f876])).
% 48.35/8.42 thf(f948,plain,(
% 48.35/8.42 ($false = $true) | (~spl1_57 | ~spl1_60)),
% 48.35/8.42 inference(forward_demodulation,[],[f943,f886])).
% 48.35/8.42 thf(f949,plain,(
% 48.35/8.42 $false | (~spl1_57 | ~spl1_60)),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f948])).
% 48.35/8.42 thf(f950,plain,(
% 48.35/8.42 ~spl1_57 | ~spl1_60),
% 48.35/8.42 inference(avatar_contradiction_clause,[],[f949])).
% 48.35/8.42 thf(f1027,plain,(
% 48.35/8.42 ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ~spl1_50),
% 48.35/8.42 inference(not_proxy_clausification,[],[f803])).
% 48.35/8.42 thf(f1032,plain,(
% 48.35/8.42 ($false = $true) | (~spl1_49 | ~spl1_50)),
% 48.35/8.42 inference(forward_demodulation,[],[f1027,f799])).
% 48.35/8.42 thf(f1033,plain,(
% 48.35/8.42 $false | (~spl1_49 | ~spl1_50)),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f1032])).
% 48.35/8.42 thf(f1034,plain,(
% 48.35/8.42 ~spl1_49 | ~spl1_50),
% 48.35/8.42 inference(avatar_contradiction_clause,[],[f1033])).
% 48.35/8.42 thf(f1071,plain,(
% 48.35/8.42 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ X1)) = $true)) ) | ~spl1_50),
% 48.35/8.42 inference(pi_proxy_clausification,[],[f1027])).
% 48.35/8.42 thf(f1072,plain,(
% 48.35/8.42 ( ! [X1 : $i] : (((((irel @ sK7 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0)))))))) = $true)) ) | ~spl1_50),
% 48.35/8.42 inference(beta-eta_normalization,[],[f1071])).
% 48.35/8.42 thf(f1143,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK8) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | $true)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))) | ~spl1_58),
% 48.35/8.42 inference(constrained_superposition,[],[f879,f80])).
% 48.35/8.42 thf(f1145,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK8) => ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))))) | ~spl1_58),
% 48.35/8.42 inference(constrained_superposition,[],[f879,f80])).
% 48.35/8.42 thf(f1153,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))) | ($false = (((irel @ sK7 @ sK8) => $true))) | ~spl1_58),
% 48.35/8.42 inference(boolean_simplification,[],[f1143])).
% 48.35/8.42 thf(f1154,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))) | ($false = $true) | ~spl1_58),
% 48.35/8.42 inference(boolean_simplification,[],[f1153])).
% 48.35/8.42 thf(f1155,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))) | ~spl1_58),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f1154])).
% 48.35/8.42 thf(f1156,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK8) => $true))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))))) | ~spl1_58),
% 48.35/8.42 inference(boolean_simplification,[],[f1145])).
% 48.35/8.42 thf(f1157,plain,(
% 48.35/8.42 ($false = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))))) | ~spl1_58),
% 48.35/8.42 inference(boolean_simplification,[],[f1156])).
% 48.35/8.42 thf(f1158,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))))) | ~spl1_58),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f1157])).
% 48.35/8.42 thf(f1165,plain,(
% 48.35/8.42 spl1_60 | ~spl1_58),
% 48.35/8.42 inference(avatar_split_clause,[],[f1155,f878,f885])).
% 48.35/8.42 thf(f1167,plain,(
% 48.35/8.42 spl1_62 | ~spl1_58),
% 48.35/8.42 inference(avatar_split_clause,[],[f1158,f878,f900])).
% 48.35/8.42 thf(f1312,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | ~spl1_55),
% 48.35/8.42 inference(or_proxy_clausification,[],[f826])).
% 48.35/8.42 thf(f1315,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | ($false = (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))))) | ~spl1_55),
% 48.35/8.42 inference(constrained_superposition,[],[f826,f80])).
% 48.35/8.42 thf(f1317,plain,(
% 48.35/8.42 ($false = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | ~spl1_55),
% 48.35/8.42 inference(boolean_simplification,[],[f1315])).
% 48.35/8.42 thf(f1318,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | ~spl1_55),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f1317])).
% 48.35/8.42 thf(f1383,plain,(
% 48.35/8.42 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) = $true) | ~spl1_3),
% 48.35/8.42 inference(not_proxy_clausification,[],[f132])).
% 48.35/8.42 thf(f1388,plain,(
% 48.35/8.42 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))) @ X1)))) ) | ~spl1_3),
% 48.35/8.42 inference(pi_proxy_clausification,[],[f1383])).
% 48.35/8.42 thf(f1389,plain,(
% 48.35/8.42 ( ! [X1 : $i] : (($true = (((irel @ sK0 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a4 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))))))) ) | ~spl1_3),
% 48.35/8.42 inference(beta-eta_normalization,[],[f1388])).
% 48.35/8.42 thf(f1399,plain,(
% 48.35/8.42 ($true = (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))))) | (~spl1_3 | ~spl1_6)),
% 48.35/8.42 inference(constrained_superposition,[],[f1389,f479])).
% 48.35/8.42 thf(f1401,plain,(
% 48.35/8.42 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) = $true) | (~spl1_3 | ~spl1_6)),
% 48.35/8.42 inference(boolean_simplification,[],[f1399])).
% 48.35/8.42 thf(f1419,plain,(
% 48.35/8.42 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $true) & ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_36)),
% 48.35/8.42 inference(forward_demodulation,[],[f1401,f737])).
% 48.35/8.42 thf(f1420,plain,(
% 48.35/8.42 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $true) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_36)),
% 48.35/8.42 inference(boolean_simplification,[],[f1419])).
% 48.35/8.42 thf(f1421,plain,(
% 48.35/8.42 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $true) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_36)),
% 48.35/8.42 inference(boolean_simplification,[],[f1420])).
% 48.35/8.42 thf(f1422,plain,(
% 48.35/8.42 ($true = (($true & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_36)),
% 48.35/8.42 inference(boolean_simplification,[],[f1421])).
% 48.35/8.42 thf(f1423,plain,(
% 48.35/8.42 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_36)),
% 48.35/8.42 inference(boolean_simplification,[],[f1422])).
% 48.35/8.42 thf(f1429,plain,(
% 48.35/8.42 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))) @ X1)) = $true)) ) | (~spl1_3 | ~spl1_6 | ~spl1_36)),
% 48.35/8.42 inference(pi_proxy_clausification,[],[f1423])).
% 48.35/8.42 thf(f1430,plain,(
% 48.35/8.42 ( ! [X1 : $i] : (($true = (((irel @ sK5 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))))) ) | (~spl1_3 | ~spl1_6 | ~spl1_36)),
% 48.35/8.42 inference(beta-eta_normalization,[],[f1429])).
% 48.35/8.42 thf(f1441,plain,(
% 48.35/8.42 ((($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36)),
% 48.35/8.42 inference(constrained_superposition,[],[f1430,f766])).
% 48.35/8.42 thf(f1448,plain,(
% 48.35/8.42 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36)),
% 48.35/8.42 inference(boolean_simplification,[],[f1441])).
% 48.35/8.42 thf(f1462,plain,(
% 48.35/8.42 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(forward_demodulation,[],[f1448,f813])).
% 48.35/8.42 thf(f1463,plain,(
% 48.35/8.42 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(boolean_simplification,[],[f1462])).
% 48.35/8.42 thf(f1464,plain,(
% 48.35/8.42 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) & $true))) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(boolean_simplification,[],[f1463])).
% 48.35/8.42 thf(f1465,plain,(
% 48.35/8.42 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false)) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(boolean_simplification,[],[f1464])).
% 48.35/8.42 thf(f1466,plain,(
% 48.35/8.42 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(boolean_simplification,[],[f1465])).
% 48.35/8.42 thf(f1468,plain,(
% 48.35/8.42 (((~ $true)) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(constrained_superposition,[],[f1466,f80])).
% 48.35/8.42 thf(f1469,plain,(
% 48.35/8.42 ($false = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(boolean_simplification,[],[f1468])).
% 48.35/8.42 thf(f1470,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f1469])).
% 48.35/8.42 thf(f1471,plain,(
% 48.35/8.42 ($false = (((^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ sK12))) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(sigma_proxy_clausification,[],[f1470])).
% 48.35/8.42 thf(f1473,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK12) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(beta-eta_normalization,[],[f1471])).
% 48.35/8.42 thf(f1476,plain,(
% 48.35/8.42 ($true = ((irel @ sK7 @ sK12))) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(imp_proxy_clausification,[],[f1473])).
% 48.35/8.42 thf(f1478,plain,(
% 48.35/8.42 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))))) | ($false = (((irel @ sK7 @ sK12) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) & $true)))) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(constrained_superposition,[],[f1473,f80])).
% 48.35/8.42 thf(f1482,plain,(
% 48.35/8.42 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))))) | ($false = (((irel @ sK7 @ sK12) => ($true & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(constrained_superposition,[],[f1473,f80])).
% 48.35/8.42 thf(f1490,plain,(
% 48.35/8.42 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))))) | ($false = (((irel @ sK7 @ sK12) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0)))))))) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(boolean_simplification,[],[f1478])).
% 48.35/8.42 thf(f1498,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK12) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0)))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))))) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(boolean_simplification,[],[f1482])).
% 48.35/8.42 thf(f1512,definition,(
% 48.35/8.42 spl1_79 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0)))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_79])],[avatar_definition])).
% 48.35/8.42 thf(f1513,plain,(
% 48.35/8.42 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))))) | ~spl1_79),
% 48.35/8.42 inference(avatar_component_clause,[],[f1512])).
% 48.35/8.42 thf(f1515,definition,(
% 48.35/8.42 spl1_80 <=> ($false = (((irel @ sK7 @ sK12) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_80])],[avatar_definition])).
% 48.35/8.42 thf(f1516,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK12) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0)))))))) | ~spl1_80),
% 48.35/8.42 inference(avatar_component_clause,[],[f1515])).
% 48.35/8.42 thf(f1517,plain,(
% 48.35/8.42 spl1_79 | spl1_80 | ~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53),
% 48.35/8.42 inference(avatar_split_clause,[],[f1490,f812,f545,f511,f142,f131,f1515,f1512])).
% 48.35/8.42 thf(f1529,plain,(
% 48.35/8.42 ($false = (($true => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0)))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))))) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(forward_demodulation,[],[f1498,f1476])).
% 48.35/8.42 thf(f1530,plain,(
% 48.35/8.42 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))))) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53)),
% 48.35/8.42 inference(boolean_simplification,[],[f1529])).
% 48.35/8.42 thf(f1534,definition,(
% 48.35/8.42 spl1_84 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0)))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_84])],[avatar_definition])).
% 48.35/8.42 thf(f1535,plain,(
% 48.35/8.42 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))))) | ~spl1_84),
% 48.35/8.42 inference(avatar_component_clause,[],[f1534])).
% 48.35/8.42 thf(f1536,plain,(
% 48.35/8.42 spl1_84 | spl1_79 | ~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53),
% 48.35/8.42 inference(avatar_split_clause,[],[f1530,f812,f545,f511,f142,f131,f1512,f1534])).
% 48.35/8.42 thf(f1549,plain,(
% 48.35/8.42 ((($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0)))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_50 | ~spl1_53)),
% 48.35/8.42 inference(constrained_superposition,[],[f1072,f1476])).
% 48.35/8.42 thf(f1550,plain,(
% 48.35/8.42 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0)))))))) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_50 | ~spl1_53)),
% 48.35/8.42 inference(boolean_simplification,[],[f1549])).
% 48.35/8.42 thf(f1552,plain,(
% 48.35/8.42 ((($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_50 | ~spl1_53 | ~spl1_79)),
% 48.35/8.42 inference(forward_demodulation,[],[f1550,f1513])).
% 48.35/8.42 thf(f1553,plain,(
% 48.35/8.42 ($false = $true) | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_50 | ~spl1_53 | ~spl1_79)),
% 48.35/8.42 inference(boolean_simplification,[],[f1552])).
% 48.35/8.42 thf(f1554,plain,(
% 48.35/8.42 $false | (~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_50 | ~spl1_53 | ~spl1_79)),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f1553])).
% 48.35/8.42 thf(f1555,plain,(
% 48.35/8.42 ~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_50 | ~spl1_53 | ~spl1_79),
% 48.35/8.42 inference(avatar_contradiction_clause,[],[f1554])).
% 48.35/8.42 thf(f1595,plain,(
% 48.35/8.42 ($false = (((irel @ sK7 @ sK12) => $false))) | (~spl1_80 | ~spl1_84)),
% 48.35/8.42 inference(forward_demodulation,[],[f1516,f1535])).
% 48.35/8.42 thf(f1596,plain,(
% 48.35/8.42 ($false = ((~ (irel @ sK7 @ sK12)))) | (~spl1_80 | ~spl1_84)),
% 48.35/8.42 inference(boolean_simplification,[],[f1595])).
% 48.35/8.42 thf(f1603,plain,(
% 48.35/8.42 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $false) & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(forward_demodulation,[],[f1401,f526])).
% 48.35/8.42 thf(f1604,plain,(
% 48.35/8.42 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $false) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f1603])).
% 48.35/8.42 thf(f1605,plain,(
% 48.35/8.42 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $false) & $true)) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f1604])).
% 48.35/8.42 thf(f1606,plain,(
% 48.35/8.42 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $false)) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f1605])).
% 48.35/8.42 thf(f1607,plain,(
% 48.35/8.42 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f1606])).
% 48.35/8.42 thf(f1632,plain,(
% 48.35/8.42 ($true = ((irel @ sK7 @ sK12))) | (~spl1_80 | ~spl1_84)),
% 48.35/8.42 inference(not_proxy_clausification,[],[f1596])).
% 48.35/8.42 thf(f1638,plain,(
% 48.35/8.42 ((($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0)))))))) = $true) | (~spl1_50 | ~spl1_80 | ~spl1_84)),
% 48.35/8.42 inference(constrained_superposition,[],[f1072,f1632])).
% 48.35/8.42 thf(f1640,plain,(
% 48.35/8.42 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0)))))))) | (~spl1_50 | ~spl1_80 | ~spl1_84)),
% 48.35/8.42 inference(boolean_simplification,[],[f1638])).
% 48.35/8.42 thf(f1641,plain,(
% 48.35/8.42 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK12 @ Y0) => (a1 @ Y0))))) & $false)) = $true) | (~spl1_50 | ~spl1_80 | ~spl1_84)),
% 48.35/8.42 inference(forward_demodulation,[],[f1640,f1535])).
% 48.35/8.42 thf(f1642,plain,(
% 48.35/8.42 ($false = $true) | (~spl1_50 | ~spl1_80 | ~spl1_84)),
% 48.35/8.42 inference(boolean_simplification,[],[f1641])).
% 48.35/8.42 thf(f1643,plain,(
% 48.35/8.42 $false | (~spl1_50 | ~spl1_80 | ~spl1_84)),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f1642])).
% 48.35/8.42 thf(f1644,plain,(
% 48.35/8.42 ~spl1_50 | ~spl1_80 | ~spl1_84),
% 48.35/8.42 inference(avatar_contradiction_clause,[],[f1643])).
% 48.35/8.42 thf(f1806,plain,(
% 48.35/8.42 ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) | ~spl1_35),
% 48.35/8.42 inference(not_proxy_clausification,[],[f542])).
% 48.35/8.42 thf(f1811,plain,(
% 48.35/8.42 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))) @ X1)))) ) | ~spl1_35),
% 48.35/8.42 inference(pi_proxy_clausification,[],[f1806])).
% 48.35/8.42 thf(f1812,plain,(
% 48.35/8.42 ( ! [X1 : $i] : (($true = (((irel @ sK5 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0)))))))))) ) | ~spl1_35),
% 48.35/8.42 inference(beta-eta_normalization,[],[f1811])).
% 48.35/8.42 thf(f1853,plain,(
% 48.35/8.42 (((~ $true)) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(constrained_superposition,[],[f1607,f80])).
% 48.35/8.42 thf(f1854,plain,(
% 48.35/8.42 ($false = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f1853])).
% 48.35/8.42 thf(f1855,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f1854])).
% 48.35/8.42 thf(f1856,plain,(
% 48.35/8.42 ($false = (((^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))) @ sK13))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(sigma_proxy_clausification,[],[f1855])).
% 48.35/8.42 thf(f1859,plain,(
% 48.35/8.42 ($false = (((irel @ sK5 @ sK13) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(beta-eta_normalization,[],[f1856])).
% 48.35/8.42 thf(f1860,plain,(
% 48.35/8.42 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(imp_proxy_clausification,[],[f1859])).
% 48.35/8.42 thf(f1861,plain,(
% 48.35/8.42 (((irel @ sK5 @ sK13)) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(imp_proxy_clausification,[],[f1859])).
% 48.35/8.42 thf(f1862,plain,(
% 48.35/8.42 ($false = (((irel @ sK5 @ sK13) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(constrained_superposition,[],[f1859,f80])).
% 48.35/8.42 thf(f1866,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | ($false = (((irel @ sK5 @ sK13) => (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(constrained_superposition,[],[f1859,f80])).
% 48.35/8.42 thf(f1875,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))))) | ($false = (((irel @ sK5 @ sK13) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) & $true)))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f1862])).
% 48.35/8.42 thf(f1876,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))))) | ($false = (((irel @ sK5 @ sK13) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f1875])).
% 48.35/8.42 thf(f1885,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | ($false = (((irel @ sK5 @ sK13) => ($true & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f1866])).
% 48.35/8.42 thf(f1886,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | ($false = (((irel @ sK5 @ sK13) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f1885])).
% 48.35/8.42 thf(f1890,definition,(
% 48.35/8.42 spl1_89 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_89])],[avatar_definition])).
% 48.35/8.42 thf(f1891,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | ~spl1_89),
% 48.35/8.42 inference(avatar_component_clause,[],[f1890])).
% 48.35/8.42 thf(f1897,definition,(
% 48.35/8.42 spl1_91 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_91])],[avatar_definition])).
% 48.35/8.42 thf(f1898,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))))) | ~spl1_91),
% 48.35/8.42 inference(avatar_component_clause,[],[f1897])).
% 48.35/8.42 thf(f1900,definition,(
% 48.35/8.42 spl1_92 <=> ($false = (((irel @ sK5 @ sK13) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_92])],[avatar_definition])).
% 48.35/8.42 thf(f1901,plain,(
% 48.35/8.42 ($false = (((irel @ sK5 @ sK13) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))))) | ~spl1_92),
% 48.35/8.42 inference(avatar_component_clause,[],[f1900])).
% 48.35/8.42 thf(f1902,plain,(
% 48.35/8.42 spl1_91 | spl1_92 | ~spl1_3 | ~spl1_6 | ~spl1_33),
% 48.35/8.42 inference(avatar_split_clause,[],[f1876,f525,f142,f131,f1900,f1897])).
% 48.35/8.42 thf(f1909,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | ($false = (($true => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(forward_demodulation,[],[f1886,f1861])).
% 48.35/8.42 thf(f1910,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f1909])).
% 48.35/8.42 thf(f1912,definition,(
% 48.35/8.42 spl1_93 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_93])],[avatar_definition])).
% 48.35/8.42 thf(f1913,plain,(
% 48.35/8.42 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | ~spl1_93),
% 48.35/8.42 inference(avatar_component_clause,[],[f1912])).
% 48.35/8.42 thf(f1915,definition,(
% 48.35/8.42 spl1_94 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_94])],[avatar_definition])).
% 48.35/8.42 thf(f1916,plain,(
% 48.35/8.42 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))))) | ~spl1_94),
% 48.35/8.42 inference(avatar_component_clause,[],[f1915])).
% 48.35/8.42 thf(f1919,definition,(
% 48.35/8.42 spl1_95 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_95])],[avatar_definition])).
% 48.35/8.42 thf(f1920,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))) | ~spl1_95),
% 48.35/8.42 inference(avatar_component_clause,[],[f1919])).
% 48.35/8.42 thf(f1924,definition,(
% 48.35/8.42 spl1_96 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_96])],[avatar_definition])).
% 48.35/8.42 thf(f1925,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | ~spl1_96),
% 48.35/8.42 inference(avatar_component_clause,[],[f1924])).
% 48.35/8.42 thf(f1926,plain,(
% 48.35/8.42 spl1_96 | spl1_93 | ~spl1_3 | ~spl1_6 | ~spl1_33),
% 48.35/8.42 inference(avatar_split_clause,[],[f1910,f525,f142,f131,f1912,f1924])).
% 48.35/8.42 thf(f1931,plain,(
% 48.35/8.42 ($false = (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))))) | (~spl1_89 | ~spl1_94)),
% 48.35/8.42 inference(forward_demodulation,[],[f1916,f1891])).
% 48.35/8.42 thf(f1932,plain,(
% 48.35/8.42 ($false = (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))))) | (~spl1_89 | ~spl1_94)),
% 48.35/8.42 inference(boolean_simplification,[],[f1931])).
% 48.35/8.42 thf(f1933,plain,(
% 48.35/8.42 ($false = $true) | (~spl1_89 | ~spl1_94)),
% 48.35/8.42 inference(boolean_simplification,[],[f1932])).
% 48.35/8.42 thf(f1934,plain,(
% 48.35/8.42 $false | (~spl1_89 | ~spl1_94)),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f1933])).
% 48.35/8.42 thf(f1935,plain,(
% 48.35/8.42 ~spl1_89 | ~spl1_94),
% 48.35/8.42 inference(avatar_contradiction_clause,[],[f1934])).
% 48.35/8.42 thf(f1939,plain,(
% 48.35/8.42 ((($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35)),
% 48.35/8.42 inference(constrained_superposition,[],[f1812,f1861])).
% 48.35/8.42 thf(f1940,plain,(
% 48.35/8.42 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35)),
% 48.35/8.42 inference(boolean_simplification,[],[f1939])).
% 48.35/8.42 thf(f1949,plain,(
% 48.35/8.42 ($false = (($true => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_92)),
% 48.35/8.42 inference(forward_demodulation,[],[f1901,f1861])).
% 48.35/8.42 thf(f1950,plain,(
% 48.35/8.42 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_92)),
% 48.35/8.42 inference(boolean_simplification,[],[f1949])).
% 48.35/8.42 thf(f1951,plain,(
% 48.35/8.42 (((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $false))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(forward_demodulation,[],[f1940,f1920])).
% 48.35/8.42 thf(f1952,plain,(
% 48.35/8.42 ($true = ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(boolean_simplification,[],[f1951])).
% 48.35/8.42 thf(f1953,plain,(
% 48.35/8.42 ($true = ((($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(boolean_simplification,[],[f1952])).
% 48.35/8.42 thf(f1954,plain,(
% 48.35/8.42 ($true = (($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(boolean_simplification,[],[f1953])).
% 48.35/8.42 thf(f1955,plain,(
% 48.35/8.42 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(boolean_simplification,[],[f1954])).
% 48.35/8.42 thf(f2185,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(not_proxy_clausification,[],[f1955])).
% 48.35/8.42 thf(f2189,plain,(
% 48.35/8.42 ($false = (((^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ sK17))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(sigma_proxy_clausification,[],[f2185])).
% 48.35/8.42 thf(f2192,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK17) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(beta-eta_normalization,[],[f2189])).
% 48.35/8.42 thf(f2194,plain,(
% 48.35/8.42 ($true = ((irel @ sK13 @ sK17))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(imp_proxy_clausification,[],[f2192])).
% 48.35/8.42 thf(f2198,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK17) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) | $true))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0)))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(constrained_superposition,[],[f2192,f80])).
% 48.35/8.42 thf(f2215,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0)))))) | ($false = (((irel @ sK13 @ sK17) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) & $true)))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(boolean_simplification,[],[f2198])).
% 48.35/8.42 thf(f2216,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0)))))) | ($false = (((irel @ sK13 @ sK17) => ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0)))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(boolean_simplification,[],[f2215])).
% 48.35/8.42 thf(f2217,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK17) => ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0)))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(boolean_simplification,[],[f2216])).
% 48.35/8.42 thf(f2218,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK17) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0)))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(boolean_simplification,[],[f2217])).
% 48.35/8.42 thf(f2230,plain,(
% 48.35/8.42 ($false = (($true => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0)))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(forward_demodulation,[],[f2218,f2194])).
% 48.35/8.42 thf(f2231,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0)))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0)))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95)),
% 48.35/8.42 inference(boolean_simplification,[],[f2230])).
% 48.35/8.42 thf(f2235,definition,(
% 48.35/8.42 spl1_106 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_106])],[avatar_definition])).
% 48.35/8.42 thf(f2236,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0)))))) | ~spl1_106),
% 48.35/8.42 inference(avatar_component_clause,[],[f2235])).
% 48.35/8.42 thf(f2238,definition,(
% 48.35/8.42 spl1_107 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_107])],[avatar_definition])).
% 48.35/8.42 thf(f2239,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0)))))) | ~spl1_107),
% 48.35/8.42 inference(avatar_component_clause,[],[f2238])).
% 48.35/8.42 thf(f2249,definition,(
% 48.35/8.42 spl1_110 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0)))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_110])],[avatar_definition])).
% 48.35/8.42 thf(f2250,plain,(
% 48.35/8.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))) | ~spl1_110),
% 48.35/8.42 inference(avatar_component_clause,[],[f2249])).
% 48.35/8.42 thf(f2253,plain,(
% 48.35/8.42 spl1_107 | spl1_106 | ~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95),
% 48.35/8.42 inference(avatar_split_clause,[],[f2231,f1919,f541,f525,f142,f131,f2235,f2238])).
% 48.35/8.42 thf(f2276,plain,(
% 48.35/8.42 spl1_94 | ~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_92),
% 48.35/8.42 inference(avatar_split_clause,[],[f1950,f1900,f525,f142,f131,f1915])).
% 48.35/8.42 thf(f2315,plain,(
% 48.35/8.42 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) = $true) | ~spl1_91),
% 48.35/8.42 inference(not_proxy_clausification,[],[f1898])).
% 48.35/8.42 thf(f2339,plain,(
% 48.35/8.42 ($false = (((^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ sK19))) | ~spl1_89),
% 48.35/8.42 inference(sigma_proxy_clausification,[],[f1891])).
% 48.35/8.42 thf(f2341,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK19) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))))))) | ~spl1_89),
% 48.35/8.42 inference(beta-eta_normalization,[],[f2339])).
% 48.35/8.42 thf(f2349,plain,(
% 48.35/8.42 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0)))))))) | ~spl1_89),
% 48.35/8.42 inference(imp_proxy_clausification,[],[f2341])).
% 48.35/8.42 thf(f2350,plain,(
% 48.35/8.42 (((irel @ sK13 @ sK19)) = $true) | ~spl1_89),
% 48.35/8.42 inference(imp_proxy_clausification,[],[f2341])).
% 48.35/8.42 thf(f2351,plain,(
% 48.35/8.42 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))) = $false) | ($false = (((irel @ sK13 @ sK19) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))))))) | ~spl1_89),
% 48.35/8.42 inference(constrained_superposition,[],[f2341,f80])).
% 48.35/8.42 thf(f2354,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK19) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))) | $true))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0)))))) | ~spl1_89),
% 48.35/8.42 inference(constrained_superposition,[],[f2341,f80])).
% 48.35/8.42 thf(f2367,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK19) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))) & $true)))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))) = $false) | ~spl1_89),
% 48.35/8.42 inference(boolean_simplification,[],[f2351])).
% 48.35/8.42 thf(f2368,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK19) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))) = $false) | ~spl1_89),
% 48.35/8.42 inference(boolean_simplification,[],[f2367])).
% 48.35/8.42 thf(f2374,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0)))))) | ($false = (((irel @ sK13 @ sK19) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))) & $true)))) | ~spl1_89),
% 48.35/8.42 inference(boolean_simplification,[],[f2354])).
% 48.35/8.42 thf(f2375,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK19) => ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0)))))) | ~spl1_89),
% 48.35/8.42 inference(boolean_simplification,[],[f2374])).
% 48.35/8.42 thf(f2376,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK19) => ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0)))))) | ~spl1_89),
% 48.35/8.42 inference(boolean_simplification,[],[f2375])).
% 48.35/8.42 thf(f2377,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK19) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0)))))) | ~spl1_89),
% 48.35/8.42 inference(boolean_simplification,[],[f2376])).
% 48.35/8.42 thf(f2392,definition,(
% 48.35/8.42 spl1_115 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_115])],[avatar_definition])).
% 48.35/8.42 thf(f2393,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))) | ~spl1_115),
% 48.35/8.42 inference(avatar_component_clause,[],[f2392])).
% 48.35/8.42 thf(f2396,definition,(
% 48.35/8.42 spl1_116 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))) = $false)),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_116])],[avatar_definition])).
% 48.35/8.42 thf(f2397,plain,(
% 48.35/8.42 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))) = $false) | ~spl1_116),
% 48.35/8.42 inference(avatar_component_clause,[],[f2396])).
% 48.35/8.42 thf(f2399,definition,(
% 48.35/8.42 spl1_117 <=> ($false = (((irel @ sK13 @ sK19) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_117])],[avatar_definition])).
% 48.35/8.42 thf(f2400,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK19) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))))) | ~spl1_117),
% 48.35/8.42 inference(avatar_component_clause,[],[f2399])).
% 48.35/8.42 thf(f2401,plain,(
% 48.35/8.42 spl1_116 | spl1_117 | ~spl1_89),
% 48.35/8.42 inference(avatar_split_clause,[],[f2368,f1890,f2399,f2396])).
% 48.35/8.42 thf(f2410,plain,(
% 48.35/8.42 ($false = (($true => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0)))))) | ~spl1_89),
% 48.35/8.42 inference(forward_demodulation,[],[f2377,f2350])).
% 48.35/8.42 thf(f2411,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0)))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))) | ~spl1_89),
% 48.35/8.42 inference(boolean_simplification,[],[f2410])).
% 48.35/8.42 thf(f2413,definition,(
% 48.35/8.42 spl1_120 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_120])],[avatar_definition])).
% 48.35/8.42 thf(f2414,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0)))))) | ~spl1_120),
% 48.35/8.42 inference(avatar_component_clause,[],[f2413])).
% 48.35/8.42 thf(f2415,plain,(
% 48.35/8.42 spl1_120 | spl1_115 | ~spl1_89),
% 48.35/8.42 inference(avatar_split_clause,[],[f2411,f1890,f2392,f2413])).
% 48.35/8.42 thf(f2531,plain,(
% 48.35/8.42 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))))) | ~spl1_89),
% 48.35/8.42 inference(and_proxy_clausification,[],[f2349])).
% 48.35/8.42 thf(f2566,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | ~spl1_93),
% 48.35/8.42 inference(or_proxy_clausification,[],[f1913])).
% 48.35/8.42 thf(f2582,plain,(
% 48.35/8.42 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $true) & ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(constrained_superposition,[],[f1860,f80])).
% 48.35/8.42 thf(f2591,plain,(
% 48.35/8.42 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $true) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f2582])).
% 48.35/8.42 thf(f2592,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $true) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f2591])).
% 48.35/8.42 thf(f2593,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))) | ($false = (($true & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f2592])).
% 48.35/8.42 thf(f2594,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))) | (~spl1_3 | ~spl1_6 | ~spl1_33)),
% 48.35/8.42 inference(boolean_simplification,[],[f2593])).
% 48.35/8.42 thf(f2606,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) | $true) & ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35)),
% 48.35/8.42 inference(constrained_superposition,[],[f1940,f80])).
% 48.35/8.42 thf(f2607,plain,(
% 48.35/8.42 (((((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $true))) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35)),
% 48.35/8.42 inference(constrained_superposition,[],[f1940,f80])).
% 48.35/8.42 thf(f2613,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))) | (((((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & $true)) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35)),
% 48.35/8.42 inference(boolean_simplification,[],[f2607])).
% 48.35/8.42 thf(f2614,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))) | ((((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35)),
% 48.35/8.42 inference(boolean_simplification,[],[f2613])).
% 48.35/8.42 thf(f2615,plain,(
% 48.35/8.42 ($true = (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35)),
% 48.35/8.42 inference(boolean_simplification,[],[f2614])).
% 48.35/8.42 thf(f2616,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0)))))) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35)),
% 48.35/8.42 inference(boolean_simplification,[],[f2615])).
% 48.35/8.42 thf(f2617,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) | $true) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35)),
% 48.35/8.42 inference(boolean_simplification,[],[f2606])).
% 48.35/8.42 thf(f2618,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) | $true) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35)),
% 48.35/8.42 inference(boolean_simplification,[],[f2617])).
% 48.35/8.42 thf(f2619,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ($true = (($true & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35)),
% 48.35/8.42 inference(boolean_simplification,[],[f2618])).
% 48.35/8.42 thf(f2620,plain,(
% 48.35/8.42 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35)),
% 48.35/8.42 inference(boolean_simplification,[],[f2619])).
% 48.35/8.42 thf(f2628,plain,(
% 48.35/8.42 ($false = $true) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_91)),
% 48.35/8.42 inference(forward_demodulation,[],[f2616,f2315])).
% 48.35/8.42 thf(f2629,plain,(
% 48.35/8.42 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_91)),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f2628])).
% 48.35/8.42 thf(f2639,plain,(
% 48.35/8.42 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ X1)) = $true)) ) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_91)),
% 48.35/8.42 inference(pi_proxy_clausification,[],[f2629])).
% 48.35/8.42 thf(f2640,plain,(
% 48.35/8.42 ( ! [X1 : $i] : (((((irel @ sK13 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0)))))))) = $true)) ) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_91)),
% 48.35/8.42 inference(beta-eta_normalization,[],[f2639])).
% 48.35/8.42 thf(f2651,plain,(
% 48.35/8.42 ($true = (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91)),
% 48.35/8.42 inference(constrained_superposition,[],[f2640,f2350])).
% 48.35/8.42 thf(f2659,plain,(
% 48.35/8.42 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91)),
% 48.35/8.42 inference(boolean_simplification,[],[f2651])).
% 48.35/8.42 thf(f2672,plain,(
% 48.35/8.42 ($true = ((($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_116)),
% 48.35/8.42 inference(forward_demodulation,[],[f2659,f2397])).
% 48.35/8.42 thf(f2673,plain,(
% 48.35/8.42 ((((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0)))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_116)),
% 48.35/8.42 inference(boolean_simplification,[],[f2672])).
% 48.35/8.42 thf(f2674,plain,(
% 48.35/8.42 ((($false & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_116 | ~spl1_120)),
% 48.35/8.42 inference(forward_demodulation,[],[f2673,f2414])).
% 48.35/8.42 thf(f2675,plain,(
% 48.35/8.42 ($false = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_116 | ~spl1_120)),
% 48.35/8.42 inference(boolean_simplification,[],[f2674])).
% 48.35/8.42 thf(f2676,plain,(
% 48.35/8.42 $false | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_116 | ~spl1_120)),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f2675])).
% 48.35/8.42 thf(f2677,plain,(
% 48.35/8.42 ~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_116 | ~spl1_120),
% 48.35/8.42 inference(avatar_contradiction_clause,[],[f2676])).
% 48.35/8.42 thf(f2720,plain,(
% 48.35/8.42 (((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | $false))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_115)),
% 48.35/8.42 inference(forward_demodulation,[],[f2659,f2393])).
% 48.35/8.42 thf(f2721,plain,(
% 48.35/8.42 (((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_115)),
% 48.35/8.42 inference(boolean_simplification,[],[f2720])).
% 48.35/8.42 thf(f2722,plain,(
% 48.35/8.42 ($true = ((($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0)))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_115)),
% 48.35/8.42 inference(boolean_simplification,[],[f2721])).
% 48.35/8.42 thf(f2723,plain,(
% 48.35/8.42 ((($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_115)),
% 48.35/8.42 inference(boolean_simplification,[],[f2722])).
% 48.35/8.42 thf(f2724,plain,(
% 48.35/8.42 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_115)),
% 48.35/8.42 inference(boolean_simplification,[],[f2723])).
% 48.35/8.42 thf(f2731,plain,(
% 48.35/8.42 ($false = (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))))) | (~spl1_89 | ~spl1_115)),
% 48.35/8.42 inference(forward_demodulation,[],[f2531,f2393])).
% 48.35/8.42 thf(f2732,plain,(
% 48.35/8.42 ($false = (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))))) | (~spl1_89 | ~spl1_115)),
% 48.35/8.42 inference(boolean_simplification,[],[f2731])).
% 48.35/8.42 thf(f2733,plain,(
% 48.35/8.42 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))))) | ($false = $true) | (~spl1_89 | ~spl1_115)),
% 48.35/8.42 inference(boolean_simplification,[],[f2732])).
% 48.35/8.42 thf(f2734,plain,(
% 48.35/8.42 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))))) | (~spl1_89 | ~spl1_115)),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f2733])).
% 48.35/8.42 thf(f2750,plain,(
% 48.35/8.42 ($false = (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0))))))) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_115)),
% 48.35/8.42 inference(forward_demodulation,[],[f2734,f2724])).
% 48.35/8.42 thf(f2751,plain,(
% 48.35/8.42 ($false = $true) | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_115)),
% 48.35/8.42 inference(boolean_simplification,[],[f2750])).
% 48.35/8.42 thf(f2752,plain,(
% 48.35/8.42 $false | (~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_115)),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f2751])).
% 48.35/8.42 thf(f2753,plain,(
% 48.35/8.42 ~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_115),
% 48.35/8.42 inference(avatar_contradiction_clause,[],[f2752])).
% 48.35/8.42 thf(f2754,plain,(
% 48.35/8.42 spl1_89 | ~spl1_93),
% 48.35/8.42 inference(avatar_split_clause,[],[f2566,f1912,f1890])).
% 48.35/8.42 thf(f2756,definition,(
% 48.35/8.42 spl1_123 <=> (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) = $true)),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_123])],[avatar_definition])).
% 48.35/8.42 thf(f2757,plain,(
% 48.35/8.42 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a3 @ Y0))))) = $true) | ~spl1_123),
% 48.35/8.42 inference(avatar_component_clause,[],[f2756])).
% 48.35/8.42 thf(f2759,definition,(
% 48.35/8.42 spl1_124 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))),
% 48.35/8.42 introduced(definition,[new_symbols(definition,[spl1_124])],[avatar_definition])).
% 48.35/8.42 thf(f2760,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ~spl1_124),
% 48.35/8.42 inference(avatar_component_clause,[],[f2759])).
% 48.35/8.42 thf(f2761,plain,(
% 48.35/8.42 spl1_123 | spl1_124 | ~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35),
% 48.35/8.42 inference(avatar_split_clause,[],[f2620,f541,f525,f142,f131,f2759,f2756])).
% 48.35/8.42 thf(f2763,plain,(
% 48.35/8.42 spl1_95 | spl1_89 | ~spl1_3 | ~spl1_6 | ~spl1_33),
% 48.35/8.42 inference(avatar_split_clause,[],[f2594,f525,f142,f131,f1890,f1919])).
% 48.35/8.42 thf(f2803,plain,(
% 48.35/8.42 ($false = $true) | (~spl1_95 | ~spl1_123)),
% 48.35/8.42 inference(forward_demodulation,[],[f2757,f1920])).
% 48.35/8.42 thf(f2804,plain,(
% 48.35/8.42 $false | (~spl1_95 | ~spl1_123)),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f2803])).
% 48.35/8.42 thf(f2805,plain,(
% 48.35/8.42 ~spl1_95 | ~spl1_123),
% 48.35/8.42 inference(avatar_contradiction_clause,[],[f2804])).
% 48.35/8.42 thf(f3001,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))) | ($false = (((irel @ sK13 @ sK19) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a1 @ Y0))))) | $true)))) | ~spl1_117),
% 48.35/8.42 inference(constrained_superposition,[],[f2400,f80])).
% 48.35/8.42 thf(f3010,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK19) => $true))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))) | ~spl1_117),
% 48.35/8.42 inference(boolean_simplification,[],[f3001])).
% 48.35/8.42 thf(f3011,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))) | ($false = $true) | ~spl1_117),
% 48.35/8.42 inference(boolean_simplification,[],[f3010])).
% 48.35/8.42 thf(f3012,plain,(
% 48.35/8.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a2 @ Y0)))))) | ~spl1_117),
% 48.35/8.42 inference(trivial_inequality_removal,[],[f3011])).
% 48.35/8.42 thf(f3020,plain,(
% 48.35/8.42 spl1_115 | ~spl1_117),
% 48.35/8.42 inference(avatar_split_clause,[],[f3012,f2399,f2392])).
% 48.35/8.42 thf(f3165,plain,(
% 48.35/8.42 ($false = (((^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ sK17))) | ~spl1_124),
% 48.35/8.42 inference(sigma_proxy_clausification,[],[f2760])).
% 48.35/8.42 thf(f3168,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK17) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))))) | ~spl1_124),
% 48.35/8.42 inference(beta-eta_normalization,[],[f3165])).
% 48.35/8.42 thf(f3169,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK17) => (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))))) | (~spl1_110 | ~spl1_124)),
% 48.35/8.42 inference(forward_demodulation,[],[f3168,f2250])).
% 48.35/8.42 thf(f3170,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK17) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0)))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))))) | (~spl1_110 | ~spl1_124)),
% 48.35/8.42 inference(boolean_simplification,[],[f3169])).
% 48.35/8.42 thf(f3171,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK17) => ($false & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))))) | (~spl1_107 | ~spl1_110 | ~spl1_124)),
% 48.35/8.42 inference(forward_demodulation,[],[f3170,f2239])).
% 48.35/8.42 thf(f3172,plain,(
% 48.35/8.42 ($false = (((irel @ sK13 @ sK17) => $false))) | (~spl1_107 | ~spl1_110 | ~spl1_124)),
% 48.35/8.42 inference(boolean_simplification,[],[f3171])).
% 48.35/8.42 thf(f3173,plain,(
% 48.35/8.42 ($false = ((~ (irel @ sK13 @ sK17)))) | (~spl1_107 | ~spl1_110 | ~spl1_124)),
% 48.35/8.42 inference(boolean_simplification,[],[f3172])).
% 48.35/8.42 thf(f3174,plain,(
% 48.35/8.42 ($true = ((irel @ sK13 @ sK17))) | (~spl1_107 | ~spl1_110 | ~spl1_124)),
% 48.35/8.42 inference(not_proxy_clausification,[],[f3173])).
% 48.35/8.42 thf(f3181,plain,(
% 48.35/8.42 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) = $true) | ~spl1_96),
% 48.35/8.42 inference(not_proxy_clausification,[],[f1925])).
% 48.35/8.42 thf(f3186,plain,(
% 48.35/8.42 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((irel @ sK13 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ X1)))) ) | ~spl1_96),
% 48.35/8.42 inference(pi_proxy_clausification,[],[f3181])).
% 48.35/8.42 thf(f3187,plain,(
% 48.35/8.42 ( ! [X1 : $i] : (($true = (((irel @ sK13 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0)))))))))) ) | ~spl1_96),
% 48.35/8.42 inference(beta-eta_normalization,[],[f3186])).
% 48.35/8.42 thf(f3197,plain,(
% 48.35/8.42 ($true = (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))))))) | (~spl1_96 | ~spl1_107 | ~spl1_110 | ~spl1_124)),
% 48.35/8.42 inference(constrained_superposition,[],[f3187,f3174])).
% 48.35/8.42 thf(f3217,plain,(
% 48.35/8.42 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_96 | ~spl1_107 | ~spl1_110 | ~spl1_124)),
% 48.35/8.42 inference(boolean_simplification,[],[f3197])).
% 48.35/8.42 thf(f3221,plain,(
% 48.35/8.42 (((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) | $false))) = $true) | (~spl1_96 | ~spl1_107 | ~spl1_110 | ~spl1_124)),
% 48.35/8.42 inference(forward_demodulation,[],[f3217,f2239])).
% 48.35/8.42 thf(f3222,plain,(
% 48.35/8.42 (((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl1_96 | ~spl1_107 | ~spl1_110 | ~spl1_124)),
% 48.35/8.42 inference(boolean_simplification,[],[f3221])).
% 48.35/8.42 thf(f3223,plain,(
% 48.35/8.42 (((($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl1_96 | ~spl1_107 | ~spl1_110 | ~spl1_124)),
% 48.35/8.42 inference(boolean_simplification,[],[f3222])).
% 48.35/8.42 thf(f3224,plain,(
% 48.35/8.42 ($true = (($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0)))))))) | (~spl1_96 | ~spl1_107 | ~spl1_110 | ~spl1_124)),
% 48.35/8.42 inference(boolean_simplification,[],[f3223])).
% 48.35/8.42 thf(f3225,plain,(
% 48.35/8.42 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))) | (~spl1_96 | ~spl1_107 | ~spl1_110 | ~spl1_124)),
% 48.35/8.42 inference(boolean_simplification,[],[f3224])).
% 48.35/8.42 thf(f3235,plain,(
% 48.35/8.42 ($false = $true) | (~spl1_96 | ~spl1_107 | ~spl1_110 | ~spl1_124)),
% 48.35/8.42 inference(forward_demodulation,[],[f3225,f2250])).
% 48.35/8.42 thf(f3236,plain,(
% 48.35/8.42 $false | (~spl1_96 | ~spl1_107 | ~spl1_110 | ~spl1_124)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f3235])).
% 48.35/8.43 thf(f3237,plain,(
% 48.35/8.43 ~spl1_96 | ~spl1_107 | ~spl1_110 | ~spl1_124),
% 48.35/8.43 inference(avatar_contradiction_clause,[],[f3236])).
% 48.35/8.43 thf(f3246,plain,(
% 48.35/8.43 ($false = (((irel @ sK13 @ sK17) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) | $false) & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))))) | (~spl1_107 | ~spl1_124)),
% 48.35/8.43 inference(forward_demodulation,[],[f3168,f2239])).
% 48.35/8.43 thf(f3247,plain,(
% 48.35/8.43 ($false = (((irel @ sK13 @ sK17) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) | $false) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))))) | (~spl1_107 | ~spl1_124)),
% 48.35/8.43 inference(boolean_simplification,[],[f3246])).
% 48.35/8.43 thf(f3248,plain,(
% 48.35/8.43 ((((irel @ sK13 @ sK17) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) | $false) & $true))) = $false) | (~spl1_107 | ~spl1_124)),
% 48.35/8.43 inference(boolean_simplification,[],[f3247])).
% 48.35/8.43 thf(f3249,plain,(
% 48.35/8.43 ($false = (((irel @ sK13 @ sK17) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) | $false)))) | (~spl1_107 | ~spl1_124)),
% 48.35/8.43 inference(boolean_simplification,[],[f3248])).
% 48.35/8.43 thf(f3250,plain,(
% 48.35/8.43 ($false = (((irel @ sK13 @ sK17) => (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0)))))))) | (~spl1_107 | ~spl1_124)),
% 48.35/8.43 inference(boolean_simplification,[],[f3249])).
% 48.35/8.43 thf(f3258,plain,(
% 48.35/8.43 spl1_50 | ~spl1_55),
% 48.35/8.43 inference(avatar_split_clause,[],[f1318,f825,f802])).
% 48.35/8.43 thf(f3274,plain,(
% 48.35/8.43 ($false = ((~ $false))) | (~spl1_49 | ~spl1_55)),
% 48.35/8.43 inference(forward_demodulation,[],[f1312,f799])).
% 48.35/8.43 thf(f3275,plain,(
% 48.35/8.43 ($false = $true) | (~spl1_49 | ~spl1_55)),
% 48.35/8.43 inference(boolean_simplification,[],[f3274])).
% 48.35/8.43 thf(f3276,plain,(
% 48.35/8.43 $false | (~spl1_49 | ~spl1_55)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f3275])).
% 48.35/8.43 thf(f3277,plain,(
% 48.35/8.43 ~spl1_49 | ~spl1_55),
% 48.35/8.43 inference(avatar_contradiction_clause,[],[f3276])).
% 48.35/8.43 thf(f3285,plain,(
% 48.35/8.43 ($false = (((irel @ sK5 @ sK7) => $false))) | (~spl1_49 | ~spl1_52)),
% 48.35/8.43 inference(forward_demodulation,[],[f810,f799])).
% 48.35/8.43 thf(f3286,plain,(
% 48.35/8.43 ($false = ((~ (irel @ sK5 @ sK7)))) | (~spl1_49 | ~spl1_52)),
% 48.35/8.43 inference(boolean_simplification,[],[f3285])).
% 48.35/8.43 thf(f3310,plain,(
% 48.35/8.43 ($true = ((irel @ sK5 @ sK7))) | (~spl1_49 | ~spl1_52)),
% 48.35/8.43 inference(not_proxy_clausification,[],[f3286])).
% 48.35/8.43 thf(f3419,plain,(
% 48.35/8.43 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))) = $true) | ~spl1_56),
% 48.35/8.43 inference(not_proxy_clausification,[],[f830])).
% 48.35/8.43 thf(f3424,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))) @ X1)) = $true)) ) | ~spl1_56),
% 48.35/8.43 inference(pi_proxy_clausification,[],[f3419])).
% 48.35/8.43 thf(f3425,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (((((irel @ sK7 @ X1) => (a3 @ X1))) = $true)) ) | ~spl1_56),
% 48.35/8.43 inference(beta-eta_normalization,[],[f3424])).
% 48.35/8.43 thf(f3527,plain,(
% 48.35/8.43 ($true = ((irel @ sK7 @ sK8))) | ~spl1_59),
% 48.35/8.43 inference(imp_proxy_clausification,[],[f883])).
% 48.35/8.43 thf(f3560,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))) | (~spl1_107 | ~spl1_124)),
% 48.35/8.43 inference(imp_proxy_clausification,[],[f3250])).
% 48.35/8.43 thf(f3573,definition,(
% 48.35/8.43 spl1_129 <=> ($false = ((~ (irel @ sK13 @ sK17))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_129])],[avatar_definition])).
% 48.35/8.43 thf(f3574,plain,(
% 48.35/8.43 ($false = ((~ (irel @ sK13 @ sK17)))) | ~spl1_129),
% 48.35/8.43 inference(avatar_component_clause,[],[f3573])).
% 48.35/8.43 thf(f3580,plain,(
% 48.35/8.43 spl1_110 | ~spl1_107 | ~spl1_124),
% 48.35/8.43 inference(avatar_split_clause,[],[f3560,f2759,f2238,f2249])).
% 48.35/8.43 thf(f3585,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0)))))) | ($false = (((irel @ sK13 @ sK17) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) | $true) & ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))))) | ~spl1_124),
% 48.35/8.43 inference(constrained_superposition,[],[f3168,f80])).
% 48.35/8.43 thf(f3592,plain,(
% 48.35/8.43 ($false = (((irel @ sK13 @ sK17) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) | $true) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0)))))) | ~spl1_124),
% 48.35/8.43 inference(boolean_simplification,[],[f3585])).
% 48.35/8.43 thf(f3593,plain,(
% 48.35/8.43 ($false = (((irel @ sK13 @ sK17) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) | $true) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0)))))) | ~spl1_124),
% 48.35/8.43 inference(boolean_simplification,[],[f3592])).
% 48.35/8.43 thf(f3594,plain,(
% 48.35/8.43 ($false = (((irel @ sK13 @ sK17) => ($true & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0)))))) | ~spl1_124),
% 48.35/8.43 inference(boolean_simplification,[],[f3593])).
% 48.35/8.43 thf(f3595,plain,(
% 48.35/8.43 ($false = (((irel @ sK13 @ sK17) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0)))))) | ~spl1_124),
% 48.35/8.43 inference(boolean_simplification,[],[f3594])).
% 48.35/8.43 thf(f3611,definition,(
% 48.35/8.43 spl1_131 <=> ($false = (((irel @ sK13 @ sK17) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0)))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_131])],[avatar_definition])).
% 48.35/8.43 thf(f3612,plain,(
% 48.35/8.43 ($false = (((irel @ sK13 @ sK17) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))))) | ~spl1_131),
% 48.35/8.43 inference(avatar_component_clause,[],[f3611])).
% 48.35/8.43 thf(f3613,plain,(
% 48.35/8.43 spl1_131 | spl1_107 | ~spl1_124),
% 48.35/8.43 inference(avatar_split_clause,[],[f3595,f2759,f2238,f3611])).
% 48.35/8.43 thf(f3652,plain,(
% 48.35/8.43 ($false = (((irel @ sK13 @ sK17) => $false))) | (~spl1_106 | ~spl1_131)),
% 48.35/8.43 inference(forward_demodulation,[],[f3612,f2236])).
% 48.35/8.43 thf(f3653,plain,(
% 48.35/8.43 ($false = ((~ (irel @ sK13 @ sK17)))) | (~spl1_106 | ~spl1_131)),
% 48.35/8.43 inference(boolean_simplification,[],[f3652])).
% 48.35/8.43 thf(f3656,plain,(
% 48.35/8.43 spl1_129 | ~spl1_106 | ~spl1_131),
% 48.35/8.43 inference(avatar_split_clause,[],[f3653,f3611,f2235,f3573])).
% 48.35/8.43 thf(f3657,plain,(
% 48.35/8.43 ($true = ((irel @ sK13 @ sK17))) | ~spl1_129),
% 48.35/8.43 inference(not_proxy_clausification,[],[f3574])).
% 48.35/8.43 thf(f3663,plain,(
% 48.35/8.43 ($true = (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))))))) | (~spl1_96 | ~spl1_129)),
% 48.35/8.43 inference(constrained_superposition,[],[f3187,f3657])).
% 48.35/8.43 thf(f3664,plain,(
% 48.35/8.43 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_96 | ~spl1_129)),
% 48.35/8.43 inference(boolean_simplification,[],[f3663])).
% 48.35/8.43 thf(f3666,plain,(
% 48.35/8.43 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) | $false) & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_96 | ~spl1_106 | ~spl1_129)),
% 48.35/8.43 inference(forward_demodulation,[],[f3664,f2236])).
% 48.35/8.43 thf(f3667,plain,(
% 48.35/8.43 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) | $false) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_96 | ~spl1_106 | ~spl1_129)),
% 48.35/8.43 inference(boolean_simplification,[],[f3666])).
% 48.35/8.43 thf(f3668,plain,(
% 48.35/8.43 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) | $false) & $true)) = $true) | (~spl1_96 | ~spl1_106 | ~spl1_129)),
% 48.35/8.43 inference(boolean_simplification,[],[f3667])).
% 48.35/8.43 thf(f3669,plain,(
% 48.35/8.43 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))) | $false)) = $true) | (~spl1_96 | ~spl1_106 | ~spl1_129)),
% 48.35/8.43 inference(boolean_simplification,[],[f3668])).
% 48.35/8.43 thf(f3670,plain,(
% 48.35/8.43 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0))))))) | (~spl1_96 | ~spl1_106 | ~spl1_129)),
% 48.35/8.43 inference(boolean_simplification,[],[f3669])).
% 48.35/8.43 thf(f3710,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a1 @ Y0)))))) | (~spl1_96 | ~spl1_106 | ~spl1_129)),
% 48.35/8.43 inference(not_proxy_clausification,[],[f3670])).
% 48.35/8.43 thf(f3714,plain,(
% 48.35/8.43 spl1_107 | ~spl1_96 | ~spl1_106 | ~spl1_129),
% 48.35/8.43 inference(avatar_split_clause,[],[f3710,f3573,f2235,f1924,f2238])).
% 48.35/8.43 thf(f3742,plain,(
% 48.35/8.43 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) = $true) | (~spl1_3 | ~spl1_6)),
% 48.35/8.43 inference(and_proxy_clausification,[],[f1401])).
% 48.35/8.43 thf(f3771,plain,(
% 48.35/8.43 ($true = (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | (~spl1_3 | ~spl1_6 | ~spl1_36)),
% 48.35/8.43 inference(forward_demodulation,[],[f3742,f546])).
% 48.35/8.43 thf(f3772,plain,(
% 48.35/8.43 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) = $true) | (~spl1_3 | ~spl1_6 | ~spl1_36)),
% 48.35/8.43 inference(boolean_simplification,[],[f3771])).
% 48.35/8.43 thf(f3783,definition,(
% 48.35/8.43 spl1_136 <=> (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) = $true)),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_136])],[avatar_definition])).
% 48.35/8.43 thf(f3784,plain,(
% 48.35/8.43 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) = $true) | ~spl1_136),
% 48.35/8.43 inference(avatar_component_clause,[],[f3783])).
% 48.35/8.43 thf(f3786,plain,(
% 48.35/8.43 spl1_136 | ~spl1_3 | ~spl1_6 | ~spl1_36),
% 48.35/8.43 inference(avatar_split_clause,[],[f3772,f545,f142,f131,f3783])).
% 48.35/8.43 thf(f3787,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))) @ X1)) = $true)) ) | ~spl1_136),
% 48.35/8.43 inference(pi_proxy_clausification,[],[f3784])).
% 48.35/8.43 thf(f3788,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (($true = (((irel @ sK5 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))))) ) | ~spl1_136),
% 48.35/8.43 inference(beta-eta_normalization,[],[f3787])).
% 48.35/8.43 thf(f3799,plain,(
% 48.35/8.43 ((($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) = $true) | (~spl1_49 | ~spl1_52 | ~spl1_136)),
% 48.35/8.43 inference(constrained_superposition,[],[f3788,f3310])).
% 48.35/8.43 thf(f3819,plain,(
% 48.35/8.43 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl1_49 | ~spl1_52 | ~spl1_136)),
% 48.35/8.43 inference(boolean_simplification,[],[f3799])).
% 48.35/8.43 thf(f3824,plain,(
% 48.35/8.43 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $true) & ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_136)),
% 48.35/8.43 inference(forward_demodulation,[],[f3819,f3419])).
% 48.35/8.43 thf(f3825,plain,(
% 48.35/8.43 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $true) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_136)),
% 48.35/8.43 inference(boolean_simplification,[],[f3824])).
% 48.35/8.43 thf(f3826,plain,(
% 48.35/8.43 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $true) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) = $true) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_136)),
% 48.35/8.43 inference(boolean_simplification,[],[f3825])).
% 48.35/8.43 thf(f3827,plain,(
% 48.35/8.43 ((($true & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) = $true) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_136)),
% 48.35/8.43 inference(boolean_simplification,[],[f3826])).
% 48.35/8.43 thf(f3828,plain,(
% 48.35/8.43 ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_136)),
% 48.35/8.43 inference(boolean_simplification,[],[f3827])).
% 48.35/8.43 thf(f3872,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ X1)))) ) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_136)),
% 48.35/8.43 inference(pi_proxy_clausification,[],[f3828])).
% 48.35/8.43 thf(f3873,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (((((irel @ sK7 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0)))))))) = $true)) ) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_136)),
% 48.35/8.43 inference(beta-eta_normalization,[],[f3872])).
% 48.35/8.43 thf(f3883,plain,(
% 48.35/8.43 ((($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))))) = $true) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_59 | ~spl1_136)),
% 48.35/8.43 inference(constrained_superposition,[],[f3873,f3527])).
% 48.35/8.43 thf(f3904,plain,(
% 48.35/8.43 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_59 | ~spl1_136)),
% 48.35/8.43 inference(boolean_simplification,[],[f3883])).
% 48.35/8.43 thf(f3905,plain,(
% 48.35/8.43 ($true = ((($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))))) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_57 | ~spl1_59 | ~spl1_136)),
% 48.35/8.43 inference(forward_demodulation,[],[f3904,f876])).
% 48.35/8.43 thf(f3906,plain,(
% 48.35/8.43 ((((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0)))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_57 | ~spl1_59 | ~spl1_136)),
% 48.35/8.43 inference(boolean_simplification,[],[f3905])).
% 48.35/8.43 thf(f3907,plain,(
% 48.35/8.43 ((($false & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_57 | ~spl1_59 | ~spl1_64 | ~spl1_136)),
% 48.35/8.43 inference(forward_demodulation,[],[f3906,f910])).
% 48.35/8.43 thf(f3908,plain,(
% 48.35/8.43 ($false = $true) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_57 | ~spl1_59 | ~spl1_64 | ~spl1_136)),
% 48.35/8.43 inference(boolean_simplification,[],[f3907])).
% 48.35/8.43 thf(f3909,plain,(
% 48.35/8.43 $false | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_57 | ~spl1_59 | ~spl1_64 | ~spl1_136)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f3908])).
% 48.35/8.43 thf(f3910,plain,(
% 48.35/8.43 ~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_57 | ~spl1_59 | ~spl1_64 | ~spl1_136),
% 48.35/8.43 inference(avatar_contradiction_clause,[],[f3909])).
% 48.35/8.43 thf(f3954,plain,(
% 48.35/8.43 ($false = (((irel @ sK7 @ sK8) => ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))))) | (~spl1_58 | ~spl1_62)),
% 48.35/8.43 inference(forward_demodulation,[],[f879,f901])).
% 48.35/8.43 thf(f3955,plain,(
% 48.35/8.43 ($false = (((irel @ sK7 @ sK8) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))))) | (~spl1_58 | ~spl1_62)),
% 48.35/8.43 inference(boolean_simplification,[],[f3954])).
% 48.35/8.43 thf(f3958,plain,(
% 48.35/8.43 ($false = (((irel @ sK7 @ sK8) => $false))) | (~spl1_58 | ~spl1_60 | ~spl1_62)),
% 48.35/8.43 inference(forward_demodulation,[],[f3955,f886])).
% 48.35/8.43 thf(f3959,plain,(
% 48.35/8.43 ($false = ((~ (irel @ sK7 @ sK8)))) | (~spl1_58 | ~spl1_60 | ~spl1_62)),
% 48.35/8.43 inference(boolean_simplification,[],[f3958])).
% 48.35/8.43 thf(f3969,plain,(
% 48.35/8.43 ($true = ((irel @ sK7 @ sK8))) | (~spl1_58 | ~spl1_60 | ~spl1_62)),
% 48.35/8.43 inference(not_proxy_clausification,[],[f3959])).
% 48.35/8.43 thf(f3983,plain,(
% 48.35/8.43 ((($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0)))))))) = $true) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_58 | ~spl1_60 | ~spl1_62 | ~spl1_136)),
% 48.35/8.43 inference(constrained_superposition,[],[f3873,f3969])).
% 48.35/8.43 thf(f3989,plain,(
% 48.35/8.43 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_58 | ~spl1_60 | ~spl1_62 | ~spl1_136)),
% 48.35/8.43 inference(boolean_simplification,[],[f3983])).
% 48.35/8.43 thf(f3991,plain,(
% 48.35/8.43 ($true = ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) | $false)))) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_58 | ~spl1_60 | ~spl1_62 | ~spl1_136)),
% 48.35/8.43 inference(forward_demodulation,[],[f3989,f886])).
% 48.35/8.43 thf(f3992,plain,(
% 48.35/8.43 ($true = ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0)))))))) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_58 | ~spl1_60 | ~spl1_62 | ~spl1_136)),
% 48.35/8.43 inference(boolean_simplification,[],[f3991])).
% 48.35/8.43 thf(f3993,plain,(
% 48.35/8.43 ($true = ((($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0)))))))) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_58 | ~spl1_60 | ~spl1_62 | ~spl1_136)),
% 48.35/8.43 inference(boolean_simplification,[],[f3992])).
% 48.35/8.43 thf(f3994,plain,(
% 48.35/8.43 ((($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_58 | ~spl1_60 | ~spl1_62 | ~spl1_136)),
% 48.35/8.43 inference(boolean_simplification,[],[f3993])).
% 48.35/8.43 thf(f3995,plain,(
% 48.35/8.43 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a2 @ Y0))))))) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_58 | ~spl1_60 | ~spl1_62 | ~spl1_136)),
% 48.35/8.43 inference(boolean_simplification,[],[f3994])).
% 48.35/8.43 thf(f3996,plain,(
% 48.35/8.43 ($false = $true) | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_58 | ~spl1_60 | ~spl1_62 | ~spl1_136)),
% 48.35/8.43 inference(forward_demodulation,[],[f3995,f901])).
% 48.35/8.43 thf(f3997,plain,(
% 48.35/8.43 $false | (~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_58 | ~spl1_60 | ~spl1_62 | ~spl1_136)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f3996])).
% 48.35/8.43 thf(f3998,plain,(
% 48.35/8.43 ~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_58 | ~spl1_60 | ~spl1_62 | ~spl1_136),
% 48.35/8.43 inference(avatar_contradiction_clause,[],[f3997])).
% 48.35/8.43 thf(f4054,plain,(
% 48.35/8.43 ($false = (((^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a3 @ Y0))) @ sK10))) | ~spl1_53),
% 48.35/8.43 inference(sigma_proxy_clausification,[],[f813])).
% 48.35/8.43 thf(f4057,plain,(
% 48.35/8.43 ($false = (((irel @ sK7 @ sK10) => (a3 @ sK10)))) | ~spl1_53),
% 48.35/8.43 inference(beta-eta_normalization,[],[f4054])).
% 48.35/8.43 thf(f4058,plain,(
% 48.35/8.43 ($false = $true) | (~spl1_53 | ~spl1_56)),
% 48.35/8.43 inference(forward_demodulation,[],[f4057,f3425])).
% 48.35/8.43 thf(f4059,plain,(
% 48.35/8.43 $false | (~spl1_53 | ~spl1_56)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f4058])).
% 48.35/8.43 thf(f4060,plain,(
% 48.35/8.43 ~spl1_53 | ~spl1_56),
% 48.35/8.43 inference(avatar_contradiction_clause,[],[f4059])).
% 48.35/8.43 thf(f4072,plain,(
% 48.35/8.43 ($false = (((irel @ sK5 @ sK7) => ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))))) | (~spl1_51 | ~spl1_56)),
% 48.35/8.43 inference(forward_demodulation,[],[f806,f830])).
% 48.35/8.43 thf(f4073,plain,(
% 48.35/8.43 ($false = (((irel @ sK5 @ sK7) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | (~spl1_51 | ~spl1_56)),
% 48.35/8.43 inference(boolean_simplification,[],[f4072])).
% 48.35/8.43 thf(f4076,plain,(
% 48.35/8.43 ($false = (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))))) | (~spl1_8 | ~spl1_16)),
% 48.35/8.43 inference(forward_demodulation,[],[f217,f188])).
% 48.35/8.43 thf(f4077,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))) | (~spl1_8 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f4076])).
% 48.35/8.43 thf(f4089,plain,(
% 48.35/8.43 spl1_52 | ~spl1_51 | ~spl1_56),
% 48.35/8.43 inference(avatar_split_clause,[],[f4073,f829,f805,f809])).
% 48.35/8.43 thf(f4090,plain,(
% 48.35/8.43 spl1_11 | ~spl1_8 | ~spl1_16),
% 48.35/8.43 inference(avatar_split_clause,[],[f4077,f216,f187,f198])).
% 48.35/8.43 thf(f4096,plain,(
% 48.35/8.43 ($false = (((irel @ sK0 @ sK2) => $false))) | (~spl1_7 | ~spl1_10)),
% 48.35/8.43 inference(forward_demodulation,[],[f185,f195])).
% 48.35/8.43 thf(f4097,plain,(
% 48.35/8.43 ($false = ((~ (irel @ sK0 @ sK2)))) | (~spl1_7 | ~spl1_10)),
% 48.35/8.43 inference(boolean_simplification,[],[f4096])).
% 48.35/8.43 thf(f4100,plain,(
% 48.35/8.43 (((irel @ sK0 @ sK2)) = $true) | (~spl1_7 | ~spl1_10)),
% 48.35/8.43 inference(not_proxy_clausification,[],[f4097])).
% 48.35/8.43 thf(f4242,plain,(
% 48.35/8.43 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) = $true) | ~spl1_13),
% 48.35/8.43 inference(not_proxy_clausification,[],[f206])).
% 48.35/8.43 thf(f4549,plain,(
% 48.35/8.43 ($false = ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | $false)))) | (~spl1_24 | ~spl1_26)),
% 48.35/8.43 inference(forward_demodulation,[],[f319,f331])).
% 48.35/8.43 thf(f4550,plain,(
% 48.35/8.43 ($false = ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))))) | (~spl1_24 | ~spl1_26)),
% 48.35/8.43 inference(boolean_simplification,[],[f4549])).
% 48.35/8.43 thf(f4551,plain,(
% 48.35/8.43 ($false = ((($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))))) | (~spl1_24 | ~spl1_26)),
% 48.35/8.43 inference(boolean_simplification,[],[f4550])).
% 48.35/8.43 thf(f4552,plain,(
% 48.35/8.43 ($false = (($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))))) | (~spl1_24 | ~spl1_26)),
% 48.35/8.43 inference(boolean_simplification,[],[f4551])).
% 48.35/8.43 thf(f4553,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))))) | (~spl1_24 | ~spl1_26)),
% 48.35/8.43 inference(boolean_simplification,[],[f4552])).
% 48.35/8.43 thf(f4562,plain,(
% 48.35/8.43 spl1_21 | ~spl1_24 | ~spl1_26),
% 48.35/8.43 inference(avatar_split_clause,[],[f4553,f330,f318,f307])).
% 48.35/8.43 thf(f4565,plain,(
% 48.35/8.43 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) = $true) | ~spl1_21),
% 48.35/8.43 inference(not_proxy_clausification,[],[f308])).
% 48.35/8.43 thf(f4624,plain,(
% 48.35/8.43 ($false = (((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ sK26))) | ~spl1_26),
% 48.35/8.43 inference(sigma_proxy_clausification,[],[f331])).
% 48.35/8.43 thf(f4626,plain,(
% 48.35/8.43 ($false = (((irel @ sK3 @ sK26) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))))) | ~spl1_26),
% 48.35/8.43 inference(beta-eta_normalization,[],[f4624])).
% 48.35/8.43 thf(f4628,plain,(
% 48.35/8.43 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))))))) | ~spl1_26),
% 48.35/8.43 inference(imp_proxy_clausification,[],[f4626])).
% 48.35/8.43 thf(f4634,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))) | ($false = (((irel @ sK3 @ sK26) => (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))))) | ~spl1_26),
% 48.35/8.43 inference(constrained_superposition,[],[f4626,f80])).
% 48.35/8.43 thf(f4639,plain,(
% 48.35/8.43 ($false = (((irel @ sK3 @ sK26) => ($true & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))) | ~spl1_26),
% 48.35/8.43 inference(boolean_simplification,[],[f4634])).
% 48.35/8.43 thf(f4640,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))) | ($false = (((irel @ sK3 @ sK26) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))))))) | ~spl1_26),
% 48.35/8.43 inference(boolean_simplification,[],[f4639])).
% 48.35/8.43 thf(f4658,definition,(
% 48.35/8.43 spl1_147 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_147])],[avatar_definition])).
% 48.35/8.43 thf(f4659,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))) | ~spl1_147),
% 48.35/8.43 inference(avatar_component_clause,[],[f4658])).
% 48.35/8.43 thf(f4661,definition,(
% 48.35/8.43 spl1_148 <=> ($false = (((irel @ sK3 @ sK26) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_148])],[avatar_definition])).
% 48.35/8.43 thf(f4662,plain,(
% 48.35/8.43 ($false = (((irel @ sK3 @ sK26) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))))))) | ~spl1_148),
% 48.35/8.43 inference(avatar_component_clause,[],[f4661])).
% 48.35/8.43 thf(f4663,plain,(
% 48.35/8.43 spl1_147 | spl1_148 | ~spl1_26),
% 48.35/8.43 inference(avatar_split_clause,[],[f4640,f330,f4661,f4658])).
% 48.35/8.43 thf(f4668,definition,(
% 48.35/8.43 spl1_150 <=> ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_150])],[avatar_definition])).
% 48.35/8.43 thf(f4669,plain,(
% 48.35/8.43 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))))))) | ~spl1_150),
% 48.35/8.43 inference(avatar_component_clause,[],[f4668])).
% 48.35/8.43 thf(f4671,plain,(
% 48.35/8.43 spl1_150 | ~spl1_26),
% 48.35/8.43 inference(avatar_split_clause,[],[f4628,f330,f4668])).
% 48.35/8.43 thf(f4680,definition,(
% 48.35/8.43 spl1_153 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_153])],[avatar_definition])).
% 48.35/8.43 thf(f4681,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))))) | ~spl1_153),
% 48.35/8.43 inference(avatar_component_clause,[],[f4680])).
% 48.35/8.43 thf(f4693,definition,(
% 48.35/8.43 spl1_155 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_155])],[avatar_definition])).
% 48.35/8.43 thf(f4694,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0)))))) | ~spl1_155),
% 48.35/8.43 inference(avatar_component_clause,[],[f4693])).
% 48.35/8.43 thf(f4700,definition,(
% 48.35/8.43 spl1_157 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0)))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_157])],[avatar_definition])).
% 48.35/8.43 thf(f4701,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) | ~spl1_157),
% 48.35/8.43 inference(avatar_component_clause,[],[f4700])).
% 48.35/8.43 thf(f4705,plain,(
% 48.35/8.43 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $true) & ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl1_21 | ~spl1_24)),
% 48.35/8.43 inference(forward_demodulation,[],[f319,f4565])).
% 48.35/8.43 thf(f4706,plain,(
% 48.35/8.43 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $true) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl1_21 | ~spl1_24)),
% 48.35/8.43 inference(boolean_simplification,[],[f4705])).
% 48.35/8.43 thf(f4707,plain,(
% 48.35/8.43 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $true) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl1_21 | ~spl1_24)),
% 48.35/8.43 inference(boolean_simplification,[],[f4706])).
% 48.35/8.43 thf(f4708,plain,(
% 48.35/8.43 ($false = (($true & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl1_21 | ~spl1_24)),
% 48.35/8.43 inference(boolean_simplification,[],[f4707])).
% 48.35/8.43 thf(f4709,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | (~spl1_21 | ~spl1_24)),
% 48.35/8.43 inference(boolean_simplification,[],[f4708])).
% 48.35/8.43 thf(f4712,plain,(
% 48.35/8.43 spl1_26 | ~spl1_21 | ~spl1_24),
% 48.35/8.43 inference(avatar_split_clause,[],[f4709,f318,f307,f330])).
% 48.35/8.43 thf(f4724,plain,(
% 48.35/8.43 ($false = (((irel @ sK2 @ sK3) => ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl1_19 | ~spl1_25)),
% 48.35/8.43 inference(forward_demodulation,[],[f301,f328])).
% 48.35/8.43 thf(f4725,plain,(
% 48.35/8.43 ($false = (((irel @ sK2 @ sK3) => ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl1_19 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f4724])).
% 48.35/8.43 thf(f4726,plain,(
% 48.35/8.43 ((((irel @ sK2 @ sK3) => $true)) = $false) | (~spl1_19 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f4725])).
% 48.35/8.43 thf(f4727,plain,(
% 48.35/8.43 ($false = $true) | (~spl1_19 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f4726])).
% 48.35/8.43 thf(f4728,plain,(
% 48.35/8.43 $false | (~spl1_19 | ~spl1_25)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f4727])).
% 48.35/8.43 thf(f4729,plain,(
% 48.35/8.43 ~spl1_19 | ~spl1_25),
% 48.35/8.43 inference(avatar_contradiction_clause,[],[f4728])).
% 48.35/8.43 thf(f4735,plain,(
% 48.35/8.43 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl1_24 | ~spl1_25)),
% 48.35/8.43 inference(forward_demodulation,[],[f319,f328])).
% 48.35/8.43 thf(f4736,plain,(
% 48.35/8.43 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl1_24 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f4735])).
% 48.35/8.43 thf(f4737,plain,(
% 48.35/8.43 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) & $true))) | (~spl1_24 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f4736])).
% 48.35/8.43 thf(f4738,plain,(
% 48.35/8.43 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false))) | (~spl1_24 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f4737])).
% 48.35/8.43 thf(f4739,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl1_24 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f4738])).
% 48.35/8.43 thf(f4740,plain,(
% 48.35/8.43 spl1_22 | ~spl1_24 | ~spl1_25),
% 48.35/8.43 inference(avatar_split_clause,[],[f4739,f327,f318,f311])).
% 48.35/8.43 thf(f4748,plain,(
% 48.35/8.43 ($false = (((irel @ sK2 @ sK3) => ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl1_19 | ~spl1_21)),
% 48.35/8.43 inference(forward_demodulation,[],[f301,f308])).
% 48.35/8.43 thf(f4749,plain,(
% 48.35/8.43 ($false = (((irel @ sK2 @ sK3) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl1_19 | ~spl1_21)),
% 48.35/8.43 inference(boolean_simplification,[],[f4748])).
% 48.35/8.43 thf(f4750,plain,(
% 48.35/8.43 ($false = (((irel @ sK2 @ sK3) => $false))) | (~spl1_19 | ~spl1_21 | ~spl1_26)),
% 48.35/8.43 inference(forward_demodulation,[],[f4749,f331])).
% 48.35/8.43 thf(f4751,plain,(
% 48.35/8.43 ($false = ((~ (irel @ sK2 @ sK3)))) | (~spl1_19 | ~spl1_21 | ~spl1_26)),
% 48.35/8.43 inference(boolean_simplification,[],[f4750])).
% 48.35/8.43 thf(f4752,plain,(
% 48.35/8.43 ($true = ((irel @ sK2 @ sK3))) | (~spl1_19 | ~spl1_21 | ~spl1_26)),
% 48.35/8.43 inference(not_proxy_clausification,[],[f4751])).
% 48.35/8.43 thf(f4825,plain,(
% 48.35/8.43 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) = $true) | ~spl1_21),
% 48.35/8.43 inference(not_proxy_clausification,[],[f308])).
% 48.35/8.43 thf(f4945,plain,(
% 48.35/8.43 (((irel @ sK3 @ sK26)) = $true) | ~spl1_148),
% 48.35/8.43 inference(imp_proxy_clausification,[],[f4662])).
% 48.35/8.43 thf(f4946,plain,(
% 48.35/8.43 ($false = (((irel @ sK3 @ sK26) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | $true)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))))) | ~spl1_148),
% 48.35/8.43 inference(constrained_superposition,[],[f4662,f80])).
% 48.35/8.43 thf(f4952,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))))) | ($false = (((irel @ sK3 @ sK26) => $true))) | ~spl1_148),
% 48.35/8.43 inference(boolean_simplification,[],[f4946])).
% 48.35/8.43 thf(f4953,plain,(
% 48.35/8.43 ($false = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))))) | ~spl1_148),
% 48.35/8.43 inference(boolean_simplification,[],[f4952])).
% 48.35/8.43 thf(f4954,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))))) | ~spl1_148),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f4953])).
% 48.35/8.43 thf(f4988,plain,(
% 48.35/8.43 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) | ~spl1_150),
% 48.35/8.43 inference(and_proxy_clausification,[],[f4669])).
% 48.35/8.43 thf(f4991,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0)))))) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | $true) & ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))))))) | ~spl1_150),
% 48.35/8.43 inference(constrained_superposition,[],[f4669,f80])).
% 48.35/8.43 thf(f5005,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0)))))) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | $true) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))))))) | ~spl1_150),
% 48.35/8.43 inference(boolean_simplification,[],[f4991])).
% 48.35/8.43 thf(f5006,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0)))))) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | $true) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))) | ~spl1_150),
% 48.35/8.43 inference(boolean_simplification,[],[f5005])).
% 48.35/8.43 thf(f5007,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0)))))) | ($false = (($true & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))) | ~spl1_150),
% 48.35/8.43 inference(boolean_simplification,[],[f5006])).
% 48.35/8.43 thf(f5008,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0)))))) | ~spl1_150),
% 48.35/8.43 inference(boolean_simplification,[],[f5007])).
% 48.35/8.43 thf(f5023,plain,(
% 48.35/8.43 ($false = (((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ sK26))) | ~spl1_26),
% 48.35/8.43 inference(sigma_proxy_clausification,[],[f331])).
% 48.35/8.43 thf(f5026,plain,(
% 48.35/8.43 ($false = (((irel @ sK3 @ sK26) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))))) | ~spl1_26),
% 48.35/8.43 inference(beta-eta_normalization,[],[f5023])).
% 48.35/8.43 thf(f5029,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ~spl1_52),
% 48.35/8.43 inference(imp_proxy_clausification,[],[f810])).
% 48.35/8.43 thf(f5041,plain,(
% 48.35/8.43 spl1_49 | ~spl1_52),
% 48.35/8.43 inference(avatar_split_clause,[],[f5029,f809,f798])).
% 48.35/8.43 thf(f5077,plain,(
% 48.35/8.43 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) = $true) | ~spl1_8),
% 48.35/8.43 inference(not_proxy_clausification,[],[f188])).
% 48.35/8.43 thf(f5082,plain,(
% 48.35/8.43 ($false = $true) | (~spl1_8 | ~spl1_14)),
% 48.35/8.43 inference(forward_demodulation,[],[f5077,f210])).
% 48.35/8.43 thf(f5083,plain,(
% 48.35/8.43 $false | (~spl1_8 | ~spl1_14)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f5082])).
% 48.35/8.43 thf(f5084,plain,(
% 48.35/8.43 ~spl1_8 | ~spl1_14),
% 48.35/8.43 inference(avatar_contradiction_clause,[],[f5083])).
% 48.35/8.43 thf(f5101,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK5 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) | ~spl1_32),
% 48.35/8.43 inference(imp_proxy_clausification,[],[f523])).
% 48.35/8.43 thf(f5111,plain,(
% 48.35/8.43 spl1_29 | ~spl1_32),
% 48.35/8.43 inference(avatar_split_clause,[],[f5101,f522,f511])).
% 48.35/8.43 thf(f5125,plain,(
% 48.35/8.43 ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))))))))) | ~spl1_4),
% 48.35/8.43 inference(not_proxy_clausification,[],[f136])).
% 48.35/8.43 thf(f5130,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))) @ X1)) = $true)) ) | ~spl1_4),
% 48.35/8.43 inference(pi_proxy_clausification,[],[f5125])).
% 48.35/8.43 thf(f5131,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (((((irel @ sK0 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a4 @ Y0)))))))) = $true)) ) | ~spl1_4),
% 48.35/8.43 inference(beta-eta_normalization,[],[f5130])).
% 48.35/8.43 thf(f5140,plain,(
% 48.35/8.43 ((($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10)),
% 48.35/8.43 inference(constrained_superposition,[],[f5131,f4100])).
% 48.35/8.43 thf(f5142,plain,(
% 48.35/8.43 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))))) | (~spl1_4 | ~spl1_7 | ~spl1_10)),
% 48.35/8.43 inference(boolean_simplification,[],[f5140])).
% 48.35/8.43 thf(f5159,plain,(
% 48.35/8.43 (((($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13)),
% 48.35/8.43 inference(forward_demodulation,[],[f5142,f206])).
% 48.35/8.43 thf(f5160,plain,(
% 48.35/8.43 ($true = (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13)),
% 48.35/8.43 inference(boolean_simplification,[],[f5159])).
% 48.35/8.43 thf(f5161,plain,(
% 48.35/8.43 ((((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | $true))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13)),
% 48.35/8.43 inference(forward_demodulation,[],[f5160,f4242])).
% 48.35/8.43 thf(f5162,plain,(
% 48.35/8.43 ((((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))) & $true)) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13)),
% 48.35/8.43 inference(boolean_simplification,[],[f5161])).
% 48.35/8.43 thf(f5163,plain,(
% 48.35/8.43 ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13)),
% 48.35/8.43 inference(boolean_simplification,[],[f5162])).
% 48.35/8.43 thf(f5164,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))) @ X1)) = $true)) ) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13)),
% 48.35/8.43 inference(pi_proxy_clausification,[],[f5163])).
% 48.35/8.43 thf(f5165,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (($true = (((irel @ sK2 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0)))))))))) ) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13)),
% 48.35/8.43 inference(beta-eta_normalization,[],[f5164])).
% 48.35/8.43 thf(f5175,plain,(
% 48.35/8.43 ((($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26)),
% 48.35/8.43 inference(constrained_superposition,[],[f5165,f4752])).
% 48.35/8.43 thf(f5188,plain,(
% 48.35/8.43 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26)),
% 48.35/8.43 inference(boolean_simplification,[],[f5175])).
% 48.35/8.43 thf(f5195,plain,(
% 48.35/8.43 (((($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26)),
% 48.35/8.43 inference(forward_demodulation,[],[f5188,f308])).
% 48.35/8.43 thf(f5196,plain,(
% 48.35/8.43 ((((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26)),
% 48.35/8.43 inference(boolean_simplification,[],[f5195])).
% 48.35/8.43 thf(f5197,plain,(
% 48.35/8.43 ((((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $true))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26)),
% 48.35/8.43 inference(forward_demodulation,[],[f5196,f4825])).
% 48.35/8.43 thf(f5198,plain,(
% 48.35/8.43 ((((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))) & $true)) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26)),
% 48.35/8.43 inference(boolean_simplification,[],[f5197])).
% 48.35/8.43 thf(f5199,plain,(
% 48.35/8.43 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26)),
% 48.35/8.43 inference(boolean_simplification,[],[f5198])).
% 48.35/8.43 thf(f5213,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ X1)))) ) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26)),
% 48.35/8.43 inference(pi_proxy_clausification,[],[f5199])).
% 48.35/8.43 thf(f5214,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (((((irel @ sK3 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0)))))))) = $true)) ) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26)),
% 48.35/8.43 inference(beta-eta_normalization,[],[f5213])).
% 48.35/8.43 thf(f5225,plain,(
% 48.35/8.43 ((($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0)))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_148)),
% 48.35/8.43 inference(constrained_superposition,[],[f5214,f4945])).
% 48.35/8.43 thf(f5242,plain,(
% 48.35/8.43 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_148)),
% 48.35/8.43 inference(boolean_simplification,[],[f5225])).
% 48.35/8.43 thf(f5246,plain,(
% 48.35/8.43 ($true = ((($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0)))))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_148 | ~spl1_157)),
% 48.35/8.43 inference(forward_demodulation,[],[f5242,f4701])).
% 48.35/8.43 thf(f5247,plain,(
% 48.35/8.43 ((((!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_148 | ~spl1_157)),
% 48.35/8.43 inference(boolean_simplification,[],[f5246])).
% 48.35/8.43 thf(f5248,plain,(
% 48.35/8.43 ($true = (($false & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0)))))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_148 | ~spl1_153 | ~spl1_157)),
% 48.35/8.43 inference(forward_demodulation,[],[f5247,f4681])).
% 48.35/8.43 thf(f5249,plain,(
% 48.35/8.43 ($false = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_148 | ~spl1_153 | ~spl1_157)),
% 48.35/8.43 inference(boolean_simplification,[],[f5248])).
% 48.35/8.43 thf(f5250,plain,(
% 48.35/8.43 $false | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_148 | ~spl1_153 | ~spl1_157)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f5249])).
% 48.35/8.43 thf(f5251,plain,(
% 48.35/8.43 ~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_148 | ~spl1_153 | ~spl1_157),
% 48.35/8.43 inference(avatar_contradiction_clause,[],[f5250])).
% 48.35/8.43 thf(f5271,plain,(
% 48.35/8.43 spl1_153 | ~spl1_148),
% 48.35/8.43 inference(avatar_split_clause,[],[f4954,f4661,f4680])).
% 48.35/8.43 thf(f5285,plain,(
% 48.35/8.43 ($false = (((irel @ sK3 @ sK26) => $false))) | (~spl1_26 | ~spl1_150)),
% 48.35/8.43 inference(forward_demodulation,[],[f5026,f4669])).
% 48.35/8.43 thf(f5286,plain,(
% 48.35/8.43 ($false = ((~ (irel @ sK3 @ sK26)))) | (~spl1_26 | ~spl1_150)),
% 48.35/8.43 inference(boolean_simplification,[],[f5285])).
% 48.35/8.43 thf(f5287,plain,(
% 48.35/8.43 ($false = ((~ $false))) | (~spl1_147 | ~spl1_153)),
% 48.35/8.43 inference(forward_demodulation,[],[f4659,f4681])).
% 48.35/8.43 thf(f5288,plain,(
% 48.35/8.43 ($false = $true) | (~spl1_147 | ~spl1_153)),
% 48.35/8.43 inference(boolean_simplification,[],[f5287])).
% 48.35/8.43 thf(f5289,plain,(
% 48.35/8.43 $false | (~spl1_147 | ~spl1_153)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f5288])).
% 48.35/8.43 thf(f5290,plain,(
% 48.35/8.43 ~spl1_147 | ~spl1_153),
% 48.35/8.43 inference(avatar_contradiction_clause,[],[f5289])).
% 48.35/8.43 thf(f5319,plain,(
% 48.35/8.43 spl1_155 | spl1_153 | ~spl1_150),
% 48.35/8.43 inference(avatar_split_clause,[],[f5008,f4668,f4680,f4693])).
% 48.35/8.43 thf(f5327,plain,(
% 48.35/8.43 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | $false))) | (~spl1_150 | ~spl1_153)),
% 48.35/8.43 inference(forward_demodulation,[],[f4988,f4681])).
% 48.35/8.43 thf(f5328,plain,(
% 48.35/8.43 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) | (~spl1_150 | ~spl1_153)),
% 48.35/8.43 inference(boolean_simplification,[],[f5327])).
% 48.35/8.43 thf(f5332,plain,(
% 48.35/8.43 ($false = (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) | (~spl1_150 | ~spl1_153)),
% 48.35/8.43 inference(forward_demodulation,[],[f5328,f4681])).
% 48.35/8.43 thf(f5333,plain,(
% 48.35/8.43 ($false = (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) | (~spl1_150 | ~spl1_153)),
% 48.35/8.43 inference(boolean_simplification,[],[f5332])).
% 48.35/8.43 thf(f5334,plain,(
% 48.35/8.43 ($false = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) | (~spl1_150 | ~spl1_153)),
% 48.35/8.43 inference(boolean_simplification,[],[f5333])).
% 48.35/8.43 thf(f5335,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) | (~spl1_150 | ~spl1_153)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f5334])).
% 48.35/8.43 thf(f5340,plain,(
% 48.35/8.43 spl1_157 | ~spl1_150 | ~spl1_153),
% 48.35/8.43 inference(avatar_split_clause,[],[f5335,f4680,f4668,f4700])).
% 48.35/8.43 thf(f5352,plain,(
% 48.35/8.43 (((irel @ sK3 @ sK26)) = $true) | (~spl1_26 | ~spl1_150)),
% 48.35/8.43 inference(not_proxy_clausification,[],[f5286])).
% 48.35/8.43 thf(f5368,plain,(
% 48.35/8.43 ((($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0)))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_150)),
% 48.35/8.43 inference(constrained_superposition,[],[f5214,f5352])).
% 48.35/8.43 thf(f5375,plain,(
% 48.35/8.43 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_150)),
% 48.35/8.43 inference(boolean_simplification,[],[f5368])).
% 48.35/8.43 thf(f5376,plain,(
% 48.35/8.43 (((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | $false))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_150 | ~spl1_155)),
% 48.35/8.43 inference(forward_demodulation,[],[f5375,f4694])).
% 48.35/8.43 thf(f5377,plain,(
% 48.35/8.43 (((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_150 | ~spl1_155)),
% 48.35/8.43 inference(boolean_simplification,[],[f5376])).
% 48.35/8.43 thf(f5378,plain,(
% 48.35/8.43 (((($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_150 | ~spl1_155)),
% 48.35/8.43 inference(boolean_simplification,[],[f5377])).
% 48.35/8.43 thf(f5379,plain,(
% 48.35/8.43 ((($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_150 | ~spl1_155)),
% 48.35/8.43 inference(boolean_simplification,[],[f5378])).
% 48.35/8.43 thf(f5380,plain,(
% 48.35/8.43 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_150 | ~spl1_155)),
% 48.35/8.43 inference(boolean_simplification,[],[f5379])).
% 48.35/8.43 thf(f5381,plain,(
% 48.35/8.43 ($false = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_147 | ~spl1_150 | ~spl1_155)),
% 48.35/8.43 inference(forward_demodulation,[],[f5380,f4659])).
% 48.35/8.43 thf(f5382,plain,(
% 48.35/8.43 $false | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_147 | ~spl1_150 | ~spl1_155)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f5381])).
% 48.35/8.43 thf(f5383,plain,(
% 48.35/8.43 ~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_147 | ~spl1_150 | ~spl1_155),
% 48.35/8.43 inference(avatar_contradiction_clause,[],[f5382])).
% 48.35/8.43 thf(f5394,plain,(
% 48.35/8.43 ($false = ((~ $false))) | (~spl1_22 | ~spl1_26)),
% 48.35/8.43 inference(forward_demodulation,[],[f312,f331])).
% 48.35/8.43 thf(f5395,plain,(
% 48.35/8.43 ($false = $true) | (~spl1_22 | ~spl1_26)),
% 48.35/8.43 inference(boolean_simplification,[],[f5394])).
% 48.35/8.43 thf(f5396,plain,(
% 48.35/8.43 $false | (~spl1_22 | ~spl1_26)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f5395])).
% 48.35/8.43 thf(f5397,plain,(
% 48.35/8.43 ~spl1_22 | ~spl1_26),
% 48.35/8.43 inference(avatar_contradiction_clause,[],[f5396])).
% 48.35/8.43 thf(f5405,plain,(
% 48.35/8.43 ($false = (((irel @ sK2 @ sK3) => $false))) | (~spl1_17 | ~spl1_20)),
% 48.35/8.43 inference(forward_demodulation,[],[f294,f304])).
% 48.35/8.43 thf(f5406,plain,(
% 48.35/8.43 ($false = ((~ (irel @ sK2 @ sK3)))) | (~spl1_17 | ~spl1_20)),
% 48.35/8.43 inference(boolean_simplification,[],[f5405])).
% 48.35/8.43 thf(f5419,plain,(
% 48.35/8.43 ($true = ((irel @ sK2 @ sK3))) | (~spl1_17 | ~spl1_20)),
% 48.35/8.43 inference(not_proxy_clausification,[],[f5406])).
% 48.35/8.43 thf(f5433,plain,(
% 48.35/8.43 ((($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20)),
% 48.35/8.43 inference(constrained_superposition,[],[f5165,f5419])).
% 48.35/8.43 thf(f5437,plain,(
% 48.35/8.43 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a3 @ Y0)))))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20)),
% 48.35/8.43 inference(boolean_simplification,[],[f5433])).
% 48.35/8.43 thf(f5441,plain,(
% 48.35/8.43 (((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $false))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(forward_demodulation,[],[f5437,f328])).
% 48.35/8.43 thf(f5442,plain,(
% 48.35/8.43 (((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f5441])).
% 48.35/8.43 thf(f5443,plain,(
% 48.35/8.43 (((($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f5442])).
% 48.35/8.43 thf(f5444,plain,(
% 48.35/8.43 ((($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f5443])).
% 48.35/8.43 thf(f5445,plain,(
% 48.35/8.43 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f5444])).
% 48.35/8.43 thf(f5696,plain,(
% 48.35/8.43 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) = $true) | ~spl1_22),
% 48.35/8.43 inference(not_proxy_clausification,[],[f312])).
% 48.35/8.43 thf(f5701,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ X1)) = $true)) ) | ~spl1_22),
% 48.35/8.43 inference(pi_proxy_clausification,[],[f5696])).
% 48.35/8.43 thf(f5702,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (((((irel @ sK3 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0)))))))) = $true)) ) | ~spl1_22),
% 48.35/8.43 inference(beta-eta_normalization,[],[f5701])).
% 48.35/8.43 thf(f5737,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(not_proxy_clausification,[],[f5445])).
% 48.35/8.43 thf(f5741,plain,(
% 48.35/8.43 ($false = (((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ sK31))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(sigma_proxy_clausification,[],[f5737])).
% 48.35/8.43 thf(f5743,plain,(
% 48.35/8.43 ($false = (((irel @ sK3 @ sK31) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(beta-eta_normalization,[],[f5741])).
% 48.35/8.43 thf(f5746,plain,(
% 48.35/8.43 ($true = ((irel @ sK3 @ sK31))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(imp_proxy_clausification,[],[f5743])).
% 48.35/8.43 thf(f5748,plain,(
% 48.35/8.43 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0)))))) = $false) | ($false = (((irel @ sK3 @ sK31) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))) & $true)))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(constrained_superposition,[],[f5743,f80])).
% 48.35/8.43 thf(f5749,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0)))))) | ($false = (((irel @ sK3 @ sK31) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) | $true) & ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(constrained_superposition,[],[f5743,f80])).
% 48.35/8.43 thf(f5768,plain,(
% 48.35/8.43 ($false = (((irel @ sK3 @ sK31) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) | $true) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0)))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f5749])).
% 48.35/8.43 thf(f5769,plain,(
% 48.35/8.43 ($false = (((irel @ sK3 @ sK31) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) | $true) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0)))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f5768])).
% 48.35/8.43 thf(f5770,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0)))))) | ($false = (((irel @ sK3 @ sK31) => ($true & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0)))))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f5769])).
% 48.35/8.43 thf(f5771,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0)))))) | ($false = (((irel @ sK3 @ sK31) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f5770])).
% 48.35/8.43 thf(f5773,plain,(
% 48.35/8.43 ($false = (((irel @ sK3 @ sK31) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0)))))))) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0)))))) = $false) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f5748])).
% 48.35/8.43 thf(f5778,definition,(
% 48.35/8.43 spl1_161 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_161])],[avatar_definition])).
% 48.35/8.43 thf(f5779,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0)))))) | ~spl1_161),
% 48.35/8.43 inference(avatar_component_clause,[],[f5778])).
% 48.35/8.43 thf(f5782,definition,(
% 48.35/8.43 spl1_162 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0)))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_162])],[avatar_definition])).
% 48.35/8.43 thf(f5783,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))))) | ~spl1_162),
% 48.35/8.43 inference(avatar_component_clause,[],[f5782])).
% 48.35/8.43 thf(f5796,definition,(
% 48.35/8.43 spl1_166 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0)))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_166])],[avatar_definition])).
% 48.35/8.43 thf(f5797,plain,(
% 48.35/8.43 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))))) | ~spl1_166),
% 48.35/8.43 inference(avatar_component_clause,[],[f5796])).
% 48.35/8.43 thf(f5800,definition,(
% 48.35/8.43 spl1_167 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_167])],[avatar_definition])).
% 48.35/8.43 thf(f5801,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0)))))) | ~spl1_167),
% 48.35/8.43 inference(avatar_component_clause,[],[f5800])).
% 48.35/8.43 thf(f5803,definition,(
% 48.35/8.43 spl1_168 <=> ($false = (((irel @ sK3 @ sK31) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0)))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_168])],[avatar_definition])).
% 48.35/8.43 thf(f5804,plain,(
% 48.35/8.43 ($false = (((irel @ sK3 @ sK31) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))))) | ~spl1_168),
% 48.35/8.43 inference(avatar_component_clause,[],[f5803])).
% 48.35/8.43 thf(f5805,plain,(
% 48.35/8.43 spl1_167 | spl1_168 | ~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25),
% 48.35/8.43 inference(avatar_split_clause,[],[f5771,f327,f303,f293,f205,f194,f184,f135,f5803,f5800])).
% 48.35/8.43 thf(f5806,plain,(
% 48.35/8.43 ($false = (($true => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0)))))))) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0)))))) = $false) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(forward_demodulation,[],[f5773,f5746])).
% 48.35/8.43 thf(f5807,plain,(
% 48.35/8.43 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))))) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0)))))) = $false) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f5806])).
% 48.35/8.43 thf(f5809,definition,(
% 48.35/8.43 spl1_169 <=> ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0)))))) = $false)),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_169])],[avatar_definition])).
% 48.35/8.43 thf(f5810,plain,(
% 48.35/8.43 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0)))))) = $false) | ~spl1_169),
% 48.35/8.43 inference(avatar_component_clause,[],[f5809])).
% 48.35/8.43 thf(f5811,plain,(
% 48.35/8.43 spl1_169 | spl1_166 | ~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25),
% 48.35/8.43 inference(avatar_split_clause,[],[f5807,f327,f303,f293,f205,f194,f184,f135,f5796,f5809])).
% 48.35/8.43 thf(f5816,plain,(
% 48.35/8.43 ($false = (($true => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25 | ~spl1_168)),
% 48.35/8.43 inference(forward_demodulation,[],[f5804,f5746])).
% 48.35/8.43 thf(f5817,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0)))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25 | ~spl1_168)),
% 48.35/8.43 inference(boolean_simplification,[],[f5816])).
% 48.35/8.43 thf(f5819,plain,(
% 48.35/8.43 spl1_161 | ~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25 | ~spl1_168),
% 48.35/8.43 inference(avatar_split_clause,[],[f5817,f5803,f327,f303,f293,f205,f194,f184,f135,f5778])).
% 48.35/8.43 thf(f5821,plain,(
% 48.35/8.43 ($true = (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))))))) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25)),
% 48.35/8.43 inference(constrained_superposition,[],[f5702,f5746])).
% 48.35/8.43 thf(f5823,plain,(
% 48.35/8.43 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25)),
% 48.35/8.43 inference(boolean_simplification,[],[f5821])).
% 48.35/8.43 thf(f5824,plain,(
% 48.35/8.43 ((($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25 | ~spl1_169)),
% 48.35/8.43 inference(forward_demodulation,[],[f5823,f5810])).
% 48.35/8.43 thf(f5825,plain,(
% 48.35/8.43 ($false = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25 | ~spl1_169)),
% 48.35/8.43 inference(boolean_simplification,[],[f5824])).
% 48.35/8.43 thf(f5826,plain,(
% 48.35/8.43 $false | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25 | ~spl1_169)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f5825])).
% 48.35/8.43 thf(f5827,plain,(
% 48.35/8.43 ~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25 | ~spl1_169),
% 48.35/8.43 inference(avatar_contradiction_clause,[],[f5826])).
% 48.35/8.43 thf(f5828,plain,(
% 48.35/8.43 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) | $false))) | (~spl1_166 | ~spl1_167)),
% 48.35/8.43 inference(forward_demodulation,[],[f5797,f5801])).
% 48.35/8.43 thf(f5829,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))))) | (~spl1_166 | ~spl1_167)),
% 48.35/8.43 inference(boolean_simplification,[],[f5828])).
% 48.35/8.43 thf(f5834,plain,(
% 48.35/8.43 spl1_162 | ~spl1_166 | ~spl1_167),
% 48.35/8.43 inference(avatar_split_clause,[],[f5829,f5800,f5796,f5782])).
% 48.35/8.43 thf(f5841,plain,(
% 48.35/8.43 ($false = (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))))) | (~spl1_161 | ~spl1_166)),
% 48.35/8.43 inference(forward_demodulation,[],[f5797,f5779])).
% 48.35/8.43 thf(f5842,plain,(
% 48.35/8.43 ($false = (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a1 @ Y0))))))) | (~spl1_161 | ~spl1_166)),
% 48.35/8.43 inference(boolean_simplification,[],[f5841])).
% 48.35/8.43 thf(f5843,plain,(
% 48.35/8.43 ($false = $true) | (~spl1_161 | ~spl1_166)),
% 48.35/8.43 inference(boolean_simplification,[],[f5842])).
% 48.35/8.43 thf(f5844,plain,(
% 48.35/8.43 $false | (~spl1_161 | ~spl1_166)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f5843])).
% 48.35/8.43 thf(f5845,plain,(
% 48.35/8.43 ~spl1_161 | ~spl1_166),
% 48.35/8.43 inference(avatar_contradiction_clause,[],[f5844])).
% 48.35/8.43 thf(f5855,plain,(
% 48.35/8.43 (((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) | $false))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25 | ~spl1_167)),
% 48.35/8.43 inference(forward_demodulation,[],[f5823,f5801])).
% 48.35/8.43 thf(f5856,plain,(
% 48.35/8.43 (((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25 | ~spl1_167)),
% 48.35/8.43 inference(boolean_simplification,[],[f5855])).
% 48.35/8.43 thf(f5857,plain,(
% 48.35/8.43 (((($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25 | ~spl1_167)),
% 48.35/8.43 inference(boolean_simplification,[],[f5856])).
% 48.35/8.43 thf(f5858,plain,(
% 48.35/8.43 ((($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25 | ~spl1_167)),
% 48.35/8.43 inference(boolean_simplification,[],[f5857])).
% 48.35/8.43 thf(f5859,plain,(
% 48.35/8.43 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK31 @ Y0) => (a2 @ Y0)))))) = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25 | ~spl1_167)),
% 48.35/8.43 inference(boolean_simplification,[],[f5858])).
% 48.35/8.43 thf(f5864,plain,(
% 48.35/8.43 ($false = $true) | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25 | ~spl1_162 | ~spl1_167)),
% 48.35/8.43 inference(forward_demodulation,[],[f5859,f5783])).
% 48.35/8.43 thf(f5865,plain,(
% 48.35/8.43 $false | (~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25 | ~spl1_162 | ~spl1_167)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f5864])).
% 48.35/8.43 thf(f5866,plain,(
% 48.35/8.43 ~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25 | ~spl1_162 | ~spl1_167),
% 48.35/8.43 inference(avatar_contradiction_clause,[],[f5865])).
% 48.35/8.43 thf(f5880,plain,(
% 48.35/8.43 ($false = (((irel @ sK0 @ sK2) => $false))) | (~spl1_9 | ~spl1_16)),
% 48.35/8.43 inference(forward_demodulation,[],[f192,f217])).
% 48.35/8.43 thf(f5881,plain,(
% 48.35/8.43 ($false = ((~ (irel @ sK0 @ sK2)))) | (~spl1_9 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f5880])).
% 48.35/8.43 thf(f5898,plain,(
% 48.35/8.43 (((irel @ sK0 @ sK2)) = $true) | (~spl1_9 | ~spl1_16)),
% 48.35/8.43 inference(not_proxy_clausification,[],[f5881])).
% 48.35/8.43 thf(f5904,plain,(
% 48.35/8.43 ((($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))))) = $true) | (~spl1_4 | ~spl1_9 | ~spl1_16)),
% 48.35/8.43 inference(constrained_superposition,[],[f5131,f5898])).
% 48.35/8.43 thf(f5905,plain,(
% 48.35/8.43 ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a4 @ Y0)))))))) | (~spl1_4 | ~spl1_9 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f5904])).
% 48.35/8.43 thf(f5907,plain,(
% 48.35/8.43 ($true = ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | $false)))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(forward_demodulation,[],[f5905,f199])).
% 48.35/8.43 thf(f5908,plain,(
% 48.35/8.43 (((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))))) = $true) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f5907])).
% 48.35/8.43 thf(f5909,plain,(
% 48.35/8.43 ($true = ((($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f5908])).
% 48.35/8.43 thf(f5910,plain,(
% 48.35/8.43 ((($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))))) = $true) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f5909])).
% 48.35/8.43 thf(f5911,plain,(
% 48.35/8.43 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) = $true) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f5910])).
% 48.35/8.43 thf(f6355,plain,(
% 48.35/8.43 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) = $true) | ~spl1_8),
% 48.35/8.43 inference(not_proxy_clausification,[],[f188])).
% 48.35/8.43 thf(f6360,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))) @ X1)))) ) | ~spl1_8),
% 48.35/8.43 inference(pi_proxy_clausification,[],[f6355])).
% 48.35/8.43 thf(f6361,plain,(
% 48.35/8.43 ( ! [X1 : $i] : (($true = (((irel @ sK2 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))))) ) | ~spl1_8),
% 48.35/8.43 inference(beta-eta_normalization,[],[f6360])).
% 48.35/8.43 thf(f6730,plain,(
% 48.35/8.43 (((~ $true)) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(constrained_superposition,[],[f5911,f80])).
% 48.35/8.43 thf(f6731,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) | ($false = $true) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f6730])).
% 48.35/8.43 thf(f6732,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f6731])).
% 48.35/8.43 thf(f6733,plain,(
% 48.35/8.43 ($false = (((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))) @ sK35))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(sigma_proxy_clausification,[],[f6732])).
% 48.35/8.43 thf(f6736,plain,(
% 48.35/8.43 ($false = (((irel @ sK2 @ sK35) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(beta-eta_normalization,[],[f6733])).
% 48.35/8.43 thf(f6738,plain,(
% 48.35/8.43 (((irel @ sK2 @ sK35)) = $true) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(imp_proxy_clausification,[],[f6736])).
% 48.35/8.43 thf(f6741,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ($false = (((irel @ sK2 @ sK35) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) | $true) & ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(constrained_superposition,[],[f6736,f80])).
% 48.35/8.43 thf(f6743,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))) | ($false = (((irel @ sK2 @ sK35) => (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(constrained_superposition,[],[f6736,f80])).
% 48.35/8.43 thf(f6745,plain,(
% 48.35/8.43 ($false = (((irel @ sK2 @ sK35) => $true))) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0)))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(constrained_superposition,[],[f6736,f80])).
% 48.35/8.43 thf(f6755,plain,(
% 48.35/8.43 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0)))))))) | ($false = $true) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f6745])).
% 48.35/8.43 thf(f6756,plain,(
% 48.35/8.43 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0)))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(trivial_inequality_removal,[],[f6755])).
% 48.35/8.43 thf(f6760,plain,(
% 48.35/8.43 ($false = (((irel @ sK2 @ sK35) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) | $true) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f6741])).
% 48.35/8.43 thf(f6761,plain,(
% 48.35/8.43 ($false = (((irel @ sK2 @ sK35) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) | $true) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f6760])).
% 48.35/8.43 thf(f6762,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ($false = (((irel @ sK2 @ sK35) => ($true & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0)))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f6761])).
% 48.35/8.43 thf(f6763,plain,(
% 48.35/8.43 ($false = (((irel @ sK2 @ sK35) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f6762])).
% 48.35/8.43 thf(f6764,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))) | ($false = (((irel @ sK2 @ sK35) => ($true & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f6743])).
% 48.35/8.43 thf(f6765,plain,(
% 48.35/8.43 ($false = (((irel @ sK2 @ sK35) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0)))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f6764])).
% 48.35/8.43 thf(f6770,definition,(
% 48.35/8.43 spl1_191 <=> ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_191])],[avatar_definition])).
% 48.35/8.43 thf(f6771,plain,(
% 48.35/8.43 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0)))))))) | ~spl1_191),
% 48.35/8.43 inference(avatar_component_clause,[],[f6770])).
% 48.35/8.43 thf(f6777,definition,(
% 48.35/8.43 spl1_193 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_193])],[avatar_definition])).
% 48.35/8.43 thf(f6778,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | ~spl1_193),
% 48.35/8.43 inference(avatar_component_clause,[],[f6777])).
% 48.35/8.43 thf(f6784,definition,(
% 48.35/8.43 spl1_195 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_195])],[avatar_definition])).
% 48.35/8.43 thf(f6785,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0)))))) | ~spl1_195),
% 48.35/8.43 inference(avatar_component_clause,[],[f6784])).
% 48.35/8.43 thf(f6787,plain,(
% 48.35/8.43 spl1_191 | ~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16),
% 48.35/8.43 inference(avatar_split_clause,[],[f6756,f216,f198,f191,f135,f6770])).
% 48.35/8.43 thf(f6792,plain,(
% 48.35/8.43 ($false = (($true => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(forward_demodulation,[],[f6763,f6738])).
% 48.35/8.43 thf(f6793,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0)))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f6792])).
% 48.35/8.43 thf(f6794,plain,(
% 48.35/8.43 ($false = (($true => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0)))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(forward_demodulation,[],[f6765,f6738])).
% 48.35/8.43 thf(f6795,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))) | (~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f6794])).
% 48.35/8.43 thf(f6800,definition,(
% 48.35/8.43 spl1_197 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0)))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_197])],[avatar_definition])).
% 48.35/8.43 thf(f6801,plain,(
% 48.35/8.43 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))) | ~spl1_197),
% 48.35/8.43 inference(avatar_component_clause,[],[f6800])).
% 48.35/8.43 thf(f6805,definition,(
% 48.35/8.43 spl1_198 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_198])],[avatar_definition])).
% 48.35/8.43 thf(f6806,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ~spl1_198),
% 48.35/8.43 inference(avatar_component_clause,[],[f6805])).
% 48.35/8.43 thf(f6807,plain,(
% 48.35/8.43 spl1_198 | spl1_195 | ~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16),
% 48.35/8.43 inference(avatar_split_clause,[],[f6793,f216,f198,f191,f135,f6784,f6805])).
% 48.35/8.43 thf(f6809,definition,(
% 48.35/8.43 spl1_199 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0)))))))),
% 48.35/8.43 introduced(definition,[new_symbols(definition,[spl1_199])],[avatar_definition])).
% 48.35/8.43 thf(f6810,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))) | ~spl1_199),
% 48.35/8.43 inference(avatar_component_clause,[],[f6809])).
% 48.35/8.43 thf(f6811,plain,(
% 48.35/8.43 spl1_199 | spl1_197 | ~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16),
% 48.35/8.43 inference(avatar_split_clause,[],[f6795,f216,f198,f191,f135,f6800,f6809])).
% 48.35/8.43 thf(f6821,plain,(
% 48.35/8.43 ((($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(constrained_superposition,[],[f6361,f6738])).
% 48.35/8.43 thf(f6822,plain,(
% 48.35/8.43 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.43 inference(boolean_simplification,[],[f6821])).
% 48.35/8.43 thf(f6824,plain,(
% 48.35/8.43 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_199)),
% 48.35/8.43 inference(forward_demodulation,[],[f6822,f6810])).
% 48.35/8.43 thf(f6825,plain,(
% 48.35/8.43 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_199)),
% 48.35/8.43 inference(boolean_simplification,[],[f6824])).
% 48.35/8.43 thf(f6860,plain,(
% 48.35/8.43 ($false = (((^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ sK36))) | ~spl1_198),
% 48.35/8.43 inference(sigma_proxy_clausification,[],[f6806])).
% 48.35/8.43 thf(f6862,plain,(
% 48.35/8.43 ($false = (((irel @ sK35 @ sK36) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))))) | ~spl1_198),
% 48.35/8.43 inference(beta-eta_normalization,[],[f6860])).
% 48.35/8.43 thf(f6865,plain,(
% 48.35/8.43 ($true = ((irel @ sK35 @ sK36))) | ~spl1_198),
% 48.35/8.43 inference(imp_proxy_clausification,[],[f6862])).
% 48.35/8.43 thf(f6866,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))))) | ($false = (((irel @ sK35 @ sK36) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))))) | ~spl1_198),
% 48.35/8.43 inference(constrained_superposition,[],[f6862,f80])).
% 48.35/8.43 thf(f6867,plain,(
% 48.35/8.43 ($false = (((irel @ sK35 @ sK36) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) & $true)))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))) | ~spl1_198),
% 48.35/8.43 inference(constrained_superposition,[],[f6862,f80])).
% 48.35/8.43 thf(f6869,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0)))))) | ($false = (((irel @ sK35 @ sK36) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | $true))))) | ~spl1_198),
% 48.35/8.43 inference(constrained_superposition,[],[f6862,f80])).
% 48.35/8.43 thf(f6870,plain,(
% 48.35/8.43 ($false = (((irel @ sK35 @ sK36) => (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))) | ~spl1_198),
% 48.35/8.43 inference(constrained_superposition,[],[f6862,f80])).
% 48.35/8.43 thf(f6876,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))))) | ($false = (((irel @ sK35 @ sK36) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) & $true)))) | ~spl1_198),
% 48.35/8.43 inference(boolean_simplification,[],[f6866])).
% 48.35/8.43 thf(f6877,plain,(
% 48.35/8.43 ($false = (((irel @ sK35 @ sK36) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0)))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))))) | ~spl1_198),
% 48.35/8.43 inference(boolean_simplification,[],[f6876])).
% 48.35/8.43 thf(f6885,plain,(
% 48.35/8.43 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))) | ($false = (((irel @ sK35 @ sK36) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0)))))))) | ~spl1_198),
% 48.35/8.43 inference(boolean_simplification,[],[f6867])).
% 48.35/8.43 thf(f6887,plain,(
% 48.35/8.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))) | ($false = (((irel @ sK35 @ sK36) => ($true & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))))) | ~spl1_198),
% 48.35/8.43 inference(boolean_simplification,[],[f6870])).
% 48.35/8.43 thf(f6888,plain,(
% 48.35/8.43 ($false = (((irel @ sK35 @ sK36) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0)))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))) | ~spl1_198),
% 48.35/8.43 inference(boolean_simplification,[],[f6887])).
% 48.35/8.43 thf(f6889,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0)))))) | ($false = (((irel @ sK35 @ sK36) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) & $true)))) | ~spl1_198),
% 48.35/8.43 inference(boolean_simplification,[],[f6869])).
% 48.35/8.43 thf(f6890,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0)))))) | ($false = (((irel @ sK35 @ sK36) => ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0)))))))) | ~spl1_198),
% 48.35/8.43 inference(boolean_simplification,[],[f6889])).
% 48.35/8.43 thf(f6891,plain,(
% 48.35/8.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0)))))) | ($false = (((irel @ sK35 @ sK36) => ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0)))))))) | ~spl1_198),
% 48.35/8.43 inference(boolean_simplification,[],[f6890])).
% 48.35/8.44 thf(f6892,plain,(
% 48.35/8.44 ($false = (((irel @ sK35 @ sK36) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0)))))) | ~spl1_198),
% 48.35/8.44 inference(boolean_simplification,[],[f6891])).
% 48.35/8.44 thf(f6901,definition,(
% 48.35/8.44 spl1_202 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0)))))))),
% 48.35/8.44 introduced(definition,[new_symbols(definition,[spl1_202])],[avatar_definition])).
% 48.35/8.44 thf(f6902,plain,(
% 48.35/8.44 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))))) | ~spl1_202),
% 48.35/8.44 inference(avatar_component_clause,[],[f6901])).
% 48.35/8.44 thf(f6904,definition,(
% 48.35/8.44 spl1_203 <=> ($false = (((irel @ sK35 @ sK36) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))))))),
% 48.35/8.44 introduced(definition,[new_symbols(definition,[spl1_203])],[avatar_definition])).
% 48.35/8.44 thf(f6905,plain,(
% 48.35/8.44 ($false = (((irel @ sK35 @ sK36) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0)))))))) | ~spl1_203),
% 48.35/8.44 inference(avatar_component_clause,[],[f6904])).
% 48.35/8.44 thf(f6906,plain,(
% 48.35/8.44 spl1_202 | spl1_203 | ~spl1_198),
% 48.35/8.44 inference(avatar_split_clause,[],[f6877,f6805,f6904,f6901])).
% 48.35/8.44 thf(f6912,plain,(
% 48.35/8.44 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))) | ($false = (($true => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0)))))))) | ~spl1_198),
% 48.35/8.44 inference(forward_demodulation,[],[f6885,f6865])).
% 48.35/8.44 thf(f6913,plain,(
% 48.35/8.44 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))) | ~spl1_198),
% 48.35/8.44 inference(boolean_simplification,[],[f6912])).
% 48.35/8.44 thf(f6914,plain,(
% 48.35/8.44 ($false = (($true => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0)))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))) | ~spl1_198),
% 48.35/8.44 inference(forward_demodulation,[],[f6888,f6865])).
% 48.35/8.44 thf(f6915,plain,(
% 48.35/8.44 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))) | ~spl1_198),
% 48.35/8.44 inference(boolean_simplification,[],[f6914])).
% 48.35/8.44 thf(f6916,plain,(
% 48.35/8.44 ($false = (($true => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0)))))) | ~spl1_198),
% 48.35/8.44 inference(forward_demodulation,[],[f6892,f6865])).
% 48.35/8.44 thf(f6917,plain,(
% 48.35/8.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0)))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0)))))) | ~spl1_198),
% 48.35/8.44 inference(boolean_simplification,[],[f6916])).
% 48.35/8.44 thf(f6919,definition,(
% 48.35/8.44 spl1_204 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0)))))))),
% 48.35/8.44 introduced(definition,[new_symbols(definition,[spl1_204])],[avatar_definition])).
% 48.35/8.44 thf(f6920,plain,(
% 48.35/8.44 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))) | ~spl1_204),
% 48.35/8.44 inference(avatar_component_clause,[],[f6919])).
% 48.35/8.44 thf(f6922,definition,(
% 48.35/8.44 spl1_205 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0)))))))),
% 48.35/8.44 introduced(definition,[new_symbols(definition,[spl1_205])],[avatar_definition])).
% 48.35/8.44 thf(f6923,plain,(
% 48.35/8.44 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))))) | ~spl1_205),
% 48.35/8.44 inference(avatar_component_clause,[],[f6922])).
% 48.35/8.44 thf(f6926,definition,(
% 48.35/8.44 spl1_206 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))),
% 48.35/8.44 introduced(definition,[new_symbols(definition,[spl1_206])],[avatar_definition])).
% 48.35/8.44 thf(f6927,plain,(
% 48.35/8.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0)))))) | ~spl1_206),
% 48.35/8.44 inference(avatar_component_clause,[],[f6926])).
% 48.35/8.44 thf(f6929,definition,(
% 48.35/8.44 spl1_207 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))))),
% 48.35/8.44 introduced(definition,[new_symbols(definition,[spl1_207])],[avatar_definition])).
% 48.35/8.44 thf(f6930,plain,(
% 48.35/8.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0)))))) | ~spl1_207),
% 48.35/8.44 inference(avatar_component_clause,[],[f6929])).
% 48.35/8.44 thf(f6932,plain,(
% 48.35/8.44 spl1_204 | spl1_205 | ~spl1_198),
% 48.35/8.44 inference(avatar_split_clause,[],[f6913,f6805,f6922,f6919])).
% 48.35/8.44 thf(f6934,definition,(
% 48.35/8.44 spl1_208 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0)))))))),
% 48.35/8.44 introduced(definition,[new_symbols(definition,[spl1_208])],[avatar_definition])).
% 48.35/8.44 thf(f6935,plain,(
% 48.35/8.44 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))) | ~spl1_208),
% 48.35/8.44 inference(avatar_component_clause,[],[f6934])).
% 48.35/8.44 thf(f6936,plain,(
% 48.35/8.44 spl1_204 | spl1_208 | ~spl1_198),
% 48.35/8.44 inference(avatar_split_clause,[],[f6915,f6805,f6934,f6919])).
% 48.35/8.44 thf(f6937,plain,(
% 48.35/8.44 spl1_207 | spl1_206 | ~spl1_198),
% 48.35/8.44 inference(avatar_split_clause,[],[f6917,f6805,f6926,f6929])).
% 48.35/8.44 thf(f7013,plain,(
% 48.35/8.44 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) = $true) | ~spl1_202),
% 48.35/8.44 inference(not_proxy_clausification,[],[f6902])).
% 48.35/8.44 thf(f7018,plain,(
% 48.35/8.44 ($false = $true) | (~spl1_202 | ~spl1_207)),
% 48.35/8.44 inference(forward_demodulation,[],[f7013,f6930])).
% 48.35/8.44 thf(f7019,plain,(
% 48.35/8.44 $false | (~spl1_202 | ~spl1_207)),
% 48.35/8.44 inference(trivial_inequality_removal,[],[f7018])).
% 48.35/8.44 thf(f7020,plain,(
% 48.35/8.44 ~spl1_202 | ~spl1_207),
% 48.35/8.44 inference(avatar_contradiction_clause,[],[f7019])).
% 48.35/8.44 thf(f7230,plain,(
% 48.35/8.44 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) = $true) | ~spl1_208),
% 48.35/8.44 inference(not_proxy_clausification,[],[f6935])).
% 48.35/8.44 thf(f7235,plain,(
% 48.35/8.44 ($false = $true) | (~spl1_206 | ~spl1_208)),
% 48.35/8.44 inference(forward_demodulation,[],[f7230,f6927])).
% 48.35/8.44 thf(f7236,plain,(
% 48.35/8.44 $false | (~spl1_206 | ~spl1_208)),
% 48.35/8.44 inference(trivial_inequality_removal,[],[f7235])).
% 48.35/8.44 thf(f7237,plain,(
% 48.35/8.44 ~spl1_206 | ~spl1_208),
% 48.35/8.44 inference(avatar_contradiction_clause,[],[f7236])).
% 48.35/8.44 thf(f7256,plain,(
% 48.35/8.44 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $true) | ~spl1_193),
% 48.35/8.44 inference(not_proxy_clausification,[],[f6778])).
% 48.35/8.44 thf(f7261,plain,(
% 48.35/8.44 ($false = $true) | (~spl1_193 | ~spl1_198)),
% 48.35/8.44 inference(forward_demodulation,[],[f7256,f6806])).
% 48.35/8.44 thf(f7262,plain,(
% 48.35/8.44 $false | (~spl1_193 | ~spl1_198)),
% 48.35/8.44 inference(trivial_inequality_removal,[],[f7261])).
% 48.35/8.44 thf(f7263,plain,(
% 48.35/8.44 ~spl1_193 | ~spl1_198),
% 48.35/8.44 inference(avatar_contradiction_clause,[],[f7262])).
% 48.35/8.44 thf(f7287,plain,(
% 48.35/8.44 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_199)),
% 48.35/8.44 inference(and_proxy_clausification,[],[f6825])).
% 48.35/8.44 thf(f7305,definition,(
% 48.35/8.44 spl1_210 <=> (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) = $true)),
% 48.35/8.44 introduced(definition,[new_symbols(definition,[spl1_210])],[avatar_definition])).
% 48.35/8.44 thf(f7306,plain,(
% 48.35/8.44 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) = $true) | ~spl1_210),
% 48.35/8.44 inference(avatar_component_clause,[],[f7305])).
% 48.35/8.44 thf(f7315,plain,(
% 48.35/8.44 spl1_210 | ~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_199),
% 48.35/8.44 inference(avatar_split_clause,[],[f7287,f6809,f216,f198,f191,f187,f135,f7305])).
% 48.35/8.44 thf(f7316,plain,(
% 48.35/8.44 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ X1)))) ) | ~spl1_210),
% 48.35/8.44 inference(pi_proxy_clausification,[],[f7306])).
% 48.35/8.44 thf(f7317,plain,(
% 48.35/8.44 ( ! [X1 : $i] : (((((irel @ sK35 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0)))))))) = $true)) ) | ~spl1_210),
% 48.35/8.44 inference(beta-eta_normalization,[],[f7316])).
% 48.35/8.44 thf(f7327,plain,(
% 48.35/8.44 ($true = (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))))))) | (~spl1_198 | ~spl1_210)),
% 48.35/8.44 inference(constrained_superposition,[],[f7317,f6865])).
% 48.35/8.44 thf(f7329,plain,(
% 48.35/8.44 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_198 | ~spl1_210)),
% 48.35/8.44 inference(boolean_simplification,[],[f7327])).
% 48.35/8.44 thf(f7347,plain,(
% 48.35/8.44 ((($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_198 | ~spl1_204 | ~spl1_210)),
% 48.35/8.44 inference(forward_demodulation,[],[f7329,f6920])).
% 48.35/8.44 thf(f7348,plain,(
% 48.35/8.44 ($false = $true) | (~spl1_198 | ~spl1_204 | ~spl1_210)),
% 48.35/8.44 inference(boolean_simplification,[],[f7347])).
% 48.35/8.44 thf(f7349,plain,(
% 48.35/8.44 $false | (~spl1_198 | ~spl1_204 | ~spl1_210)),
% 48.35/8.44 inference(trivial_inequality_removal,[],[f7348])).
% 48.35/8.44 thf(f7350,plain,(
% 48.35/8.44 ~spl1_198 | ~spl1_204 | ~spl1_210),
% 48.35/8.44 inference(avatar_contradiction_clause,[],[f7349])).
% 48.35/8.44 thf(f7351,plain,(
% 48.35/8.44 ($false = (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))) | (~spl1_197 | ~spl1_198)),
% 48.35/8.44 inference(forward_demodulation,[],[f6801,f6806])).
% 48.35/8.44 thf(f7352,plain,(
% 48.35/8.44 ($false = (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))) | (~spl1_197 | ~spl1_198)),
% 48.35/8.44 inference(boolean_simplification,[],[f7351])).
% 48.35/8.44 thf(f7353,plain,(
% 48.35/8.44 ($false = $true) | (~spl1_197 | ~spl1_198)),
% 48.35/8.44 inference(boolean_simplification,[],[f7352])).
% 48.35/8.44 thf(f7354,plain,(
% 48.35/8.44 $false | (~spl1_197 | ~spl1_198)),
% 48.35/8.44 inference(trivial_inequality_removal,[],[f7353])).
% 48.35/8.44 thf(f7355,plain,(
% 48.35/8.44 ~spl1_197 | ~spl1_198),
% 48.35/8.44 inference(avatar_contradiction_clause,[],[f7354])).
% 48.35/8.44 thf(f7359,plain,(
% 48.35/8.44 ($false = ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $false)))) | (~spl1_191 | ~spl1_195)),
% 48.35/8.44 inference(forward_demodulation,[],[f6771,f6785])).
% 48.35/8.44 thf(f7360,plain,(
% 48.35/8.44 ($false = ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))))) | (~spl1_191 | ~spl1_195)),
% 48.35/8.44 inference(boolean_simplification,[],[f7359])).
% 48.35/8.44 thf(f7361,plain,(
% 48.35/8.44 ($false = ((($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))))) | (~spl1_191 | ~spl1_195)),
% 48.35/8.44 inference(boolean_simplification,[],[f7360])).
% 48.35/8.44 thf(f7362,plain,(
% 48.35/8.44 ($false = (($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))))) | (~spl1_191 | ~spl1_195)),
% 48.35/8.44 inference(boolean_simplification,[],[f7361])).
% 48.35/8.44 thf(f7363,plain,(
% 48.35/8.44 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | (~spl1_191 | ~spl1_195)),
% 48.35/8.44 inference(boolean_simplification,[],[f7362])).
% 48.35/8.44 thf(f7376,plain,(
% 48.35/8.44 spl1_193 | ~spl1_191 | ~spl1_195),
% 48.35/8.44 inference(avatar_split_clause,[],[f7363,f6784,f6770,f6777])).
% 48.35/8.44 thf(f7382,plain,(
% 48.35/8.44 ($false = (((irel @ sK35 @ sK36) => $false))) | (~spl1_203 | ~spl1_205)),
% 48.35/8.44 inference(forward_demodulation,[],[f6905,f6923])).
% 48.35/8.44 thf(f7383,plain,(
% 48.35/8.44 ($false = ((~ (irel @ sK35 @ sK36)))) | (~spl1_203 | ~spl1_205)),
% 48.35/8.44 inference(boolean_simplification,[],[f7382])).
% 48.35/8.44 thf(f7386,plain,(
% 48.35/8.44 ($true = ((irel @ sK35 @ sK36))) | (~spl1_203 | ~spl1_205)),
% 48.35/8.44 inference(not_proxy_clausification,[],[f7383])).
% 48.35/8.44 thf(f7606,plain,(
% 48.35/8.44 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ X1)))) ) | ~spl1_210),
% 48.35/8.44 inference(pi_proxy_clausification,[],[f7306])).
% 48.35/8.44 thf(f7607,plain,(
% 48.35/8.44 ( ! [X1 : $i] : (((((irel @ sK35 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0)))))))) = $true)) ) | ~spl1_210),
% 48.35/8.44 inference(beta-eta_normalization,[],[f7606])).
% 48.35/8.44 thf(f7618,plain,(
% 48.35/8.44 ($true = (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))))))) | (~spl1_203 | ~spl1_205 | ~spl1_210)),
% 48.35/8.44 inference(constrained_superposition,[],[f7607,f7386])).
% 48.35/8.44 thf(f7632,plain,(
% 48.35/8.44 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_203 | ~spl1_205 | ~spl1_210)),
% 48.35/8.44 inference(boolean_simplification,[],[f7618])).
% 48.35/8.44 thf(f7639,plain,(
% 48.35/8.44 ($true = ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) | $false)))) | (~spl1_203 | ~spl1_205 | ~spl1_207 | ~spl1_210)),
% 48.35/8.44 inference(forward_demodulation,[],[f7632,f6930])).
% 48.35/8.44 thf(f7640,plain,(
% 48.35/8.44 ($true = ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0)))))))) | (~spl1_203 | ~spl1_205 | ~spl1_207 | ~spl1_210)),
% 48.35/8.44 inference(boolean_simplification,[],[f7639])).
% 48.35/8.44 thf(f7641,plain,(
% 48.35/8.44 (((($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl1_203 | ~spl1_205 | ~spl1_207 | ~spl1_210)),
% 48.35/8.44 inference(boolean_simplification,[],[f7640])).
% 48.35/8.44 thf(f7642,plain,(
% 48.35/8.44 ($true = (($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0)))))))) | (~spl1_203 | ~spl1_205 | ~spl1_207 | ~spl1_210)),
% 48.35/8.44 inference(boolean_simplification,[],[f7641])).
% 48.35/8.44 thf(f7643,plain,(
% 48.35/8.44 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK36 @ Y0) => (a2 @ Y0))))))) | (~spl1_203 | ~spl1_205 | ~spl1_207 | ~spl1_210)),
% 48.35/8.44 inference(boolean_simplification,[],[f7642])).
% 48.35/8.44 thf(f7644,plain,(
% 48.35/8.44 ($false = $true) | (~spl1_203 | ~spl1_205 | ~spl1_207 | ~spl1_208 | ~spl1_210)),
% 48.35/8.44 inference(forward_demodulation,[],[f7643,f6935])).
% 48.35/8.44 thf(f7645,plain,(
% 48.35/8.44 $false | (~spl1_203 | ~spl1_205 | ~spl1_207 | ~spl1_208 | ~spl1_210)),
% 48.35/8.44 inference(trivial_inequality_removal,[],[f7644])).
% 48.35/8.44 thf(f7646,plain,(
% 48.35/8.44 ~spl1_203 | ~spl1_205 | ~spl1_207 | ~spl1_208 | ~spl1_210),
% 48.35/8.44 inference(avatar_contradiction_clause,[],[f7645])).
% 48.35/8.44 thf(f8022,plain,(
% 48.35/8.44 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $true) | ~spl1_193),
% 48.35/8.44 inference(not_proxy_clausification,[],[f6778])).
% 48.35/8.44 thf(f8027,plain,(
% 48.35/8.44 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ X1)))) ) | ~spl1_193),
% 48.35/8.44 inference(pi_proxy_clausification,[],[f8022])).
% 48.35/8.44 thf(f8028,plain,(
% 48.35/8.44 ( ! [X1 : $i] : (($true = (((irel @ sK35 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0)))))))))) ) | ~spl1_193),
% 48.35/8.44 inference(beta-eta_normalization,[],[f8027])).
% 48.35/8.44 thf(f8066,plain,(
% 48.35/8.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | (((((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) | $true))) = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.44 inference(constrained_superposition,[],[f6822,f80])).
% 48.35/8.44 thf(f8079,plain,(
% 48.35/8.44 (((((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))) & $true)) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.44 inference(boolean_simplification,[],[f8066])).
% 48.35/8.44 thf(f8080,plain,(
% 48.35/8.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | ((((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0)))))) = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.44 inference(boolean_simplification,[],[f8079])).
% 48.35/8.44 thf(f8081,plain,(
% 48.35/8.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | ($true = (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0))))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.44 inference(boolean_simplification,[],[f8080])).
% 48.35/8.44 thf(f8082,plain,(
% 48.35/8.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (a3 @ Y0)))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16)),
% 48.35/8.44 inference(boolean_simplification,[],[f8081])).
% 48.35/8.44 thf(f8132,plain,(
% 48.35/8.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | ($false = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195)),
% 48.35/8.44 inference(forward_demodulation,[],[f8082,f6785])).
% 48.35/8.44 thf(f8133,plain,(
% 48.35/8.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195)),
% 48.35/8.44 inference(trivial_inequality_removal,[],[f8132])).
% 48.35/8.44 thf(f8139,plain,(
% 48.35/8.44 ($false = (((^[Y0 : $i]: ((irel @ sK35 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ sK42))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195)),
% 48.35/8.44 inference(sigma_proxy_clausification,[],[f8133])).
% 48.35/8.44 thf(f8142,plain,(
% 48.35/8.44 ($false = (((irel @ sK35 @ sK42) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195)),
% 48.35/8.44 inference(beta-eta_normalization,[],[f8139])).
% 48.35/8.44 thf(f8144,plain,(
% 48.35/8.44 ($true = ((irel @ sK35 @ sK42))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195)),
% 48.35/8.44 inference(imp_proxy_clausification,[],[f8142])).
% 48.35/8.44 thf(f8149,plain,(
% 48.35/8.44 ($false = (((irel @ sK35 @ sK42) => (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195)),
% 48.35/8.44 inference(constrained_superposition,[],[f8142,f80])).
% 48.35/8.44 thf(f8150,plain,(
% 48.35/8.44 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))))) | ($false = (((irel @ sK35 @ sK42) => ($true & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195)),
% 48.35/8.44 inference(constrained_superposition,[],[f8142,f80])).
% 48.35/8.44 thf(f8163,plain,(
% 48.35/8.44 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))))) | ($false = (((irel @ sK35 @ sK42) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0)))))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195)),
% 48.35/8.44 inference(boolean_simplification,[],[f8150])).
% 48.35/8.44 thf(f8165,plain,(
% 48.35/8.44 ($false = (((irel @ sK35 @ sK42) => ($true & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195)),
% 48.35/8.44 inference(boolean_simplification,[],[f8149])).
% 48.35/8.44 thf(f8166,plain,(
% 48.35/8.44 ($false = (((irel @ sK35 @ sK42) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0)))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195)),
% 48.35/8.44 inference(boolean_simplification,[],[f8165])).
% 48.35/8.44 thf(f8178,plain,(
% 48.35/8.44 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))))) | ($false = (($true => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0)))))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195)),
% 48.35/8.44 inference(forward_demodulation,[],[f8163,f8144])).
% 48.35/8.44 thf(f8179,plain,(
% 48.35/8.44 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195)),
% 48.35/8.44 inference(boolean_simplification,[],[f8178])).
% 48.35/8.44 thf(f8180,plain,(
% 48.35/8.44 ($false = (($true => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0)))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195)),
% 48.35/8.44 inference(forward_demodulation,[],[f8166,f8144])).
% 48.35/8.44 thf(f8181,plain,(
% 48.35/8.44 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195)),
% 48.35/8.44 inference(boolean_simplification,[],[f8180])).
% 48.35/8.44 thf(f8188,definition,(
% 48.35/8.44 spl1_224 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))))),
% 48.35/8.44 introduced(definition,[new_symbols(definition,[spl1_224])],[avatar_definition])).
% 48.35/8.44 thf(f8189,plain,(
% 48.35/8.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0)))))) | ~spl1_224),
% 48.35/8.44 inference(avatar_component_clause,[],[f8188])).
% 48.35/8.44 thf(f8192,definition,(
% 48.35/8.44 spl1_225 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0)))))))),
% 48.35/8.44 introduced(definition,[new_symbols(definition,[spl1_225])],[avatar_definition])).
% 48.35/8.44 thf(f8193,plain,(
% 48.35/8.44 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))))) | ~spl1_225),
% 48.35/8.44 inference(avatar_component_clause,[],[f8192])).
% 48.35/8.44 thf(f8199,definition,(
% 48.35/8.44 spl1_227 <=> ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0)))))))),
% 48.35/8.44 introduced(definition,[new_symbols(definition,[spl1_227])],[avatar_definition])).
% 48.35/8.44 thf(f8200,plain,(
% 48.35/8.44 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))))) | ~spl1_227),
% 48.35/8.44 inference(avatar_component_clause,[],[f8199])).
% 48.35/8.44 thf(f8202,plain,(
% 48.35/8.44 spl1_227 | spl1_225 | ~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195),
% 48.35/8.44 inference(avatar_split_clause,[],[f8179,f6784,f216,f198,f191,f187,f135,f8192,f8199])).
% 48.35/8.44 thf(f8204,definition,(
% 48.35/8.44 spl1_228 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0)))))))),
% 48.35/8.44 introduced(definition,[new_symbols(definition,[spl1_228])],[avatar_definition])).
% 48.35/8.44 thf(f8205,plain,(
% 48.35/8.44 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))))) | ~spl1_228),
% 48.35/8.44 inference(avatar_component_clause,[],[f8204])).
% 48.35/8.44 thf(f8206,plain,(
% 48.35/8.44 spl1_228 | spl1_227 | ~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195),
% 48.35/8.44 inference(avatar_split_clause,[],[f8181,f6784,f216,f198,f191,f187,f135,f8199,f8204])).
% 48.35/8.44 thf(f8216,plain,(
% 48.35/8.44 ((($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0)))))))) = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195)),
% 48.35/8.44 inference(constrained_superposition,[],[f8028,f8144])).
% 48.35/8.44 thf(f8218,plain,(
% 48.35/8.44 (((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195)),
% 48.35/8.44 inference(boolean_simplification,[],[f8216])).
% 48.35/8.44 thf(f8219,plain,(
% 48.35/8.44 ((($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195 | ~spl1_227)),
% 48.35/8.44 inference(forward_demodulation,[],[f8218,f8200])).
% 48.35/8.44 thf(f8220,plain,(
% 48.35/8.44 ($false = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195 | ~spl1_227)),
% 48.35/8.44 inference(boolean_simplification,[],[f8219])).
% 48.35/8.44 thf(f8221,plain,(
% 48.35/8.44 $false | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195 | ~spl1_227)),
% 48.35/8.44 inference(trivial_inequality_removal,[],[f8220])).
% 48.35/8.44 thf(f8222,plain,(
% 48.35/8.44 ~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195 | ~spl1_227),
% 48.35/8.44 inference(avatar_contradiction_clause,[],[f8221])).
% 48.35/8.44 thf(f8223,plain,(
% 48.35/8.44 (((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) | $false))) = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195 | ~spl1_224)),
% 48.35/8.44 inference(forward_demodulation,[],[f8218,f8189])).
% 48.35/8.44 thf(f8224,plain,(
% 48.35/8.44 (((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195 | ~spl1_224)),
% 48.35/8.44 inference(boolean_simplification,[],[f8223])).
% 48.35/8.44 thf(f8225,plain,(
% 48.35/8.44 ($true = ((($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0)))))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195 | ~spl1_224)),
% 48.35/8.44 inference(boolean_simplification,[],[f8224])).
% 48.35/8.44 thf(f8226,plain,(
% 48.35/8.44 ($true = (($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0)))))))) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195 | ~spl1_224)),
% 48.35/8.44 inference(boolean_simplification,[],[f8225])).
% 48.35/8.44 thf(f8227,plain,(
% 48.35/8.44 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a1 @ Y0)))))) = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195 | ~spl1_224)),
% 48.35/8.44 inference(boolean_simplification,[],[f8226])).
% 48.35/8.44 thf(f8228,plain,(
% 48.35/8.44 ($false = $true) | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195 | ~spl1_224 | ~spl1_228)),
% 48.35/8.44 inference(forward_demodulation,[],[f8227,f8205])).
% 48.35/8.44 thf(f8229,plain,(
% 48.35/8.44 $false | (~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195 | ~spl1_224 | ~spl1_228)),
% 48.35/8.44 inference(trivial_inequality_removal,[],[f8228])).
% 48.35/8.44 thf(f8230,plain,(
% 48.35/8.44 ~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195 | ~spl1_224 | ~spl1_228),
% 48.35/8.44 inference(avatar_contradiction_clause,[],[f8229])).
% 48.35/8.44 thf(f8233,plain,(
% 48.35/8.44 ($false = (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0))))))) | (~spl1_225 | ~spl1_228)),
% 48.35/8.44 inference(forward_demodulation,[],[f8193,f8205])).
% 48.35/8.44 thf(f8234,plain,(
% 48.35/8.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK42 @ Y0) => (a2 @ Y0)))))) | (~spl1_225 | ~spl1_228)),
% 48.35/8.44 inference(boolean_simplification,[],[f8233])).
% 48.35/8.44 thf(f8240,plain,(
% 48.35/8.44 spl1_224 | ~spl1_225 | ~spl1_228),
% 48.35/8.44 inference(avatar_split_clause,[],[f8234,f8204,f8192,f8188])).
% 48.35/8.44 thf(f8243,plain,(
% 48.35/8.44 ($false = (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))))) | (~spl1_1 | ~spl1_5)),
% 48.35/8.44 inference(forward_demodulation,[],[f125,f140])).
% 48.35/8.44 thf(f8244,plain,(
% 48.35/8.44 ($false = (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))))) | (~spl1_1 | ~spl1_5)),
% 48.35/8.44 inference(boolean_simplification,[],[f8243])).
% 48.35/8.44 thf(f8245,plain,(
% 48.35/8.44 ($false = $true) | (~spl1_1 | ~spl1_5)),
% 48.35/8.44 inference(boolean_simplification,[],[f8244])).
% 48.35/8.44 thf(f8246,plain,(
% 48.35/8.44 $false | (~spl1_1 | ~spl1_5)),
% 48.35/8.44 inference(trivial_inequality_removal,[],[f8245])).
% 48.35/8.44 thf(f8247,plain,(
% 48.35/8.44 ~spl1_1 | ~spl1_5),
% 48.35/8.44 inference(avatar_contradiction_clause,[],[f8246])).
% 48.35/8.44 cnf(s3, plain, spl1_1 | spl1_4, inference(sat_conversion,[],[f137])).
% 48.35/8.44 cnf(s6, plain, spl1_5 | spl1_6, inference(sat_conversion,[],[f146])).
% 48.35/8.44 cnf(s7, plain, spl1_1 | spl1_2, inference(sat_conversion,[],[f147])).
% 48.35/8.44 cnf(s8, plain, ~spl1_5 | spl1_7 | spl1_8, inference(sat_conversion,[],[f189])).
% 48.35/8.44 cnf(s9, plain, ~spl1_5 | spl1_9 | spl1_10, inference(sat_conversion,[],[f196])).
% 48.35/8.44 cnf(s11, plain, ~spl1_5 | spl1_9 | spl1_13, inference(sat_conversion,[],[f207])).
% 48.35/8.44 cnf(s12, plain, ~spl1_5 | spl1_14 | spl1_15, inference(sat_conversion,[],[f214])).
% 48.35/8.44 cnf(s13, plain, ~spl1_5 | spl1_7 | spl1_16, inference(sat_conversion,[],[f218])).
% 48.35/8.44 cnf(s14, plain, ~spl1_2 | ~spl1_4 | spl1_5, inference(sat_conversion,[],[f219])).
% 48.35/8.44 cnf(s15, plain, ~spl1_7 | ~spl1_11, inference(sat_conversion,[],[f225])).
% 48.35/8.44 cnf(s16, plain, ~spl1_9 | ~spl1_14, inference(sat_conversion,[],[f231])).
% 48.35/8.44 cnf(s18, plain, ~spl1_14 | spl1_19 | spl1_20, inference(sat_conversion,[],[f305])).
% 48.35/8.44 cnf(s19, plain, ~spl1_14 | spl1_17 | spl1_21, inference(sat_conversion,[],[f309])).
% 48.35/8.44 cnf(s20, plain, ~spl1_14 | spl1_19 | spl1_22, inference(sat_conversion,[],[f313])).
% 48.35/8.44 cnf(s22, plain, ~spl1_14 | spl1_24, inference(sat_conversion,[],[f323])).
% 48.35/8.44 cnf(s25, plain, ~spl1_14 | spl1_25 | spl1_26, inference(sat_conversion,[],[f333])).
% 48.35/8.44 cnf(s28, plain, spl1_11 | ~spl1_15, inference(sat_conversion,[],[f363])).
% 48.35/8.44 cnf(s34, plain, ~spl1_1 | spl1_3 | ~spl1_6, inference(sat_conversion,[],[f378])).
% 48.35/8.44 cnf(s39, plain, ~spl1_10 | spl1_14, inference(sat_conversion,[],[f430])).
% 48.35/8.44 cnf(s50, plain, ~spl1_6 | spl1_32 | spl1_33, inference(sat_conversion,[],[f527])).
% 48.35/8.44 cnf(s51, plain, ~spl1_6 | spl1_30, inference(sat_conversion,[],[f528])).
% 48.35/8.44 cnf(s54, plain, ~spl1_6 | spl1_36 | spl1_37, inference(sat_conversion,[],[f550])).
% 48.35/8.44 cnf(s60, plain, ~spl1_29 | ~spl1_37, inference(sat_conversion,[],[f614])).
% 48.35/8.44 cnf(s64, plain, ~spl1_30 | ~spl1_33 | spl1_35, inference(sat_conversion,[],[f631])).
% 48.35/8.44 cnf(s76, plain, ~spl1_29 | spl1_50 | spl1_51, inference(sat_conversion,[],[f807])).
% 48.35/8.44 cnf(s77, plain, ~spl1_29 | spl1_52 | spl1_53, inference(sat_conversion,[],[f814])).
% 48.35/8.44 cnf(s79, plain, ~spl1_29 | spl1_55 | spl1_56, inference(sat_conversion,[],[f831])).
% 48.35/8.44 cnf(s81, plain, ~spl1_49 | spl1_57 | spl1_58, inference(sat_conversion,[],[f880])).
% 48.35/8.44 cnf(s82, plain, ~spl1_49 | spl1_59 | spl1_60, inference(sat_conversion,[],[f887])).
% 48.35/8.44 cnf(s86, plain, ~spl1_49 | spl1_60 | spl1_64, inference(sat_conversion,[],[f911])).
% 48.35/8.44 cnf(s90, plain, ~spl1_57 | ~spl1_60, inference(sat_conversion,[],[f950])).
% 48.35/8.44 cnf(s96, plain, ~spl1_49 | ~spl1_50, inference(sat_conversion,[],[f1034])).
% 48.35/8.44 cnf(s102, plain, ~spl1_58 | spl1_60, inference(sat_conversion,[],[f1165])).
% 48.35/8.44 cnf(s104, plain, ~spl1_58 | spl1_62, inference(sat_conversion,[],[f1167])).
% 48.35/8.44 cnf(s122, plain, ~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53 | spl1_79 | spl1_80, inference(sat_conversion,[],[f1517])).
% 48.35/8.44 cnf(s125, plain, ~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_53 | spl1_79 | spl1_84, inference(sat_conversion,[],[f1536])).
% 48.35/8.44 cnf(s128, plain, ~spl1_3 | ~spl1_6 | ~spl1_29 | ~spl1_36 | ~spl1_50 | ~spl1_53 | ~spl1_79, inference(sat_conversion,[],[f1555])).
% 48.35/8.44 cnf(s134, plain, ~spl1_50 | ~spl1_80 | ~spl1_84, inference(sat_conversion,[],[f1644])).
% 48.35/8.44 cnf(s155, plain, ~spl1_3 | ~spl1_6 | ~spl1_33 | spl1_91 | spl1_92, inference(sat_conversion,[],[f1902])).
% 48.35/8.44 cnf(s159, plain, ~spl1_3 | ~spl1_6 | ~spl1_33 | spl1_93 | spl1_96, inference(sat_conversion,[],[f1926])).
% 48.35/8.44 cnf(s161, plain, ~spl1_89 | ~spl1_94, inference(sat_conversion,[],[f1935])).
% 48.35/8.44 cnf(s177, plain, ~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_95 | spl1_106 | spl1_107, inference(sat_conversion,[],[f2253])).
% 48.35/8.44 cnf(s182, plain, ~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_92 | spl1_94, inference(sat_conversion,[],[f2276])).
% 48.35/8.44 cnf(s186, plain, ~spl1_89 | spl1_116 | spl1_117, inference(sat_conversion,[],[f2401])).
% 48.35/8.44 cnf(s189, plain, ~spl1_89 | spl1_115 | spl1_120, inference(sat_conversion,[],[f2415])).
% 48.35/8.44 cnf(s195, plain, ~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_116 | ~spl1_120, inference(sat_conversion,[],[f2677])).
% 48.35/8.44 cnf(s208, plain, ~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | ~spl1_89 | ~spl1_91 | ~spl1_115, inference(sat_conversion,[],[f2753])).
% 48.35/8.44 cnf(s211, plain, spl1_89 | ~spl1_93, inference(sat_conversion,[],[f2754])).
% 48.35/8.44 cnf(s212, plain, ~spl1_3 | ~spl1_6 | ~spl1_33 | ~spl1_35 | spl1_123 | spl1_124, inference(sat_conversion,[],[f2761])).
% 48.35/8.44 cnf(s214, plain, ~spl1_3 | ~spl1_6 | ~spl1_33 | spl1_89 | spl1_95, inference(sat_conversion,[],[f2763])).
% 48.35/8.44 cnf(s221, plain, ~spl1_95 | ~spl1_123, inference(sat_conversion,[],[f2805])).
% 48.35/8.44 cnf(s239, plain, spl1_115 | ~spl1_117, inference(sat_conversion,[],[f3020])).
% 48.35/8.44 cnf(s247, plain, ~spl1_96 | ~spl1_107 | ~spl1_110 | ~spl1_124, inference(sat_conversion,[],[f3237])).
% 48.35/8.44 cnf(s251, plain, spl1_50 | ~spl1_55, inference(sat_conversion,[],[f3258])).
% 48.35/8.44 cnf(s253, plain, ~spl1_49 | ~spl1_55, inference(sat_conversion,[],[f3277])).
% 48.35/8.44 cnf(s266, plain, ~spl1_107 | spl1_110 | ~spl1_124, inference(sat_conversion,[],[f3580])).
% 48.35/8.44 cnf(s268, plain, spl1_107 | ~spl1_124 | spl1_131, inference(sat_conversion,[],[f3613])).
% 48.35/8.44 cnf(s279, plain, ~spl1_106 | spl1_129 | ~spl1_131, inference(sat_conversion,[],[f3656])).
% 48.35/8.44 cnf(s280, plain, ~spl1_96 | ~spl1_106 | spl1_107 | ~spl1_129, inference(sat_conversion,[],[f3714])).
% 48.35/8.44 cnf(s286, plain, ~spl1_3 | ~spl1_6 | ~spl1_36 | spl1_136, inference(sat_conversion,[],[f3786])).
% 48.35/8.44 cnf(s291, plain, ~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_57 | ~spl1_59 | ~spl1_64 | ~spl1_136, inference(sat_conversion,[],[f3910])).
% 48.35/8.44 cnf(s301, plain, ~spl1_49 | ~spl1_52 | ~spl1_56 | ~spl1_58 | ~spl1_60 | ~spl1_62 | ~spl1_136, inference(sat_conversion,[],[f3998])).
% 48.35/8.44 cnf(s302, plain, ~spl1_53 | ~spl1_56, inference(sat_conversion,[],[f4060])).
% 48.35/8.44 cnf(s307, plain, ~spl1_51 | spl1_52 | ~spl1_56, inference(sat_conversion,[],[f4089])).
% 48.35/8.44 cnf(s308, plain, ~spl1_8 | spl1_11 | ~spl1_16, inference(sat_conversion,[],[f4090])).
% 48.35/8.44 cnf(s325, plain, spl1_21 | ~spl1_24 | ~spl1_26, inference(sat_conversion,[],[f4562])).
% 48.35/8.44 cnf(s326, plain, ~spl1_26 | spl1_147 | spl1_148, inference(sat_conversion,[],[f4663])).
% 48.35/8.44 cnf(s328, plain, ~spl1_26 | spl1_150, inference(sat_conversion,[],[f4671])).
% 48.35/8.44 cnf(s336, plain, ~spl1_21 | ~spl1_24 | spl1_26, inference(sat_conversion,[],[f4712])).
% 48.35/8.44 cnf(s338, plain, ~spl1_19 | ~spl1_25, inference(sat_conversion,[],[f4729])).
% 48.35/8.44 cnf(s340, plain, spl1_22 | ~spl1_24 | ~spl1_25, inference(sat_conversion,[],[f4740])).
% 48.35/8.44 cnf(s341, plain, spl1_49 | ~spl1_52, inference(sat_conversion,[],[f5041])).
% 48.35/8.44 cnf(s344, plain, ~spl1_8 | ~spl1_14, inference(sat_conversion,[],[f5084])).
% 48.35/8.44 cnf(s346, plain, spl1_29 | ~spl1_32, inference(sat_conversion,[],[f5111])).
% 48.35/8.44 cnf(s348, plain, ~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_148 | ~spl1_153 | ~spl1_157, inference(sat_conversion,[],[f5251])).
% 48.35/8.44 cnf(s354, plain, ~spl1_148 | spl1_153, inference(sat_conversion,[],[f5271])).
% 48.35/8.44 cnf(s362, plain, ~spl1_147 | ~spl1_153, inference(sat_conversion,[],[f5290])).
% 48.35/8.44 cnf(s368, plain, ~spl1_150 | spl1_153 | spl1_155, inference(sat_conversion,[],[f5319])).
% 48.35/8.44 cnf(s371, plain, ~spl1_150 | ~spl1_153 | spl1_157, inference(sat_conversion,[],[f5340])).
% 48.35/8.44 cnf(s374, plain, ~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_19 | ~spl1_21 | ~spl1_26 | ~spl1_147 | ~spl1_150 | ~spl1_155, inference(sat_conversion,[],[f5383])).
% 48.35/8.44 cnf(s376, plain, ~spl1_22 | ~spl1_26, inference(sat_conversion,[],[f5397])).
% 48.35/8.44 cnf(s394, plain, ~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25 | spl1_167 | spl1_168, inference(sat_conversion,[],[f5805])).
% 48.35/8.44 cnf(s395, plain, ~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25 | spl1_166 | spl1_169, inference(sat_conversion,[],[f5811])).
% 48.35/8.44 cnf(s397, plain, ~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_25 | spl1_161 | ~spl1_168, inference(sat_conversion,[],[f5819])).
% 48.35/8.44 cnf(s398, plain, ~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25 | ~spl1_169, inference(sat_conversion,[],[f5827])).
% 48.35/8.44 cnf(s399, plain, spl1_162 | ~spl1_166 | ~spl1_167, inference(sat_conversion,[],[f5834])).
% 48.35/8.44 cnf(s402, plain, ~spl1_161 | ~spl1_166, inference(sat_conversion,[],[f5845])).
% 48.35/8.44 cnf(s404, plain, ~spl1_4 | ~spl1_7 | ~spl1_10 | ~spl1_13 | ~spl1_17 | ~spl1_20 | ~spl1_22 | ~spl1_25 | ~spl1_162 | ~spl1_167, inference(sat_conversion,[],[f5866])).
% 48.35/8.44 cnf(s430, plain, ~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16 | spl1_191, inference(sat_conversion,[],[f6787])).
% 48.35/8.44 cnf(s434, plain, ~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16 | spl1_195 | spl1_198, inference(sat_conversion,[],[f6807])).
% 48.35/8.44 cnf(s435, plain, ~spl1_4 | ~spl1_9 | ~spl1_11 | ~spl1_16 | spl1_197 | spl1_199, inference(sat_conversion,[],[f6811])).
% 48.35/8.44 cnf(s438, plain, ~spl1_198 | spl1_202 | spl1_203, inference(sat_conversion,[],[f6906])).
% 48.35/8.44 cnf(s443, plain, ~spl1_198 | spl1_204 | spl1_205, inference(sat_conversion,[],[f6932])).
% 48.35/8.44 cnf(s444, plain, ~spl1_198 | spl1_204 | spl1_208, inference(sat_conversion,[],[f6936])).
% 48.35/8.44 cnf(s445, plain, ~spl1_198 | spl1_206 | spl1_207, inference(sat_conversion,[],[f6937])).
% 48.35/8.44 cnf(s447, plain, ~spl1_202 | ~spl1_207, inference(sat_conversion,[],[f7020])).
% 48.35/8.44 cnf(s448, plain, ~spl1_206 | ~spl1_208, inference(sat_conversion,[],[f7237])).
% 48.35/8.44 cnf(s449, plain, ~spl1_193 | ~spl1_198, inference(sat_conversion,[],[f7263])).
% 48.35/8.44 cnf(s451, plain, ~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_199 | spl1_210, inference(sat_conversion,[],[f7315])).
% 48.35/8.44 cnf(s454, plain, ~spl1_198 | ~spl1_204 | ~spl1_210, inference(sat_conversion,[],[f7350])).
% 48.35/8.44 cnf(s455, plain, ~spl1_197 | ~spl1_198, inference(sat_conversion,[],[f7355])).
% 48.35/8.44 cnf(s461, plain, ~spl1_191 | spl1_193 | ~spl1_195, inference(sat_conversion,[],[f7376])).
% 48.35/8.44 cnf(s463, plain, ~spl1_203 | ~spl1_205 | ~spl1_207 | ~spl1_208 | ~spl1_210, inference(sat_conversion,[],[f7646])).
% 48.35/8.44 cnf(s483, plain, ~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195 | spl1_225 | spl1_227, inference(sat_conversion,[],[f8202])).
% 48.35/8.44 cnf(s484, plain, ~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_195 | spl1_227 | spl1_228, inference(sat_conversion,[],[f8206])).
% 48.35/8.44 cnf(s488, plain, ~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195 | ~spl1_227, inference(sat_conversion,[],[f8222])).
% 48.35/8.44 cnf(s489, plain, ~spl1_4 | ~spl1_8 | ~spl1_9 | ~spl1_11 | ~spl1_16 | ~spl1_193 | ~spl1_195 | ~spl1_224 | ~spl1_228, inference(sat_conversion,[],[f8230])).
% 48.35/8.44 cnf(s491, plain, spl1_224 | ~spl1_225 | ~spl1_228, inference(sat_conversion,[],[f8240])).
% 48.35/8.44 cnf(s492, plain, ~spl1_1 | ~spl1_5, inference(sat_conversion,[],[f8247])).
% 48.35/8.44 cnf(s494, plain, ~spl1_195 | ~spl1_193 | ~spl1_4 | ~spl1_8 | ~spl1_16 | ~spl1_11 | ~spl1_9, inference(rat,[],[s489,s491,s484,s483,s488])).
% 48.35/8.44 cnf(s495, plain, ~spl1_193 | ~spl1_9 | ~spl1_8 | ~spl1_16 | ~spl1_4, inference(rat,[],[s494,s434,s449,s308])).
% 48.35/8.44 cnf(s496, plain, ~spl1_210 | ~spl1_198, inference(rat,[],[s438,s463,s447,s445,s448,s443,s444,s454])).
% 48.35/8.44 cnf(s497, plain, spl1_7 | spl1_1, inference(rat,[],[s496,s451,s435,s455,s434,s461,s495,s430,s9,s39,s308,s344,s8,s13,s14,s7,s3])).
% 48.35/8.44 cnf(s498, plain, ~spl1_148 | ~spl1_21 | spl1_1, inference(rat,[],[s348,s371,s354,s11,s9,s16,s328,s20,s376,s336,s22,s12,s28,s15,s497,s14,s7,s3])).
% 48.35/8.44 cnf(s499, plain, ~spl1_21 | spl1_1, inference(rat,[],[s368,s374,s362,s326,s498,s20,s328,s376,s336,s22,s11,s9,s16,s12,s28,s15,s497,s14,s7,s3])).
% 48.35/8.44 cnf(s500, plain, ~spl1_20 | ~spl1_22 | ~spl1_4 | ~spl1_7 | ~spl1_13 | ~spl1_10 | ~spl1_17 | ~spl1_25, inference(rat,[],[s404,s399,s394,s397,s402,s395,s398])).
% 48.35/8.44 cnf(s501, plain, spl1_1, inference(rat,[],[s500,s18,s340,s338,s25,s325,s19,s499,s9,s11,s16,s22,s12,s28,s15,s497,s14,s3,s7])).
% 48.35/8.44 cnf(s502, plain, ~spl1_5, inference(rat,[],[s492,s501])).
% 48.35/8.44 cnf(s503, plain, spl1_6, inference(rat,[],[s6,s502])).
% 48.35/8.44 cnf(s504, plain, spl1_30, inference(rat,[],[s51,s503])).
% 48.35/8.44 cnf(s506, plain, spl1_3, inference(rat,[],[s34,s501,s503])).
% 48.35/8.44 cnf(s508, plain, ~spl1_58 | ~spl1_52 | ~spl1_56 | ~spl1_49 | ~spl1_136, inference(rat,[],[s301,s102,s104])).
% 48.35/8.44 cnf(s509, plain, ~spl1_52 | ~spl1_56 | ~spl1_136 | ~spl1_49, inference(rat,[],[s291,s86,s82,s90,s81,s508])).
% 48.35/8.44 cnf(s510, plain, ~spl1_49 | ~spl1_29, inference(rat,[],[s509,s307,s76,s79,s96,s253,s286,s54,s60,s506,s503])).
% 48.35/8.44 cnf(s511, plain, ~spl1_50 | ~spl1_53 | ~spl1_29 | ~spl1_36, inference(rat,[],[s134,s122,s125,s128,s506,s503])).
% 48.35/8.44 cnf(s512, plain, ~spl1_29, inference(rat,[],[s511,s251,s79,s302,s77,s341,s510,s54,s60,s503])).
% 48.35/8.44 cnf(s513, plain, ~spl1_32, inference(rat,[],[s346,s512])).
% 48.35/8.44 cnf(s516, plain, spl1_33, inference(rat,[],[s50,s503,s513])).
% 48.35/8.44 cnf(s519, plain, spl1_35, inference(rat,[],[s64,s504,s516])).
% 48.35/8.44 cnf(s523, plain, ~spl1_107 | spl1_89, inference(rat,[],[s247,s266,s159,s211,s212,s221,s214,s519,s516,s506,s503])).
% 48.35/8.44 cnf(s524, plain, spl1_89, inference(rat,[],[s279,s280,s268,s177,s523,s212,s221,s159,s214,s211,s503,s506,s516,s519])).
% 48.35/8.44 cnf(s525, plain, ~spl1_94, inference(rat,[],[s161,s524])).
% 48.35/8.44 cnf(s528, plain, ~spl1_92, inference(rat,[],[s182,s516,s506,s503,s525])).
% 48.35/8.44 cnf(s530, plain, spl1_91, inference(rat,[],[s155,s516,s506,s503,s528])).
% 48.35/8.44 cnf(s532, plain, ~spl1_115, inference(rat,[],[s208,s524,s519,s516,s506,s503,s530])).
% 48.35/8.44 cnf(s533, plain, ~spl1_117, inference(rat,[],[s239,s532])).
% 48.35/8.44 cnf(s534, plain, spl1_120, inference(rat,[],[s189,s524,s532])).
% 48.35/8.44 cnf(s537, plain, spl1_116, inference(rat,[],[s186,s524,s533])).
% 48.35/8.44 cnf(s539, plain, $false, inference(rat,[],[s195,s530,s524,s519,s516,s506,s503,s534,s537])).
% 48.35/8.44 thf(f8249,plain,(
% 48.35/8.44 $false),
% 48.35/8.44 inference(avatar_sat_refutation,[],[s539])).
% 48.35/8.44 % SZS output end Proof for theBenchmark
% 48.35/8.44 % (547067)------------------------------
% 48.35/8.44 % (547067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/8.44 % (547067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/8.44 % (547067)CaDiCaL version: 2.1.3
% 48.35/8.44 % (547067)Termination reason: Refutation
% 48.35/8.44 % (547067)Time elapsed: 1.049 s
% 48.35/8.44 % (547067)Peak memory usage: 18 MB
% 48.35/8.44 % (547067)Instructions burned: 1328 (million)
% 48.35/8.44 % (546654)Success in time 8.112 s
% 48.35/8.44 % Vampire exiting
%------------------------------------------------------------------------------