%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX179^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:40:39 AM UTC 2026
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX179^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n004.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 16:09:52 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.36 % (1487808)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.36 % (1487814)lrs+10_16_si=on:nwc=1.5:random_seed=3751497782:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.36 % (1487814)Instruction limit reached!
% 0.21/0.36 % (1487814)------------------------------
% 0.21/0.36 % (1487814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1487814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1487814)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1487814)Termination reason: Instruction limit
% 0.21/0.36 % (1487814)Termination phase: Saturation
% 0.21/0.36 % (1487814)Time elapsed: 0.005 s
% 0.21/0.36 % (1487814)Peak memory usage: 12 MB
% 0.21/0.36 % (1487814)Instructions burned: 19 (million)
% 0.21/0.36 % (1487813)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3572596033:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.36 % (1487815)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=102515535:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.36 % (1487816)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=311401167: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)
% 0.21/0.36 % (1487817)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2017778158:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.36 % (1487815)Instruction limit reached!
% 0.21/0.36 % (1487815)------------------------------
% 0.21/0.36 % (1487815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1487815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1487815)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1487815)Termination reason: Instruction limit
% 0.21/0.36 % (1487815)Termination phase: Property scanning
% 0.21/0.36 % (1487815)Time elapsed: 0.002 s
% 0.21/0.36 % (1487815)Peak memory usage: 10 MB
% 0.21/0.36 % (1487815)Instructions burned: 4 (million)
% 0.21/0.36 % (1487819)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.36 % (1487819)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
% 0.21/0.36 % (1487821)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1353024648:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.36 % (1487818)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1959309718:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.36 % (1487819)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=55062080:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.36 % (1487821)Instruction limit reached!
% 0.21/0.36 % (1487821)------------------------------
% 0.21/0.36 % (1487821)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1487821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1487821)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1487821)Termination reason: Instruction limit
% 0.21/0.36 % (1487821)Termination phase: Saturation
% 0.21/0.36 % (1487821)Time elapsed: 0.002 s
% 0.21/0.36 % (1487821)Peak memory usage: 12 MB
% 0.21/0.36 % (1487821)Instructions burned: 8 (million)
% 0.21/0.36 % (1487817)Instruction limit reached!
% 0.21/0.36 % (1487817)------------------------------
% 0.21/0.36 % (1487817)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1487817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1487817)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1487817)Termination reason: Instruction limit
% 0.21/0.36 % (1487817)Termination phase: Saturation
% 0.21/0.36 % (1487817)Time elapsed: 0.014 s
% 0.21/0.36 % (1487817)Peak memory usage: 12 MB
% 0.21/0.36 % (1487817)Instructions burned: 25 (million)
% 0.21/0.36 % (1487830)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.38 % (1487826)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2289437341:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.38 % (1487830)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1743506448:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.38 % (1487830)Instruction limit reached!
% 0.21/0.38 % (1487830)------------------------------
% 0.21/0.38 % (1487830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1487826)Instruction limit reached!
% 0.21/0.38 % (1487826)------------------------------
% 0.21/0.38 % (1487826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1487830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1487830)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1487830)Termination reason: Instruction limit
% 0.21/0.38 % (1487830)Termination phase: Saturation
% 0.21/0.38 % (1487826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1487830)Time elapsed: 0.003 s
% 0.21/0.38 % (1487830)Peak memory usage: 12 MB
% 0.21/0.38 % (1487830)Instructions burned: 11 (million)
% 0.21/0.38 % (1487826)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1487826)Termination reason: Instruction limit
% 0.21/0.38 % (1487826)Termination phase: Property scanning
% 0.21/0.38 % (1487826)Time elapsed: 0.003 s
% 0.21/0.38 % (1487826)Peak memory usage: 10 MB
% 0.21/0.38 % (1487826)Instructions burned: 7 (million)
% 0.21/0.38 % (1487831)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2875332512:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.38 % (1487834)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
% 0.21/0.38 % (1487834)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.38 % (1487834)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=623466966:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.38 % (1487813)Instruction limit reached!
% 0.21/0.38 % (1487813)------------------------------
% 0.21/0.38 % (1487813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1487813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1487813)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1487813)Termination reason: Instruction limit
% 0.21/0.38 % (1487813)Termination phase: Saturation
% 0.21/0.38 % (1487813)Time elapsed: 0.040 s
% 0.21/0.38 % (1487813)Peak memory usage: 13 MB
% 0.21/0.38 % (1487813)Instructions burned: 89 (million)
% 0.21/0.38 % (1487831)Instruction limit reached!
% 0.21/0.38 % (1487831)------------------------------
% 0.21/0.38 % (1487831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1487831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1487831)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1487831)Termination reason: Instruction limit
% 0.21/0.38 % (1487831)Termination phase: Saturation
% 0.21/0.38 % (1487831)Time elapsed: 0.007 s
% 0.21/0.38 % (1487831)Peak memory usage: 12 MB
% 0.21/0.38 % (1487831)Instructions burned: 12 (million)
% 0.21/0.38 % (1487818)Instruction limit reached!
% 0.21/0.38 % (1487818)------------------------------
% 0.21/0.38 % (1487818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1487818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1487818)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1487818)Termination reason: Instruction limit
% 0.21/0.38 % (1487818)Termination phase: Saturation
% 0.21/0.38 % (1487818)Time elapsed: 0.033 s
% 0.21/0.38 % (1487818)Peak memory usage: 13 MB
% 0.21/0.38 % (1487818)Instructions burned: 76 (million)
% 0.21/0.38 % (1487834)Instruction limit reached!
% 0.21/0.38 % (1487834)------------------------------
% 0.21/0.38 % (1487834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1487834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1487834)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1487834)Termination reason: Instruction limit
% 0.21/0.38 % (1487834)Termination phase: Saturation
% 0.21/0.38 % (1487834)Time elapsed: 0.007 s
% 0.21/0.38 % (1487834)Peak memory usage: 12 MB
% 0.21/0.38 % (1487834)Instructions burned: 31 (million)
% 0.21/0.38 % (1487835)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=435757364:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.38 % (1487841)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2792770476:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.21/0.38 % (1487839)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.38 % (1487819) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1487808-1487819"...
% 0.21/0.38 % (1487838)lrs+10_1_si=on:cs=on:random_seed=1008077075:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.21/0.38 % (1487839)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=100373140:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38 % (1487840)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=630596605:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.21/0.38 % (1487839)Instruction limit reached!
% 0.21/0.38 % (1487839)------------------------------
% 0.21/0.38 % (1487839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1487839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1487839)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1487839)Termination reason: Instruction limit
% 0.21/0.38 % (1487839)Termination phase: Property scanning
% 0.21/0.38 % (1487839)Time elapsed: 0.003 s
% 0.21/0.38 % (1487839)Peak memory usage: 10 MB
% 0.21/0.38 % (1487839)Instructions burned: 6 (million)
% 0.21/0.38 % (1487838)Instruction limit reached!
% 0.21/0.38 % (1487838)------------------------------
% 0.21/0.38 % (1487838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1487838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1487838)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1487838)Termination reason: Instruction limit
% 0.21/0.38 % (1487838)Termination phase: Saturation
% 0.21/0.38 % (1487838)Time elapsed: 0.004 s
% 0.21/0.38 % (1487838)Peak memory usage: 11 MB
% 0.21/0.38 % (1487838)Instructions burned: 9 (million)
% 0.21/0.38 % (1487840)Refutation not found, incomplete strategy
% 0.21/0.38 % (1487840)------------------------------
% 0.21/0.38 % (1487840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1487840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1487840)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1487840)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38 % (1487840)Time elapsed: 0.003 s
% 0.21/0.38 % (1487840)Peak memory usage: 12 MB
% 0.21/0.38 % (1487840)Instructions burned: 5 (million)
% 0.21/0.38 % (1487840)------------------------------
% 0.21/0.38 % (1487840)------------------------------
% 0.21/0.38 % (1487835)Instruction limit reached!
% 0.21/0.38 % (1487835)------------------------------
% 0.21/0.38 % (1487835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1487835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1487835)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1487835)Termination reason: Instruction limit
% 0.21/0.38 % (1487835)Termination phase: Saturation
% 0.21/0.38 % (1487835)Time elapsed: 0.038 s
% 0.21/0.38 % (1487835)Peak memory usage: 13 MB
% 0.21/0.38 % (1487835)Instructions burned: 87 (million)
% 0.21/0.38 % (1487847)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2229015501:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.21/0.38 % (1487848)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=385030648:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.21/0.38 % (1487849)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1780838450:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.21/0.38 % (1487848)Instruction limit reached!
% 0.21/0.38 % (1487848)------------------------------
% 0.21/0.38 % (1487848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1487848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1487848)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1487848)Termination reason: Instruction limit
% 0.21/0.38 % (1487848)Termination phase: Saturation
% 0.21/0.38 % (1487848)Time elapsed: 0.007 s
% 0.21/0.38 % (1487848)Peak memory usage: 12 MB
% 0.21/0.38 % (1487848)Instructions burned: 14 (million)
% 0.21/0.38 % (1487847)Instruction limit reached!
% 0.21/0.38 % (1487847)------------------------------
% 0.21/0.38 % (1487847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1487847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1487847)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1487847)Termination reason: Instruction limit
% 0.21/0.38 % (1487847)Termination phase: Saturation
% 0.21/0.38 % (1487847)Time elapsed: 0.014 s
% 0.21/0.38 % (1487847)Peak memory usage: 12 MB
% 0.21/0.38 % (1487847)Instructions burned: 26 (million)
% 0.21/0.38 % (1487852)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1421418686:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.21/0.38 % (1487819)...printing done.
% 0.21/0.38 % (1487819)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% 0.21/0.38 thf(type_def_5, type, unsorted: $tType).
% 0.21/0.38 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.38 thf(type_def_7, type, d_unsorted: $tType).
% 0.21/0.38 thf(func_def_0, type, irel: ($i > $i > $o)).
% 0.21/0.38 thf(func_def_1, type, mnot: (($i > $o) > $i > $o)).
% 0.21/0.38 thf(func_def_2, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.21/0.38 thf(func_def_3, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.21/0.38 thf(func_def_4, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 0.21/0.38 thf(func_def_5, type, mbox_s4: (($i > $o) > $i > $o)).
% 0.21/0.38 thf(func_def_6, type, iatom: (($i > $o) > $i > $o)).
% 0.21/0.38 thf(func_def_7, type, inot: (($i > $o) > $i > $o)).
% 0.21/0.38 thf(func_def_8, type, itrue: ($i > $o)).
% 0.21/0.38 thf(func_def_9, type, ifalse: ($i > $o)).
% 0.21/0.38 thf(func_def_10, type, iand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.21/0.38 thf(func_def_11, type, ior: (($i > $o) > ($i > $o) > $i > $o)).
% 0.21/0.38 thf(func_def_12, type, iimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 0.21/0.38 thf(func_def_13, type, iimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 0.21/0.38 thf(func_def_14, type, iequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 0.21/0.38 thf(func_def_15, type, ixor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.21/0.38 thf(func_def_16, type, ivalid: (($i > $o) > $o)).
% 0.21/0.38 thf(func_def_17, type, isatisfiable: (($i > $o) > $o)).
% 0.21/0.38 thf(func_def_18, type, icountersatisfiable: (($i > $o) > $o)).
% 0.21/0.38 thf(func_def_19, type, iinvalid: (($i > $o) > $o)).
% 0.21/0.38 thf(func_def_20, type, d2unsorted: (d_unsorted > $i)).
% 0.21/0.38 thf(func_def_21, type, d_unsorted_0: d_unsorted).
% 0.21/0.38 thf(func_def_23, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.38 thf(func_def_24, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.38 thf(func_def_25, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.38 thf(func_def_26, type, vNOT: ($o > $o)).
% 0.21/0.38 thf(func_def_27, type, vAND: ($o > $o > $o)).
% 0.21/0.38 thf(func_def_28, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.38 thf(func_def_29, type, vOR: ($o > $o > $o)).
% 0.21/0.38 thf(func_def_30, type, db4: !>[X0: $tType]:(X0)).
% 0.21/0.38 thf(func_def_31, type, db2: !>[X0: $tType]:(X0)).
% 0.21/0.38 thf(func_def_32, type, db3: !>[X0: $tType]:(X0)).
% 0.21/0.38 thf(func_def_33, type, db5: !>[X0: $tType]:(X0)).
% 0.21/0.38 thf(func_def_34, type, db8: !>[X0: $tType]:(X0)).
% 0.21/0.38 thf(func_def_35, type, db6: !>[X0: $tType]:(X0)).
% 0.21/0.38 thf(func_def_36, type, db7: !>[X0: $tType]:(X0)).
% 0.21/0.38 thf(func_def_39, type, sK0: ($i > d_unsorted)).
% 0.21/0.38 thf(func_def_40, type, sK1: ($i > $o)).
% 0.21/0.38 thf(func_def_41, type, sK2: ($i > $o)).
% 0.21/0.38 thf(func_def_43, type, sK4: ($i > $i)).
% 0.21/0.38 thf(func_def_44, type, sK5: ($i > $i)).
% 0.21/0.38 thf(func_def_45, type, sK6: ($i > $i)).
% 0.21/0.38 thf(func_def_46, type, sK7: ($i > $i)).
% 0.21/0.38 thf(func_def_47, type, sK8: ($i > $i)).
% 0.21/0.38 thf(func_def_48, type, sK9: ($i > $i)).
% 0.21/0.38 thf(func_def_49, type, sK10: ($i > $i)).
% 0.21/0.38 thf(func_def_50, type, sK11: ($i > $i)).
% 0.21/0.38 thf(func_def_51, type, sK12: ($i > $i)).
% 0.21/0.38 thf(func_def_52, type, sK13: ($i > $i)).
% 0.21/0.38 thf(f1,axiom,(
% 0.21/0.38 ((^[X18 : ($i > $o)] : (~ ! [X19 : $i] : (X18 @ X19))) = icountersatisfiable) & ! [X1 : d_unsorted] : (X1 = d_unsorted_0) & ((^[X4 : ($i > $o), X5 : ($i > $o), X0 : $i] : ((X5 @ X0) | (X4 @ X0))) = mor) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (~ ! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)))) = iimplied) & (iinvalid = (^[X18 : ($i > $o)] : (! [X19 : $i] : ~(X18 @ X19)))) & ((^[X8 : ($i > $o), X7 : $i] : ((X8 @ X7))) = iatom) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (~ ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)))) = iimplies) & (mbox_s4 = (^[X8 : ($i > $o), X4 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X4 @ X5))))) & ((^[X18 : ($i > $o)] : (~ ! [X19 : $i] : ~(X18 @ X19))) = isatisfiable) & (itrue @ (d2unsorted @ d_unsorted_0)) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ((^[X18 : ($i > $o)] : (! [X19 : $i] : (X18 @ X19))) = ivalid) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & ((^[X0 : ($i > $o), X6 : ($i > $o), X7 : $i] : (~(X0 @ X7) | (X6 @ X7))) = mimplies) & (ior = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5))))) & (mand = (^[X4 : ($i > $o), X5 : ($i > $o), X0 : $i] : ((X5 @ X0) & (X4 @ X0)))) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)) & ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)))) = iand) & ! [X0 : $i] : ? [X1 : d_unsorted] : (X0 = ((d2unsorted @ X1))) & (inot = (^[X8 : ($i > $o), X7 : $i] : (~ ! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5))))) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (ixor = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (~ ! [X17 : $i,X5 : $i,X15 : $i,X14 : $i,X16 : $i] : (~(irel @ X7 @ X5) | ((~(irel @ X16 @ X17) | ~(irel @ X5 @ X16) | (X8 @ X17) | ~ ! [X13 : $i] : ((X9 @ X13) | ~(irel @ X16 @ X13))) & (~(irel @ X14 @ X15) | ~(irel @ X5 @ X14) | (X9 @ X15) | ~ ! [X11 : $i] : ((X8 @ X11) | ~(irel @ X14 @ X11)))))))) & (iequiv = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i,X10 : $i] : (~ ! [X11 : $i] : (~(irel @ X5 @ X11) | (X8 @ X11)) | (X9 @ X10) | ~(irel @ X5 @ X10) | ~(irel @ X7 @ X5)) & ! [X12 : $i,X5 : $i] : (~(irel @ X5 @ X12) | ~ ! [X13 : $i] : ((X9 @ X13) | ~(irel @ X5 @ X13)) | ~(irel @ X7 @ X5) | (X8 @ X12))))) & (mnot = (^[X4 : ($i > $o), X0 : $i] : (~(X4 @ X0))))),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',lcl696_1)).
% 0.21/0.38 thf(f2,conjecture,(
% 0.21/0.38 ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((inot @ (iequiv @ X0 @ X1)))) = ixor)),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ixor)).
% 0.21/0.38 thf(f3,negated_conjecture,(
% 0.21/0.38 ~ ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((inot @ (iequiv @ X0 @ X1)))) = ixor)),
% 0.21/0.38 inference(negated_conjecture,[status(cth)],[f2])).
% 0.21/0.38 thf(f4,plain,(
% 0.21/0.38 ~ (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (inot @ (iequiv @ Y0 @ Y1))))))),
% 0.21/0.38 inference(fool_elimination,[],[f3])).
% 0.21/0.38 thf(f5,plain,(
% 0.21/0.38 ((^[X0 : ($i > $o)] : (~ ! [X1 : $i] : (X0 @ X1))) = icountersatisfiable) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & ((^[X3 : ($i > $o), X4 : ($i > $o), X5 : $i] : ((X4 @ X5) | (X3 @ X5))) = mor) & ((^[X6 : ($i > $o), X7 : ($i > $o), X8 : $i] : (~ ! [X9 : $i] : ((X7 @ X9) | ~(irel @ X8 @ X9)) | ! [X10 : $i] : ((X6 @ X10) | ~(irel @ X8 @ X10)))) = iimplied) & (iinvalid = (^[X11 : ($i > $o)] : (! [X12 : $i] : ~(X11 @ X12)))) & ((^[X13 : ($i > $o), X14 : $i] : ((X13 @ X14))) = iatom) & ((^[X15 : ($i > $o), X16 : ($i > $o), X17 : $i] : (~ ! [X18 : $i] : ((X15 @ X18) | ~(irel @ X17 @ X18)) | ! [X19 : $i] : ((X16 @ X19) | ~(irel @ X17 @ X19)))) = iimplies) & (mbox_s4 = (^[X20 : ($i > $o), X21 : $i] : (! [X22 : $i] : ((X20 @ X22) | ~(irel @ X21 @ X22))))) & ((^[X23 : ($i > $o)] : (~ ! [X24 : $i] : ~(X23 @ X24))) = isatisfiable) & (itrue @ (d2unsorted @ d_unsorted_0)) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ((^[X25 : ($i > $o)] : (! [X26 : $i] : (X25 @ X26))) = ivalid) & ! [X27 : d_unsorted,X28 : d_unsorted] : ((((d2unsorted @ X27)) = ((d2unsorted @ X28))) => (X27 = X28)) & ((^[X29 : ($i > $o), X30 : ($i > $o), X31 : $i] : (~(X29 @ X31) | (X30 @ X31))) = mimplies) & (ior = (^[X32 : ($i > $o), X33 : ($i > $o), X34 : $i] : (! [X35 : $i] : ((X32 @ X35) | ~(irel @ X34 @ X35)) | ! [X36 : $i] : (~(irel @ X34 @ X36) | (X33 @ X36))))) & (mand = (^[X37 : ($i > $o), X38 : ($i > $o), X39 : $i] : ((X38 @ X39) & (X37 @ X39)))) & ((^[X40 : ($i > $o), X41 : ($i > $o), X42 : $i] : (! [X43 : $i] : (~(irel @ X42 @ X43) | (X41 @ X43)) & ! [X44 : $i] : ((X40 @ X44) | ~(irel @ X42 @ X44)))) = iand) & ! [X45 : $i] : ? [X46 : d_unsorted] : (((d2unsorted @ X46)) = X45) & (inot = (^[X47 : ($i > $o), X48 : $i] : (~ ! [X49 : $i] : (~(irel @ X48 @ X49) | (X47 @ X49))))) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (ixor = (^[X50 : ($i > $o), X51 : ($i > $o), X52 : $i] : (~ ! [X53 : $i,X54 : $i,X55 : $i,X56 : $i,X57 : $i] : (~(irel @ X52 @ X54) | ((~(irel @ X57 @ X53) | ~(irel @ X54 @ X57) | (X50 @ X53) | ~ ! [X58 : $i] : ((X51 @ X58) | ~(irel @ X57 @ X58))) & (~(irel @ X56 @ X55) | ~(irel @ X54 @ X56) | (X51 @ X55) | ~ ! [X59 : $i] : ((X50 @ X59) | ~(irel @ X56 @ X59)))))))) & (iequiv = (^[X60 : ($i > $o), X61 : ($i > $o), X62 : $i] : (! [X63 : $i,X64 : $i] : (~ ! [X65 : $i] : (~(irel @ X63 @ X65) | (X60 @ X65)) | (X61 @ X64) | ~(irel @ X63 @ X64) | ~(irel @ X62 @ X63)) & ! [X66 : $i,X67 : $i] : (~(irel @ X67 @ X66) | ~ ! [X68 : $i] : ((X61 @ X68) | ~(irel @ X67 @ X68)) | ~(irel @ X62 @ X67) | (X60 @ X66))))) & (mnot = (^[X69 : ($i > $o), X70 : $i] : (~(X69 @ X70))))),
% 0.21/0.38 inference(rectify,[],[f1])).
% 0.21/0.38 thf(f6,plain,(
% 0.21/0.38 (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ! [X27 : d_unsorted,X28 : d_unsorted] : ((((d2unsorted @ X27)) = ((d2unsorted @ X28))) => (X27 = X28)) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X45 : $i] : ? [X46 : d_unsorted] : (((d2unsorted @ X46)) = X45) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8))))) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y4))) | (~ (irel @ Y4 @ Y5))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y7)) | (~ (irel @ Y6 @ Y3))) | (~ (irel @ Y3 @ Y7)))) | (~ (irel @ Y2 @ Y6)))))))))))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5)))))))))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.38 inference(fool_elimination,[],[f5])).
% 0.21/0.38 thf(f7,plain,(
% 0.21/0.38 (ixor != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (inot @ (iequiv @ Y0 @ Y1))))))),
% 0.21/0.38 inference(flattening,[],[f4])).
% 0.21/0.38 thf(f8,plain,(
% 0.21/0.38 (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ! [X1 : d_unsorted,X2 : d_unsorted] : ((((d2unsorted @ X1)) = ((d2unsorted @ X2))) => (X1 = X2)) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8))))) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y4))) | (~ (irel @ Y4 @ Y5))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y7)) | (~ (irel @ Y6 @ Y3))) | (~ (irel @ Y3 @ Y7)))) | (~ (irel @ Y2 @ Y6)))))))))))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5)))))))))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.38 inference(rectify,[],[f6])).
% 0.21/0.38 thf(f9,plain,(
% 0.21/0.38 (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8))))) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y4))) | (~ (irel @ Y4 @ Y5))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y7)) | (~ (irel @ Y6 @ Y3))) | (~ (irel @ Y3 @ Y7)))) | (~ (irel @ Y2 @ Y6)))))))))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X1 : d_unsorted,X2 : d_unsorted] : ((((d2unsorted @ X1)) = ((d2unsorted @ X2))) => (X1 = X2)) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5)))))))))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0)),
% 0.21/0.38 inference(flattening,[],[f8])).
% 0.21/0.38 thf(f10,plain,(
% 0.21/0.38 (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X2 : d_unsorted,X1 : d_unsorted] : ((((d2unsorted @ X1)) != ((d2unsorted @ X2))) | (X1 = X2)) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8))))) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y4))) | (~ (irel @ Y4 @ Y5))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y7)) | (~ (irel @ Y6 @ Y3))) | (~ (irel @ Y3 @ Y7)))) | (~ (irel @ Y2 @ Y6)))))))))))))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5)))))))))))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.38 inference(ennf_transformation,[],[f9])).
% 0.21/0.38 thf(f11,plain,(
% 0.21/0.38 (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((((d2unsorted @ X1)) != ((d2unsorted @ X0))) | (X0 = X1)) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ! [X2 : $i] : ? [X3 : d_unsorted] : (((d2unsorted @ X3)) = X2) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8))))) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y4))) | (~ (irel @ Y4 @ Y5))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y7)) | (~ (irel @ Y6 @ Y3))) | (~ (irel @ Y3 @ Y7)))) | (~ (irel @ Y2 @ Y6)))))))))))))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5)))))))))))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.38 inference(rectify,[],[f10])).
% 0.21/0.38 thf(f12,plain,(
% 0.21/0.38 (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((((d2unsorted @ X1)) != ((d2unsorted @ X0))) | (X0 = X1)) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ! [X2 : $i] : (((d2unsorted @ (sK0 @ X2))) = X2) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8))))) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y4))) | (~ (irel @ Y4 @ Y5))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y7)) | (~ (irel @ Y6 @ Y3))) | (~ (irel @ Y3 @ Y7)))) | (~ (irel @ Y2 @ Y6)))))))))))))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5)))))))))))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X2)],[f11])).
% 0.21/0.38 thf(f16,plain,(
% 0.21/0.38 (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))))),
% 0.21/0.38 inference(cnf_transformation,[],[f12])).
% 0.21/0.38 thf(f19,plain,(
% 0.21/0.38 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5))))))))))))))))))),
% 0.21/0.38 inference(cnf_transformation,[],[f12])).
% 0.21/0.38 thf(f23,plain,(
% 0.21/0.38 (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8))))) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y4))) | (~ (irel @ Y4 @ Y5))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y7)) | (~ (irel @ Y6 @ Y3))) | (~ (irel @ Y3 @ Y7)))) | (~ (irel @ Y2 @ Y6))))))))))))))))))))),
% 0.21/0.38 inference(cnf_transformation,[],[f12])).
% 0.21/0.38 thf(f25,plain,(
% 0.21/0.38 (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f12])).
% 0.21/0.38 thf(f28,plain,(
% 0.21/0.38 ( ! [X4 : d_unsorted] : ((d_unsorted_0 = X4)) )),
% 0.21/0.38 inference(cnf_transformation,[],[f12])).
% 0.21/0.38 thf(f29,plain,(
% 0.21/0.38 ( ! [X2 : $i] : ((((d2unsorted @ (sK0 @ X2))) = X2)) )),
% 0.21/0.38 inference(cnf_transformation,[],[f12])).
% 0.21/0.38 thf(f36,plain,(
% 0.21/0.38 (ixor != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (inot @ (iequiv @ Y0 @ Y1))))))),
% 0.21/0.38 inference(cnf_transformation,[],[f7])).
% 0.21/0.38 thf(f39,plain,(
% 0.21/0.38 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (irel @ Y3 @ Y4))))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((((Y2 @ Y6) | (~ (irel @ Y4 @ Y5))) | (~ (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y5 @ Y7)) | (Y3 @ Y7)))))) | (~ (irel @ Y5 @ Y6))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((((~ (irel @ Y4 @ Y6)) | (~ (irel @ Y6 @ Y5))) | (Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7) | (~ (irel @ Y6 @ Y7))))))))))))))))) @ Y0 @ Y1))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8))))) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y4))) | (~ (irel @ Y4 @ Y5))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y7)) | (~ (irel @ Y6 @ Y3))) | (~ (irel @ Y3 @ Y7)))) | (~ (irel @ Y2 @ Y6))))))))))))))))))))),
% 0.21/0.38 inference(definition_unfolding,[],[f36,f23,f16,f19])).
% 0.21/0.38 thf(f40,plain,(
% 0.21/0.38 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8))))) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y4))) | (~ (irel @ Y4 @ Y5))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y7)) | (~ (irel @ Y6 @ Y3))) | (~ (irel @ Y3 @ Y7)))) | (~ (irel @ Y2 @ Y6))))))))))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((Y0 @ Y5) | (~ (irel @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (Y1 @ Y6)))))) | (~ (irel @ Y4 @ Y5))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((~ (irel @ Y3 @ Y5)) | (~ (irel @ Y5 @ Y4))) | (Y1 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6)))))))))))) | (~ (irel @ Y2 @ Y3))))))))))))),
% 0.21/0.38 inference(beta-eta_normalization,[],[f39])).
% 0.21/0.38 thf(f54,plain,(
% 0.21/0.38 ( ! [X2 : $i] : ((((d2unsorted @ d_unsorted_0)) = X2)) )),
% 0.21/0.38 inference(forward_demodulation,[],[f29,f28])).
% 0.21/0.38 thf(f58,plain,(
% 0.21/0.38 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 0.21/0.38 inference(constrained_superposition,[],[f54,f54])).
% 0.21/0.38 thf(f81,plain,(
% 0.21/0.38 ( ! [X0 : $i] : ((((irel @ X0 @ X0)) = $true)) )),
% 0.21/0.38 inference(constrained_superposition,[],[f25,f54])).
% 0.21/0.38 thf(f84,plain,(
% 0.21/0.38 ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((Y0 @ Y5) | (~ (irel @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (Y1 @ Y6)))))) | (~ (irel @ Y4 @ Y5))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((~ (irel @ Y3 @ Y5)) | (~ (irel @ Y5 @ Y4))) | (Y1 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6)))))))))))) | (~ (irel @ Y2 @ Y3))))))))))) @ sK1)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8))))) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y4))) | (~ (irel @ Y4 @ Y5))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y7)) | (~ (irel @ Y6 @ Y3))) | (~ (irel @ Y3 @ Y7)))) | (~ (irel @ Y2 @ Y6))))))))))))))))))) @ sK1)))),
% 0.21/0.38 inference(negative_extensionality,[],[f40])).
% 0.21/0.38 thf(f85,plain,(
% 0.21/0.38 ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((((((~ (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y3 @ Y7)) | (sK1 @ Y7))))) | (Y0 @ Y4)) | (~ (irel @ Y5 @ Y3))) | (~ (irel @ Y3 @ Y4))) & ((((~ (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y7)) | (Y0 @ Y7))))) | (sK1 @ Y6)) | (~ (irel @ Y5 @ Y2))) | (~ (irel @ Y2 @ Y6)))) | (~ (irel @ Y1 @ Y5))))))))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((sK1 @ Y4) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5) | (~ (irel @ Y4 @ Y5)))))))))))) | (~ (irel @ Y1 @ Y2))))))))))),
% 0.21/0.38 inference(beta-eta_normalization,[],[f84])).
% 0.21/0.38 thf(f86,plain,(
% 0.21/0.38 ((((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((((((~ (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y3 @ Y7)) | (sK1 @ Y7))))) | (Y0 @ Y4)) | (~ (irel @ Y5 @ Y3))) | (~ (irel @ Y3 @ Y4))) & ((((~ (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y7)) | (Y0 @ Y7))))) | (sK1 @ Y6)) | (~ (irel @ Y5 @ Y2))) | (~ (irel @ Y2 @ Y6)))) | (~ (irel @ Y1 @ Y5))))))))))))))))) @ sK2)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((sK1 @ Y4) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5) | (~ (irel @ Y4 @ Y5)))))))))))) | (~ (irel @ Y1 @ Y2))))))))) @ sK2)))),
% 0.21/0.38 inference(negative_extensionality,[],[f85])).
% 0.21/0.38 thf(f87,plain,(
% 0.21/0.38 ((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y2 @ Y6)) | (sK1 @ Y6))))) | (sK2 @ Y3)) | (~ (irel @ Y4 @ Y2))) | (~ (irel @ Y2 @ Y3))) & ((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y1 @ Y6)) | (sK2 @ Y6))))) | (sK1 @ Y5)) | (~ (irel @ Y4 @ Y1))) | (~ (irel @ Y1 @ Y5)))) | (~ (irel @ Y0 @ Y4))))))))))))))) != (^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((sK1 @ Y3) | (~ (irel @ Y1 @ Y2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4)))))) | (~ (irel @ Y2 @ Y3))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (irel @ Y1 @ Y3)) | (~ (irel @ Y3 @ Y2))) | (sK2 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y3 @ Y4)))))))))))) | (~ (irel @ Y0 @ Y1))))))))),
% 0.21/0.38 inference(beta-eta_normalization,[],[f86])).
% 0.21/0.38 thf(f88,plain,(
% 0.21/0.38 ((((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y2 @ Y6)) | (sK1 @ Y6))))) | (sK2 @ Y3)) | (~ (irel @ Y4 @ Y2))) | (~ (irel @ Y2 @ Y3))) & ((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y1 @ Y6)) | (sK2 @ Y6))))) | (sK1 @ Y5)) | (~ (irel @ Y4 @ Y1))) | (~ (irel @ Y1 @ Y5)))) | (~ (irel @ Y0 @ Y4))))))))))))))) @ sK3)) != (((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((sK1 @ Y3) | (~ (irel @ Y1 @ Y2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4)))))) | (~ (irel @ Y2 @ Y3))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (irel @ Y1 @ Y3)) | (~ (irel @ Y3 @ Y2))) | (sK2 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y3 @ Y4)))))))))))) | (~ (irel @ Y0 @ Y1))))))) @ sK3)))),
% 0.21/0.38 inference(negative_extensionality,[],[f87])).
% 0.21/0.38 thf(f89,plain,(
% 0.21/0.38 ((((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((sK1 @ Y3) | (~ (irel @ Y1 @ Y2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4)))))) | (~ (irel @ Y2 @ Y3))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (irel @ Y1 @ Y3)) | (~ (irel @ Y3 @ Y2))) | (sK2 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y3 @ Y4)))))))))))) | (~ (irel @ Y0 @ Y1))))))) @ sK3)) = $true) | ((((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y2 @ Y6)) | (sK1 @ Y6))))) | (sK2 @ Y3)) | (~ (irel @ Y4 @ Y2))) | (~ (irel @ Y2 @ Y3))) & ((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y1 @ Y6)) | (sK2 @ Y6))))) | (sK1 @ Y5)) | (~ (irel @ Y4 @ Y1))) | (~ (irel @ Y1 @ Y5)))) | (~ (irel @ Y0 @ Y4))))))))))))))) @ sK3)) = $true)),
% 0.21/0.38 inference(xor_proxy_clausification,[],[f88])).
% 0.21/0.38 thf(f90,plain,(
% 0.21/0.38 ($false = (((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((sK1 @ Y3) | (~ (irel @ Y1 @ Y2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4)))))) | (~ (irel @ Y2 @ Y3))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (irel @ Y1 @ Y3)) | (~ (irel @ Y3 @ Y2))) | (sK2 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y3 @ Y4)))))))))))) | (~ (irel @ Y0 @ Y1))))))) @ sK3))) | ($false = (((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y2 @ Y6)) | (sK1 @ Y6))))) | (sK2 @ Y3)) | (~ (irel @ Y4 @ Y2))) | (~ (irel @ Y2 @ Y3))) & ((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y1 @ Y6)) | (sK2 @ Y6))))) | (sK1 @ Y5)) | (~ (irel @ Y4 @ Y1))) | (~ (irel @ Y1 @ Y5)))) | (~ (irel @ Y0 @ Y4))))))))))))))) @ sK3)))),
% 0.21/0.38 inference(xor_proxy_clausification,[],[f88])).
% 0.21/0.38 thf(f91,plain,(
% 0.21/0.38 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK1 @ Y2) | (~ (irel @ Y0 @ Y1))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3)))))) | (~ (irel @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y0 @ Y2)) | (~ (irel @ Y2 @ Y1))) | (sK2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) | (~ (irel @ sK3 @ Y0)))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y1 @ Y5)) | (sK1 @ Y5))))) | (sK2 @ Y2)) | (~ (irel @ Y3 @ Y1))) | (~ (irel @ Y1 @ Y2))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y4)) | (~ (irel @ Y3 @ Y0))) | (~ (irel @ Y0 @ Y4)))) | (~ (irel @ sK3 @ Y3))))))))))))))))),
% 0.21/0.38 inference(beta-eta_normalization,[],[f90])).
% 0.21/0.38 thf(f92,plain,(
% 0.21/0.38 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y1 @ Y5)) | (sK1 @ Y5))))) | (sK2 @ Y2)) | (~ (irel @ Y3 @ Y1))) | (~ (irel @ Y1 @ Y2))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y4)) | (~ (irel @ Y3 @ Y0))) | (~ (irel @ Y0 @ Y4)))) | (~ (irel @ sK3 @ Y3)))))))))))))))) | (((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK1 @ Y2) | (~ (irel @ Y0 @ Y1))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3)))))) | (~ (irel @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y0 @ Y2)) | (~ (irel @ Y2 @ Y1))) | (sK2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) | (~ (irel @ sK3 @ Y0)))))) = $true)),
% 0.21/0.38 inference(not_proxy_clausification,[],[f91])).
% 0.21/0.38 thf(f93,plain,(
% 0.21/0.38 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y1 @ Y5)) | (sK1 @ Y5))))) | (sK2 @ Y2)) | (~ (irel @ Y3 @ Y1))) | (~ (irel @ Y1 @ Y2))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y4)) | (~ (irel @ Y3 @ Y0))) | (~ (irel @ Y0 @ Y4)))) | (~ (irel @ sK3 @ Y3))))))))))))))) | (((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK1 @ Y2) | (~ (irel @ Y0 @ Y1))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3)))))) | (~ (irel @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y0 @ Y2)) | (~ (irel @ Y2 @ Y1))) | (sK2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) | (~ (irel @ sK3 @ Y0)))))) = $true)),
% 0.21/0.38 inference(not_proxy_clausification,[],[f92])).
% 0.21/0.38 thf(f94,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK1 @ Y2) | (~ (irel @ Y0 @ Y1))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3)))))) | (~ (irel @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y0 @ Y2)) | (~ (irel @ Y2 @ Y1))) | (sK2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) | (~ (irel @ sK3 @ Y0)))))) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y1 @ Y5)) | (sK1 @ Y5))))) | (sK2 @ Y2)) | (~ (irel @ Y3 @ Y1))) | (~ (irel @ Y1 @ Y2))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y4)) | (~ (irel @ Y3 @ Y0))) | (~ (irel @ Y0 @ Y4)))) | (~ (irel @ sK3 @ Y3)))))))))))) @ X1)) = $true)) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f93])).
% 0.21/0.38 thf(f95,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK1 @ Y2) | (~ (irel @ Y0 @ Y1))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3)))))) | (~ (irel @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y0 @ Y2)) | (~ (irel @ Y2 @ Y1))) | (sK2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) | (~ (irel @ sK3 @ Y0)))) @ X2))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y1 @ Y5)) | (sK1 @ Y5))))) | (sK2 @ Y2)) | (~ (irel @ Y3 @ Y1))) | (~ (irel @ Y1 @ Y2))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y4)) | (~ (irel @ Y3 @ Y0))) | (~ (irel @ Y0 @ Y4)))) | (~ (irel @ sK3 @ Y3)))))))))))) @ X1)) = $true)) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f94])).
% 0.21/0.38 thf(f96,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y0 @ Y4)) | (sK1 @ Y4))))) | (sK2 @ Y1)) | (~ (irel @ Y2 @ Y0))) | (~ (irel @ Y0 @ Y1))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X1 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ X1))) | (~ (irel @ X1 @ Y3)))) | (~ (irel @ sK3 @ Y2))))))))))))) | ($true = ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (irel @ X2 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ X2 @ Y1)) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))))) | (~ (irel @ sK3 @ X2)))))) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f95])).
% 0.21/0.38 thf(f97,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (irel @ X2 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ X2 @ Y1)) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))))) | (~ (irel @ sK3 @ X2))))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y0 @ Y4)) | (sK1 @ Y4))))) | (sK2 @ Y1)) | (~ (irel @ Y2 @ Y0))) | (~ (irel @ Y0 @ Y1))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X1 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ X1))) | (~ (irel @ X1 @ Y3)))) | (~ (irel @ sK3 @ Y2)))))))))) @ X3)) = $true)) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f96])).
% 0.21/0.38 thf(f98,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (irel @ X2 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ X2 @ Y1)) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))))))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y0 @ Y4)) | (sK1 @ Y4))))) | (sK2 @ Y1)) | (~ (irel @ Y2 @ Y0))) | (~ (irel @ Y0 @ Y1))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X1 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ X1))) | (~ (irel @ X1 @ Y3)))) | (~ (irel @ sK3 @ Y2)))))))))) @ X3)) = $true) | ($true = ((~ (irel @ sK3 @ X2))))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f97])).
% 0.21/0.38 thf(f99,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ X2 @ Y1)) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))))) = $true) | ($true = ((~ (irel @ sK3 @ X2)))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y0 @ Y4)) | (sK1 @ Y4))))) | (sK2 @ Y1)) | (~ (irel @ Y2 @ Y0))) | (~ (irel @ Y0 @ Y1))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X1 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ X1))) | (~ (irel @ X1 @ Y3)))) | (~ (irel @ sK3 @ Y2)))))))))) @ X3)) = $true)) )),
% 0.21/0.38 inference(and_proxy_clausification,[],[f98])).
% 0.21/0.38 thf(f100,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((~ (irel @ sK3 @ X2)))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y0 @ Y4)) | (sK1 @ Y4))))) | (sK2 @ Y1)) | (~ (irel @ Y2 @ Y0))) | (~ (irel @ Y0 @ Y1))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X1 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ X1))) | (~ (irel @ X1 @ Y3)))) | (~ (irel @ sK3 @ Y2)))))))))) @ X3)) = $true) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (irel @ X2 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ Y0 @ Y1)))))))) = $true)) )),
% 0.21/0.38 inference(and_proxy_clausification,[],[f98])).
% 0.21/0.38 thf(f101,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((irel @ sK3 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (irel @ X2 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ Y0 @ Y1)))))))) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y0 @ Y4)) | (sK1 @ Y4))))) | (sK2 @ Y1)) | (~ (irel @ Y2 @ Y0))) | (~ (irel @ Y0 @ Y1))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X1 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ X1))) | (~ (irel @ X1 @ Y3)))) | (~ (irel @ sK3 @ Y2)))))))))) @ X3)) = $true)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f100])).
% 0.21/0.38 thf(f102,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y0 @ Y4)) | (sK1 @ Y4))))) | (sK2 @ Y1)) | (~ (irel @ Y2 @ Y0))) | (~ (irel @ Y0 @ Y1))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X1 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ X1))) | (~ (irel @ X1 @ Y3)))) | (~ (irel @ sK3 @ Y2)))))))))) @ X3)) = $true) | ($false = ((irel @ sK3 @ X2))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (irel @ X2 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ Y0 @ Y1)))))) @ X4)) = $true)) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f101])).
% 0.21/0.38 thf(f103,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((((sK1 @ Y0) | (~ (irel @ X2 @ X4))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X4 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ X4 @ Y0))))))) | ($false = ((irel @ sK3 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X3 @ Y3)) | (sK1 @ Y3))))) | (sK2 @ Y0)) | (~ (irel @ Y1 @ X3))) | (~ (irel @ X3 @ Y0))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ Y2)) | (~ (irel @ Y1 @ X1))) | (~ (irel @ X1 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))))) = $true)) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f102])).
% 0.21/0.38 thf(f104,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (((((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (irel @ X2 @ X4))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X4 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ X4 @ Y0)))) @ X5)) = $true) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X3 @ Y3)) | (sK1 @ Y3))))) | (sK2 @ Y0)) | (~ (irel @ Y1 @ X3))) | (~ (irel @ X3 @ Y0))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ Y2)) | (~ (irel @ Y1 @ X1))) | (~ (irel @ X1 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))))) = $true) | ($false = ((irel @ sK3 @ X2)))) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f103])).
% 0.21/0.38 thf(f105,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X3 @ Y3)) | (sK1 @ Y3))))) | (sK2 @ Y0)) | (~ (irel @ Y1 @ X3))) | (~ (irel @ X3 @ Y0))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ Y2)) | (~ (irel @ Y1 @ X1))) | (~ (irel @ X1 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))) @ X6)) = $true) | ($false = ((irel @ sK3 @ X2))) | ((((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (irel @ X2 @ X4))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X4 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ X4 @ Y0)))) @ X5)) = $true)) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f104])).
% 0.21/0.38 thf(f106,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((((((sK1 @ X5) | (~ (irel @ X2 @ X4))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X4 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ X4 @ X5)))) = $true) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X6)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X6))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))) = $true) | ($false = ((irel @ sK3 @ X2)))) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f105])).
% 0.21/0.38 thf(f107,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | (((~ (irel @ X4 @ X5))) = $true) | ($true = ((((sK1 @ X5) | (~ (irel @ X2 @ X4))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X4 @ Y0)) | (sK2 @ Y0)))))))) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X6)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X6))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f106])).
% 0.21/0.38 thf(f108,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : ((((irel @ X4 @ X5)) = $false) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X6)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X6))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))) = $true) | ($true = ((((sK1 @ X5) | (~ (irel @ X2 @ X4))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X4 @ Y0)) | (sK2 @ Y0)))))))) | ($false = ((irel @ sK3 @ X2)))) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f107])).
% 0.21/0.38 thf(f109,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X6)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X6))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X7)) = $true) | ($true = ((((sK1 @ X5) | (~ (irel @ X2 @ X4))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X4 @ Y0)) | (sK2 @ Y0)))))))) | ($false = ((irel @ sK3 @ X2))) | (((irel @ X4 @ X5)) = $false)) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f108])).
% 0.21/0.38 thf(f110,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X6)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X6))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X7)) = $true) | (((irel @ X4 @ X5)) = $false) | ((((sK1 @ X5) | (~ (irel @ X2 @ X4)))) = $true) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X4 @ Y0)) | (sK2 @ Y0)))))))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f109])).
% 0.21/0.38 thf(f111,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X4 @ Y0)) | (sK2 @ Y0))))))) | (((irel @ X4 @ X5)) = $false) | (((sK1 @ X5)) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X6)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X6))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X7)) = $true) | ($false = ((irel @ sK3 @ X2))) | (((~ (irel @ X2 @ X4))) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f110])).
% 0.21/0.38 thf(f112,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK1 @ X5)) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X4 @ Y0)) | (sK2 @ Y0)))))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X6)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X6))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X7)) = $true) | ($false = ((irel @ sK3 @ X2))) | (((~ (irel @ X2 @ X4))) = $true) | (((irel @ X4 @ X5)) = $false)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f111])).
% 0.21/0.38 thf(f113,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((irel @ X4 @ X5)) = $false) | (((sK1 @ X5)) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X6)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X6))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X7)) = $true) | (((~ (irel @ X2 @ X4))) = $true) | ($false = (((^[Y0 : $i]: ((~ (irel @ X4 @ Y0)) | (sK2 @ Y0))) @ (sK4 @ X4)))) | ($false = ((irel @ sK3 @ X2)))) )),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f112])).
% 0.21/0.38 thf(f114,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK1 @ X5)) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X6)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X6))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X7)) = $true) | (((irel @ X4 @ X5)) = $false) | ($false = ((irel @ sK3 @ X2))) | ($false = ((irel @ X2 @ X4))) | ($false = (((^[Y0 : $i]: ((~ (irel @ X4 @ Y0)) | (sK2 @ Y0))) @ (sK4 @ X4))))) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f113])).
% 0.21/0.38 thf(f115,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | (((irel @ X4 @ X5)) = $false) | ($false = ((irel @ X2 @ X4))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ X6)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X3 @ X6))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X1 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ X7 @ X1))) | (~ (irel @ X1 @ Y0)))) | (~ (irel @ sK3 @ X7))))))) | (((sK1 @ X5)) = $true) | ($false = (((~ (irel @ X4 @ (sK4 @ X4))) | (sK2 @ (sK4 @ X4)))))) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f114])).
% 0.21/0.38 thf(f116,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((((^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ X6)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X3 @ X6))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X1 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ X7 @ X1))) | (~ (irel @ X1 @ Y0)))) | (~ (irel @ sK3 @ X7)))) @ X8)) = $true) | (((irel @ X4 @ X5)) = $false) | ($false = ((irel @ sK3 @ X2))) | (((sK1 @ X5)) = $true) | ($false = ((irel @ X2 @ X4))) | ($false = (((~ (irel @ X4 @ (sK4 @ X4))) | (sK2 @ (sK4 @ X4)))))) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f115])).
% 0.21/0.38 thf(f117,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | ($false = ((irel @ X2 @ X4))) | (((irel @ X4 @ X5)) = $false) | ($false = ((sK2 @ (sK4 @ X4)))) | ((((^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ X6)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X3 @ X6))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X1 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ X7 @ X1))) | (~ (irel @ X1 @ Y0)))) | (~ (irel @ sK3 @ X7)))) @ X8)) = $true) | (((sK1 @ X5)) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f116])).
% 0.21/0.38 thf(f148,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X2 @ X4))) | ($false = ((irel @ sK3 @ X2))) | (((sK1 @ X5)) = $true) | (((irel @ X4 @ X5)) = $false) | ($false = ((sK2 @ (sK4 @ X4)))) | ((((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ X6)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X3 @ X6))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X8)) | (~ (irel @ X7 @ X1))) | (~ (irel @ X1 @ X8)))) | (~ (irel @ sK3 @ X7)))) = $true)) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f117])).
% 0.21/0.38 thf(f149,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ X6)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X3 @ X6))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X8)) | (~ (irel @ X7 @ X1))) | (~ (irel @ X1 @ X8))))) = $true) | ($false = ((irel @ sK3 @ X2))) | ($false = ((sK2 @ (sK4 @ X4)))) | (((irel @ X4 @ X5)) = $false) | (((~ (irel @ sK3 @ X7))) = $true) | ($false = ((irel @ X2 @ X4))) | (((sK1 @ X5)) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f148])).
% 0.21/0.38 thf(f150,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((irel @ X4 @ X5)) = $false) | ($false = ((irel @ X2 @ X4))) | (((sK1 @ X5)) = $true) | ($false = ((sK2 @ (sK4 @ X4)))) | (((~ (irel @ sK3 @ X7))) = $true) | ($false = ((irel @ sK3 @ X2))) | ((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X8)) | (~ (irel @ X7 @ X1))) | (~ (irel @ X1 @ X8)))) = $true)) )),
% 0.21/0.38 inference(and_proxy_clausification,[],[f149])).
% 0.21/0.38 thf(f164,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((sK2 @ (sK4 @ X4)))) | (((irel @ X4 @ X5)) = $false) | ($false = ((irel @ X2 @ X4))) | ((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X8)) | (~ (irel @ X7 @ X1))) | (~ (irel @ X1 @ X8)))) = $true) | ($false = ((irel @ sK3 @ X7))) | ($false = ((irel @ sK3 @ X2))) | (((sK1 @ X5)) = $true)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f150])).
% 0.21/0.38 thf(f165,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((irel @ X4 @ X5)) = $false) | (((~ (irel @ X1 @ X8))) = $true) | ($false = ((irel @ X2 @ X4))) | (((sK1 @ X5)) = $true) | ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X8)) | (~ (irel @ X7 @ X1))))) | ($false = ((sK2 @ (sK4 @ X4)))) | ($false = ((irel @ sK3 @ X2))) | ($false = ((irel @ sK3 @ X7)))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f164])).
% 0.21/0.38 thf(f166,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X7))) | (((irel @ X4 @ X5)) = $false) | ($false = ((irel @ X2 @ X4))) | ($false = ((irel @ sK3 @ X2))) | ($false = ((irel @ X1 @ X8))) | ($false = ((sK2 @ (sK4 @ X4)))) | ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X8)) | (~ (irel @ X7 @ X1))))) | (((sK1 @ X5)) = $true)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f165])).
% 0.21/0.38 thf(f167,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((irel @ X4 @ X5)) = $false) | ($false = ((irel @ X2 @ X4))) | ($false = ((sK2 @ (sK4 @ X4)))) | ($false = ((irel @ sK3 @ X2))) | ($false = ((irel @ sK3 @ X7))) | (((sK1 @ X5)) = $true) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X8)))) | ($false = ((irel @ X1 @ X8))) | (((~ (irel @ X7 @ X1))) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f166])).
% 0.21/0.38 thf(f168,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK1 @ X8)) = $true) | (((irel @ X4 @ X5)) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0)))))) = $true) | (((~ (irel @ X7 @ X1))) = $true) | ($false = ((sK2 @ (sK4 @ X4)))) | ($false = ((irel @ sK3 @ X2))) | ($false = ((irel @ X2 @ X4))) | ($false = ((irel @ X1 @ X8))) | ($false = ((irel @ sK3 @ X7))) | (((sK1 @ X5)) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f167])).
% 0.21/0.38 thf(f169,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | ($false = ((irel @ X1 @ X8))) | (((irel @ X4 @ X5)) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0)))))) | (((sK1 @ X8)) = $true) | ($false = ((irel @ X2 @ X4))) | ($false = ((irel @ sK3 @ X7))) | (((~ (irel @ X7 @ X1))) = $true) | (((sK1 @ X5)) = $true) | ($false = ((sK2 @ (sK4 @ X4))))) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f168])).
% 0.21/0.38 thf(f170,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X1 @ X8))) | (((~ (irel @ X7 @ X1))) = $true) | ($false = ((irel @ sK3 @ X7))) | ($false = ((irel @ X2 @ X4))) | (((sK1 @ X5)) = $true) | ($false = (((^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))) @ (sK8 @ X1)))) | (((sK1 @ X8)) = $true) | (((irel @ X4 @ X5)) = $false) | ($false = ((sK2 @ (sK4 @ X4)))) | ($false = ((irel @ sK3 @ X2)))) )),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f169])).
% 0.21/0.38 thf(f171,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK1 @ X8)) = $true) | ($false = ((irel @ X7 @ X1))) | (((irel @ X4 @ X5)) = $false) | ($false = ((irel @ X2 @ X4))) | ($false = (((^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))) @ (sK8 @ X1)))) | ($false = ((irel @ sK3 @ X2))) | (((sK1 @ X5)) = $true) | ($false = ((sK2 @ (sK4 @ X4)))) | ($false = ((irel @ sK3 @ X7))) | ($false = ((irel @ X1 @ X8)))) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f170])).
% 0.21/0.38 thf(f172,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X1 @ X8))) | (((irel @ X4 @ X5)) = $false) | ($false = ((sK2 @ (sK4 @ X4)))) | (((sK1 @ X8)) = $true) | ($false = ((irel @ sK3 @ X7))) | ($false = (((~ (irel @ X1 @ (sK8 @ X1))) | (sK2 @ (sK8 @ X1))))) | ($false = ((irel @ sK3 @ X2))) | ($false = ((irel @ X7 @ X1))) | ($false = ((irel @ X2 @ X4))) | (((sK1 @ X5)) = $true)) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f171])).
% 0.21/0.38 thf(f173,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X7 @ X1))) | (((irel @ X4 @ X5)) = $false) | (((sK1 @ X8)) = $true) | ($false = ((irel @ sK3 @ X2))) | ($false = ((sK2 @ (sK4 @ X4)))) | ($false = ((sK2 @ (sK8 @ X1)))) | (((sK1 @ X5)) = $true) | ($false = ((irel @ sK3 @ X7))) | ($false = ((irel @ X2 @ X4))) | ($false = ((irel @ X1 @ X8)))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f172])).
% 0.21/0.38 thf(f176,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ X2 @ Y1)) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) @ X4)) = $true) | ($true = ((~ (irel @ sK3 @ X2)))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y0 @ Y4)) | (sK1 @ Y4))))) | (sK2 @ Y1)) | (~ (irel @ Y2 @ Y0))) | (~ (irel @ Y0 @ Y1))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X1 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ X1))) | (~ (irel @ X1 @ Y3)))) | (~ (irel @ sK3 @ Y2)))))))))) @ X3)) = $true)) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f99])).
% 0.21/0.38 thf(f177,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK3 @ X2))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y0 @ Y4)) | (sK1 @ Y4))))) | (sK2 @ Y1)) | (~ (irel @ Y2 @ Y0))) | (~ (irel @ Y0 @ Y1))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X1 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ X1))) | (~ (irel @ X1 @ Y3)))) | (~ (irel @ sK3 @ Y2)))))))))) @ X3)) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ X2 @ Y1)) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) @ X4)) = $true)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f176])).
% 0.21/0.38 thf(f178,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X3 @ Y3)) | (sK1 @ Y3))))) | (sK2 @ Y0)) | (~ (irel @ Y1 @ X3))) | (~ (irel @ X3 @ Y0))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ Y2)) | (~ (irel @ Y1 @ X1))) | (~ (irel @ X1 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))))) = $true) | ($false = ((irel @ sK3 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ X2 @ Y0)) | (~ (irel @ Y0 @ X4))) | (sK2 @ X4)) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))))))) = $true)) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f177])).
% 0.21/0.38 thf(f179,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ X2 @ Y0)) | (~ (irel @ Y0 @ X4))) | (sK2 @ X4)) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))))))) = $true) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X3 @ Y3)) | (sK1 @ Y3))))) | (sK2 @ Y0)) | (~ (irel @ Y1 @ X3))) | (~ (irel @ X3 @ Y0))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ Y2)) | (~ (irel @ Y1 @ X1))) | (~ (irel @ X1 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))) @ X5))) | ($false = ((irel @ sK3 @ X2)))) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f178])).
% 0.21/0.38 thf(f180,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: ((((~ (irel @ X2 @ Y0)) | (~ (irel @ Y0 @ X4))) | (sK2 @ X4)) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))))) @ X6))) | ($false = ((irel @ sK3 @ X2))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X3 @ Y3)) | (sK1 @ Y3))))) | (sK2 @ Y0)) | (~ (irel @ Y1 @ X3))) | (~ (irel @ X3 @ Y0))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ Y2)) | (~ (irel @ Y1 @ X1))) | (~ (irel @ X1 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))) @ X5)))) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f179])).
% 0.21/0.38 thf(f181,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = (((((~ (irel @ X2 @ X6)) | (~ (irel @ X6 @ X4))) | (sK2 @ X4)) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0))))))))) | ($false = ((irel @ sK3 @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X5)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X5))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))))) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f180])).
% 0.21/0.38 thf(f182,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((((~ (irel @ X2 @ X6)) | (~ (irel @ X6 @ X4))) | (sK2 @ X4)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X5)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X5))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))) | ($false = ((irel @ sK3 @ X2))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0))))))))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f181])).
% 0.21/0.38 thf(f183,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0)))))))) | (((sK2 @ X4)) = $true) | ($true = (((~ (irel @ X2 @ X6)) | (~ (irel @ X6 @ X4))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X5)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X5))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f182])).
% 0.21/0.38 thf(f184,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | (((sK2 @ X4)) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0))))))) | ($true = (((~ (irel @ X2 @ X6)) | (~ (irel @ X6 @ X4))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X5)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X5))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))))) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f183])).
% 0.21/0.38 thf(f185,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | (((sK2 @ X4)) = $true) | ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0)))) @ (sK9 @ X6)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X5)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X5))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))) | ($true = (((~ (irel @ X2 @ X6)) | (~ (irel @ X6 @ X4)))))) )),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f184])).
% 0.21/0.38 thf(f186,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X5)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X5))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X7)) = $true) | (((sK2 @ X4)) = $true) | ($false = ((irel @ sK3 @ X2))) | ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0)))) @ (sK9 @ X6)))) | ($true = (((~ (irel @ X2 @ X6)) | (~ (irel @ X6 @ X4)))))) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f185])).
% 0.21/0.38 thf(f187,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X5)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X5))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X7)) = $true) | (((sK2 @ X4)) = $true) | (((~ (irel @ X2 @ X6))) = $true) | ($false = ((irel @ sK3 @ X2))) | (((~ (irel @ X6 @ X4))) = $true) | ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0)))) @ (sK9 @ X6))))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f186])).
% 0.21/0.38 thf(f188,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X5)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X5))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X7)) = $true) | (((~ (irel @ X6 @ X4))) = $true) | ($false = ((irel @ X2 @ X6))) | ($false = ((irel @ sK3 @ X2))) | (((sK2 @ X4)) = $true) | ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0)))) @ (sK9 @ X6))))) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f187])).
% 0.21/0.38 thf(f189,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X2 @ X6))) | ($false = ((irel @ sK3 @ X2))) | ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0)))) @ (sK9 @ X6)))) | (((sK2 @ X4)) = $true) | ($false = ((irel @ X6 @ X4))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X3 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ X5)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X3 @ X5))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X1 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ X1))) | (~ (irel @ X1 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X7)) = $true)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f188])).
% 0.21/0.38 thf(f190,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | (((sK2 @ X4)) = $true) | ($false = ((irel @ X6 @ X4))) | ($false = ((irel @ X2 @ X6))) | (((!! @ $i @ (^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ X5)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X3 @ X5))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X1 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ X7 @ X1))) | (~ (irel @ X1 @ Y0)))) | (~ (irel @ sK3 @ X7)))))) = $true) | ($false = (((sK1 @ (sK9 @ X6)) | (~ (irel @ X6 @ (sK9 @ X6))))))) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f189])).
% 0.21/0.38 thf(f191,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | (((sK2 @ X4)) = $true) | ($false = ((irel @ X6 @ X4))) | ($true = (((^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ X5)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X3 @ X5))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X1 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ X7 @ X1))) | (~ (irel @ X1 @ Y0)))) | (~ (irel @ sK3 @ X7)))) @ X8))) | ($false = (((sK1 @ (sK9 @ X6)) | (~ (irel @ X6 @ (sK9 @ X6)))))) | ($false = ((irel @ X2 @ X6)))) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f190])).
% 0.21/0.38 thf(f193,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | (((sK2 @ X4)) = $true) | ($false = ((irel @ X6 @ X4))) | ($false = ((irel @ X2 @ X6))) | (((sK1 @ (sK9 @ X6))) = $false) | ($true = (((^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ X5)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X3 @ X5))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X1 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ X7 @ X1))) | (~ (irel @ X1 @ Y0)))) | (~ (irel @ sK3 @ X7)))) @ X8)))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f191])).
% 0.21/0.38 thf(f194,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK2 @ X4)) = $true) | ((((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ X5)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X3 @ X5))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X8)) | (~ (irel @ X7 @ X1))) | (~ (irel @ X1 @ X8)))) | (~ (irel @ sK3 @ X7)))) = $true) | ($false = ((irel @ sK3 @ X2))) | (((sK1 @ (sK9 @ X6))) = $false) | ($false = ((irel @ X2 @ X6))) | ($false = ((irel @ X6 @ X4)))) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f193])).
% 0.21/0.38 thf(f195,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK2 @ X4)) = $true) | ($false = ((irel @ X6 @ X4))) | (((~ (irel @ sK3 @ X7))) = $true) | (((sK1 @ (sK9 @ X6))) = $false) | ($false = ((irel @ sK3 @ X2))) | (((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ X5)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X3 @ X5))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X8)) | (~ (irel @ X7 @ X1))) | (~ (irel @ X1 @ X8))))) = $true) | ($false = ((irel @ X2 @ X6)))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f194])).
% 0.21/0.38 thf(f196,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X6 @ X4))) | ($false = ((irel @ X2 @ X6))) | ($false = ((irel @ sK3 @ X2))) | (((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ X5)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X3 @ X5))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X8)) | (~ (irel @ X7 @ X1))) | (~ (irel @ X1 @ X8))))) = $true) | (((sK2 @ X4)) = $true) | (((sK1 @ (sK9 @ X6))) = $false) | ($false = ((irel @ sK3 @ X7)))) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f195])).
% 0.21/0.38 thf(f198,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X7))) | (((sK1 @ (sK9 @ X6))) = $false) | ($false = ((irel @ X2 @ X6))) | ((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ X5)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X3 @ X5)))) = $true) | ($false = ((irel @ sK3 @ X2))) | (((sK2 @ X4)) = $true) | ($false = ((irel @ X6 @ X4)))) )),
% 0.21/0.38 inference(and_proxy_clausification,[],[f196])).
% 0.21/0.38 thf(f199,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X2 @ X6))) | ($false = ((irel @ sK3 @ X7))) | ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ X5)) | (~ (irel @ X7 @ X3))))) | (((sK2 @ X4)) = $true) | ($false = ((irel @ X6 @ X4))) | (((sK1 @ (sK9 @ X6))) = $false) | (((~ (irel @ X3 @ X5))) = $true) | ($false = ((irel @ sK3 @ X2)))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f198])).
% 0.21/0.38 thf(f200,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ X5))) = $true) | (((sK2 @ X4)) = $true) | (((~ (irel @ X7 @ X3))) = $true) | (((sK1 @ (sK9 @ X6))) = $false) | (((~ (irel @ X3 @ X5))) = $true) | ($false = ((irel @ X2 @ X6))) | ($false = ((irel @ X6 @ X4))) | ($false = ((irel @ sK3 @ X7)))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f199])).
% 0.21/0.38 thf(f201,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0)))))) = $true) | (((sK1 @ (sK9 @ X6))) = $false) | ($true = ((sK2 @ X5))) | (((~ (irel @ X3 @ X5))) = $true) | ($false = ((irel @ X2 @ X6))) | ($false = ((irel @ sK3 @ X2))) | (((~ (irel @ X7 @ X3))) = $true) | (((sK2 @ X4)) = $true) | ($false = ((irel @ X6 @ X4))) | ($false = ((irel @ sK3 @ X7)))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f200])).
% 0.21/0.38 thf(f202,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((sK2 @ X5))) | ($false = ((irel @ sK3 @ X7))) | (((~ (irel @ X7 @ X3))) = $true) | (((~ (irel @ X3 @ X5))) = $true) | ($false = ((irel @ sK3 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) = $false) | ($false = ((irel @ X2 @ X6))) | (((sK1 @ (sK9 @ X6))) = $false) | ($false = ((irel @ X6 @ X4))) | (((sK2 @ X4)) = $true)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f201])).
% 0.21/0.38 thf(f203,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((irel @ X7 @ X3)) = $false) | ($false = ((irel @ sK3 @ X7))) | (((sK1 @ (sK9 @ X6))) = $false) | ($false = ((irel @ X6 @ X4))) | (((~ (irel @ X3 @ X5))) = $true) | ($false = ((irel @ sK3 @ X2))) | (((sK2 @ X4)) = $true) | ($false = ((irel @ X2 @ X6))) | ($true = ((sK2 @ X5))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) = $false)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f202])).
% 0.21/0.38 thf(f204,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | (((sK2 @ X4)) = $true) | ($false = ((irel @ X6 @ X4))) | ($false = ((irel @ X3 @ X5))) | (((irel @ X7 @ X3)) = $false) | ($false = ((irel @ X2 @ X6))) | ($true = ((sK2 @ X5))) | ($false = ((irel @ sK3 @ X7))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) = $false) | (((sK1 @ (sK9 @ X6))) = $false)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f203])).
% 0.21/0.38 thf(f205,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | ($false = ((irel @ X2 @ X6))) | ($false = ((irel @ sK3 @ X7))) | ($false = ((irel @ X6 @ X4))) | (((sK1 @ (sK9 @ X6))) = $false) | ($true = ((sK2 @ X5))) | (((irel @ X7 @ X3)) = $false) | (((sK2 @ X4)) = $true) | ($false = ((irel @ X3 @ X5))) | ($false = (((^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))) @ (sK10 @ X3))))) )),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f204])).
% 0.21/0.38 thf(f206,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | ($false = ((irel @ X6 @ X4))) | (((sK2 @ X4)) = $true) | ($false = ((irel @ X3 @ X5))) | ($false = (((~ (irel @ X3 @ (sK10 @ X3))) | (sK1 @ (sK10 @ X3))))) | ($false = ((irel @ X2 @ X6))) | (((sK1 @ (sK9 @ X6))) = $false) | ($false = ((irel @ sK3 @ X7))) | ($true = ((sK2 @ X5))) | (((irel @ X7 @ X3)) = $false)) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f205])).
% 0.21/0.38 thf(f207,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK1 @ (sK9 @ X6))) = $false) | ($false = ((irel @ X2 @ X6))) | ($false = ((sK1 @ (sK10 @ X3)))) | (((irel @ X7 @ X3)) = $false) | (((sK2 @ X4)) = $true) | ($true = ((sK2 @ X5))) | ($false = ((irel @ X3 @ X5))) | ($false = ((irel @ sK3 @ X2))) | ($false = ((irel @ sK3 @ X7))) | ($false = ((irel @ X6 @ X4)))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f206])).
% 0.21/0.38 thf(f249,plain,(
% 0.21/0.38 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y1 @ Y5)) | (sK1 @ Y5))))) | (sK2 @ Y2)) | (~ (irel @ Y3 @ Y1))) | (~ (irel @ Y1 @ Y2))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y4)) | (~ (irel @ Y3 @ Y0))) | (~ (irel @ Y0 @ Y4)))) | (~ (irel @ sK3 @ Y3)))))))))))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK1 @ Y2) | (~ (irel @ Y0 @ Y1))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3)))))) | (~ (irel @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y0 @ Y2)) | (~ (irel @ Y2 @ Y1))) | (sK2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) | (~ (irel @ sK3 @ Y0))))))))),
% 0.21/0.38 inference(beta-eta_normalization,[],[f89])).
% 0.21/0.38 thf(f250,plain,(
% 0.21/0.38 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK1 @ Y2) | (~ (irel @ Y0 @ Y1))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3)))))) | (~ (irel @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y0 @ Y2)) | (~ (irel @ Y2 @ Y1))) | (sK2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) | (~ (irel @ sK3 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y1 @ Y5)) | (sK1 @ Y5))))) | (sK2 @ Y2)) | (~ (irel @ Y3 @ Y1))) | (~ (irel @ Y1 @ Y2))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y4)) | (~ (irel @ Y3 @ Y0))) | (~ (irel @ Y0 @ Y4)))) | (~ (irel @ sK3 @ Y3)))))))))))))))),
% 0.21/0.38 inference(not_proxy_clausification,[],[f249])).
% 0.21/0.38 thf(f251,plain,(
% 0.21/0.38 ($false = ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK1 @ Y2) | (~ (irel @ Y0 @ Y1))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3)))))) | (~ (irel @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y0 @ Y2)) | (~ (irel @ Y2 @ Y1))) | (sK2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) | (~ (irel @ sK3 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y1 @ Y5)) | (sK1 @ Y5))))) | (sK2 @ Y2)) | (~ (irel @ Y3 @ Y1))) | (~ (irel @ Y1 @ Y2))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y4)) | (~ (irel @ Y3 @ Y0))) | (~ (irel @ Y0 @ Y4)))) | (~ (irel @ sK3 @ Y3)))))))))))))))),
% 0.21/0.38 inference(not_proxy_clausification,[],[f250])).
% 0.21/0.38 thf(f252,plain,(
% 0.21/0.38 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y1 @ Y5)) | (sK1 @ Y5))))) | (sK2 @ Y2)) | (~ (irel @ Y3 @ Y1))) | (~ (irel @ Y1 @ Y2))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y4)) | (~ (irel @ Y3 @ Y0))) | (~ (irel @ Y0 @ Y4)))) | (~ (irel @ sK3 @ Y3))))))))))))))) | ($false = (((^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK1 @ Y2) | (~ (irel @ Y0 @ Y1))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3)))))) | (~ (irel @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y0 @ Y2)) | (~ (irel @ Y2 @ Y1))) | (sK2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) | (~ (irel @ sK3 @ Y0)))) @ sK14)))),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f251])).
% 0.21/0.38 thf(f253,plain,(
% 0.21/0.38 ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y1 @ Y5)) | (sK1 @ Y5))))) | (sK2 @ Y2)) | (~ (irel @ Y3 @ Y1))) | (~ (irel @ Y1 @ Y2))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y4)) | (~ (irel @ Y3 @ Y0))) | (~ (irel @ Y0 @ Y4)))) | (~ (irel @ sK3 @ Y3)))))))))))) @ sK15))) | ($false = (((^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK1 @ Y2) | (~ (irel @ Y0 @ Y1))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3)))))) | (~ (irel @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y0 @ Y2)) | (~ (irel @ Y2 @ Y1))) | (sK2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) | (~ (irel @ sK3 @ Y0)))) @ sK14)))),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f252])).
% 0.21/0.38 thf(f254,plain,(
% 0.21/0.38 ($false = ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (irel @ sK14 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ sK14 @ Y1)) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))))) | (~ (irel @ sK3 @ sK14))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y0 @ Y4)) | (sK1 @ Y4))))) | (sK2 @ Y1)) | (~ (irel @ Y2 @ Y0))) | (~ (irel @ Y0 @ Y1))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ sK15 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ sK15))) | (~ (irel @ sK15 @ Y3)))) | (~ (irel @ sK3 @ Y2)))))))))))))),
% 0.21/0.38 inference(beta-eta_normalization,[],[f253])).
% 0.21/0.38 thf(f256,plain,(
% 0.21/0.38 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (irel @ sK14 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ sK14 @ Y1)) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y0 @ Y4)) | (sK1 @ Y4))))) | (sK2 @ Y1)) | (~ (irel @ Y2 @ Y0))) | (~ (irel @ Y0 @ Y1))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ sK15 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ sK15))) | (~ (irel @ sK15 @ Y3)))) | (~ (irel @ sK3 @ Y2)))))))))))))),
% 0.21/0.38 inference(or_proxy_clausification,[],[f254])).
% 0.21/0.38 thf(f257,plain,(
% 0.21/0.38 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (irel @ sK14 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ Y0 @ Y1)))))))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ sK14 @ Y1)) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y0 @ Y4)) | (sK1 @ Y4))))) | (sK2 @ Y1)) | (~ (irel @ Y2 @ Y0))) | (~ (irel @ Y0 @ Y1))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ sK15 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ sK15))) | (~ (irel @ sK15 @ Y3)))) | (~ (irel @ sK3 @ Y2)))))))))))))),
% 0.21/0.38 inference(and_proxy_clausification,[],[f256])).
% 0.21/0.38 thf(f258,plain,(
% 0.21/0.38 ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (irel @ sK14 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ Y0 @ Y1)))))) @ sK16))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ sK14 @ Y1)) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y0 @ Y4)) | (sK1 @ Y4))))) | (sK2 @ Y1)) | (~ (irel @ Y2 @ Y0))) | (~ (irel @ Y0 @ Y1))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ sK15 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ sK15))) | (~ (irel @ sK15 @ Y3)))) | (~ (irel @ sK3 @ Y2)))))))))))))),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f257])).
% 0.21/0.38 thf(f259,plain,(
% 0.21/0.38 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y0 @ Y4)) | (sK1 @ Y4))))) | (sK2 @ Y1)) | (~ (irel @ Y2 @ Y0))) | (~ (irel @ Y0 @ Y1))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ sK15 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ sK15))) | (~ (irel @ sK15 @ Y3)))) | (~ (irel @ sK3 @ Y2))))))))))))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ sK14 @ Y1)) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) @ sK17))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (irel @ sK14 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ Y0 @ Y1)))))) @ sK16)))),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f258])).
% 0.21/0.38 thf(f260,plain,(
% 0.21/0.38 ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y0 @ Y4)) | (sK1 @ Y4))))) | (sK2 @ Y1)) | (~ (irel @ Y2 @ Y0))) | (~ (irel @ Y0 @ Y1))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ sK15 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ sK15))) | (~ (irel @ sK15 @ Y3)))) | (~ (irel @ sK3 @ Y2)))))))))) @ sK18)) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (irel @ sK14 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ Y0 @ Y1)))))) @ sK16))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ sK14 @ Y1)) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) @ sK17)))),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f259])).
% 0.21/0.38 thf(f261,plain,(
% 0.21/0.38 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ sK18 @ Y3)) | (sK1 @ Y3))))) | (sK2 @ Y0)) | (~ (irel @ Y1 @ sK18))) | (~ (irel @ sK18 @ Y0))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ sK15 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ Y2)) | (~ (irel @ Y1 @ sK15))) | (~ (irel @ sK15 @ Y2)))) | (~ (irel @ sK3 @ Y1))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK14 @ Y0)) | (~ (irel @ Y0 @ sK17))) | (sK2 @ sK17)) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((((sK1 @ Y0) | (~ (irel @ sK14 @ sK16))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK16 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK16 @ Y0)))))))),
% 0.21/0.38 inference(beta-eta_normalization,[],[f260])).
% 0.21/0.38 thf(f262,plain,(
% 0.21/0.38 ($false = ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK14 @ Y0)) | (~ (irel @ Y0 @ sK17))) | (sK2 @ sK17)) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((((sK1 @ Y0) | (~ (irel @ sK14 @ sK16))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK16 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK16 @ Y0))))))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ sK18 @ Y3)) | (sK1 @ Y3))))) | (sK2 @ Y0)) | (~ (irel @ Y1 @ sK18))) | (~ (irel @ sK18 @ Y0))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ sK15 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ Y2)) | (~ (irel @ Y1 @ sK15))) | (~ (irel @ sK15 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))) @ sK19)))),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f261])).
% 0.21/0.38 thf(f263,plain,(
% 0.21/0.38 ($false = ((!! @ $i @ (^[Y0 : $i]: ((((sK1 @ Y0) | (~ (irel @ sK14 @ sK16))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK16 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK16 @ Y0))))))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ sK18 @ Y3)) | (sK1 @ Y3))))) | (sK2 @ Y0)) | (~ (irel @ Y1 @ sK18))) | (~ (irel @ sK18 @ Y0))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ sK15 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ Y2)) | (~ (irel @ Y1 @ sK15))) | (~ (irel @ sK15 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))) @ sK19))) | ($false = (((^[Y0 : $i]: ((((~ (irel @ sK14 @ Y0)) | (~ (irel @ Y0 @ sK17))) | (sK2 @ sK17)) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))))) @ sK20)))),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f262])).
% 0.21/0.38 thf(f264,plain,(
% 0.21/0.38 ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (irel @ sK14 @ sK16))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK16 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK16 @ Y0)))) @ sK21))) | ($false = (((^[Y0 : $i]: ((((~ (irel @ sK14 @ Y0)) | (~ (irel @ Y0 @ sK17))) | (sK2 @ sK17)) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))))) @ sK20))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ sK18 @ Y3)) | (sK1 @ Y3))))) | (sK2 @ Y0)) | (~ (irel @ Y1 @ sK18))) | (~ (irel @ sK18 @ Y0))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ sK15 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ Y2)) | (~ (irel @ Y1 @ sK15))) | (~ (irel @ sK15 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))) @ sK19)))),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f263])).
% 0.21/0.38 thf(f265,plain,(
% 0.21/0.38 ($false = (((((sK1 @ sK21) | (~ (irel @ sK14 @ sK16))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK16 @ sK21))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))) | ($false = (((((~ (irel @ sK14 @ sK20)) | (~ (irel @ sK20 @ sK17))) | (sK2 @ sK17)) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK20 @ Y0)))))))))),
% 0.21/0.38 inference(beta-eta_normalization,[],[f264])).
% 0.21/0.38 thf(f267,plain,(
% 0.21/0.38 ($false = (((((~ (irel @ sK14 @ sK20)) | (~ (irel @ sK20 @ sK17))) | (sK2 @ sK17)) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK20 @ Y0))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))) | ($false = ((((sK1 @ sK21) | (~ (irel @ sK14 @ sK16))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK2 @ Y0))))))))),
% 0.21/0.38 inference(or_proxy_clausification,[],[f265])).
% 0.21/0.38 thf(f268,plain,(
% 0.21/0.38 (((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK20 @ Y0))))))) = $false) | ($false = ((((sK1 @ sK21) | (~ (irel @ sK14 @ sK16))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK2 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))))),
% 0.21/0.38 inference(or_proxy_clausification,[],[f267])).
% 0.21/0.38 thf(f269,plain,(
% 0.21/0.38 ($false = ((((sK1 @ sK21) | (~ (irel @ sK14 @ sK16))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK2 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))) | ($false = ((((~ (irel @ sK14 @ sK20)) | (~ (irel @ sK20 @ sK17))) | (sK2 @ sK17))))),
% 0.21/0.38 inference(or_proxy_clausification,[],[f267])).
% 0.21/0.38 thf(f271,plain,(
% 0.21/0.38 ($false = ((((~ (irel @ sK14 @ sK20)) | (~ (irel @ sK20 @ sK17))) | (sK2 @ sK17)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))) | ($false = (((sK1 @ sK21) | (~ (irel @ sK14 @ sK16)))))),
% 0.21/0.38 inference(or_proxy_clausification,[],[f269])).
% 0.21/0.38 thf(f272,plain,(
% 0.21/0.38 ($false = ((sK2 @ sK17))) | ($false = (((sK1 @ sK21) | (~ (irel @ sK14 @ sK16))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))))),
% 0.21/0.38 inference(or_proxy_clausification,[],[f271])).
% 0.21/0.38 thf(f634,plain,(
% 0.21/0.38 ($false = ((sK2 @ sK17))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))) | (((sK1 @ sK21)) = $false)),
% 0.21/0.38 inference(or_proxy_clausification,[],[f272])).
% 0.21/0.38 thf(f635,plain,(
% 0.21/0.38 ($false = ((sK2 @ sK17))) | (((sK1 @ sK21)) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK30)))),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f634])).
% 0.21/0.38 thf(f636,plain,(
% 0.21/0.38 ($false = ((sK2 @ sK17))) | (((sK1 @ sK21)) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ sK19)) | (~ (irel @ sK30 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK15 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ sK30 @ sK15))) | (~ (irel @ sK15 @ Y0)))) | (~ (irel @ sK3 @ sK30)))))) = $false)),
% 0.21/0.38 inference(beta-eta_normalization,[],[f635])).
% 0.21/0.38 thf(f637,plain,(
% 0.21/0.38 ($false = (((^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ sK19)) | (~ (irel @ sK30 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK15 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ sK30 @ sK15))) | (~ (irel @ sK15 @ Y0)))) | (~ (irel @ sK3 @ sK30)))) @ sK31))) | ($false = ((sK2 @ sK17))) | (((sK1 @ sK21)) = $false)),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f636])).
% 0.21/0.38 thf(f638,plain,(
% 0.21/0.38 ($false = (((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK30 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK31)) | (~ (irel @ sK30 @ sK15))) | (~ (irel @ sK15 @ sK31)))) | (~ (irel @ sK3 @ sK30))))) | ($false = ((sK2 @ sK17))) | (((sK1 @ sK21)) = $false)),
% 0.21/0.38 inference(beta-eta_normalization,[],[f637])).
% 0.21/0.38 thf(f640,plain,(
% 0.21/0.38 ($false = ((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK30 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK31)) | (~ (irel @ sK30 @ sK15))) | (~ (irel @ sK15 @ sK31)))))) | ($false = ((sK2 @ sK17))) | (((sK1 @ sK21)) = $false)),
% 0.21/0.38 inference(or_proxy_clausification,[],[f638])).
% 0.21/0.38 thf(f641,plain,(
% 0.21/0.38 (((sK1 @ sK21)) = $false) | ((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK31)) | (~ (irel @ sK30 @ sK15))) | (~ (irel @ sK15 @ sK31)))) = $false) | ($false = ((sK2 @ sK17))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK30 @ sK18))) | (~ (irel @ sK18 @ sK19)))))),
% 0.21/0.38 inference(and_proxy_clausification,[],[f640])).
% 0.21/0.38 thf(f643,plain,(
% 0.21/0.38 ($false = ((sK2 @ sK17))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK30 @ sK18))) | (~ (irel @ sK18 @ sK19))))) | (((sK1 @ sK21)) = $false) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK31)) | (~ (irel @ sK30 @ sK15)))))),
% 0.21/0.38 inference(or_proxy_clausification,[],[f641])).
% 0.21/0.38 thf(f645,plain,(
% 0.21/0.38 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK31)) | (~ (irel @ sK30 @ sK15))))) | ($false = ((sK2 @ sK17))) | (((sK1 @ sK21)) = $false) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK30 @ sK18)))))),
% 0.21/0.38 inference(or_proxy_clausification,[],[f643])).
% 0.21/0.38 thf(f647,plain,(
% 0.21/0.38 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK30 @ sK18))))) | (((sK1 @ sK21)) = $false) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK31)))) | ($false = ((sK2 @ sK17)))),
% 0.21/0.38 inference(or_proxy_clausification,[],[f645])).
% 0.21/0.38 thf(f649,plain,(
% 0.21/0.38 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)))) | (((sK1 @ sK21)) = $false) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK31)))) | ($false = ((sK2 @ sK17)))),
% 0.21/0.38 inference(or_proxy_clausification,[],[f647])).
% 0.21/0.38 thf(f650,plain,(
% 0.21/0.38 ($false = ((sK2 @ sK17))) | ($false = ((sK2 @ sK19))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK31)))) | (((sK1 @ sK21)) = $false)),
% 0.21/0.38 inference(or_proxy_clausification,[],[f649])).
% 0.21/0.38 thf(f668,plain,(
% 0.21/0.38 (((sK1 @ sK31)) = $false) | ($false = ((sK2 @ sK19))) | ($false = ((sK2 @ sK17))) | (((sK1 @ sK21)) = $false)),
% 0.21/0.38 inference(or_proxy_clausification,[],[f650])).
% 0.21/0.38 thf(f669,plain,(
% 0.21/0.38 ($false = ((sK2 @ sK19))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))))) | (((sK1 @ sK21)) = $false) | ($false = ((sK2 @ sK17)))),
% 0.21/0.38 inference(or_proxy_clausification,[],[f650])).
% 0.21/0.38 thf(f670,plain,(
% 0.21/0.38 (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) = $true) | ($false = ((sK2 @ sK19))) | ($false = ((sK2 @ sK17))) | (((sK1 @ sK21)) = $false)),
% 0.21/0.38 inference(not_proxy_clausification,[],[f669])).
% 0.21/0.38 thf(f671,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((sK1 @ sK21)) = $false) | ($false = ((sK2 @ sK17))) | ((((^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))) @ X1)) = $true) | ($false = ((sK2 @ sK19)))) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f670])).
% 0.21/0.38 thf(f672,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($false = ((sK2 @ sK17))) | ((((~ (irel @ sK15 @ X1)) | (sK2 @ X1))) = $true) | (((sK1 @ sK21)) = $false) | ($false = ((sK2 @ sK19)))) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f671])).
% 0.21/0.38 thf(f673,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((sK2 @ X1)) = $true) | ($false = ((sK2 @ sK17))) | (((sK1 @ sK21)) = $false) | ($false = ((sK2 @ sK19))) | (((~ (irel @ sK15 @ X1))) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f672])).
% 0.21/0.38 thf(f674,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((irel @ sK15 @ X1)) = $false) | ($false = ((sK2 @ sK19))) | (((sK1 @ sK21)) = $false) | ($false = ((sK2 @ sK17))) | (((sK2 @ X1)) = $true)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f673])).
% 0.21/0.38 thf(f1091,plain,(
% 0.21/0.38 (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK20 @ Y0)))))) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))) | ($false = ((((sK1 @ sK21) | (~ (irel @ sK14 @ sK16))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK2 @ Y0))))))))),
% 0.21/0.38 inference(not_proxy_clausification,[],[f268])).
% 0.21/0.38 thf(f1092,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($false = ((((sK1 @ sK21) | (~ (irel @ sK14 @ sK16))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK2 @ Y0)))))))) | ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK20 @ Y0)))) @ X1)) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))))) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f1091])).
% 0.21/0.38 thf(f1093,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK20 @ Y0)))) @ X1)) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK2 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1092])).
% 0.21/0.38 thf(f1094,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($false = (((sK1 @ sK21) | (~ (irel @ sK14 @ sK16))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))) | ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK20 @ Y0)))) @ X1)) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1092])).
% 0.21/0.38 thf(f1096,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((sK1 @ sK21)) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))) | ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK20 @ Y0)))) @ X1)) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1094])).
% 0.21/0.38 thf(f1097,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK20 @ Y0)))) @ X1)) = $true) | (((sK1 @ sK21)) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK40)))) )),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f1096])).
% 0.21/0.38 thf(f1098,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ sK19)) | (~ (irel @ sK40 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK15 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ sK40 @ sK15))) | (~ (irel @ sK15 @ Y0)))) | (~ (irel @ sK3 @ sK40))))))) | (((sK1 @ sK21)) = $false) | ((((sK1 @ X1) | (~ (irel @ sK20 @ X1)))) = $true)) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f1097])).
% 0.21/0.38 thf(f1099,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((sK1 @ sK21)) = $false) | ((((sK1 @ X1) | (~ (irel @ sK20 @ X1)))) = $true) | ($false = (((^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ sK19)) | (~ (irel @ sK40 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK15 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ sK40 @ sK15))) | (~ (irel @ sK15 @ Y0)))) | (~ (irel @ sK3 @ sK40)))) @ sK41)))) )),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f1098])).
% 0.21/0.38 thf(f1100,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((~ (irel @ sK20 @ X1))) = $true) | (((sK1 @ sK21)) = $false) | (((sK1 @ X1)) = $true) | ($false = (((^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ sK19)) | (~ (irel @ sK40 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK15 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ sK40 @ sK15))) | (~ (irel @ sK15 @ Y0)))) | (~ (irel @ sK3 @ sK40)))) @ sK41)))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1099])).
% 0.21/0.38 thf(f1101,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($false = ((irel @ sK20 @ X1))) | (((sK1 @ sK21)) = $false) | ($false = (((^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ sK19)) | (~ (irel @ sK40 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK15 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ sK40 @ sK15))) | (~ (irel @ sK15 @ Y0)))) | (~ (irel @ sK3 @ sK40)))) @ sK41))) | (((sK1 @ X1)) = $true)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f1100])).
% 0.21/0.38 thf(f1102,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((sK1 @ X1)) = $true) | ($false = ((irel @ sK20 @ X1))) | ($false = (((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK40 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK41)) | (~ (irel @ sK40 @ sK15))) | (~ (irel @ sK15 @ sK41)))) | (~ (irel @ sK3 @ sK40))))) | (((sK1 @ sK21)) = $false)) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f1101])).
% 0.21/0.38 thf(f1104,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($false = ((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK40 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK41)) | (~ (irel @ sK40 @ sK15))) | (~ (irel @ sK15 @ sK41)))))) | (((sK1 @ sK21)) = $false) | ($false = ((irel @ sK20 @ X1))) | (((sK1 @ X1)) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1102])).
% 0.21/0.38 thf(f1105,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((sK1 @ X1)) = $true) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK41)) | (~ (irel @ sK40 @ sK15))) | (~ (irel @ sK15 @ sK41))))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK40 @ sK18))) | (~ (irel @ sK18 @ sK19))))) | ($false = ((irel @ sK20 @ X1))) | (((sK1 @ sK21)) = $false)) )),
% 0.21/0.38 inference(and_proxy_clausification,[],[f1104])).
% 0.21/0.38 thf(f1107,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((sK1 @ X1)) = $true) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK41)) | (~ (irel @ sK40 @ sK15))))) | (((sK1 @ sK21)) = $false) | ($false = ((irel @ sK20 @ X1))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK40 @ sK18))) | (~ (irel @ sK18 @ sK19)))))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1105])).
% 0.21/0.38 thf(f1109,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK40 @ sK18))) | (~ (irel @ sK18 @ sK19))))) | ($false = ((irel @ sK20 @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK41)))) | (((sK1 @ X1)) = $true) | (((sK1 @ sK21)) = $false)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1107])).
% 0.21/0.38 thf(f1111,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((sK1 @ sK21)) = $false) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK40 @ sK18))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK41)))) | ($false = ((irel @ sK20 @ X1))) | (((sK1 @ X1)) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1109])).
% 0.21/0.38 thf(f1113,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($false = ((irel @ sK20 @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)))) | (((sK1 @ sK21)) = $false) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK41)))) | (((sK1 @ X1)) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1111])).
% 0.21/0.38 thf(f1115,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((sK1 @ sK21)) = $false) | (((sK1 @ X1)) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK41)))) | ($false = ((irel @ sK20 @ X1)))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1113])).
% 0.21/0.38 thf(f1116,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) = $true) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK41)))) | (((sK1 @ X1)) = $true) | (((sK1 @ sK21)) = $false) | ($false = ((irel @ sK20 @ X1)))) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f1115])).
% 0.21/0.38 thf(f1117,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : ((((sK1 @ sK21)) = $false) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))) @ X2))) | ($false = ((irel @ sK20 @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK41)))) | (((sK1 @ X1)) = $true)) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f1116])).
% 0.21/0.38 thf(f1119,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK20 @ X1))) | (((sK1 @ sK21)) = $false) | (((sK1 @ X1)) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))))) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))) @ X2)))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1117])).
% 0.21/0.38 thf(f1120,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) = $true) | (((sK1 @ sK21)) = $false) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))) @ X2))) | ($false = ((irel @ sK20 @ X1))) | (((sK1 @ X1)) = $true)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f1119])).
% 0.21/0.38 thf(f1121,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((irel @ sK20 @ X1))) | (((sK1 @ X1)) = $true) | ((((^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))) @ X3)) = $true) | (((sK1 @ sK21)) = $false) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))) @ X2)))) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f1120])).
% 0.21/0.38 thf(f1122,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((sK1 @ sK21)) = $false) | ((((~ (irel @ sK18 @ X2)) | (sK1 @ X2))) = $true) | (((sK1 @ X1)) = $true) | ((((~ (irel @ sK15 @ X3)) | (sK2 @ X3))) = $true) | ($false = ((irel @ sK20 @ X1)))) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f1121])).
% 0.21/0.38 thf(f1123,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((sK1 @ sK21)) = $false) | ($false = ((irel @ sK20 @ X1))) | (((sK1 @ X2)) = $true) | ($true = ((~ (irel @ sK18 @ X2)))) | (((sK1 @ X1)) = $true) | ((((~ (irel @ sK15 @ X3)) | (sK2 @ X3))) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1122])).
% 0.21/0.38 thf(f1124,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((sK1 @ X1)) = $true) | ($false = ((irel @ sK18 @ X2))) | (((sK1 @ sK21)) = $false) | ((((~ (irel @ sK15 @ X3)) | (sK2 @ X3))) = $true) | (((sK1 @ X2)) = $true) | ($false = ((irel @ sK20 @ X1)))) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f1123])).
% 0.21/0.38 thf(f1125,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((sK1 @ X1)) = $true) | ($true = ((sK2 @ X3))) | ($false = ((irel @ sK20 @ X1))) | (((sK1 @ X2)) = $true) | (((sK1 @ sK21)) = $false) | ($true = ((~ (irel @ sK15 @ X3)))) | ($false = ((irel @ sK18 @ X2)))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1124])).
% 0.21/0.38 thf(f1126,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((sK1 @ X2)) = $true) | (((irel @ sK15 @ X3)) = $false) | ($true = ((sK2 @ X3))) | (((sK1 @ X1)) = $true) | ($false = ((irel @ sK18 @ X2))) | ($false = ((irel @ sK20 @ X1))) | (((sK1 @ sK21)) = $false)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f1125])).
% 0.21/0.38 thf(f1274,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK2 @ Y0)))))) | ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK20 @ Y0)))) @ X1)) = $true)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f1093])).
% 0.21/0.38 thf(f1275,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK20 @ Y0)))) @ X1)) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK2 @ Y0)))))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK44)))) )),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f1274])).
% 0.21/0.38 thf(f1276,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (((((^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK2 @ Y0))) @ X2)) = $true) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK1 @ Y2))))) | (sK2 @ sK19)) | (~ (irel @ Y0 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK15 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ sK15))) | (~ (irel @ sK15 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK44))) | ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK20 @ Y0)))) @ X1)) = $true)) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f1275])).
% 0.21/0.38 thf(f1277,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (((((~ (irel @ sK16 @ X2)) | (sK2 @ X2))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ sK19)) | (~ (irel @ sK44 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK15 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ sK44 @ sK15))) | (~ (irel @ sK15 @ Y0)))) | (~ (irel @ sK3 @ sK44)))))) = $false) | ((((sK1 @ X1) | (~ (irel @ sK20 @ X1)))) = $true)) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f1276])).
% 0.21/0.38 thf(f1278,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (($true = ((sK2 @ X2))) | ((((sK1 @ X1) | (~ (irel @ sK20 @ X1)))) = $true) | (((~ (irel @ sK16 @ X2))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ sK19)) | (~ (irel @ sK44 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK15 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ sK44 @ sK15))) | (~ (irel @ sK15 @ Y0)))) | (~ (irel @ sK3 @ sK44)))))) = $false)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1277])).
% 0.21/0.38 thf(f1279,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (($true = ((sK2 @ X2))) | (((~ (irel @ sK20 @ X1))) = $true) | (((sK1 @ X1)) = $true) | (((~ (irel @ sK16 @ X2))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ sK19)) | (~ (irel @ sK44 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK15 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ sK44 @ sK15))) | (~ (irel @ sK15 @ Y0)))) | (~ (irel @ sK3 @ sK44)))))) = $false)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1278])).
% 0.21/0.38 thf(f1280,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK20 @ X1))) | (((sK1 @ X1)) = $true) | (((~ (irel @ sK16 @ X2))) = $true) | ($true = ((sK2 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ sK19)) | (~ (irel @ sK44 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK15 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ sK44 @ sK15))) | (~ (irel @ sK15 @ Y0)))) | (~ (irel @ sK3 @ sK44)))))) = $false)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f1279])).
% 0.21/0.38 thf(f1281,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : ((((sK1 @ X1)) = $true) | ($false = ((irel @ sK20 @ X1))) | ($true = ((sK2 @ X2))) | ($false = ((irel @ sK16 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ sK19)) | (~ (irel @ sK44 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK15 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ sK44 @ sK15))) | (~ (irel @ sK15 @ Y0)))) | (~ (irel @ sK3 @ sK44)))))) = $false)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f1280])).
% 0.21/0.38 thf(f1282,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK20 @ X1))) | ($false = (((^[Y0 : $i]: ((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (sK2 @ sK19)) | (~ (irel @ sK44 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK15 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ Y0)) | (~ (irel @ sK44 @ sK15))) | (~ (irel @ sK15 @ Y0)))) | (~ (irel @ sK3 @ sK44)))) @ sK45))) | (((sK1 @ X1)) = $true) | ($true = ((sK2 @ X2))) | ($false = ((irel @ sK16 @ X2)))) )),
% 0.21/0.38 inference(sigma_proxy_clausification,[],[f1281])).
% 0.21/0.38 thf(f1283,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (($true = ((sK2 @ X2))) | ($false = ((irel @ sK16 @ X2))) | (((sK1 @ X1)) = $true) | ($false = (((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK44 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK45)) | (~ (irel @ sK44 @ sK15))) | (~ (irel @ sK15 @ sK45)))) | (~ (irel @ sK3 @ sK44))))) | ($false = ((irel @ sK20 @ X1)))) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f1282])).
% 0.21/0.38 thf(f1285,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK20 @ X1))) | (((sK1 @ X1)) = $true) | ($false = ((irel @ sK16 @ X2))) | ($true = ((sK2 @ X2))) | ($false = ((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK44 @ sK18))) | (~ (irel @ sK18 @ sK19))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK45)) | (~ (irel @ sK44 @ sK15))) | (~ (irel @ sK15 @ sK45))))))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1283])).
% 0.21/0.38 thf(f1286,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK20 @ X1))) | (((sK1 @ X1)) = $true) | ($false = ((irel @ sK16 @ X2))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK45)) | (~ (irel @ sK44 @ sK15))) | (~ (irel @ sK15 @ sK45))))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK44 @ sK18))) | (~ (irel @ sK18 @ sK19))))) | ($true = ((sK2 @ X2)))) )),
% 0.21/0.38 inference(and_proxy_clausification,[],[f1285])).
% 0.21/0.38 thf(f1288,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK45)) | (~ (irel @ sK44 @ sK15))))) | ($false = ((irel @ sK16 @ X2))) | (((sK1 @ X1)) = $true) | ($true = ((sK2 @ X2))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK44 @ sK18))) | (~ (irel @ sK18 @ sK19))))) | ($false = ((irel @ sK20 @ X1)))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1286])).
% 0.21/0.38 thf(f1290,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK20 @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK45)))) | ($false = ((irel @ sK16 @ X2))) | (((sK1 @ X1)) = $true) | ($true = ((sK2 @ X2))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK44 @ sK18))) | (~ (irel @ sK18 @ sK19)))))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1288])).
% 0.21/0.38 thf(f1292,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (($true = ((sK2 @ X2))) | (((sK1 @ X1)) = $true) | ($false = ((irel @ sK16 @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))))) | ($false = ((irel @ sK20 @ X1))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK44 @ sK18))) | (~ (irel @ sK18 @ sK19)))))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1290])).
% 0.21/0.38 thf(f1293,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) = $true) | ($false = ((irel @ sK20 @ X1))) | (((sK1 @ X1)) = $true) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK44 @ sK18))) | (~ (irel @ sK18 @ sK19))))) | ($true = ((sK2 @ X2))) | ($false = ((irel @ sK16 @ X2)))) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f1292])).
% 0.21/0.38 thf(f1294,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((sK1 @ X1)) = $true) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK44 @ sK18))) | (~ (irel @ sK18 @ sK19))))) | ($false = ((irel @ sK20 @ X1))) | ((((^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))) @ X3)) = $true) | ($true = ((sK2 @ X2))) | ($false = ((irel @ sK16 @ X2)))) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f1293])).
% 0.21/0.38 thf(f1296,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((sK2 @ X2))) | ($false = ((irel @ sK20 @ X1))) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)) | (~ (irel @ sK44 @ sK18))))) | ($false = ((irel @ sK16 @ X2))) | ((((^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))) @ X3)) = $true) | (((sK1 @ X1)) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1294])).
% 0.21/0.38 thf(f1298,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((sK2 @ X2))) | ($false = ((irel @ sK16 @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (sK2 @ sK19)))) | ((((^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))) @ X3)) = $true) | ($false = ((irel @ sK20 @ X1))) | (((sK1 @ X1)) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1296])).
% 0.21/0.38 thf(f1300,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((sK2 @ X2))) | (((sK1 @ X1)) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))))) | ($false = ((irel @ sK20 @ X1))) | ((((^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))) @ X3)) = $true) | ($false = ((irel @ sK16 @ X2)))) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1298])).
% 0.21/0.38 thf(f1301,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((sK2 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) = $true) | (((sK1 @ X1)) = $true) | ($false = ((irel @ sK16 @ X2))) | ((((^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))) @ X3)) = $true) | ($false = ((irel @ sK20 @ X1)))) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f1300])).
% 0.21/0.38 thf(f1302,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK16 @ X2))) | ($true = ((sK2 @ X2))) | (((sK1 @ X1)) = $true) | ((((^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))) @ X4)) = $true) | ($false = ((irel @ sK20 @ X1))) | ((((^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))) @ X3)) = $true)) )),
% 0.21/0.38 inference(pi_proxy_clausification,[],[f1301])).
% 0.21/0.38 thf(f1303,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK16 @ X2))) | ((((~ (irel @ sK18 @ X4)) | (sK1 @ X4))) = $true) | ((((~ (irel @ sK15 @ X3)) | (sK2 @ X3))) = $true) | (((sK1 @ X1)) = $true) | ($true = ((sK2 @ X2))) | ($false = ((irel @ sK20 @ X1)))) )),
% 0.21/0.38 inference(beta-eta_normalization,[],[f1302])).
% 0.21/0.38 thf(f1304,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK16 @ X2))) | ($false = ((irel @ sK20 @ X1))) | ($true = ((sK2 @ X2))) | ((((~ (irel @ sK15 @ X3)) | (sK2 @ X3))) = $true) | (((sK1 @ X4)) = $true) | (((sK1 @ X1)) = $true) | (((~ (irel @ sK18 @ X4))) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1303])).
% 0.21/0.38 thf(f1305,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((sK1 @ X1)) = $true) | ($false = ((irel @ sK20 @ X1))) | ($true = ((sK2 @ X3))) | ($true = ((sK2 @ X2))) | ($false = ((irel @ sK16 @ X2))) | (((sK1 @ X4)) = $true) | ($true = ((~ (irel @ sK15 @ X3)))) | (((~ (irel @ sK18 @ X4))) = $true)) )),
% 0.21/0.38 inference(or_proxy_clausification,[],[f1304])).
% 0.21/0.38 thf(f1306,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK20 @ X1))) | (((sK1 @ X4)) = $true) | ($false = ((irel @ sK16 @ X2))) | (((sK1 @ X1)) = $true) | ($true = ((sK2 @ X3))) | (((~ (irel @ sK18 @ X4))) = $true) | ($true = ((sK2 @ X2))) | (((irel @ sK15 @ X3)) = $false)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f1305])).
% 0.21/0.38 thf(f1307,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK18 @ X4))) | ($true = ((sK2 @ X3))) | ($false = ((irel @ sK16 @ X2))) | (((sK1 @ X1)) = $true) | ($false = ((irel @ sK20 @ X1))) | (((irel @ sK15 @ X3)) = $false) | (((sK1 @ X4)) = $true) | ($true = ((sK2 @ X2)))) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f1306])).
% 0.21/0.38 thf(f1818,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((irel @ X4 @ X5)) = $false) | ($false = ((irel @ X1 @ X8))) | ($false = ((sK2 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((irel @ X2 @ X4))) | ($false = ((irel @ sK3 @ X7))) | ($false = ((irel @ sK3 @ X2))) | ($false = ((irel @ X7 @ X1))) | (((sK1 @ X8)) = $true) | (((sK1 @ X5)) = $true) | ($false = ((sK2 @ (sK8 @ X1))))) )),
% 0.21/0.38 inference(forward_demodulation,[],[f173,f54])).
% 0.21/0.38 thf(f1820,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((sK1 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((irel @ X6 @ X4))) | (((sK2 @ X4)) = $true) | ($false = ((irel @ X2 @ X6))) | ($false = ((sK1 @ (sK10 @ X3)))) | ($false = ((irel @ X3 @ X5))) | ($true = ((sK2 @ X5))) | (((irel @ X7 @ X3)) = $false) | ($false = ((irel @ sK3 @ X2))) | ($false = ((irel @ sK3 @ X7)))) )),
% 0.21/0.38 inference(forward_demodulation,[],[f207,f54])).
% 0.21/0.38 thf(f1828,definition,(
% 0.21/0.38 spl56_1 <=> (((sK1 @ sK21)) = $false)),
% 0.21/0.38 introduced(definition,[new_symbols(definition,[spl56_1])],[avatar_definition])).
% 0.21/0.38 thf(f1830,plain,(
% 0.21/0.38 (((sK1 @ sK21)) = $false) | ~spl56_1),
% 0.21/0.38 inference(avatar_component_clause,[],[f1828])).
% 0.21/0.38 thf(f1832,definition,(
% 0.21/0.38 spl56_2 <=> ! [X1 : $i] : ((((irel @ sK15 @ X1)) = $false) | (((sK2 @ X1)) = $true))),
% 0.21/0.38 introduced(definition,[new_symbols(definition,[spl56_2])],[avatar_definition])).
% 0.21/0.38 thf(f1833,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((irel @ sK15 @ X1)) = $false) | (((sK2 @ X1)) = $true)) ) | ~spl56_2),
% 0.21/0.38 inference(avatar_component_clause,[],[f1832])).
% 0.21/0.38 thf(f1839,definition,(
% 0.21/0.38 spl56_4 <=> ! [X2 : $i] : ((((sK1 @ X2)) = $true) | ($false = ((irel @ sK18 @ X2))))),
% 0.21/0.38 introduced(definition,[new_symbols(definition,[spl56_4])],[avatar_definition])).
% 0.21/0.38 thf(f1840,plain,(
% 0.21/0.38 ( ! [X2 : $i] : (($false = ((irel @ sK18 @ X2))) | (((sK1 @ X2)) = $true)) ) | ~spl56_4),
% 0.21/0.38 inference(avatar_component_clause,[],[f1839])).
% 0.21/0.38 thf(f1858,definition,(
% 0.21/0.38 spl56_8 <=> ($false = ((sK2 @ sK19)))),
% 0.21/0.38 introduced(definition,[new_symbols(definition,[spl56_8])],[avatar_definition])).
% 0.21/0.38 thf(f1860,plain,(
% 0.21/0.38 ($false = ((sK2 @ sK19))) | ~spl56_8),
% 0.21/0.38 inference(avatar_component_clause,[],[f1858])).
% 0.21/0.38 thf(f2006,definition,(
% 0.21/0.38 spl56_29 <=> ($false = ((sK2 @ sK17)))),
% 0.21/0.38 introduced(definition,[new_symbols(definition,[spl56_29])],[avatar_definition])).
% 0.21/0.38 thf(f2008,plain,(
% 0.21/0.38 ($false = ((sK2 @ sK17))) | ~spl56_29),
% 0.21/0.38 inference(avatar_component_clause,[],[f2006])).
% 0.21/0.38 thf(f2011,definition,(
% 0.21/0.38 spl56_30 <=> (((sK1 @ sK31)) = $false)),
% 0.21/0.38 introduced(definition,[new_symbols(definition,[spl56_30])],[avatar_definition])).
% 0.21/0.38 thf(f2013,plain,(
% 0.21/0.38 (((sK1 @ sK31)) = $false) | ~spl56_30),
% 0.21/0.38 inference(avatar_component_clause,[],[f2011])).
% 0.21/0.38 thf(f2015,plain,(
% 0.21/0.38 spl56_29 | spl56_1 | spl56_2 | spl56_8),
% 0.21/0.38 inference(avatar_split_clause,[],[f674,f1858,f1832,f1828,f2006])).
% 0.21/0.38 thf(f2016,plain,(
% 0.21/0.38 spl56_29 | spl56_30 | spl56_8 | spl56_1),
% 0.21/0.38 inference(avatar_split_clause,[],[f668,f1828,f1858,f2011,f2006])).
% 0.21/0.38 thf(f2084,definition,(
% 0.21/0.38 spl56_40 <=> ! [X1 : $i] : ((((sK2 @ X1)) = $true) | ($false = ((irel @ sK16 @ X1))))),
% 0.21/0.38 introduced(definition,[new_symbols(definition,[spl56_40])],[avatar_definition])).
% 0.21/0.38 thf(f2085,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($false = ((irel @ sK16 @ X1))) | (((sK2 @ X1)) = $true)) ) | ~spl56_40),
% 0.21/0.38 inference(avatar_component_clause,[],[f2084])).
% 0.21/0.38 thf(f2198,definition,(
% 0.21/0.38 spl56_56 <=> ! [X1 : $i] : ((((sK1 @ X1)) = $true) | ($false = ((irel @ sK20 @ X1))))),
% 0.21/0.38 introduced(definition,[new_symbols(definition,[spl56_56])],[avatar_definition])).
% 0.21/0.38 thf(f2199,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((sK1 @ X1)) = $true) | ($false = ((irel @ sK20 @ X1)))) ) | ~spl56_56),
% 0.21/0.38 inference(avatar_component_clause,[],[f2198])).
% 0.21/0.38 thf(f2200,plain,(
% 0.21/0.38 spl56_2 | spl56_4 | spl56_1 | spl56_56),
% 0.21/0.38 inference(avatar_split_clause,[],[f1126,f2198,f1828,f1839,f1832])).
% 0.21/0.38 thf(f2274,plain,(
% 0.21/0.38 spl56_56 | spl56_2 | spl56_40 | spl56_4),
% 0.21/0.38 inference(avatar_split_clause,[],[f1307,f1839,f2084,f1832,f2198])).
% 0.21/0.38 thf(f2440,definition,(
% 0.21/0.38 spl56_87 <=> (((irel @ sK3 @ sK14)) = $true)),
% 0.21/0.38 introduced(definition,[new_symbols(definition,[spl56_87])],[avatar_definition])).
% 0.21/0.38 thf(f2441,plain,(
% 0.21/0.38 (((irel @ sK3 @ sK14)) != $true) | spl56_87),
% 0.21/0.38 inference(avatar_component_clause,[],[f2440])).
% 0.21/0.38 thf(f2442,plain,(
% 0.21/0.38 (((irel @ sK3 @ sK14)) = $true) | ~spl56_87),
% 0.21/0.38 inference(avatar_component_clause,[],[f2440])).
% 0.21/0.38 thf(f2458,definition,(
% 0.21/0.38 spl56_91 <=> ($false = ((sK2 @ sK53)))),
% 0.21/0.38 introduced(definition,[new_symbols(definition,[spl56_91])],[avatar_definition])).
% 0.21/0.38 thf(f2459,plain,(
% 0.21/0.38 ($false != ((sK2 @ sK53))) | spl56_91),
% 0.21/0.38 inference(avatar_component_clause,[],[f2458])).
% 0.21/0.38 thf(f2460,plain,(
% 0.21/0.38 ($false = ((sK2 @ sK53))) | ~spl56_91),
% 0.21/0.38 inference(avatar_component_clause,[],[f2458])).
% 0.21/0.38 thf(f2487,definition,(
% 0.21/0.38 spl56_95 <=> (((irel @ sK3 @ sK54)) = $true)),
% 0.21/0.38 introduced(definition,[new_symbols(definition,[spl56_95])],[avatar_definition])).
% 0.21/0.38 thf(f2488,plain,(
% 0.21/0.38 (((irel @ sK3 @ sK54)) != $true) | spl56_95),
% 0.21/0.38 inference(avatar_component_clause,[],[f2487])).
% 0.21/0.38 thf(f2489,plain,(
% 0.21/0.38 (((irel @ sK3 @ sK54)) = $true) | ~spl56_95),
% 0.21/0.38 inference(avatar_component_clause,[],[f2487])).
% 0.21/0.38 thf(f2498,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((sK2 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((irel @ sK3 @ X7))) | ($false = ((irel @ sK3 @ X2))) | ($false = ((irel @ X7 @ X1))) | ($false = ((sK2 @ (d2unsorted @ d_unsorted_0)))) | (((sK1 @ X5)) = $true) | (((irel @ X4 @ X5)) = $false) | ($false = ((irel @ X2 @ X4))) | (((sK1 @ X8)) = $true) | ($false = ((irel @ X1 @ X8)))) )),
% 0.21/0.38 inference(forward_demodulation,[],[f1818,f54])).
% 0.21/0.38 thf(f2499,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK1 @ X5)) = $true) | ($false = ((irel @ sK3 @ X7))) | ($false = ((irel @ X7 @ X1))) | ($false = ((irel @ sK3 @ X2))) | ($false = ((sK2 @ (d2unsorted @ d_unsorted_0)))) | (((sK1 @ X8)) = $true) | ($false = ((irel @ X2 @ X4))) | (((irel @ X4 @ X5)) = $false) | ($false = ((irel @ X1 @ X8)))) )),
% 0.21/0.38 inference(duplicate_literal_removal,[],[f2498])).
% 0.21/0.38 thf(f2501,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X2))) | ($false = ((irel @ X3 @ X5))) | ($false = ((sK1 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((irel @ X6 @ X4))) | ($true = ((sK2 @ X5))) | (((sK2 @ X4)) = $true) | (((irel @ X7 @ X3)) = $false) | ($false = ((irel @ X2 @ X6))) | ($false = ((irel @ sK3 @ X7))) | ($false = ((sK1 @ (d2unsorted @ d_unsorted_0))))) )),
% 0.21/0.38 inference(forward_demodulation,[],[f1820,f54])).
% 0.21/0.38 thf(f2502,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X2 @ X6))) | ($true = ((sK2 @ X5))) | ($false = ((irel @ sK3 @ X2))) | ($false = ((sK1 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((irel @ sK3 @ X7))) | ($false = ((irel @ X6 @ X4))) | ($false = ((irel @ X3 @ X5))) | (((sK2 @ X4)) = $true) | (((irel @ X7 @ X3)) = $false)) )),
% 0.21/0.38 inference(duplicate_literal_removal,[],[f2501])).
% 0.21/0.38 thf(f2517,definition,(
% 0.21/0.38 spl56_98 <=> ($false = ((sK1 @ (d2unsorted @ d_unsorted_0))))),
% 0.21/0.38 introduced(definition,[new_symbols(definition,[spl56_98])],[avatar_definition])).
% 0.21/0.38 thf(f2519,plain,(
% 0.21/0.38 ($false = ((sK1 @ (d2unsorted @ d_unsorted_0)))) | ~spl56_98),
% 0.21/0.38 inference(avatar_component_clause,[],[f2517])).
% 0.21/0.38 thf(f2521,definition,(
% 0.21/0.38 spl56_99 <=> ! [X6 : $i,X7 : $i,X3 : $i] : ((((irel @ X7 @ X3)) = $false) | ($false = ((irel @ sK3 @ X7))) | ($false = ((irel @ X3 @ X6))) | (((sK2 @ X6)) = $true))),
% 0.21/0.38 introduced(definition,[new_symbols(definition,[spl56_99])],[avatar_definition])).
% 0.21/0.38 thf(f2522,plain,(
% 0.21/0.38 ( ! [X3 : $i,X6 : $i,X7 : $i] : (($false = ((irel @ sK3 @ X7))) | (((irel @ X7 @ X3)) = $false) | (((sK2 @ X6)) = $true) | ($false = ((irel @ X3 @ X6)))) ) | ~spl56_99),
% 0.21/0.38 inference(avatar_component_clause,[],[f2521])).
% 0.21/0.38 thf(f2526,definition,(
% 0.21/0.38 spl56_100 <=> ! [X1 : $i,X8 : $i,X7 : $i] : ((((sK1 @ X8)) = $true) | ($false = ((irel @ sK3 @ X7))) | ($false = ((irel @ X7 @ X1))) | ($false = ((irel @ X1 @ X8))))),
% 0.21/0.38 introduced(definition,[new_symbols(definition,[spl56_100])],[avatar_definition])).
% 0.21/0.38 thf(f2527,plain,(
% 0.21/0.38 ( ! [X1 : $i,X8 : $i,X7 : $i] : ((((sK1 @ X8)) = $true) | ($false = ((irel @ X1 @ X8))) | ($false = ((irel @ sK3 @ X7))) | ($false = ((irel @ X7 @ X1)))) ) | ~spl56_100),
% 0.21/0.38 inference(avatar_component_clause,[],[f2526])).
% 0.21/0.38 thf(f2529,definition,(
% 0.21/0.38 spl56_101 <=> ($false = ((sK2 @ (d2unsorted @ d_unsorted_0))))),
% 0.21/0.38 introduced(definition,[new_symbols(definition,[spl56_101])],[avatar_definition])).
% 0.21/0.38 thf(f2531,plain,(
% 0.21/0.38 ($false = ((sK2 @ (d2unsorted @ d_unsorted_0)))) | ~spl56_101),
% 0.21/0.38 inference(avatar_component_clause,[],[f2529])).
% 0.21/0.38 thf(f2536,plain,(
% 0.21/0.38 spl56_101 | spl56_100 | spl56_100),
% 0.21/0.38 inference(avatar_split_clause,[],[f2499,f2526,f2526,f2529])).
% 0.21/0.38 thf(f2538,plain,(
% 0.21/0.38 spl56_99 | spl56_98 | spl56_99),
% 0.21/0.38 inference(avatar_split_clause,[],[f2502,f2521,f2517,f2521])).
% 0.21/0.38 thf(f2548,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($false = ((sK1 @ X0)))) ) | ~spl56_98),
% 0.21/0.38 inference(constrained_superposition,[],[f2519,f54])).
% 0.21/0.38 thf(f2555,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($false = ((sK2 @ X0)))) ) | ~spl56_29),
% 0.21/0.38 inference(constrained_superposition,[],[f2008,f58])).
% 0.21/0.38 thf(f2561,plain,(
% 0.21/0.38 ( ! [X1 : $i,X8 : $i,X7 : $i] : (($false = ((irel @ sK3 @ X7))) | ($false = ((irel @ X7 @ X1))) | ($false = $true) | ($false = ((irel @ X1 @ X8)))) ) | (~spl56_98 | ~spl56_100)),
% 0.21/0.38 inference(forward_demodulation,[],[f2527,f2548])).
% 0.21/0.38 thf(f2562,plain,(
% 0.21/0.38 ( ! [X1 : $i,X8 : $i,X7 : $i] : (($false = ((irel @ X7 @ X1))) | ($false = ((irel @ X1 @ X8))) | ($false = ((irel @ sK3 @ X7)))) ) | (~spl56_98 | ~spl56_100)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2561])).
% 0.21/0.38 thf(f2563,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($true = ((irel @ sK3 @ X0)))) ) | ~spl56_87),
% 0.21/0.38 inference(constrained_superposition,[],[f2442,f58])).
% 0.21/0.38 thf(f2567,plain,(
% 0.21/0.38 ( ! [X0 : $i,X1 : $i] : ((((irel @ X0 @ X1)) = $true)) ) | ~spl56_87),
% 0.21/0.38 inference(constrained_superposition,[],[f2563,f58])).
% 0.21/0.38 thf(f2571,plain,(
% 0.21/0.38 ( ! [X1 : $i,X8 : $i,X7 : $i] : (($false = ((irel @ X7 @ X1))) | ($false = ((irel @ X1 @ X8))) | ($false = $true)) ) | (~spl56_87 | ~spl56_98 | ~spl56_100)),
% 0.21/0.38 inference(forward_demodulation,[],[f2562,f2567])).
% 0.21/0.38 thf(f2572,plain,(
% 0.21/0.38 ( ! [X1 : $i,X8 : $i,X7 : $i] : (($false = ((irel @ X7 @ X1))) | ($false = ((irel @ X1 @ X8)))) ) | (~spl56_87 | ~spl56_98 | ~spl56_100)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2571])).
% 0.21/0.38 thf(f2573,plain,(
% 0.21/0.38 ( ! [X1 : $i,X8 : $i] : (($false = ((irel @ X1 @ X8))) | ($false = $true)) ) | (~spl56_87 | ~spl56_98 | ~spl56_100)),
% 0.21/0.38 inference(forward_demodulation,[],[f2572,f2567])).
% 0.21/0.38 thf(f2574,plain,(
% 0.21/0.38 ( ! [X1 : $i,X8 : $i] : (($false = ((irel @ X1 @ X8)))) ) | (~spl56_87 | ~spl56_98 | ~spl56_100)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2573])).
% 0.21/0.38 thf(f2575,plain,(
% 0.21/0.38 ($false = $true) | (~spl56_87 | ~spl56_98 | ~spl56_100)),
% 0.21/0.38 inference(forward_demodulation,[],[f2574,f2567])).
% 0.21/0.38 thf(f2576,plain,(
% 0.21/0.38 $false | (~spl56_87 | ~spl56_98 | ~spl56_100)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2575])).
% 0.21/0.38 thf(f2577,plain,(
% 0.21/0.38 ~spl56_87 | ~spl56_98 | ~spl56_100),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f2576])).
% 0.21/0.38 thf(f2580,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($true = ((irel @ sK3 @ X0)))) ) | ~spl56_95),
% 0.21/0.38 inference(constrained_superposition,[],[f2489,f58])).
% 0.21/0.38 thf(f2584,plain,(
% 0.21/0.38 ( ! [X0 : $i,X1 : $i] : ((((irel @ X0 @ X1)) = $true)) ) | ~spl56_95),
% 0.21/0.38 inference(constrained_superposition,[],[f2580,f58])).
% 0.21/0.38 thf(f2588,plain,(
% 0.21/0.38 $false | (spl56_87 | ~spl56_95)),
% 0.21/0.38 inference(forward_subsumption_resolution,[],[f2441,f2584])).
% 0.21/0.38 thf(f2589,plain,(
% 0.21/0.38 spl56_87 | ~spl56_95),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f2588])).
% 0.21/0.38 thf(f2592,plain,(
% 0.21/0.38 ( ! [X3 : $i,X6 : $i,X7 : $i] : (($false = ((irel @ sK3 @ X7))) | ($false = $true) | ($false = ((irel @ X3 @ X6))) | (((irel @ X7 @ X3)) = $false)) ) | (~spl56_29 | ~spl56_99)),
% 0.21/0.38 inference(forward_demodulation,[],[f2522,f2555])).
% 0.21/0.38 thf(f2593,plain,(
% 0.21/0.38 ( ! [X3 : $i,X6 : $i,X7 : $i] : (($false = ((irel @ X3 @ X6))) | (((irel @ X7 @ X3)) = $false) | ($false = ((irel @ sK3 @ X7)))) ) | (~spl56_29 | ~spl56_99)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2592])).
% 0.21/0.38 thf(f2598,plain,(
% 0.21/0.38 ( ! [X3 : $i,X7 : $i] : (($false = ((irel @ sK3 @ X7))) | ($false = $true) | (((irel @ X7 @ X3)) = $false)) ) | (~spl56_29 | ~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(forward_demodulation,[],[f2593,f2584])).
% 0.21/0.38 thf(f2599,plain,(
% 0.21/0.38 ( ! [X3 : $i,X7 : $i] : ((((irel @ X7 @ X3)) = $false) | ($false = ((irel @ sK3 @ X7)))) ) | (~spl56_29 | ~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2598])).
% 0.21/0.38 thf(f2602,plain,(
% 0.21/0.38 ( ! [X7 : $i] : (($false = $true) | ($false = ((irel @ sK3 @ X7)))) ) | (~spl56_29 | ~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(forward_demodulation,[],[f2599,f2584])).
% 0.21/0.38 thf(f2603,plain,(
% 0.21/0.38 ( ! [X7 : $i] : (($false = ((irel @ sK3 @ X7)))) ) | (~spl56_29 | ~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2602])).
% 0.21/0.38 thf(f2604,plain,(
% 0.21/0.38 ($false = $true) | (~spl56_29 | ~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(forward_demodulation,[],[f2603,f2584])).
% 0.21/0.38 thf(f2605,plain,(
% 0.21/0.38 $false | (~spl56_29 | ~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2604])).
% 0.21/0.38 thf(f2606,plain,(
% 0.21/0.38 ~spl56_29 | ~spl56_95 | ~spl56_99),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f2605])).
% 0.21/0.38 thf(f2607,plain,(
% 0.21/0.38 ( ! [X3 : $i,X6 : $i,X7 : $i] : (($false = ((irel @ sK3 @ X7))) | (((sK2 @ X6)) = $true) | ($false = $true) | ($false = ((irel @ X3 @ X6)))) ) | (~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(forward_demodulation,[],[f2522,f2584])).
% 0.21/0.38 thf(f2608,plain,(
% 0.21/0.38 ( ! [X3 : $i,X6 : $i,X7 : $i] : (($false = ((irel @ X3 @ X6))) | ($false = ((irel @ sK3 @ X7))) | (((sK2 @ X6)) = $true)) ) | (~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2607])).
% 0.21/0.38 thf(f2609,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($false = $true) | (((sK2 @ X1)) = $true)) ) | (~spl56_40 | ~spl56_95)),
% 0.21/0.38 inference(forward_demodulation,[],[f2085,f2584])).
% 0.21/0.38 thf(f2610,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((sK2 @ X1)) = $true)) ) | (~spl56_40 | ~spl56_95)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2609])).
% 0.21/0.38 thf(f2611,plain,(
% 0.21/0.38 ( ! [X2 : $i] : ((((sK1 @ X2)) = $true) | ($false = $true)) ) | (~spl56_4 | ~spl56_95)),
% 0.21/0.38 inference(forward_demodulation,[],[f1840,f2584])).
% 0.21/0.38 thf(f2612,plain,(
% 0.21/0.38 ( ! [X2 : $i] : ((((sK1 @ X2)) = $true)) ) | (~spl56_4 | ~spl56_95)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2611])).
% 0.21/0.38 thf(f2613,plain,(
% 0.21/0.38 ( ! [X6 : $i,X7 : $i] : (($false = ((irel @ sK3 @ X7))) | (((sK2 @ X6)) = $true) | ($false = $true)) ) | (~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(forward_demodulation,[],[f2608,f2584])).
% 0.21/0.38 thf(f2614,plain,(
% 0.21/0.38 ( ! [X6 : $i,X7 : $i] : (($false = ((irel @ sK3 @ X7))) | (((sK2 @ X6)) = $true)) ) | (~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2613])).
% 0.21/0.38 thf(f2615,plain,(
% 0.21/0.38 ( ! [X6 : $i] : (($false = $true) | (((sK2 @ X6)) = $true)) ) | (~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(forward_demodulation,[],[f2614,f2584])).
% 0.21/0.38 thf(f2616,plain,(
% 0.21/0.38 ( ! [X6 : $i] : ((((sK2 @ X6)) = $true)) ) | (~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2615])).
% 0.21/0.38 thf(f2617,plain,(
% 0.21/0.38 ($false = $true) | (~spl56_91 | ~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(forward_demodulation,[],[f2460,f2616])).
% 0.21/0.38 thf(f2618,plain,(
% 0.21/0.38 $false | (~spl56_91 | ~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2617])).
% 0.21/0.38 thf(f2619,plain,(
% 0.21/0.38 ~spl56_91 | ~spl56_95 | ~spl56_99),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f2618])).
% 0.21/0.38 thf(f2623,plain,(
% 0.21/0.38 ($false = $true) | (~spl56_8 | ~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(forward_demodulation,[],[f1860,f2616])).
% 0.21/0.38 thf(f2624,plain,(
% 0.21/0.38 $false | (~spl56_8 | ~spl56_95 | ~spl56_99)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2623])).
% 0.21/0.38 thf(f2625,plain,(
% 0.21/0.38 ~spl56_8 | ~spl56_95 | ~spl56_99),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f2624])).
% 0.21/0.38 thf(f2626,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($false != ((sK2 @ X0)))) ) | spl56_91),
% 0.21/0.38 inference(constrained_superposition,[],[f2459,f58])).
% 0.21/0.38 thf(f2635,plain,(
% 0.21/0.38 $false | (~spl56_8 | spl56_91)),
% 0.21/0.38 inference(forward_subsumption_resolution,[],[f1860,f2626])).
% 0.21/0.38 thf(f2636,plain,(
% 0.21/0.38 ~spl56_8 | spl56_91),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f2635])).
% 0.21/0.38 thf(f2638,plain,(
% 0.21/0.38 ($false = $true) | (~spl56_40 | ~spl56_91 | ~spl56_95)),
% 0.21/0.38 inference(forward_demodulation,[],[f2460,f2610])).
% 0.21/0.38 thf(f2639,plain,(
% 0.21/0.38 $false | (~spl56_40 | ~spl56_91 | ~spl56_95)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2638])).
% 0.21/0.38 thf(f2640,plain,(
% 0.21/0.38 ~spl56_40 | ~spl56_91 | ~spl56_95),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f2639])).
% 0.21/0.38 thf(f2652,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($false = $true) | (((sK2 @ X1)) = $true)) ) | (~spl56_2 | ~spl56_95)),
% 0.21/0.38 inference(forward_demodulation,[],[f1833,f2584])).
% 0.21/0.38 thf(f2653,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((sK2 @ X1)) = $true)) ) | (~spl56_2 | ~spl56_95)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2652])).
% 0.21/0.38 thf(f2656,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($false != ((sK2 @ X0)))) ) | spl56_91),
% 0.21/0.38 inference(constrained_superposition,[],[f2459,f58])).
% 0.21/0.38 thf(f2663,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($false = ((sK1 @ X0)))) ) | ~spl56_98),
% 0.21/0.38 inference(constrained_superposition,[],[f2519,f54])).
% 0.21/0.38 thf(f2672,plain,(
% 0.21/0.38 ($false = $true) | (~spl56_4 | ~spl56_95 | ~spl56_98)),
% 0.21/0.38 inference(forward_demodulation,[],[f2612,f2663])).
% 0.21/0.38 thf(f2673,plain,(
% 0.21/0.38 $false | (~spl56_4 | ~spl56_95 | ~spl56_98)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2672])).
% 0.21/0.38 thf(f2674,plain,(
% 0.21/0.38 ~spl56_4 | ~spl56_95 | ~spl56_98),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f2673])).
% 0.21/0.38 thf(f2675,plain,(
% 0.21/0.38 $false | (spl56_91 | ~spl56_101)),
% 0.21/0.38 inference(forward_subsumption_resolution,[],[f2531,f2656])).
% 0.21/0.38 thf(f2676,plain,(
% 0.21/0.38 spl56_91 | ~spl56_101),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f2675])).
% 0.21/0.38 thf(f2677,plain,(
% 0.21/0.38 ( ! [X1 : $i,X8 : $i,X7 : $i] : ((((sK1 @ X8)) = $true) | ($false = ((irel @ X1 @ X8))) | ($false = ((irel @ sK3 @ X7))) | ($false = $true)) ) | (~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(forward_demodulation,[],[f2527,f2584])).
% 0.21/0.38 thf(f2678,plain,(
% 0.21/0.38 ( ! [X1 : $i,X8 : $i,X7 : $i] : ((((sK1 @ X8)) = $true) | ($false = ((irel @ X1 @ X8))) | ($false = ((irel @ sK3 @ X7)))) ) | (~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2677])).
% 0.21/0.38 thf(f2679,plain,(
% 0.21/0.38 ( ! [X8 : $i,X7 : $i] : (($false = ((irel @ sK3 @ X7))) | ($false = $true) | (((sK1 @ X8)) = $true)) ) | (~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(forward_demodulation,[],[f2678,f2584])).
% 0.21/0.38 thf(f2680,plain,(
% 0.21/0.38 ( ! [X8 : $i,X7 : $i] : ((((sK1 @ X8)) = $true) | ($false = ((irel @ sK3 @ X7)))) ) | (~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2679])).
% 0.21/0.38 thf(f2681,plain,(
% 0.21/0.38 ( ! [X8 : $i] : (($false = $true) | (((sK1 @ X8)) = $true)) ) | (~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(forward_demodulation,[],[f2680,f2584])).
% 0.21/0.38 thf(f2682,plain,(
% 0.21/0.38 ( ! [X8 : $i] : ((((sK1 @ X8)) = $true)) ) | (~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2681])).
% 0.21/0.38 thf(f2683,plain,(
% 0.21/0.38 ($false = $true) | (~spl56_30 | ~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(forward_demodulation,[],[f2013,f2682])).
% 0.21/0.38 thf(f2684,plain,(
% 0.21/0.38 $false | (~spl56_30 | ~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2683])).
% 0.21/0.38 thf(f2685,plain,(
% 0.21/0.38 ~spl56_30 | ~spl56_95 | ~spl56_100),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f2684])).
% 0.21/0.38 thf(f2686,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($false = ((sK2 @ X0)))) ) | ~spl56_91),
% 0.21/0.38 inference(constrained_superposition,[],[f2460,f58])).
% 0.21/0.38 thf(f2701,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($false = ((sK1 @ X0)))) ) | ~spl56_98),
% 0.21/0.38 inference(constrained_superposition,[],[f2519,f54])).
% 0.21/0.38 thf(f2708,plain,(
% 0.21/0.38 ($false = $true) | (~spl56_2 | ~spl56_91 | ~spl56_95)),
% 0.21/0.38 inference(forward_demodulation,[],[f2653,f2686])).
% 0.21/0.38 thf(f2709,plain,(
% 0.21/0.38 $false | (~spl56_2 | ~spl56_91 | ~spl56_95)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2708])).
% 0.21/0.38 thf(f2710,plain,(
% 0.21/0.38 ~spl56_2 | ~spl56_91 | ~spl56_95),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f2709])).
% 0.21/0.38 thf(f2711,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($false = $true) | ($false = ((irel @ sK20 @ X1)))) ) | (~spl56_56 | ~spl56_98)),
% 0.21/0.38 inference(forward_demodulation,[],[f2199,f2701])).
% 0.21/0.38 thf(f2712,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($false = ((irel @ sK20 @ X1)))) ) | (~spl56_56 | ~spl56_98)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2711])).
% 0.21/0.38 thf(f2713,plain,(
% 0.21/0.38 ($false = $true) | (~spl56_56 | ~spl56_95 | ~spl56_98)),
% 0.21/0.38 inference(forward_demodulation,[],[f2712,f2584])).
% 0.21/0.38 thf(f2714,plain,(
% 0.21/0.38 $false | (~spl56_56 | ~spl56_95 | ~spl56_98)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2713])).
% 0.21/0.38 thf(f2715,plain,(
% 0.21/0.38 ~spl56_56 | ~spl56_95 | ~spl56_98),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f2714])).
% 0.21/0.38 thf(f2718,plain,(
% 0.21/0.38 ( ! [X1 : $i,X8 : $i,X7 : $i] : (($false = ((irel @ X7 @ X1))) | ($false = ((irel @ sK3 @ X7))) | ($false = $true) | (((sK1 @ X8)) = $true)) ) | (~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(forward_demodulation,[],[f2527,f2584])).
% 0.21/0.38 thf(f2719,plain,(
% 0.21/0.38 ( ! [X1 : $i,X8 : $i,X7 : $i] : ((((sK1 @ X8)) = $true) | ($false = ((irel @ X7 @ X1))) | ($false = ((irel @ sK3 @ X7)))) ) | (~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2718])).
% 0.21/0.38 thf(f2722,plain,(
% 0.21/0.38 ( ! [X8 : $i,X7 : $i] : ((((sK1 @ X8)) = $true) | ($false = ((irel @ sK3 @ X7))) | ($false = $true)) ) | (~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(forward_demodulation,[],[f2719,f2584])).
% 0.21/0.38 thf(f2723,plain,(
% 0.21/0.38 ( ! [X8 : $i,X7 : $i] : ((((sK1 @ X8)) = $true) | ($false = ((irel @ sK3 @ X7)))) ) | (~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2722])).
% 0.21/0.38 thf(f2726,plain,(
% 0.21/0.38 ( ! [X8 : $i] : ((((sK1 @ X8)) = $true) | ($false = $true)) ) | (~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(forward_demodulation,[],[f2723,f2584])).
% 0.21/0.38 thf(f2727,plain,(
% 0.21/0.38 ( ! [X8 : $i] : ((((sK1 @ X8)) = $true)) ) | (~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2726])).
% 0.21/0.38 thf(f2734,plain,(
% 0.21/0.38 ($false = $true) | (~spl56_1 | ~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(forward_demodulation,[],[f1830,f2727])).
% 0.21/0.38 thf(f2735,plain,(
% 0.21/0.38 $false | (~spl56_1 | ~spl56_95 | ~spl56_100)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2734])).
% 0.21/0.38 thf(f2736,plain,(
% 0.21/0.38 ~spl56_1 | ~spl56_95 | ~spl56_100),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f2735])).
% 0.21/0.38 thf(f2745,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($true != ((irel @ sK3 @ X0)))) ) | spl56_95),
% 0.21/0.38 inference(constrained_superposition,[],[f2488,f58])).
% 0.21/0.38 thf(f2761,plain,(
% 0.21/0.38 ($true != $true) | spl56_95),
% 0.21/0.38 inference(constrained_superposition,[],[f2745,f81])).
% 0.21/0.38 thf(f2763,plain,(
% 0.21/0.38 $false | spl56_95),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f2761])).
% 0.21/0.38 thf(f2764,plain,(
% 0.21/0.38 spl56_95),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f2763])).
% 0.21/0.38 cnf(s71, plain, spl56_1 | spl56_2 | spl56_8 | spl56_29, inference(sat_conversion,[],[f2015])).
% 0.21/0.38 cnf(s72, plain, spl56_1 | spl56_8 | spl56_29 | spl56_30, inference(sat_conversion,[],[f2016])).
% 0.21/0.38 cnf(s154, plain, spl56_1 | spl56_2 | spl56_4 | spl56_56, inference(sat_conversion,[],[f2200])).
% 0.21/0.38 cnf(s188, plain, spl56_2 | spl56_4 | spl56_40 | spl56_56, inference(sat_conversion,[],[f2274])).
% 0.21/0.38 cnf(s298, plain, spl56_100 | spl56_100 | spl56_101, inference(sat_conversion,[],[f2536])).
% 0.21/0.38 cnf(s299, plain, spl56_100 | spl56_101, inference(rat,[],[s298])).
% 0.21/0.38 cnf(s301, plain, spl56_99 | spl56_98 | spl56_99, inference(sat_conversion,[],[f2538])).
% 0.21/0.38 cnf(s302, plain, spl56_98 | spl56_99, inference(rat,[],[s301])).
% 0.21/0.38 cnf(s310, plain, ~spl56_87 | ~spl56_98 | ~spl56_100, inference(sat_conversion,[],[f2577])).
% 0.21/0.38 cnf(s311, plain, spl56_87 | ~spl56_95, inference(sat_conversion,[],[f2589])).
% 0.21/0.38 cnf(s312, plain, ~spl56_29 | ~spl56_95 | ~spl56_99, inference(sat_conversion,[],[f2606])).
% 0.21/0.38 cnf(s313, plain, ~spl56_91 | ~spl56_95 | ~spl56_99, inference(sat_conversion,[],[f2619])).
% 0.21/0.38 cnf(s314, plain, ~spl56_8 | ~spl56_95 | ~spl56_99, inference(sat_conversion,[],[f2625])).
% 0.21/0.38 cnf(s316, plain, ~spl56_8 | spl56_91, inference(sat_conversion,[],[f2636])).
% 0.21/0.38 cnf(s317, plain, ~spl56_40 | ~spl56_91 | ~spl56_95, inference(sat_conversion,[],[f2640])).
% 0.21/0.38 cnf(s320, plain, ~spl56_4 | ~spl56_95 | ~spl56_98, inference(sat_conversion,[],[f2674])).
% 0.21/0.38 cnf(s321, plain, spl56_91 | ~spl56_101, inference(sat_conversion,[],[f2676])).
% 0.21/0.38 cnf(s322, plain, ~spl56_30 | ~spl56_95 | ~spl56_100, inference(sat_conversion,[],[f2685])).
% 0.21/0.38 cnf(s324, plain, ~spl56_2 | ~spl56_91 | ~spl56_95, inference(sat_conversion,[],[f2710])).
% 0.21/0.38 cnf(s325, plain, ~spl56_56 | ~spl56_95 | ~spl56_98, inference(sat_conversion,[],[f2715])).
% 0.21/0.38 cnf(s326, plain, ~spl56_1 | ~spl56_95 | ~spl56_100, inference(sat_conversion,[],[f2736])).
% 0.21/0.38 cnf(s328, plain, spl56_95, inference(sat_conversion,[],[f2764])).
% 0.21/0.38 cnf(s329, plain, ~spl56_1 | ~spl56_100, inference(rat,[],[s326,s328])).
% 0.21/0.38 cnf(s330, plain, ~spl56_56 | ~spl56_98, inference(rat,[],[s325,s328])).
% 0.21/0.38 cnf(s331, plain, ~spl56_2 | ~spl56_91, inference(rat,[],[s324,s328])).
% 0.21/0.38 cnf(s332, plain, ~spl56_30 | ~spl56_100, inference(rat,[],[s322,s328])).
% 0.21/0.38 cnf(s333, plain, ~spl56_4 | ~spl56_98, inference(rat,[],[s320,s328])).
% 0.21/0.38 cnf(s335, plain, ~spl56_40 | ~spl56_91, inference(rat,[],[s317,s328])).
% 0.21/0.38 cnf(s337, plain, ~spl56_8 | ~spl56_99, inference(rat,[],[s314,s328])).
% 0.21/0.38 cnf(s338, plain, ~spl56_91 | ~spl56_99, inference(rat,[],[s313,s328])).
% 0.21/0.38 cnf(s339, plain, ~spl56_29 | ~spl56_99, inference(rat,[],[s312,s328])).
% 0.21/0.38 cnf(s340, plain, spl56_87, inference(rat,[],[s311,s328])).
% 0.21/0.38 cnf(s341, plain, ~spl56_98 | ~spl56_100, inference(rat,[],[s310,s340])).
% 0.21/0.38 cnf(s343, plain, ~spl56_99 | spl56_2 | spl56_1, inference(rat,[],[s71,s339,s337])).
% 0.21/0.38 cnf(s344, plain, spl56_2 | spl56_1, inference(rat,[],[s154,s333,s330,s302,s343])).
% 0.21/0.38 cnf(s345, plain, spl56_1, inference(rat,[],[s339,s302,s72,s341,s332,s299,s316,s321,s331,s344])).
% 0.21/0.38 cnf(s346, plain, ~spl56_100, inference(rat,[],[s329,s345])).
% 0.21/0.38 cnf(s347, plain, spl56_101, inference(rat,[],[s299,s346])).
% 0.21/0.38 cnf(s348, plain, spl56_91, inference(rat,[],[s321,s347])).
% 0.21/0.38 cnf(s349, plain, ~spl56_2, inference(rat,[],[s331,s348])).
% 0.21/0.38 cnf(s352, plain, ~spl56_40, inference(rat,[],[s335,s348])).
% 0.21/0.38 cnf(s353, plain, ~spl56_99, inference(rat,[],[s338,s348])).
% 0.21/0.38 cnf(s354, plain, spl56_98, inference(rat,[],[s302,s353])).
% 0.21/0.38 cnf(s355, plain, ~spl56_56, inference(rat,[],[s330,s354])).
% 0.21/0.38 cnf(s356, plain, ~spl56_4, inference(rat,[],[s333,s354])).
% 0.21/0.38 cnf(s360, plain, $false, inference(rat,[],[s188,s352,s349,s355,s356])).
% 0.21/0.38 thf(f2766,plain,(
% 0.21/0.38 $false),
% 0.21/0.38 inference(avatar_sat_refutation,[],[s360])).
% 0.21/0.38 % SZS output end Proof for theBenchmark
% 0.21/0.38 % (1487819)------------------------------
% 0.21/0.38 % (1487819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1487819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1487819)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1487819)Termination reason: Refutation
% 0.21/0.38 % (1487819)Time elapsed: 0.093 s
% 0.21/0.38 % (1487819)Peak memory usage: 14 MB
% 0.21/0.38 % (1487819)Instructions burned: 168 (million)
% 0.21/0.38 % (1487808)Success in time 0.144 s
% 0.21/0.38 % Vampire exiting
%------------------------------------------------------------------------------