%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX182^1 : 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 : n010.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 08:40:40 AM UTC 2026
% Result : Theorem 3.52s 0.95s
% Output : Refutation 3.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX182^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n010.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:10:33 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.72/0.40 % (3057621)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.72/0.40 % (3057630)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1350208315:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.72/0.40 % (3057628)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=229178077:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.72/0.40 % (3057626)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=904164624:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.72/0.40 % (3057627)lrs+10_16_si=on:nwc=1.5:random_seed=2983179576:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.72/0.40 % (3057629)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=928568869: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)
% 0.72/0.40 % (3057631)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2796874493:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.72/0.40 % (3057628)Instruction limit reached!
% 0.72/0.40 % (3057628)------------------------------
% 0.72/0.40 % (3057628)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (3057628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (3057628)CaDiCaL version: 2.1.3
% 0.72/0.40 % (3057628)Termination reason: Instruction limit
% 0.72/0.40 % (3057628)Termination phase: shuffling
% 0.72/0.40 % (3057628)Time elapsed: 0.003 s
% 0.72/0.40 % (3057628)Peak memory usage: 10 MB
% 0.72/0.40 % (3057628)Instructions burned: 7 (million)
% 0.72/0.40 % (3057630)Instruction limit reached!
% 0.72/0.40 % (3057630)------------------------------
% 0.72/0.40 % (3057630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (3057630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (3057630)CaDiCaL version: 2.1.3
% 0.72/0.40 % (3057630)Termination reason: Instruction limit
% 0.72/0.40 % (3057630)Termination phase: Property scanning
% 0.72/0.40 % (3057630)Time elapsed: 0.009 s
% 0.72/0.40 % (3057630)Peak memory usage: 10 MB
% 0.72/0.40 % (3057630)Instructions burned: 27 (million)
% 0.72/0.40 % (3057627)Instruction limit reached!
% 0.72/0.40 % (3057627)------------------------------
% 0.72/0.40 % (3057627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (3057627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (3057627)CaDiCaL version: 2.1.3
% 0.72/0.40 % (3057627)Termination reason: Instruction limit
% 0.72/0.40 % (3057627)Termination phase: Property scanning
% 0.72/0.40 % (3057627)Time elapsed: 0.008 s
% 0.72/0.40 % (3057627)Peak memory usage: 10 MB
% 0.72/0.40 % (3057627)Instructions burned: 20 (million)
% 0.72/0.40 % (3057632)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.72/0.40 % (3057632)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
% 0.72/0.40 % (3057632)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=1771111678:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.72/0.40 % (3057639)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=919633227:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.72/0.40 % (3057641)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.72/0.40 % (3057639)Instruction limit reached!
% 0.72/0.40 % (3057639)------------------------------
% 0.72/0.40 % (3057639)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (3057639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (3057639)CaDiCaL version: 2.1.3
% 0.72/0.40 % (3057639)Termination reason: Instruction limit
% 0.72/0.40 % (3057639)Termination phase: shuffling
% 0.72/0.40 % (3057639)Time elapsed: 0.003 s
% 0.72/0.40 % (3057639)Peak memory usage: 10 MB
% 0.72/0.40 % (3057639)Instructions burned: 6 (million)
% 0.72/0.46 % (3057641)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1639955329:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.72/0.46 % (3057640)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1991249859:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.72/0.46 % (3057641)Instruction limit reached!
% 0.72/0.46 % (3057641)------------------------------
% 0.72/0.46 % (3057641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.46 % (3057641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.46 % (3057641)CaDiCaL version: 2.1.3
% 0.72/0.46 % (3057641)Termination reason: Instruction limit
% 0.72/0.46 % (3057641)Termination phase: shuffling
% 0.72/0.46 % (3057641)Time elapsed: 0.003 s
% 0.72/0.46 % (3057641)Peak memory usage: 9 MB
% 0.72/0.46 % (3057641)Instructions burned: 8 (million)
% 0.72/0.46 % (3057631)Instruction limit reached!
% 0.72/0.46 % (3057631)------------------------------
% 0.72/0.46 % (3057631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.46 % (3057631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.46 % (3057631)CaDiCaL version: 2.1.3
% 0.72/0.46 % (3057631)Termination reason: Instruction limit
% 0.72/0.46 % (3057631)Termination phase: Saturation
% 0.72/0.46 % (3057631)Time elapsed: 0.031 s
% 0.72/0.46 % (3057631)Peak memory usage: 13 MB
% 0.72/0.46 % (3057631)Instructions burned: 75 (million)
% 0.72/0.46 % (3057640)Instruction limit reached!
% 0.72/0.46 % (3057640)------------------------------
% 0.72/0.46 % (3057640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.46 % (3057640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.46 % (3057640)CaDiCaL version: 2.1.3
% 0.72/0.46 % (3057640)Termination reason: Instruction limit
% 0.72/0.46 % (3057640)Termination phase: shuffling
% 0.72/0.46 % (3057640)Time elapsed: 0.003 s
% 0.72/0.46 % (3057640)Peak memory usage: 10 MB
% 0.72/0.46 % (3057640)Instructions burned: 6 (million)
% 0.72/0.46 % (3057626)Instruction limit reached!
% 0.72/0.46 % (3057626)------------------------------
% 0.72/0.46 % (3057626)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.46 % (3057626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.46 % (3057626)CaDiCaL version: 2.1.3
% 0.72/0.46 % (3057626)Termination reason: Instruction limit
% 0.72/0.46 % (3057626)Termination phase: Saturation
% 0.72/0.46 % (3057626)Time elapsed: 0.041 s
% 0.72/0.46 % (3057626)Peak memory usage: 12 MB
% 0.72/0.46 % (3057626)Instructions burned: 93 (million)
% 0.72/0.46 % (3057647)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
% 0.72/0.46 % (3057647)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.72/0.46 % (3057647)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1945092179:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.72/0.46 % (3057648)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=2009771346:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.72/0.46 % (3057649)lrs+10_1_si=on:cs=on:random_seed=2721820937:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.72/0.46 % (3057644)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=151075916:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.72/0.46 % (3057649)Instruction limit reached!
% 0.72/0.46 % (3057649)------------------------------
% 0.72/0.46 % (3057649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.46 % (3057649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.46 % (3057649)CaDiCaL version: 2.1.3
% 0.72/0.46 % (3057649)Termination reason: Instruction limit
% 0.72/0.46 % (3057649)Termination phase: shuffling
% 0.72/0.46 % (3057649)Time elapsed: 0.004 s
% 0.72/0.46 % (3057649)Peak memory usage: 10 MB
% 0.72/0.46 % (3057649)Instructions burned: 9 (million)
% 0.72/0.46 % (3057650)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.44/0.51 % (3057650)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=482978802:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.44/0.51 % (3057647)Instruction limit reached!
% 1.44/0.51 % (3057647)------------------------------
% 1.44/0.51 % (3057647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.51 % (3057647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.51 % (3057647)CaDiCaL version: 2.1.3
% 1.44/0.51 % (3057647)Termination reason: Instruction limit
% 1.44/0.51 % (3057647)Termination phase: Property scanning
% 1.44/0.51 % (3057647)Time elapsed: 0.012 s
% 1.44/0.51 % (3057647)Peak memory usage: 10 MB
% 1.44/0.51 % (3057647)Instructions burned: 29 (million)
% 1.44/0.51 % (3057650)Instruction limit reached!
% 1.44/0.51 % (3057650)------------------------------
% 1.44/0.51 % (3057650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.51 % (3057650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.51 % (3057650)CaDiCaL version: 2.1.3
% 1.44/0.51 % (3057650)Termination reason: Instruction limit
% 1.44/0.51 % (3057650)Termination phase: shuffling
% 1.44/0.51 % (3057650)Time elapsed: 0.002 s
% 1.44/0.51 % (3057650)Peak memory usage: 9 MB
% 1.44/0.51 % (3057650)Instructions burned: 4 (million)
% 1.44/0.51 % (3057644)Instruction limit reached!
% 1.44/0.51 % (3057644)------------------------------
% 1.44/0.51 % (3057644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.51 % (3057644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.51 % (3057644)CaDiCaL version: 2.1.3
% 1.44/0.51 % (3057644)Termination reason: Instruction limit
% 1.44/0.51 % (3057644)Termination phase: Property scanning
% 1.44/0.51 % (3057644)Time elapsed: 0.012 s
% 1.44/0.51 % (3057644)Peak memory usage: 10 MB
% 1.44/0.51 % (3057644)Instructions burned: 18 (million)
% 1.44/0.51 % (3057655)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4032485247:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.44/0.51 % (3057657)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=134200966:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.44/0.51 % (3057648)Instruction limit reached!
% 1.44/0.51 % (3057648)------------------------------
% 1.44/0.51 % (3057648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.51 % (3057648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.51 % (3057648)CaDiCaL version: 2.1.3
% 1.44/0.51 % (3057648)Termination reason: Instruction limit
% 1.44/0.51 % (3057648)Termination phase: Saturation
% 1.44/0.51 % (3057648)Time elapsed: 0.032 s
% 1.44/0.51 % (3057648)Peak memory usage: 13 MB
% 1.44/0.51 % (3057648)Instructions burned: 89 (million)
% 1.44/0.51 % (3057658)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=569013209:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.44/0.51 % (3057659)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3577646414:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.44/0.51 % (3057658)Instruction limit reached!
% 1.44/0.51 % (3057658)------------------------------
% 1.44/0.51 % (3057658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.51 % (3057658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.51 % (3057658)CaDiCaL version: 2.1.3
% 1.44/0.51 % (3057658)Termination reason: Instruction limit
% 1.44/0.51 % (3057658)Termination phase: SInE selection
% 1.44/0.51 % (3057658)Time elapsed: 0.011 s
% 1.44/0.51 % (3057658)Peak memory usage: 10 MB
% 1.44/0.51 % (3057658)Instructions burned: 26 (million)
% 1.44/0.51 % (3057659)Instruction limit reached!
% 1.44/0.51 % (3057659)------------------------------
% 1.44/0.51 % (3057659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.51 % (3057659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.51 % (3057659)CaDiCaL version: 2.1.3
% 1.44/0.51 % (3057659)Termination reason: Instruction limit
% 1.44/0.51 % (3057659)Termination phase: Property scanning
% 1.44/0.59 % (3057659)Time elapsed: 0.006 s
% 1.44/0.59 % (3057659)Peak memory usage: 10 MB
% 1.44/0.59 % (3057659)Instructions burned: 14 (million)
% 1.44/0.59 % (3057655)Refutation not found, incomplete strategy
% 1.44/0.59 % (3057655)------------------------------
% 1.44/0.59 % (3057655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.59 % (3057655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.59 % (3057655)CaDiCaL version: 2.1.3
% 1.44/0.59 % (3057655)Termination reason: Refutation not found, incomplete strategy
% 1.44/0.59 % (3057655)Time elapsed: 0.021 s
% 1.44/0.59 % (3057655)Peak memory usage: 12 MB
% 1.44/0.59 % (3057655)Instructions burned: 28 (million)
% 1.44/0.59 % (3057655)------------------------------
% 1.44/0.59 % (3057655)------------------------------
% 1.44/0.59 % (3057663)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4010107111:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.44/0.59 % (3057666)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3009467405:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.44/0.59 % (3057666)Instruction limit reached!
% 1.44/0.59 % (3057666)------------------------------
% 1.44/0.59 % (3057666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.59 % (3057666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.59 % (3057666)CaDiCaL version: 2.1.3
% 1.44/0.59 % (3057666)Termination reason: Instruction limit
% 1.44/0.59 % (3057666)Termination phase: shuffling
% 1.44/0.59 % (3057666)Time elapsed: 0.003 s
% 1.44/0.59 % (3057666)Peak memory usage: 10 MB
% 1.44/0.59 % (3057666)Instructions burned: 8 (million)
% 1.44/0.59 % (3057665)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1501556953:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.44/0.59 % (3057667)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2351614482:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.44/0.59 % (3057665)Instruction limit reached!
% 1.44/0.59 % (3057665)------------------------------
% 1.44/0.59 % (3057665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.59 % (3057665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.59 % (3057665)CaDiCaL version: 2.1.3
% 1.44/0.59 % (3057665)Termination reason: Instruction limit
% 1.44/0.59 % (3057665)Termination phase: Property scanning
% 1.44/0.59 % (3057665)Time elapsed: 0.006 s
% 1.44/0.59 % (3057665)Peak memory usage: 10 MB
% 1.44/0.59 % (3057665)Instructions burned: 17 (million)
% 1.44/0.59 % (3057667)Instruction limit reached!
% 1.44/0.59 % (3057667)------------------------------
% 1.44/0.59 % (3057667)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.59 % (3057667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.59 % (3057667)CaDiCaL version: 2.1.3
% 1.44/0.59 % (3057667)Termination reason: Instruction limit
% 1.44/0.59 % (3057667)Termination phase: Property scanning
% 1.44/0.59 % (3057667)Time elapsed: 0.011 s
% 1.44/0.59 % (3057667)Peak memory usage: 10 MB
% 1.44/0.59 % (3057667)Instructions burned: 28 (million)
% 1.44/0.59 % (3057632)Instruction limit reached!
% 1.44/0.59 % (3057632)------------------------------
% 1.44/0.59 % (3057632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.59 % (3057632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.59 % (3057632)CaDiCaL version: 2.1.3
% 1.44/0.59 % (3057632)Termination reason: Instruction limit
% 1.44/0.59 % (3057632)Termination phase: Saturation
% 1.44/0.59 % (3057632)Time elapsed: 0.129 s
% 1.44/0.59 % (3057632)Peak memory usage: 13 MB
% 1.44/0.59 % (3057632)Instructions burned: 157 (million)
% 1.44/0.59 % (3057670)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3434291824:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.44/0.59 % (3057674)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.44/0.59 % (3057674)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.44/0.59 % (3057670)Instruction limit reached!
% 2.33/0.64 % (3057670)------------------------------
% 2.33/0.64 % (3057670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.33/0.64 % (3057670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.64 % (3057670)CaDiCaL version: 2.1.3
% 2.33/0.64 % (3057670)Termination reason: Instruction limit
% 2.33/0.64 % (3057670)Termination phase: Preprocessing 3
% 2.33/0.64 % (3057670)Time elapsed: 0.010 s
% 2.33/0.64 % (3057670)Peak memory usage: 10 MB
% 2.33/0.64 % (3057670)Instructions burned: 23 (million)
% 2.33/0.64 % (3057673)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=177824373:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.33/0.64 % (3057674)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3272651254:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.33/0.64 % (3057674)Instruction limit reached!
% 2.33/0.64 % (3057674)------------------------------
% 2.33/0.64 % (3057674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.33/0.64 % (3057674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.64 % (3057674)CaDiCaL version: 2.1.3
% 2.33/0.64 % (3057674)Termination reason: Instruction limit
% 2.33/0.64 % (3057674)Termination phase: Property scanning
% 2.33/0.64 % (3057674)Time elapsed: 0.009 s
% 2.33/0.64 % (3057674)Peak memory usage: 9 MB
% 2.33/0.64 % (3057674)Instructions burned: 14 (million)
% 2.33/0.64 % (3057675)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.33/0.64 % (3057677)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1962324787:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.33/0.64 % (3057675)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=1370426560:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.33/0.64 % (3057675)Instruction limit reached!
% 2.33/0.64 % (3057675)------------------------------
% 2.33/0.64 % (3057675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.33/0.64 % (3057675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.64 % (3057675)CaDiCaL version: 2.1.3
% 2.33/0.64 % (3057675)Termination reason: Instruction limit
% 2.33/0.64 % (3057675)Termination phase: shuffling
% 2.33/0.64 % (3057675)Time elapsed: 0.004 s
% 2.33/0.64 % (3057675)Peak memory usage: 10 MB
% 2.33/0.64 % (3057675)Instructions burned: 8 (million)
% 2.33/0.64 % (3057673)Instruction limit reached!
% 2.33/0.64 % (3057673)------------------------------
% 2.33/0.64 % (3057673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.33/0.64 % (3057673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.64 % (3057673)CaDiCaL version: 2.1.3
% 2.33/0.64 % (3057673)Termination reason: Instruction limit
% 2.33/0.64 % (3057673)Termination phase: Saturation
% 2.33/0.64 % (3057673)Time elapsed: 0.023 s
% 2.33/0.64 % (3057673)Peak memory usage: 12 MB
% 2.33/0.64 % (3057673)Instructions burned: 62 (million)
% 2.33/0.64 % (3057677)Instruction limit reached!
% 2.33/0.64 % (3057677)------------------------------
% 2.33/0.64 % (3057677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.33/0.64 % (3057677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.64 % (3057677)CaDiCaL version: 2.1.3
% 2.33/0.64 % (3057677)Termination reason: Instruction limit
% 2.33/0.64 % (3057677)Termination phase: Property scanning
% 2.33/0.64 % (3057677)Time elapsed: 0.013 s
% 2.33/0.64 % (3057677)Peak memory usage: 10 MB
% 2.33/0.64 % (3057677)Instructions burned: 31 (million)
% 2.33/0.64 % (3057680)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1607473425:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.33/0.64 % (3057680)Instruction limit reached!
% 2.33/0.64 % (3057680)------------------------------
% 2.33/0.64 % (3057680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.33/0.64 % (3057680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.64 % (3057680)CaDiCaL version: 2.1.3
% 2.33/0.64 % (3057680)Termination reason: Instruction limit
% 2.54/0.71 % (3057680)Termination phase: shuffling
% 2.54/0.71 % (3057680)Time elapsed: 0.003 s
% 2.54/0.71 % (3057680)Peak memory usage: 10 MB
% 2.54/0.71 % (3057680)Instructions burned: 7 (million)
% 2.54/0.71 % (3057683)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2697183707:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.54/0.71 % (3057684)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1100737024:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.54/0.71 % (3057685)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3802854728:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.54/0.71 % (3057684)Instruction limit reached!
% 2.54/0.71 % (3057684)------------------------------
% 2.54/0.71 % (3057684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.71 % (3057684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.71 % (3057684)CaDiCaL version: 2.1.3
% 2.54/0.71 % (3057684)Termination reason: Instruction limit
% 2.54/0.71 % (3057684)Termination phase: Property scanning
% 2.54/0.71 % (3057684)Time elapsed: 0.009 s
% 2.54/0.71 % (3057684)Peak memory usage: 10 MB
% 2.54/0.71 % (3057684)Instructions burned: 21 (million)
% 2.54/0.71 % (3057683)Instruction limit reached!
% 2.54/0.71 % (3057683)------------------------------
% 2.54/0.71 % (3057683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.71 % (3057683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.71 % (3057683)CaDiCaL version: 2.1.3
% 2.54/0.71 % (3057683)Termination reason: Instruction limit
% 2.54/0.71 % (3057683)Termination phase: Property scanning
% 2.54/0.71 % (3057683)Time elapsed: 0.010 s
% 2.54/0.71 % (3057683)Peak memory usage: 10 MB
% 2.54/0.71 % (3057683)Instructions burned: 24 (million)
% 2.54/0.71 % (3057687)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2489748925:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.54/0.71 % (3057691)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=4187933118:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.54/0.71 % (3057692)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1992015205:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.54/0.71 % (3057657)Instruction limit reached!
% 2.54/0.71 % (3057657)------------------------------
% 2.54/0.71 % (3057657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.71 % (3057657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.71 % (3057657)CaDiCaL version: 2.1.3
% 2.54/0.71 % (3057657)Termination reason: Instruction limit
% 2.54/0.71 % (3057657)Termination phase: Saturation
% 2.54/0.71 % (3057657)Time elapsed: 0.154 s
% 2.54/0.71 % (3057657)Peak memory usage: 13 MB
% 2.54/0.71 % (3057657)Instructions burned: 249 (million)
% 2.54/0.71 % (3057629)Instruction limit reached!
% 2.54/0.71 % (3057629)------------------------------
% 2.54/0.71 % (3057629)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.71 % (3057629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.71 % (3057629)CaDiCaL version: 2.1.3
% 2.54/0.71 % (3057629)Termination reason: Instruction limit
% 2.54/0.71 % (3057629)Termination phase: Saturation
% 2.54/0.71 % (3057629)Time elapsed: 0.271 s
% 2.54/0.71 % (3057629)Peak memory usage: 18 MB
% 2.54/0.71 % (3057629)Instructions burned: 636 (million)
% 2.54/0.71 % (3057692)Instruction limit reached!
% 2.54/0.71 % (3057692)------------------------------
% 2.54/0.71 % (3057692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.71 % (3057692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.71 % (3057692)CaDiCaL version: 2.1.3
% 2.54/0.71 % (3057692)Termination reason: Instruction limit
% 2.54/0.71 % (3057692)Termination phase: Saturation
% 2.54/0.71 % (3057692)Time elapsed: 0.040 s
% 2.54/0.71 % (3057692)Peak memory usage: 12 MB
% 2.54/0.71 % (3057692)Instructions burned: 44 (million)
% 2.54/0.71 % (3057696)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.54/0.71 % (3057687)Instruction limit reached!
% 2.54/0.71 % (3057687)------------------------------
% 2.54/0.71 % (3057687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.80 % (3057687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.80 % (3057687)CaDiCaL version: 2.1.3
% 2.54/0.80 % (3057687)Termination reason: Instruction limit
% 2.54/0.80 % (3057687)Termination phase: Saturation
% 2.54/0.80 % (3057687)Time elapsed: 0.061 s
% 2.54/0.80 % (3057687)Peak memory usage: 13 MB
% 2.54/0.80 % (3057687)Instructions burned: 143 (million)
% 2.54/0.80 % (3057696)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1234875513:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.54/0.80 % (3057696)Instruction limit reached!
% 2.54/0.80 % (3057696)------------------------------
% 2.54/0.80 % (3057696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.80 % (3057696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.80 % (3057696)CaDiCaL version: 2.1.3
% 2.54/0.80 % (3057696)Termination reason: Instruction limit
% 2.54/0.80 % (3057696)Termination phase: shuffling
% 2.54/0.80 % (3057696)Time elapsed: 0.008 s
% 2.54/0.80 % (3057696)Peak memory usage: 9 MB
% 2.54/0.80 % (3057696)Instructions burned: 8 (million)
% 2.54/0.80 % (3057699)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.54/0.80 % (3057699)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=4102702463:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 2.54/0.80 % (3057699)Instruction limit reached!
% 2.54/0.80 % (3057699)------------------------------
% 2.54/0.80 % (3057699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.80 % (3057699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.80 % (3057699)CaDiCaL version: 2.1.3
% 2.54/0.80 % (3057699)Termination reason: Instruction limit
% 2.54/0.80 % (3057699)Termination phase: shuffling
% 2.54/0.80 % (3057699)Time elapsed: 0.003 s
% 2.54/0.80 % (3057699)Peak memory usage: 9 MB
% 2.54/0.80 % (3057699)Instructions burned: 6 (million)
% 2.54/0.80 % (3057697)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3434679868:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 2.95/0.80 % (3057698)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3824564278:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 2.95/0.80 % (3057691)Instruction limit reached!
% 2.95/0.80 % (3057691)------------------------------
% 2.95/0.80 % (3057691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.80 % (3057691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.80 % (3057691)CaDiCaL version: 2.1.3
% 2.95/0.80 % (3057691)Termination reason: Instruction limit
% 2.95/0.80 % (3057691)Termination phase: Saturation
% 2.95/0.80 % (3057691)Time elapsed: 0.087 s
% 2.95/0.80 % (3057691)Peak memory usage: 13 MB
% 2.95/0.80 % (3057691)Instructions burned: 193 (million)
% 2.95/0.80 % (3057663)Instruction limit reached!
% 2.95/0.80 % (3057663)------------------------------
% 2.95/0.80 % (3057663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.80 % (3057663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.80 % (3057663)CaDiCaL version: 2.1.3
% 2.95/0.80 % (3057663)Termination reason: Instruction limit
% 2.95/0.80 % (3057663)Termination phase: Saturation
% 2.95/0.80 % (3057663)Time elapsed: 0.214 s
% 2.95/0.80 % (3057663)Peak memory usage: 14 MB
% 2.95/0.80 % (3057663)Instructions burned: 327 (million)
% 2.95/0.80 % (3057701)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1246510191:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.95/0.80 % (3057701)Instruction limit reached!
% 2.95/0.80 % (3057701)------------------------------
% 2.95/0.80 % (3057701)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.80 % (3057701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.80 % (3057701)CaDiCaL version: 2.1.3
% 2.95/0.80 % (3057701)Termination reason: Instruction limit
% 2.95/0.80 % (3057701)Termination phase: Preprocessing 3
% 2.95/0.80 % (3057701)Time elapsed: 0.008 s
% 2.95/0.80 % (3057701)Peak memory usage: 10 MB
% 3.52/0.92 % (3057701)Instructions burned: 23 (million)
% 3.52/0.92 % (3057697)Refutation not found, incomplete strategy
% 3.52/0.92 % (3057697)------------------------------
% 3.52/0.92 % (3057697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.92 % (3057697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.92 % (3057697)CaDiCaL version: 2.1.3
% 3.52/0.92 % (3057697)Termination reason: Refutation not found, incomplete strategy
% 3.52/0.92 % (3057697)Time elapsed: 0.031 s
% 3.52/0.92 % (3057697)Peak memory usage: 13 MB
% 3.52/0.92 % (3057697)Instructions burned: 27 (million)
% 3.52/0.92 % (3057706)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=3777130648:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 3.52/0.92 % (3057697)------------------------------
% 3.52/0.92 % (3057697)------------------------------
% 3.52/0.92 % (3057703)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2875977330:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 3.52/0.92 % (3057707)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3208668462:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 3.52/0.92 % (3057703)Instruction limit reached!
% 3.52/0.92 % (3057703)------------------------------
% 3.52/0.92 % (3057703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.92 % (3057703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.92 % (3057703)CaDiCaL version: 2.1.3
% 3.52/0.92 % (3057703)Termination reason: Instruction limit
% 3.52/0.92 % (3057703)Termination phase: Property scanning
% 3.52/0.92 % (3057703)Time elapsed: 0.008 s
% 3.52/0.92 % (3057703)Peak memory usage: 9 MB
% 3.52/0.92 % (3057703)Instructions burned: 19 (million)
% 3.52/0.92 % (3057710)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=1704783670:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 3.52/0.92 % (3057714)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=720253809:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 3.52/0.92 % (3057711)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2159956248:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.52/0.92 % (3057714)Instruction limit reached!
% 3.52/0.92 % (3057714)------------------------------
% 3.52/0.92 % (3057714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.92 % (3057714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.92 % (3057714)CaDiCaL version: 2.1.3
% 3.52/0.92 % (3057714)Termination reason: Instruction limit
% 3.52/0.92 % (3057714)Termination phase: Unused predicate definition removal
% 3.52/0.92 % (3057714)Time elapsed: 0.009 s
% 3.52/0.92 % (3057714)Peak memory usage: 10 MB
% 3.52/0.92 % (3057714)Instructions burned: 22 (million)
% 3.52/0.92 % (3057710)Instruction limit reached!
% 3.52/0.92 % (3057710)------------------------------
% 3.52/0.92 % (3057710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.92 % (3057710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.92 % (3057710)CaDiCaL version: 2.1.3
% 3.52/0.92 % (3057710)Termination reason: Instruction limit
% 3.52/0.92 % (3057710)Termination phase: Saturation
% 3.52/0.92 % (3057710)Time elapsed: 0.018 s
% 3.52/0.92 % (3057710)Peak memory usage: 12 MB
% 3.52/0.92 % (3057710)Instructions burned: 45 (million)
% 3.52/0.92 % (3057718)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.52/0.92 % (3057718)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=1564228746:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/200Mi)
% 3.52/0.92 % (3057719)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=136743641:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 3.52/0.92 % (3057711)Refutation not found, incomplete strategy
% 3.52/0.94 % (3057711)------------------------------
% 3.52/0.94 % (3057711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.94 % (3057711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.94 % (3057711)CaDiCaL version: 2.1.3
% 3.52/0.94 % (3057711)Termination reason: Refutation not found, incomplete strategy
% 3.52/0.94 % (3057711)Time elapsed: 0.024 s
% 3.52/0.94 % (3057711)Peak memory usage: 12 MB
% 3.52/0.94 % (3057711)Instructions burned: 40 (million)
% 3.52/0.94 % (3057711)------------------------------
% 3.52/0.94 % (3057711)------------------------------
% 3.52/0.94 % (3057719)Instruction limit reached!
% 3.52/0.94 % (3057719)------------------------------
% 3.52/0.94 % (3057719)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.94 % (3057719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.94 % (3057719)CaDiCaL version: 2.1.3
% 3.52/0.94 % (3057719)Termination reason: Instruction limit
% 3.52/0.94 % (3057719)Termination phase: Property scanning
% 3.52/0.94 % (3057719)Time elapsed: 0.006 s
% 3.52/0.94 % (3057719)Peak memory usage: 10 MB
% 3.52/0.94 % (3057719)Instructions burned: 15 (million)
% 3.52/0.94 % (3057723)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=2430208059:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 3.52/0.94 % (3057722)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=1284614338:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 3.52/0.94 % (3057698)Instruction limit reached!
% 3.52/0.94 % (3057698)------------------------------
% 3.52/0.94 % (3057698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.94 % (3057698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.94 % (3057698)CaDiCaL version: 2.1.3
% 3.52/0.94 % (3057698)Termination reason: Instruction limit
% 3.52/0.94 % (3057698)Termination phase: Saturation
% 3.52/0.94 % (3057698)Time elapsed: 0.126 s
% 3.52/0.94 % (3057698)Peak memory usage: 13 MB
% 3.52/0.94 % (3057698)Instructions burned: 170 (million)
% 3.52/0.94 % (3057723)Instruction limit reached!
% 3.52/0.94 % (3057723)------------------------------
% 3.52/0.94 % (3057723)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.94 % (3057723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.94 % (3057723)CaDiCaL version: 2.1.3
% 3.52/0.94 % (3057723)Termination reason: Instruction limit
% 3.52/0.94 % (3057723)Termination phase: Saturation
% 3.52/0.94 % (3057723)Time elapsed: 0.022 s
% 3.52/0.94 % (3057723)Peak memory usage: 12 MB
% 3.52/0.94 % (3057723)Instructions burned: 53 (million)
% 3.52/0.94 % (3057726)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=869439064:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 3.52/0.94 % (3057727)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=2833991082:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 3.52/0.94 % (3057726)Instruction limit reached!
% 3.52/0.94 % (3057726)------------------------------
% 3.52/0.94 % (3057726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.95 % (3057726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.95 % (3057726)CaDiCaL version: 2.1.3
% 3.52/0.95 % (3057726)Termination reason: Instruction limit
% 3.52/0.95 % (3057726)Termination phase: Property scanning
% 3.52/0.95 % (3057726)Time elapsed: 0.013 s
% 3.52/0.95 % (3057726)Peak memory usage: 10 MB
% 3.52/0.95 % (3057726)Instructions burned: 32 (million)
% 3.52/0.95 % (3057722)Instruction limit reached!
% 3.52/0.95 % (3057722)------------------------------
% 3.52/0.95 % (3057722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.95 % (3057722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.95 % (3057722)CaDiCaL version: 2.1.3
% 3.52/0.95 % (3057722)Termination reason: Instruction limit
% 3.52/0.95 % (3057722)Termination phase: Saturation
% 3.52/0.95 % (3057722)Time elapsed: 0.043 s
% 3.52/0.95 % (3057722)Peak memory usage: 13 MB
% 3.52/0.95 % (3057722)Instructions burned: 67 (million)
% 3.52/0.95 % (3057730)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=33974091:cond=on:i=34:hud=10:nm=10:rtra=on_2994 on theBenchmark for (2994ds/34Mi)
% 3.52/0.95 % (3057718)Instruction limit reached!
% 3.52/0.95 % (3057718)------------------------------
% 3.52/0.95 % (3057718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.95 % (3057718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.95 % (3057718)CaDiCaL version: 2.1.3
% 3.52/0.95 % (3057718)Termination reason: Instruction limit
% 3.52/0.95 % (3057718)Termination phase: Saturation
% 3.52/0.95 % (3057718)Time elapsed: 0.102 s
% 3.52/0.95 % (3057718)Peak memory usage: 12 MB
% 3.52/0.95 % (3057718)Instructions burned: 202 (million)
% 3.52/0.95 % (3057706)Instruction limit reached!
% 3.52/0.95 % (3057706)------------------------------
% 3.52/0.95 % (3057706)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.95 % (3057706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.95 % (3057706)CaDiCaL version: 2.1.3
% 3.52/0.95 % (3057706)Termination reason: Instruction limit
% 3.52/0.95 % (3057706)Termination phase: Saturation
% 3.52/0.95 % (3057706)Time elapsed: 0.163 s
% 3.52/0.95 % (3057706)Peak memory usage: 16 MB
% 3.52/0.95 % (3057706)Instructions burned: 316 (million)
% 3.52/0.95 % (3057735)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=2050229627:st=2:i=246:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/246Mi)
% 3.52/0.95 % (3057732)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=943254852:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2994 on theBenchmark for (2994ds/67Mi)
% 3.52/0.95 % (3057734)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 3.52/0.95 % (3057730)Instruction limit reached!
% 3.52/0.95 % (3057730)------------------------------
% 3.52/0.95 % (3057730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.95 % (3057730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.95 % (3057730)CaDiCaL version: 2.1.3
% 3.52/0.95 % (3057730)Termination reason: Instruction limit
% 3.52/0.95 % (3057730)Termination phase: Saturation
% 3.52/0.95 % (3057730)Time elapsed: 0.022 s
% 3.52/0.95 % (3057730)Peak memory usage: 11 MB
% 3.52/0.95 % (3057730)Instructions burned: 36 (million)
% 3.52/0.95 % (3057734)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=1168025982:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2994 on theBenchmark for (2994ds/180Mi)
% 3.52/0.95 % (3057732)Instruction limit reached!
% 3.52/0.95 % (3057732)------------------------------
% 3.52/0.95 % (3057732)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.95 % (3057732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.95 % (3057732)CaDiCaL version: 2.1.3
% 3.52/0.95 % (3057732)Termination reason: Instruction limit
% 3.52/0.95 % (3057732)Termination phase: Saturation
% 3.52/0.95 % (3057732)Time elapsed: 0.029 s
% 3.52/0.95 % (3057732)Peak memory usage: 12 MB
% 3.52/0.95 % (3057732)Instructions burned: 69 (million)
% 3.52/0.95 % (3057738)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=4249803683:cond=on:i=96:bd=all:rtra=on_2994 on theBenchmark for (2994ds/96Mi)
% 3.52/0.95 % (3057740)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=2600229690:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 3.52/0.95 % (3057727)Instruction limit reached!
% 3.52/0.95 % (3057727)------------------------------
% 3.52/0.95 % (3057727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.95 % (3057727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.95 % (3057727)CaDiCaL version: 2.1.3
% 3.52/0.95 % (3057727)Termination reason: Instruction limit
% 3.52/0.95 % (3057727)Termination phase: Saturation
% 3.52/0.95 % (3057727)Time elapsed: 0.103 s
% 3.52/0.95 % (3057727)Peak memory usage: 13 MB
% 3.52/0.95 % (3057727)Instructions burned: 138 (million)
% 3.52/0.95 % (3057735) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3057621-3057735"...
% 3.52/0.95 % (3057743)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2794091124:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/874Mi)
% 3.52/0.95 % (3057738)Instruction limit reached!
% 3.52/0.95 % (3057738)------------------------------
% 3.52/0.95 % (3057738)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.95 % (3057738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.95 % (3057738)CaDiCaL version: 2.1.3
% 3.52/0.95 % (3057738)Termination reason: Instruction limit
% 3.52/0.95 % (3057738)Termination phase: Saturation
% 3.52/0.95 % (3057738)Time elapsed: 0.055 s
% 3.52/0.95 % (3057738)Peak memory usage: 13 MB
% 3.52/0.95 % (3057738)Instructions burned: 98 (million)
% 3.52/0.95 % (3057745)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=1270735096:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/515Mi)
% 3.52/0.95 % (3057735)...printing done.
% 3.52/0.95 % (3057735)Refutation found. Thanks to Tanya!
% 3.52/0.95 % SZS status Theorem for theBenchmark
% 3.52/0.95 % SZS output start Proof for theBenchmark
% 3.52/0.95 thf(type_def_5, type, unsorted: $tType).
% 3.52/0.95 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 3.52/0.95 thf(type_def_7, type, d_unsorted: $tType).
% 3.52/0.95 thf(func_def_0, type, subrel: (($i > $i > $o) > ($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_1, type, inv: (($i > $i > $o) > $i > $i > $o)).
% 3.52/0.95 thf(func_def_2, type, idem: ((($i > $i > $o) > $i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_3, type, infl: ((($i > $i > $o) > $i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_4, type, mono: ((($i > $i > $o) > $i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_5, type, refl: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_6, type, irrefl: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_7, type, rc: (($i > $i > $o) > $i > $i > $o)).
% 3.52/0.95 thf(func_def_8, type, symm: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_9, type, antisymm: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_10, type, asymm: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_11, type, sc: (($i > $i > $o) > $i > $i > $o)).
% 3.52/0.95 thf(func_def_12, type, trans: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_13, type, tc: (($i > $i > $o) > $i > $i > $o)).
% 3.52/0.95 thf(func_def_14, type, trc: (($i > $i > $o) > $i > $i > $o)).
% 3.52/0.95 thf(func_def_15, type, trsc: (($i > $i > $o) > $i > $i > $o)).
% 3.52/0.95 thf(func_def_16, type, po: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_17, type, so: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_18, type, total: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_19, type, term: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_20, type, ind: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_21, type, innf: (($i > $i > $o) > $i > $o)).
% 3.52/0.95 thf(func_def_22, type, nfof: (($i > $i > $o) > $i > $i > $o)).
% 3.52/0.95 thf(func_def_23, type, norm: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_24, type, join: (($i > $i > $o) > $i > $i > $o)).
% 3.52/0.95 thf(func_def_25, type, lconfl: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_26, type, sconfl: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_27, type, confl: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_28, type, cr: (($i > $i > $o) > $o)).
% 3.52/0.95 thf(func_def_29, type, d2unsorted: (d_unsorted > $i)).
% 3.52/0.95 thf(func_def_30, type, d_unsorted_0: d_unsorted).
% 3.52/0.95 thf(func_def_32, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.52/0.95 thf(func_def_33, type, vIMP: ($o > $o > $o)).
% 3.52/0.95 thf(func_def_34, type, db3: !>[X0: $tType]:(X0)).
% 3.52/0.95 thf(func_def_35, type, db1: !>[X0: $tType]:(X0)).
% 3.52/0.95 thf(func_def_36, type, db0: !>[X0: $tType]:(X0)).
% 3.52/0.95 thf(func_def_37, type, db2: !>[X0: $tType]:(X0)).
% 3.52/0.95 thf(func_def_38, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.52/0.95 thf(func_def_39, type, vOR: ($o > $o > $o)).
% 3.52/0.95 thf(func_def_40, type, vNOT: ($o > $o)).
% 3.52/0.95 thf(func_def_41, type, db5: !>[X0: $tType]:(X0)).
% 3.52/0.95 thf(func_def_42, type, db7: !>[X0: $tType]:(X0)).
% 3.52/0.95 thf(func_def_43, type, db4: !>[X0: $tType]:(X0)).
% 3.52/0.95 thf(func_def_44, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.52/0.95 thf(func_def_45, type, vAND: ($o > $o > $o)).
% 3.52/0.95 thf(func_def_46, type, db8: !>[X0: $tType]:(X0)).
% 3.52/0.95 thf(func_def_47, type, db9: !>[X0: $tType]:(X0)).
% 3.52/0.95 thf(func_def_48, type, db6: !>[X0: $tType]:(X0)).
% 3.52/0.95 thf(func_def_49, type, sK0: ($i > d_unsorted)).
% 3.52/0.95 thf(func_def_52, type, sK1: ($i > $i > $o)).
% 3.52/0.95 thf(func_def_53, type, sK2: ($i > $o)).
% 3.52/0.95 thf(func_def_54, type, sK3: ($i > $o)).
% 3.52/0.95 thf(func_def_56, type, sK5: ($i > $i)).
% 3.52/0.95 thf(func_def_57, type, sK6: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_58, type, sK7: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_59, type, sK8: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_60, type, sK9: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_61, type, sK10: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_62, type, sK11: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_63, type, sK12: ($i > $i)).
% 3.52/0.95 thf(func_def_64, type, sK13: ($i > $i)).
% 3.52/0.95 thf(func_def_65, type, sK14: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_66, type, sK15: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_67, type, sK16: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_68, type, sK17: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_69, type, sK18: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_70, type, sK19: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_71, type, sK20: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_72, type, sK21: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_73, type, sK22: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_74, type, sK23: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_75, type, sK24: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_76, type, sK25: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_77, type, sK26: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_78, type, sK27: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_79, type, sK28: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_80, type, sK29: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_81, type, sK30: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_82, type, sK31: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_83, type, sK32: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_84, type, sK33: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_85, type, sK34: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_86, type, sK35: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_87, type, sK36: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_88, type, sK37: ($i > $i)).
% 3.52/0.95 thf(func_def_89, type, sK38: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_90, type, sK39: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_91, type, sK40: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_92, type, sK41: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_93, type, sK42: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_94, type, sK43: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_97, type, sK46: ($i > $i)).
% 3.52/0.95 thf(func_def_98, type, sK47: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_99, type, sK48: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_100, type, sK49: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_101, type, sK50: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_102, type, sK51: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_103, type, sK52: (($i > $i > $o) > $i)).
% 3.52/0.95 thf(func_def_104, type, sK53: (($i > $o) > $i)).
% 3.52/0.95 thf(func_def_105, type, sK54: (($i > $o) > $i)).
% 3.52/0.95 thf(func_def_106, type, sK55: ($i > ($i > $o) > $i > $i > $o)).
% 3.52/0.95 thf(func_def_107, type, sK56: ($i > ($i > $o) > $i > $i > $o)).
% 3.52/0.95 thf(func_def_108, type, sK57: (($i > $o) > $i > $i > $i > $o)).
% 3.52/0.95 thf(func_def_109, type, sK58: (($i > $o) > $i)).
% 3.52/0.95 thf(func_def_110, type, sK59: (($i > $o) > $i > $i > $i > $o)).
% 3.52/0.95 thf(f1,axiom,(
% 3.52/0.95 (asymm = (^[X4 : ($i > $i > $o)] : (! [X7 : $i,X6 : $i] : (~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X6))))) & ((^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : (! [X22 : $i] : ~(X4 @ X6 @ X22) & (! [X5 : ($i > $i > $o)] : (~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~ ! [X13 : $i,X11 : $i,X12 : $i] : (~(X5 @ X13 @ X11) | (X5 @ X12 @ X11) | ~(X5 @ X12 @ X13)) | (X5 @ X7 @ X6)) | (X6 = X7)))) = nfof) & ((^[X8 : (($i > $i > $o) > $i > $i > $o)] : (! [X6 : $i,X7 : $i,X4 : ($i > $i > $o)] : (~(X4 @ X6 @ X7) | (X8 @ X4 @ X6 @ X7)))) = infl) & ((^[X4 : ($i > $i > $o)] : (! [X7 : $i,X11 : $i,X6 : $i] : (~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X11) | (X4 @ X6 @ X11)))) = trans) & (antisymm = (^[X4 : ($i > $i > $o)] : (! [X7 : $i,X6 : $i] : (~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X6) | (X6 = X7))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (X0 = ((d2unsorted @ X1))) & (rc = (^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : ((X4 @ X6 @ X7) | (X6 = X7)))) & ((^[X4 : ($i > $i > $o)] : (! [X6 : $i] : (X4 @ X6 @ X6))) = refl) & ((^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : ((X4 @ X6 @ X7) | (X4 @ X7 @ X6))) = sc) & ((^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : (~((X6 != X7) & ~ ! [X5 : ($i > $i > $o)] : (~ ! [X12 : $i,X26 : $i,X13 : $i] : (~(X5 @ X13 @ X26) | (X5 @ X12 @ X26) | ~(X5 @ X12 @ X13)) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | (X5 @ X6 @ X7)) & ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X6) | ~ ! [X13 : $i,X25 : $i,X12 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13)) | ~ ! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15))) & ! [X27 : $i] : (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X27) | ~ ! [X26 : $i,X13 : $i,X12 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X26)) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15))) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X27) | ~ ! [X13 : $i,X12 : $i,X25 : $i] : (~(X5 @ X13 @ X25) | (X5 @ X12 @ X25) | ~(X5 @ X12 @ X13)) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15))))))) = join) & (symm = (^[X4 : ($i > $i > $o)] : (! [X7 : $i,X6 : $i] : ((X4 @ X7 @ X6) | ~(X4 @ X6 @ X7))))) & (norm = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X23 : $i] : (~ ! [X24 : $i] : (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X24) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~ ! [X13 : $i,X12 : $i,X11 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X11))) | ~ ! [X22 : $i] : ~(X4 @ X24 @ X22)) | ~(X4 @ X6 @ X23))))) & (inv = (^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : ((X4 @ X7 @ X6)))) & ((^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i,X11 : $i] : (~(X4 @ X7 @ X11) | (X4 @ X6 @ X11) | ~(X4 @ X6 @ X7)) & ! [X6 : $i,X7 : $i] : (~(X4 @ X7 @ X6) | ~(X4 @ X6 @ X7)))) = so) & ((^[X4 : ($i > $i > $o), X5 : ($i > $i > $o)] : (! [X7 : $i,X6 : $i] : (~(X4 @ X6 @ X7) | (X5 @ X6 @ X7)))) = subrel) & ((^[X4 : ($i > $i > $o), X6 : $i] : (! [X7 : $i] : ~(X4 @ X6 @ X7))) = innf) & (lconfl = (^[X4 : ($i > $i > $o)] : (! [X29 : ($i > $i > $o),X6 : $i,X11 : $i,X7 : $i,X28 : ($i > $i > $o)] : (~ ! [X27 : $i] : (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X27) | ~ ! [X25 : $i,X12 : $i,X13 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X25) | ~(X5 @ X13 @ X25)) | ~ ! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15))) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X11 @ X27) | ~ ! [X26 : $i,X12 : $i,X13 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X26) | ~(X5 @ X13 @ X26)) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)))) | ~(X4 @ X6 @ X7) | (X28 @ X7 @ X11) | (X29 @ X11 @ X7) | ~ ! [X12 : $i,X26 : $i,X13 : $i] : (~(X29 @ X12 @ X13) | (X29 @ X12 @ X26) | ~(X29 @ X13 @ X26)) | ~ ! [X14 : $i,X15 : $i] : ((X29 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X7 = X11) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X28 @ X14 @ X15)) | ~(X4 @ X6 @ X11) | ~ ! [X13 : $i,X12 : $i,X25 : $i] : (~(X28 @ X12 @ X13) | ~(X28 @ X13 @ X25) | (X28 @ X12 @ X25)))))) & ((^[X4 : ($i > $i > $o)] : (! [X33 : ($i > $i > $o),X6 : $i,X11 : $i,X7 : $i,X34 : ($i > $i > $o)] : (~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X33 @ X14 @ X15)) | ~ ! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X34 @ X14 @ X15)) | (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X11) | ~ ! [X12 : $i,X26 : $i,X13 : $i] : (~(X5 @ X13 @ X26) | (X5 @ X12 @ X26) | ~(X5 @ X12 @ X13)) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15))) & (X6 != X11)) | ~ ! [X27 : $i] : (~ ! [X5 : ($i > $i > $o)] : (~ ! [X13 : $i,X12 : $i,X26 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X26)) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X11 @ X27)) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X27) | ~ ! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X25 : $i,X13 : $i,X12 : $i] : (~(X5 @ X13 @ X25) | (X5 @ X12 @ X25) | ~(X5 @ X12 @ X13)))) | ((X6 != X7) & ~ ! [X5 : ($i > $i > $o)] : (~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X35 : $i] : ((X5 @ X12 @ X35) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X35)) | (X5 @ X6 @ X7))) | ~ ! [X12 : $i,X13 : $i,X25 : $i] : (~(X33 @ X13 @ X25) | (X33 @ X12 @ X25) | ~(X33 @ X12 @ X13)) | (X34 @ X11 @ X7) | (X33 @ X7 @ X11) | (X7 = X11) | ~ ! [X13 : $i,X26 : $i,X12 : $i] : (~(X34 @ X12 @ X13) | (X34 @ X12 @ X26) | ~(X34 @ X13 @ X26))))) = confl) & ((^[X4 : ($i > $i > $o)] : (! [X21 : $i,X20 : ($i > $o)] : (~ ! [X6 : $i] : (~ ! [X7 : $i] : (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X7) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X11 : $i,X13 : $i,X12 : $i] : (~(X5 @ X13 @ X11) | (X5 @ X12 @ X11) | ~(X5 @ X12 @ X13))) | (X20 @ X7)) | (X20 @ X6)) | (X20 @ X21)))) = ind) & ((^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : (! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X7) | ~ ! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X11 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13))))) = tc) & (po = (^[X4 : ($i > $i > $o)] : (! [X6 : $i] : (X4 @ X6 @ X6) & ! [X7 : $i,X6 : $i,X11 : $i] : ((X4 @ X6 @ X11) | ~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X11)) & ! [X6 : $i,X7 : $i] : (~(X4 @ X7 @ X6) | (X6 = X7) | ~(X4 @ X6 @ X7))))) & ((^[X4 : ($i > $i > $o)] : (! [X18 : ($i > $o),X19 : $i] : (~ ! [X6 : $i] : (~ ! [X7 : $i] : (~(X4 @ X6 @ X7) | ~(X18 @ X7)) | ~(X18 @ X6)) | ~(X18 @ X19)))) = term) & ! [X1 : d_unsorted] : (X1 = d_unsorted_0) & ((^[X8 : (($i > $i > $o) > $i > $i > $o)] : (! [X4 : ($i > $i > $o),X10 : $i,X5 : ($i > $i > $o),X9 : $i] : ((X8 @ X5 @ X9 @ X10) | ~(X8 @ X4 @ X9 @ X10) | ~ ! [X6 : $i,X7 : $i] : ((X5 @ X6 @ X7) | ~(X4 @ X6 @ X7))))) = mono) & (irrefl = (^[X4 : ($i > $i > $o)] : (! [X6 : $i] : ~(X4 @ X6 @ X6)))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & ((^[X4 : ($i > $i > $o), X16 : $i, X17 : $i] : ((X16 = X17) | ! [X5 : ($i > $i > $o)] : ((X5 @ X17 @ X16) | ~ ! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X13 : $i,X11 : $i,X12 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X11) | (X5 @ X12 @ X11))) | ! [X5 : ($i > $i > $o)] : (~ ! [X11 : $i,X12 : $i,X13 : $i] : (~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X11)) | (X5 @ X16 @ X17) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15))))) = trsc) & (cr = (^[X4 : ($i > $i > $o)] : (! [X7 : $i,X37 : ($i > $i > $o),X36 : ($i > $i > $o),X6 : $i] : (~ ! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X37 @ X14 @ X15)) | ~ ! [X27 : $i] : (~ ! [X5 : ($i > $i > $o)] : (~ ! [X25 : $i,X13 : $i,X12 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X25) | ~(X5 @ X13 @ X25)) | (X5 @ X7 @ X27) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15))) | ~ ! [X5 : ($i > $i > $o)] : (~ ! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X6 @ X27) | ~ ! [X26 : $i,X13 : $i,X12 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X26) | (X5 @ X12 @ X26)))) | (X36 @ X7 @ X6) | (X6 = X7) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X36 @ X14 @ X15)) | ~ ! [X25 : $i,X12 : $i,X13 : $i] : (~(X36 @ X13 @ X25) | (X36 @ X12 @ X25) | ~(X36 @ X12 @ X13)) | ((X6 != X7) & ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X7) | ~ ! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X11 : $i] : (~(X5 @ X13 @ X11) | (X5 @ X12 @ X11) | ~(X5 @ X12 @ X13))) & ~ ! [X5 : ($i > $i > $o)] : (~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X7 @ X6) | ~ ! [X12 : $i,X13 : $i,X11 : $i] : (~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X11)))) | (X37 @ X6 @ X7) | ~ ! [X26 : $i,X12 : $i,X13 : $i] : (~(X37 @ X13 @ X26) | ~(X37 @ X12 @ X13) | (X37 @ X12 @ X26)))))) & ((^[X8 : (($i > $i > $o) > $i > $i > $o)] : (! [X4 : ($i > $i > $o)] : (((X8 @ X4)) = ((X8 @ (X8 @ X4)))))) = idem) & (total = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i] : ((X4 @ X7 @ X6) | (X4 @ X6 @ X7) | (X6 = X7))))) & (trc = (^[X4 : ($i > $i > $o), X16 : $i, X17 : $i] : ((X16 = X17) | ! [X5 : ($i > $i > $o)] : ((X5 @ X16 @ X17) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~ ! [X12 : $i,X11 : $i,X13 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X11) | (X5 @ X12 @ X11)))))) & ((^[X4 : ($i > $i > $o)] : (! [X6 : $i,X31 : ($i > $i > $o),X30 : ($i > $i > $o),X7 : $i,X11 : $i] : (~ ! [X27 : $i] : (~ ! [X5 : ($i > $i > $o)] : (~ ! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X13 : $i,X25 : $i,X12 : $i] : (~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X25)) | (X5 @ X7 @ X27)) | ~ ! [X5 : ($i > $i > $o)] : (~ ! [X26 : $i,X12 : $i,X13 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X26) | (X5 @ X12 @ X26)) | (X5 @ X11 @ X27) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)))) | ~ ! [X12 : $i,X26 : $i,X13 : $i] : ((X31 @ X12 @ X26) | ~(X31 @ X13 @ X26) | ~(X31 @ X12 @ X13)) | (X31 @ X11 @ X7) | ~ ! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X30 @ X14 @ X15)) | ~(X4 @ X6 @ X11) | (~ ! [X5 : ($i > $i > $o)] : (~ ! [X32 : $i,X12 : $i,X13 : $i] : (~(X5 @ X13 @ X32) | (X5 @ X12 @ X32) | ~(X5 @ X12 @ X13)) | ~ ! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X6 @ X7)) & (X6 != X7)) | (X30 @ X7 @ X11) | (X7 = X11) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X31 @ X14 @ X15)) | ~ ! [X25 : $i,X13 : $i,X12 : $i] : (~(X30 @ X13 @ X25) | ~(X30 @ X12 @ X13) | (X30 @ X12 @ X25))))) = sconfl)),
% 3.52/0.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sev441_1)).
% 3.52/0.95 thf(f2,conjecture,(
% 3.52/0.95 (ind = (^[X0 : ($i > $i > $o)] : (! [X1 : ($i > $o)] : (! [X2 : $i] : (! [X3 : $i] : ((tc @ X0 @ X2 @ X3) => (X1 @ X3)) => (X1 @ X2)) => ! [X2 : $i] : (X1 @ X2)))))),
% 3.52/0.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satisfying_the_induction_principle)).
% 3.52/0.95 thf(f3,negated_conjecture,(
% 3.52/0.95 ~ (ind = (^[X0 : ($i > $i > $o)] : (! [X1 : ($i > $o)] : (! [X2 : $i] : (! [X3 : $i] : ((tc @ X0 @ X2 @ X3) => (X1 @ X3)) => (X1 @ X2)) => ! [X2 : $i] : (X1 @ X2)))))),
% 3.52/0.95 inference(negated_conjecture,[status(cth)],[f2])).
% 3.52/0.95 thf(f4,plain,(
% 3.52/0.95 ~ (ind = (^[X0 : ($i > $i > $o)] : (! [X1 : ($i > $o)] : (! [X2 : $i] : (! [X3 : $i] : ((tc @ X0 @ X2 @ X3) => (X1 @ X3)) => (X1 @ X2)) => ! [X4 : $i] : (X1 @ X4)))))),
% 3.52/0.95 inference(rectify,[],[f3])).
% 3.52/0.95 thf(f5,plain,(
% 3.52/0.95 ~ (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((tc @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 3.52/0.95 inference(fool_elimination,[],[f4])).
% 3.52/0.95 thf(f6,plain,(
% 3.52/0.95 (asymm = (^[X0 : ($i > $i > $o)] : (! [X1 : $i,X2 : $i] : (~(X0 @ X2 @ X1) | ~(X0 @ X1 @ X2))))) & ((^[X3 : ($i > $i > $o), X4 : $i, X5 : $i] : (! [X6 : $i] : ~(X3 @ X4 @ X6) & (! [X7 : ($i > $i > $o)] : (~ ! [X8 : $i,X9 : $i] : (~(X3 @ X8 @ X9) | (X7 @ X8 @ X9)) | ~ ! [X10 : $i,X11 : $i,X12 : $i] : (~(X7 @ X10 @ X11) | (X7 @ X12 @ X11) | ~(X7 @ X12 @ X10)) | (X7 @ X5 @ X4)) | (X4 = X5)))) = nfof) & ((^[X13 : (($i > $i > $o) > $i > $i > $o)] : (! [X14 : $i,X15 : $i,X16 : ($i > $i > $o)] : (~(X16 @ X14 @ X15) | (X13 @ X16 @ X14 @ X15)))) = infl) & ((^[X17 : ($i > $i > $o)] : (! [X18 : $i,X19 : $i,X20 : $i] : (~(X17 @ X20 @ X18) | ~(X17 @ X18 @ X19) | (X17 @ X20 @ X19)))) = trans) & (antisymm = (^[X21 : ($i > $i > $o)] : (! [X22 : $i,X23 : $i] : (~(X21 @ X23 @ X22) | ~(X21 @ X22 @ X23) | (X22 = X23))))) & ! [X24 : $i] : ? [X25 : d_unsorted] : (((d2unsorted @ X25)) = X24) & (rc = (^[X26 : ($i > $i > $o), X27 : $i, X28 : $i] : ((X26 @ X27 @ X28) | (X27 = X28)))) & ((^[X29 : ($i > $i > $o)] : (! [X30 : $i] : (X29 @ X30 @ X30))) = refl) & ((^[X31 : ($i > $i > $o), X32 : $i, X33 : $i] : ((X31 @ X32 @ X33) | (X31 @ X33 @ X32))) = sc) & ((^[X34 : ($i > $i > $o), X35 : $i, X36 : $i] : (~((X35 != X36) & ~ ! [X37 : ($i > $i > $o)] : (~ ! [X38 : $i,X39 : $i,X40 : $i] : (~(X37 @ X40 @ X39) | (X37 @ X38 @ X39) | ~(X37 @ X38 @ X40)) | ~ ! [X41 : $i,X42 : $i] : (~(X34 @ X41 @ X42) | (X37 @ X41 @ X42)) | (X37 @ X35 @ X36)) & ~ ! [X43 : ($i > $i > $o)] : ((X43 @ X36 @ X35) | ~ ! [X44 : $i,X45 : $i,X46 : $i] : ((X43 @ X46 @ X45) | ~(X43 @ X44 @ X45) | ~(X43 @ X46 @ X44)) | ~ ! [X47 : $i,X48 : $i] : ((X43 @ X48 @ X47) | ~(X34 @ X48 @ X47))) & ! [X49 : $i] : (~ ! [X50 : ($i > $i > $o)] : ((X50 @ X35 @ X49) | ~ ! [X51 : $i,X52 : $i,X53 : $i] : ((X50 @ X53 @ X51) | ~(X50 @ X53 @ X52) | ~(X50 @ X52 @ X51)) | ~ ! [X54 : $i,X55 : $i] : ((X50 @ X54 @ X55) | ~(X34 @ X54 @ X55))) | ~ ! [X56 : ($i > $i > $o)] : ((X56 @ X36 @ X49) | ~ ! [X57 : $i,X58 : $i,X59 : $i] : (~(X56 @ X57 @ X59) | (X56 @ X58 @ X59) | ~(X56 @ X58 @ X57)) | ~ ! [X60 : $i,X61 : $i] : (~(X34 @ X60 @ X61) | (X56 @ X60 @ X61))))))) = join) & (symm = (^[X62 : ($i > $i > $o)] : (! [X63 : $i,X64 : $i] : ((X62 @ X63 @ X64) | ~(X62 @ X64 @ X63))))) & (norm = (^[X65 : ($i > $i > $o)] : (! [X66 : $i,X67 : $i] : (~ ! [X68 : $i] : (~ ! [X69 : ($i > $i > $o)] : ((X69 @ X66 @ X68) | ~ ! [X70 : $i,X71 : $i] : (~(X65 @ X70 @ X71) | (X69 @ X70 @ X71)) | ~ ! [X72 : $i,X73 : $i,X74 : $i] : ((X69 @ X73 @ X74) | ~(X69 @ X73 @ X72) | ~(X69 @ X72 @ X74))) | ~ ! [X75 : $i] : ~(X65 @ X68 @ X75)) | ~(X65 @ X66 @ X67))))) & (inv = (^[X76 : ($i > $i > $o), X77 : $i, X78 : $i] : ((X76 @ X78 @ X77)))) & ((^[X79 : ($i > $i > $o)] : (! [X80 : $i,X81 : $i,X82 : $i] : (~(X79 @ X81 @ X82) | (X79 @ X80 @ X82) | ~(X79 @ X80 @ X81)) & ! [X83 : $i,X84 : $i] : (~(X79 @ X84 @ X83) | ~(X79 @ X83 @ X84)))) = so) & ((^[X85 : ($i > $i > $o), X86 : ($i > $i > $o)] : (! [X87 : $i,X88 : $i] : (~(X85 @ X88 @ X87) | (X86 @ X88 @ X87)))) = subrel) & ((^[X89 : ($i > $i > $o), X90 : $i] : (! [X91 : $i] : ~(X89 @ X90 @ X91))) = innf) & (lconfl = (^[X92 : ($i > $i > $o)] : (! [X93 : ($i > $i > $o),X94 : $i,X95 : $i,X96 : $i,X97 : ($i > $i > $o)] : (~ ! [X98 : $i] : (~ ! [X99 : ($i > $i > $o)] : ((X99 @ X96 @ X98) | ~ ! [X100 : $i,X101 : $i,X102 : $i] : (~(X99 @ X101 @ X102) | (X99 @ X101 @ X100) | ~(X99 @ X102 @ X100)) | ~ ! [X103 : $i,X104 : $i] : (~(X92 @ X104 @ X103) | (X99 @ X104 @ X103))) | ~ ! [X105 : ($i > $i > $o)] : ((X105 @ X95 @ X98) | ~ ! [X106 : $i,X107 : $i,X108 : $i] : (~(X105 @ X107 @ X108) | (X105 @ X107 @ X106) | ~(X105 @ X108 @ X106)) | ~ ! [X109 : $i,X110 : $i] : (~(X92 @ X109 @ X110) | (X105 @ X109 @ X110)))) | ~(X92 @ X94 @ X96) | (X97 @ X96 @ X95) | (X93 @ X95 @ X96) | ~ ! [X111 : $i,X112 : $i,X113 : $i] : (~(X93 @ X111 @ X113) | (X93 @ X111 @ X112) | ~(X93 @ X113 @ X112)) | ~ ! [X114 : $i,X115 : $i] : ((X93 @ X114 @ X115) | ~(X92 @ X114 @ X115)) | (X95 = X96) | ~ ! [X116 : $i,X117 : $i] : (~(X92 @ X116 @ X117) | (X97 @ X116 @ X117)) | ~(X92 @ X94 @ X95) | ~ ! [X118 : $i,X119 : $i,X120 : $i] : (~(X97 @ X119 @ X118) | ~(X97 @ X118 @ X120) | (X97 @ X119 @ X120)))))) & ((^[X121 : ($i > $i > $o)] : (! [X122 : ($i > $i > $o),X123 : $i,X124 : $i,X125 : $i,X126 : ($i > $i > $o)] : (~ ! [X127 : $i,X128 : $i] : (~(X121 @ X127 @ X128) | (X122 @ X127 @ X128)) | ~ ! [X129 : $i,X130 : $i] : (~(X121 @ X130 @ X129) | (X126 @ X130 @ X129)) | (~ ! [X131 : ($i > $i > $o)] : ((X131 @ X123 @ X124) | ~ ! [X132 : $i,X133 : $i,X134 : $i] : (~(X131 @ X134 @ X133) | (X131 @ X132 @ X133) | ~(X131 @ X132 @ X134)) | ~ ! [X135 : $i,X136 : $i] : (~(X121 @ X135 @ X136) | (X131 @ X135 @ X136))) & (X123 != X124)) | ~ ! [X137 : $i] : (~ ! [X138 : ($i > $i > $o)] : (~ ! [X139 : $i,X140 : $i,X141 : $i] : ((X138 @ X140 @ X141) | ~(X138 @ X140 @ X139) | ~(X138 @ X139 @ X141)) | ~ ! [X142 : $i,X143 : $i] : ((X138 @ X142 @ X143) | ~(X121 @ X142 @ X143)) | (X138 @ X124 @ X137)) | ~ ! [X144 : ($i > $i > $o)] : ((X144 @ X125 @ X137) | ~ ! [X145 : $i,X146 : $i] : ((X144 @ X146 @ X145) | ~(X121 @ X146 @ X145)) | ~ ! [X147 : $i,X148 : $i,X149 : $i] : (~(X144 @ X148 @ X147) | (X144 @ X149 @ X147) | ~(X144 @ X149 @ X148)))) | ((X123 != X125) & ~ ! [X150 : ($i > $i > $o)] : (~ ! [X151 : $i,X152 : $i] : ((X150 @ X151 @ X152) | ~(X121 @ X151 @ X152)) | ~ ! [X153 : $i,X154 : $i,X155 : $i] : ((X150 @ X153 @ X155) | ~(X150 @ X153 @ X154) | ~(X150 @ X154 @ X155)) | (X150 @ X123 @ X125))) | ~ ! [X156 : $i,X157 : $i,X158 : $i] : (~(X122 @ X157 @ X158) | (X122 @ X156 @ X158) | ~(X122 @ X156 @ X157)) | (X126 @ X124 @ X125) | (X122 @ X125 @ X124) | (X124 = X125) | ~ ! [X159 : $i,X160 : $i,X161 : $i] : (~(X126 @ X161 @ X159) | (X126 @ X161 @ X160) | ~(X126 @ X159 @ X160))))) = confl) & ((^[X162 : ($i > $i > $o)] : (! [X163 : $i,X164 : ($i > $o)] : (~ ! [X165 : $i] : (~ ! [X166 : $i] : (~ ! [X167 : ($i > $i > $o)] : ((X167 @ X165 @ X166) | ~ ! [X168 : $i,X169 : $i] : ((X167 @ X168 @ X169) | ~(X162 @ X168 @ X169)) | ~ ! [X170 : $i,X171 : $i,X172 : $i] : (~(X167 @ X171 @ X170) | (X167 @ X172 @ X170) | ~(X167 @ X172 @ X171))) | (X164 @ X166)) | (X164 @ X165)) | (X164 @ X163)))) = ind) & ((^[X173 : ($i > $i > $o), X174 : $i, X175 : $i] : (! [X176 : ($i > $i > $o)] : ((X176 @ X174 @ X175) | ~ ! [X177 : $i,X178 : $i] : ((X176 @ X178 @ X177) | ~(X173 @ X178 @ X177)) | ~ ! [X179 : $i,X180 : $i,X181 : $i] : ((X176 @ X179 @ X181) | ~(X176 @ X180 @ X181) | ~(X176 @ X179 @ X180))))) = tc) & (po = (^[X182 : ($i > $i > $o)] : (! [X183 : $i] : (X182 @ X183 @ X183) & ! [X184 : $i,X185 : $i,X186 : $i] : ((X182 @ X185 @ X186) | ~(X182 @ X185 @ X184) | ~(X182 @ X184 @ X186)) & ! [X187 : $i,X188 : $i] : (~(X182 @ X188 @ X187) | (X187 = X188) | ~(X182 @ X187 @ X188))))) & ((^[X189 : ($i > $i > $o)] : (! [X190 : ($i > $o),X191 : $i] : (~ ! [X192 : $i] : (~ ! [X193 : $i] : (~(X189 @ X192 @ X193) | ~(X190 @ X193)) | ~(X190 @ X192)) | ~(X190 @ X191)))) = term) & ! [X194 : d_unsorted] : (d_unsorted_0 = X194) & ((^[X195 : (($i > $i > $o) > $i > $i > $o)] : (! [X196 : ($i > $i > $o),X197 : $i,X198 : ($i > $i > $o),X199 : $i] : ((X195 @ X198 @ X199 @ X197) | ~(X195 @ X196 @ X199 @ X197) | ~ ! [X200 : $i,X201 : $i] : ((X198 @ X200 @ X201) | ~(X196 @ X200 @ X201))))) = mono) & (irrefl = (^[X202 : ($i > $i > $o)] : (! [X203 : $i] : ~(X202 @ X203 @ X203)))) & ! [X204 : d_unsorted,X205 : d_unsorted] : ((((d2unsorted @ X204)) = ((d2unsorted @ X205))) => (X204 = X205)) & ((^[X206 : ($i > $i > $o), X207 : $i, X208 : $i] : ((X207 = X208) | ! [X209 : ($i > $i > $o)] : ((X209 @ X208 @ X207) | ~ ! [X210 : $i,X211 : $i] : ((X209 @ X211 @ X210) | ~(X206 @ X211 @ X210)) | ~ ! [X212 : $i,X213 : $i,X214 : $i] : (~(X209 @ X214 @ X212) | ~(X209 @ X212 @ X213) | (X209 @ X214 @ X213))) | ! [X215 : ($i > $i > $o)] : (~ ! [X216 : $i,X217 : $i,X218 : $i] : (~(X215 @ X218 @ X216) | ~(X215 @ X217 @ X218) | (X215 @ X217 @ X216)) | (X215 @ X207 @ X208) | ~ ! [X219 : $i,X220 : $i] : (~(X206 @ X219 @ X220) | (X215 @ X219 @ X220))))) = trsc) & (cr = (^[X221 : ($i > $i > $o)] : (! [X222 : $i,X223 : ($i > $i > $o),X224 : ($i > $i > $o),X225 : $i] : (~ ! [X226 : $i,X227 : $i] : (~(X221 @ X227 @ X226) | (X223 @ X227 @ X226)) | ~ ! [X228 : $i] : (~ ! [X229 : ($i > $i > $o)] : (~ ! [X230 : $i,X231 : $i,X232 : $i] : (~(X229 @ X232 @ X231) | (X229 @ X232 @ X230) | ~(X229 @ X231 @ X230)) | (X229 @ X222 @ X228) | ~ ! [X233 : $i,X234 : $i] : (~(X221 @ X233 @ X234) | (X229 @ X233 @ X234))) | ~ ! [X235 : ($i > $i > $o)] : (~ ! [X236 : $i,X237 : $i] : ((X235 @ X237 @ X236) | ~(X221 @ X237 @ X236)) | (X235 @ X225 @ X228) | ~ ! [X238 : $i,X239 : $i,X240 : $i] : (~(X235 @ X240 @ X239) | ~(X235 @ X239 @ X238) | (X235 @ X240 @ X238)))) | (X224 @ X222 @ X225) | (X222 = X225) | ~ ! [X241 : $i,X242 : $i] : (~(X221 @ X241 @ X242) | (X224 @ X241 @ X242)) | ~ ! [X243 : $i,X244 : $i,X245 : $i] : (~(X224 @ X245 @ X243) | (X224 @ X244 @ X243) | ~(X224 @ X244 @ X245)) | ((X222 != X225) & ~ ! [X246 : ($i > $i > $o)] : ((X246 @ X225 @ X222) | ~ ! [X247 : $i,X248 : $i] : (~(X221 @ X248 @ X247) | (X246 @ X248 @ X247)) | ~ ! [X249 : $i,X250 : $i,X251 : $i] : (~(X246 @ X250 @ X251) | (X246 @ X249 @ X251) | ~(X246 @ X249 @ X250))) & ~ ! [X252 : ($i > $i > $o)] : (~ ! [X253 : $i,X254 : $i] : ((X252 @ X253 @ X254) | ~(X221 @ X253 @ X254)) | (X252 @ X222 @ X225) | ~ ! [X255 : $i,X256 : $i,X257 : $i] : (~(X252 @ X256 @ X257) | ~(X252 @ X255 @ X256) | (X252 @ X255 @ X257)))) | (X223 @ X225 @ X222) | ~ ! [X258 : $i,X259 : $i,X260 : $i] : (~(X223 @ X260 @ X258) | ~(X223 @ X259 @ X260) | (X223 @ X259 @ X258)))))) & ((^[X261 : (($i > $i > $o) > $i > $i > $o)] : (! [X262 : ($i > $i > $o)] : (((X261 @ (X261 @ X262))) = ((X261 @ X262))))) = idem) & (total = (^[X263 : ($i > $i > $o)] : (! [X264 : $i,X265 : $i] : ((X263 @ X265 @ X264) | (X263 @ X264 @ X265) | (X264 = X265))))) & (trc = (^[X266 : ($i > $i > $o), X267 : $i, X268 : $i] : ((X267 = X268) | ! [X269 : ($i > $i > $o)] : ((X269 @ X267 @ X268) | ~ ! [X270 : $i,X271 : $i] : (~(X266 @ X270 @ X271) | (X269 @ X270 @ X271)) | ~ ! [X272 : $i,X273 : $i,X274 : $i] : (~(X269 @ X272 @ X274) | ~(X269 @ X274 @ X273) | (X269 @ X272 @ X273)))))) & ((^[X275 : ($i > $i > $o)] : (! [X276 : $i,X277 : ($i > $i > $o),X278 : ($i > $i > $o),X279 : $i,X280 : $i] : (~ ! [X281 : $i] : (~ ! [X282 : ($i > $i > $o)] : (~ ! [X283 : $i,X284 : $i] : ((X282 @ X284 @ X283) | ~(X275 @ X284 @ X283)) | ~ ! [X285 : $i,X286 : $i,X287 : $i] : (~(X282 @ X285 @ X286) | ~(X282 @ X287 @ X285) | (X282 @ X287 @ X286)) | (X282 @ X279 @ X281)) | ~ ! [X288 : ($i > $i > $o)] : (~ ! [X289 : $i,X290 : $i,X291 : $i] : (~(X288 @ X290 @ X291) | ~(X288 @ X291 @ X289) | (X288 @ X290 @ X289)) | (X288 @ X280 @ X281) | ~ ! [X292 : $i,X293 : $i] : ((X288 @ X292 @ X293) | ~(X275 @ X292 @ X293)))) | ~ ! [X294 : $i,X295 : $i,X296 : $i] : ((X277 @ X294 @ X295) | ~(X277 @ X296 @ X295) | ~(X277 @ X294 @ X296)) | (X277 @ X280 @ X279) | ~ ! [X297 : $i,X298 : $i] : (~(X275 @ X298 @ X297) | (X278 @ X298 @ X297)) | ~(X275 @ X276 @ X280) | (~ ! [X299 : ($i > $i > $o)] : (~ ! [X300 : $i,X301 : $i,X302 : $i] : (~(X299 @ X302 @ X300) | (X299 @ X301 @ X300) | ~(X299 @ X301 @ X302)) | ~ ! [X303 : $i,X304 : $i] : ((X299 @ X304 @ X303) | ~(X275 @ X304 @ X303)) | (X299 @ X276 @ X279)) & (X276 != X279)) | (X278 @ X279 @ X280) | (X279 = X280) | ~ ! [X305 : $i,X306 : $i] : (~(X275 @ X305 @ X306) | (X277 @ X305 @ X306)) | ~ ! [X307 : $i,X308 : $i,X309 : $i] : (~(X278 @ X308 @ X307) | ~(X278 @ X309 @ X308) | (X278 @ X309 @ X307))))) = sconfl)),
% 3.52/0.95 inference(rectify,[],[f1])).
% 3.52/0.95 thf(f7,plain,(
% 3.52/0.95 (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2))))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y3 @ Y2))) | (~ (Y0 @ Y1 @ Y3))))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y2))))))))) & ! [X24 : $i] : ? [X25 : d_unsorted] : (((d2unsorted @ X25)) = X24) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y5))))))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7)))))))))) | (Y4 @ Y1 @ Y3)))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y4 @ Y5))))))))))))))) & (~ (Y1 = Y2)))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 @ Y2 @ Y3)))))))))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y1)))))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y3))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y1 @ Y7 @ Y6) | (~ (Y1 @ Y8 @ Y6))) | (~ (Y1 @ Y7 @ Y8)))))))))) | (~ (Y0 @ Y4 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y3 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y8 @ Y6))))))))))) | (Y5 @ Y3 @ Y2)) | (Y1 @ Y2 @ Y3)) | (~ (Y0 @ Y4 @ Y2))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y3 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y2 @ Y6)))))))))))))))))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y6 @ Y8)))))))))) | (Y3 = Y2)) | (Y5 @ Y2 @ Y3)) | (Y1 @ Y3 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y6))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y9 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) & (~ (Y4 = Y2)))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y2 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8)))))))))))))))))) | ((~ (Y4 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (Y6 @ Y4 @ Y3))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4)))))))))))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ! [X194 : d_unsorted] : (d_unsorted_0 = X194) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y4 @ Y6 @ Y5)) | (Y2 @ Y6 @ Y5))))))) | (~ (Y0 @ Y4 @ Y1 @ Y3))) | (Y0 @ Y2 @ Y1 @ Y3)))))))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & ! [X204 : d_unsorted,X205 : d_unsorted] : ((((d2unsorted @ X204)) = ((d2unsorted @ X205))) => (X204 = X205)) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y4 @ Y6))))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y6 @ Y7) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y7)))))))))) | (Y3 @ Y1 @ Y4)) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) | (~ (Y5 @ Y8 @ Y7))) | (~ (Y5 @ Y7 @ Y6)))))))))) | (Y5 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y5 @ Y1 @ Y4)))))) & (~ (Y4 = Y1)))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y6 @ Y5)) | (Y2 @ Y6 @ Y7)) | (~ (Y2 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y9) | (~ (Y6 @ Y8 @ Y9))) | (~ (Y6 @ Y7 @ Y8)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y7 @ Y8))))))))))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))))))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1)))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y2 @ Y1)) | (Y0 @ Y1 @ Y2)))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) | (Y1 = Y2)))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y6 @ Y8) | (~ (Y3 @ Y6 @ Y7))) | (~ (Y3 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y2 = Y1)) | (Y3 @ Y2 @ Y1)) | ((~ (Y5 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y5 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9)))))))))))))))) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y8 @ Y6)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y9 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y2 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y10 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))))))))))))))))),
% 3.52/0.95 inference(fool_elimination,[],[f6])).
% 3.52/0.95 thf(f8,plain,(
% 3.52/0.95 (ind != (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((tc @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 3.52/0.95 inference(flattening,[],[f5])).
% 3.52/0.95 thf(f9,plain,(
% 3.52/0.95 ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y1 @ Y7 @ Y6) | (~ (Y1 @ Y8 @ Y6))) | (~ (Y1 @ Y7 @ Y8)))))))))) | (~ (Y0 @ Y4 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y3 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y8 @ Y6))))))))))) | (Y5 @ Y3 @ Y2)) | (Y1 @ Y2 @ Y3)) | (~ (Y0 @ Y4 @ Y2))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y3 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y2 @ Y6)))))))))))))))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2))))))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 @ Y2 @ Y3)))))))))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y6 @ Y7) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y7)))))))))) | (Y3 @ Y1 @ Y4)) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) | (~ (Y5 @ Y8 @ Y7))) | (~ (Y5 @ Y7 @ Y6)))))))))) | (Y5 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y5 @ Y1 @ Y4)))))) & (~ (Y4 = Y1)))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y6 @ Y5)) | (Y2 @ Y6 @ Y7)) | (~ (Y2 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y9) | (~ (Y6 @ Y8 @ Y9))) | (~ (Y6 @ Y7 @ Y8)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y7 @ Y8))))))))))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y4 @ Y6 @ Y5)) | (Y2 @ Y6 @ Y5))))))) | (~ (Y0 @ Y4 @ Y1 @ Y3))) | (Y0 @ Y2 @ Y1 @ Y3)))))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y2))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y5))))))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7)))))))))) | (Y4 @ Y1 @ Y3)))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y4 @ Y5))))))))))))))) & (~ (Y1 = Y2)))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4)))))))))))))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y2 @ Y1)) | (Y0 @ Y1 @ Y2)))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y3 @ Y2))) | (~ (Y0 @ Y1 @ Y3))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) | (Y1 = Y2)))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y6 @ Y8) | (~ (Y3 @ Y6 @ Y7))) | (~ (Y3 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y2 = Y1)) | (Y3 @ Y2 @ Y1)) | ((~ (Y5 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y5 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9)))))))))))))))) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y8 @ Y6)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y9 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y2 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y10 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))))))))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y4 @ Y6))))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y6 @ Y8)))))))))) | (Y3 = Y2)) | (Y5 @ Y2 @ Y3)) | (Y1 @ Y3 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y6))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y9 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) & (~ (Y4 = Y2)))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y2 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8)))))))))))))))))) | ((~ (Y4 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (Y6 @ Y4 @ Y3))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))))))))))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((((d2unsorted @ X3)) = ((d2unsorted @ X4))) => (X3 = X4)) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y1)))))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4))))))))))))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 3.52/0.95 inference(rectify,[],[f7])).
% 3.52/0.95 thf(f10,plain,(
% 3.52/0.95 (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((X3 = X4) | (((d2unsorted @ X3)) != ((d2unsorted @ X4)))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y2))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y6 @ Y7) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y7)))))))))) | (Y3 @ Y1 @ Y4)) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) | (~ (Y5 @ Y8 @ Y7))) | (~ (Y5 @ Y7 @ Y6)))))))))) | (Y5 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y5 @ Y1 @ Y4)))))) & (~ (Y4 = Y1)))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y6 @ Y5)) | (Y2 @ Y6 @ Y7)) | (~ (Y2 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y9) | (~ (Y6 @ Y8 @ Y9))) | (~ (Y6 @ Y7 @ Y8)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y7 @ Y8))))))))))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4)))))))))))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y6 @ Y8) | (~ (Y3 @ Y6 @ Y7))) | (~ (Y3 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y2 = Y1)) | (Y3 @ Y2 @ Y1)) | ((~ (Y5 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y5 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9)))))))))))))))) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y8 @ Y6)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y9 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y2 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y10 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))))))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y3))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2))))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y4 @ Y6 @ Y5)) | (Y2 @ Y6 @ Y5))))))) | (~ (Y0 @ Y4 @ Y1 @ Y3))) | (Y0 @ Y2 @ Y1 @ Y3)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1)))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y6 @ Y8)))))))))) | (Y3 = Y2)) | (Y5 @ Y2 @ Y3)) | (Y1 @ Y3 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y6))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y9 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) & (~ (Y4 = Y2)))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y2 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8)))))))))))))))))) | ((~ (Y4 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (Y6 @ Y4 @ Y3))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))))))))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y2 @ Y1)) | (Y0 @ Y1 @ Y2)))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y4 @ Y6))))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4))))))))))))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y1)))))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y3 @ Y2))) | (~ (Y0 @ Y1 @ Y3))))))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y1 @ Y7 @ Y6) | (~ (Y1 @ Y8 @ Y6))) | (~ (Y1 @ Y7 @ Y8)))))))))) | (~ (Y0 @ Y4 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y3 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y8 @ Y6))))))))))) | (Y5 @ Y3 @ Y2)) | (Y1 @ Y2 @ Y3)) | (~ (Y0 @ Y4 @ Y2))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y3 @ Y6))))) | (~ (!! 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[X2 : d_unsorted] : (d_unsorted_0 = X2) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y5))))))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7)))))))))) | (Y4 @ Y1 @ Y3)))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y4 @ Y5))))))))))))))) & (~ (Y1 = Y2)))))))))) & ! 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[X2 : d_unsorted] : (d_unsorted_0 = X2) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y5))))))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7)))))))))) | (Y4 @ Y1 @ Y3)))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y4 @ Y5))))))))))))))) & (~ (Y1 = Y2)))))))))) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 @ Y2 @ Y3)))))))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) | (Y1 = Y2))))))))),
% 3.52/0.95 inference(rectify,[],[f10])).
% 3.52/0.95 thf(f12,plain,(
% 3.52/0.95 (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((X0 = X1) | (((d2unsorted @ X1)) != ((d2unsorted @ X0)))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y2))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y6 @ Y7) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y7)))))))))) | (Y3 @ Y1 @ Y4)) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) | (~ (Y5 @ Y8 @ Y7))) | (~ (Y5 @ Y7 @ Y6)))))))))) | (Y5 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y5 @ Y1 @ Y4)))))) & (~ (Y4 = Y1)))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y6 @ Y5)) | (Y2 @ Y6 @ Y7)) | (~ (Y2 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y9) | (~ (Y6 @ Y8 @ Y9))) | (~ (Y6 @ Y7 @ Y8)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y7 @ Y8))))))))))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4)))))))))))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y6 @ Y8) | (~ (Y3 @ Y6 @ Y7))) | (~ (Y3 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y2 = Y1)) | (Y3 @ Y2 @ Y1)) | ((~ (Y5 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y5 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9)))))))))))))))) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y8 @ Y6)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y9 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y2 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y10 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))))))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y3))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2))))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y4 @ Y6 @ Y5)) | (Y2 @ Y6 @ Y5))))))) | (~ (Y0 @ Y4 @ Y1 @ Y3))) | (Y0 @ Y2 @ Y1 @ Y3)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1)))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y6 @ Y8)))))))))) | (Y3 = Y2)) | (Y5 @ Y2 @ Y3)) | (Y1 @ Y3 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y6))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y9 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) & (~ (Y4 = Y2)))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y2 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8)))))))))))))))))) | ((~ (Y4 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (Y6 @ Y4 @ Y3))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))))))))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y2 @ Y1)) | (Y0 @ Y1 @ Y2)))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y4 @ Y6))))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4))))))))))))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y1)))))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y3 @ Y2))) | (~ (Y0 @ Y1 @ Y3))))))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y1 @ Y7 @ Y6) | (~ (Y1 @ Y8 @ Y6))) | (~ (Y1 @ Y7 @ Y8)))))))))) | (~ (Y0 @ Y4 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y3 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y8 @ Y6))))))))))) | (Y5 @ Y3 @ Y2)) | (Y1 @ Y2 @ Y3)) | (~ (Y0 @ Y4 @ Y2))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y3 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y2 @ Y6)))))))))))))))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y5))))))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7)))))))))) | (Y4 @ Y1 @ Y3)))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y4 @ Y5))))))))))))))) & (~ (Y1 = Y2)))))))))) & ! [X3 : $i] : (((d2unsorted @ (sK0 @ X3))) = X3) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 @ Y2 @ Y3)))))))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) | (Y1 = Y2))))))))),
% 3.52/0.95 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK0 @ X3)],[f11])).
% 3.52/0.95 thf(f15,plain,(
% 3.52/0.95 ( ! [X3 : $i] : ((((d2unsorted @ (sK0 @ X3))) = X3)) )),
% 3.52/0.95 inference(cnf_transformation,[],[f12])).
% 3.52/0.95 thf(f17,plain,(
% 3.52/0.95 ( ! [X2 : d_unsorted] : ((d_unsorted_0 = X2)) )),
% 3.52/0.95 inference(cnf_transformation,[],[f12])).
% 3.52/0.95 thf(f38,plain,(
% 3.52/0.95 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2))))))))))),
% 3.52/0.95 inference(cnf_transformation,[],[f12])).
% 3.52/0.95 thf(f39,plain,(
% 3.52/0.95 (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4))))))))))))))))))))),
% 3.52/0.95 inference(cnf_transformation,[],[f12])).
% 3.52/0.95 thf(f45,plain,(
% 3.52/0.95 (ind != (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((tc @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 3.52/0.95 inference(cnf_transformation,[],[f8])).
% 3.52/0.95 thf(f48,plain,(
% 3.52/0.95 ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4))))))))))))))))))) != (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y4 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y5 @ Y6))))))))) @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 3.52/0.95 inference(definition_unfolding,[],[f45,f39,f38])).
% 3.52/0.95 thf(f49,plain,(
% 3.52/0.95 ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4))))))))))))))))))) != (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (Y4 @ Y2 @ Y3)))) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ Y1))))))),
% 3.52/0.95 inference(beta-eta_normalization,[],[f48])).
% 3.52/0.95 thf(f50,plain,(
% 3.52/0.95 ( ! [X3 : $i] : ((((d2unsorted @ d_unsorted_0)) = X3)) )),
% 3.52/0.95 inference(forward_demodulation,[],[f15,f17])).
% 3.52/0.95 thf(f64,plain,(
% 3.52/0.95 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 3.52/0.95 inference(superposition,[],[f50,f50])).
% 3.52/0.95 thf(f76,plain,(
% 3.52/0.95 ((((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4))))))))))))))))))) @ sK1)) != (((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (Y4 @ Y2 @ Y3)))) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ Y1))))) @ sK1)))),
% 3.52/0.95 inference(negative_extensionality,[],[f49])).
% 3.52/0.95 thf(f77,plain,(
% 3.52/0.95 ($true = (((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4))))))))))))))))))) @ sK1))) | ($true = (((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (Y4 @ Y2 @ Y3)))) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ Y1))))) @ sK1)))),
% 3.52/0.95 inference(xor_proxy_clausification,[],[f76])).
% 3.52/0.95 thf(f78,plain,(
% 3.52/0.95 ($false = (((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (Y4 @ Y2 @ Y3)))) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ Y1))))) @ sK1))) | ($false = (((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4))))))))))))))))))) @ sK1)))),
% 3.52/0.95 inference(xor_proxy_clausification,[],[f76])).
% 3.52/0.95 thf(f79,plain,(
% 3.52/0.95 ($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0)))))) | (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3))))))))))))))))))) = $false)),
% 3.52/0.95 inference(beta-eta_normalization,[],[f78])).
% 3.52/0.95 thf(f80,plain,(
% 3.52/0.95 (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3))))))))))))))))))) = $false) | ($false = (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))) @ sK2)))),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f79])).
% 3.52/0.95 thf(f81,plain,(
% 3.52/0.95 ($false = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3))))))))))))))))) @ sK3))) | ($false = (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))) @ sK2)))),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f80])).
% 3.52/0.95 thf(f82,plain,(
% 3.52/0.95 ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))) | (Y2 @ Y0 @ Y1)))) => (sK2 @ Y1)))) => (sK2 @ Y0)))) => (!! @ $i @ sK2))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))))))))) = $false)),
% 3.52/0.95 inference(beta-eta_normalization,[],[f81])).
% 3.52/0.95 thf(f83,plain,(
% 3.52/0.95 (((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))))))))) = $false) | (((!! @ $i @ sK2)) = $false)),
% 3.52/0.95 inference(imp_proxy_clausification,[],[f82])).
% 3.52/0.95 thf(f84,plain,(
% 3.52/0.95 ($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))) | (Y2 @ Y0 @ Y1)))) => (sK2 @ Y1)))) => (sK2 @ Y0)))))) | (((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))))))))) = $false)),
% 3.52/0.95 inference(imp_proxy_clausification,[],[f82])).
% 3.52/0.95 thf(f85,plain,(
% 3.52/0.95 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))) | (Y2 @ Y0 @ Y1)))) => (sK2 @ Y1)))) => (sK2 @ Y0))) @ X1)) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))))))))) = $false)) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f84])).
% 3.52/0.95 thf(f86,plain,(
% 3.52/0.95 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))) | (Y2 @ Y0 @ Y1)))) => (sK2 @ Y1)))) => (sK2 @ Y0))) @ X1)) = $true) | ((((^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))))))) @ sK4)) = $false)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f85])).
% 3.52/0.95 thf(f87,plain,(
% 3.52/0.95 ( ! [X1 : $i] : (((((sK3 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))))))) = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ X1 @ Y0)))) => (sK2 @ Y0)))) => (sK2 @ X1))) = $true)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f86])).
% 3.52/0.95 thf(f88,plain,(
% 3.52/0.95 ( ! [X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1)))))))))))))) = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ X1 @ Y0)))) => (sK2 @ Y0)))) => (sK2 @ X1))) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f87])).
% 3.52/0.95 thf(f89,plain,(
% 3.52/0.95 ( ! [X1 : $i] : (((((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ X1 @ Y0)))) => (sK2 @ Y0)))) => (sK2 @ X1))) = $true) | (((sK3 @ sK4)) = $false)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f87])).
% 3.52/0.95 thf(f90,plain,(
% 3.52/0.95 ( ! [X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ X1 @ Y0)))) => (sK2 @ Y0)))))) | (((sK2 @ X1)) = $true) | (((sK3 @ sK4)) = $false)) )),
% 3.52/0.95 inference(imp_proxy_clausification,[],[f89])).
% 3.52/0.95 thf(f91,plain,(
% 3.52/0.95 ( ! [X1 : $i] : ((((sK2 @ X1)) = $true) | ($false = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ X1 @ Y0)))) => (sK2 @ Y0))) @ (sK5 @ X1)))) | (((sK3 @ sK4)) = $false)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f90])).
% 3.52/0.95 thf(f92,plain,(
% 3.52/0.95 ( ! [X1 : $i] : ((((sK3 @ sK4)) = $false) | (((sK2 @ X1)) = $true) | ((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ X1 @ (sK5 @ X1))))) => (sK2 @ (sK5 @ X1)))) = $false)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f91])).
% 3.52/0.95 thf(f94,plain,(
% 3.52/0.95 ( ! [X1 : $i] : ((((sK3 @ sK4)) = $false) | (((sK2 @ X1)) = $true) | ($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ X1 @ (sK5 @ X1)))))))) )),
% 3.52/0.95 inference(imp_proxy_clausification,[],[f92])).
% 3.52/0.95 thf(f95,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK3 @ sK4)) = $false) | ($true = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ X1 @ (sK5 @ X1)))) @ X2))) | (((sK2 @ X1)) = $true)) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f94])).
% 3.52/0.95 thf(f96,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X2 @ Y0 @ Y1)))))))) | (X2 @ X1 @ (sK5 @ X1))))) | (((sK2 @ X1)) = $true) | (((sK3 @ sK4)) = $false)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f95])).
% 3.52/0.95 thf(f97,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK5 @ X1)))) | (((sK3 @ sK4)) = $false) | (((sK2 @ X1)) = $true) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X2 @ Y0 @ Y1))))))))))) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f96])).
% 3.52/0.95 thf(f98,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X2 @ Y0 @ Y1))))))))) | (((sK3 @ sK4)) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))))) | (((sK2 @ X1)) = $true) | ($true = ((X2 @ X1 @ (sK5 @ X1))))) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f97])).
% 3.52/0.95 thf(f99,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK2 @ X1)) = $true) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X2 @ Y0 @ Y1))))))) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | (((sK3 @ sK4)) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0)))))))))))) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f98])).
% 3.52/0.95 thf(f100,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK3 @ sK4)) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))))) | (((sK2 @ X1)) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X2 @ Y0 @ Y1))))) @ (sK6 @ X2))) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1))))) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f99])).
% 3.52/0.95 thf(f101,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK2 @ X1)) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X2 @ Y0 @ Y1))))) @ (sK6 @ X2))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0)))))))))) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | (((sK3 @ sK4)) = $false)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f100])).
% 3.52/0.95 thf(f102,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))) @ (sK7 @ X2))) = $false) | (((sK3 @ sK4)) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | (((sK2 @ X1)) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X2 @ Y0 @ Y1))))) @ (sK6 @ X2))) = $false)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f101])).
% 3.52/0.95 thf(f103,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK5 @ X1)))) | (((sK3 @ sK4)) = $false) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (~ (X2 @ Y0 @ (sK7 @ X2)))) | (X2 @ Y1 @ (sK7 @ X2)))))))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ (sK6 @ X2) @ Y0)) | (X2 @ (sK6 @ X2) @ Y0)))))) | (((sK2 @ X1)) = $true)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f102])).
% 3.52/0.95 thf(f104,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (~ (X2 @ Y0 @ (sK7 @ X2)))) | (X2 @ Y1 @ (sK7 @ X2)))))) @ (sK8 @ X2))) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | (((sK2 @ X1)) = $true) | (((sK3 @ sK4)) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ (sK6 @ X2) @ Y0)) | (X2 @ (sK6 @ X2) @ Y0))))))) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f103])).
% 3.52/0.95 thf(f105,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK2 @ X1)) = $true) | ((((^[Y0 : $i]: ((~ (sK1 @ (sK6 @ X2) @ Y0)) | (X2 @ (sK6 @ X2) @ Y0))) @ (sK9 @ X2))) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (~ (X2 @ Y0 @ (sK7 @ X2)))) | (X2 @ Y1 @ (sK7 @ X2)))))) @ (sK8 @ X2))) = $false) | (((sK3 @ sK4)) = $false)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f104])).
% 3.52/0.95 thf(f106,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK2 @ X1)) = $true) | ((((~ (sK1 @ (sK6 @ X2) @ (sK9 @ X2))) | (X2 @ (sK6 @ X2) @ (sK9 @ X2)))) = $false) | (((sK3 @ sK4)) = $false) | (((!! @ $i @ (^[Y0 : $i]: (((~ (X2 @ Y0 @ (sK8 @ X2))) | (~ (X2 @ (sK8 @ X2) @ (sK7 @ X2)))) | (X2 @ Y0 @ (sK7 @ X2)))))) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1))))) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f105])).
% 3.52/0.95 thf(f108,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK2 @ X1)) = $true) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | (((sK3 @ sK4)) = $false) | ($false = ((~ (sK1 @ (sK6 @ X2) @ (sK9 @ X2))))) | (((!! @ $i @ (^[Y0 : $i]: (((~ (X2 @ Y0 @ (sK8 @ X2))) | (~ (X2 @ (sK8 @ X2) @ (sK7 @ X2)))) | (X2 @ Y0 @ (sK7 @ X2)))))) = $false)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f106])).
% 3.52/0.95 thf(f109,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: (((~ (X2 @ Y0 @ (sK8 @ X2))) | (~ (X2 @ (sK8 @ X2) @ (sK7 @ X2)))) | (X2 @ Y0 @ (sK7 @ X2)))))) = $false) | (((sK2 @ X1)) = $true) | (((sK3 @ sK4)) = $false) | (((sK1 @ (sK6 @ X2) @ (sK9 @ X2))) = $true) | ($true = ((X2 @ X1 @ (sK5 @ X1))))) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f108])).
% 3.52/0.95 thf(f110,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK3 @ sK4)) = $false) | ((((^[Y0 : $i]: (((~ (X2 @ Y0 @ (sK8 @ X2))) | (~ (X2 @ (sK8 @ X2) @ (sK7 @ X2)))) | (X2 @ Y0 @ (sK7 @ X2)))) @ (sK10 @ X2))) = $false) | (((sK2 @ X1)) = $true) | (((sK1 @ (sK6 @ X2) @ (sK9 @ X2))) = $true) | ($true = ((X2 @ X1 @ (sK5 @ X1))))) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f109])).
% 3.52/0.95 thf(f111,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($false = ((((~ (X2 @ (sK10 @ X2) @ (sK8 @ X2))) | (~ (X2 @ (sK8 @ X2) @ (sK7 @ X2)))) | (X2 @ (sK10 @ X2) @ (sK7 @ X2))))) | (((sK3 @ sK4)) = $false) | (((sK1 @ (sK6 @ X2) @ (sK9 @ X2))) = $true) | (((sK2 @ X1)) = $true) | ($true = ((X2 @ X1 @ (sK5 @ X1))))) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f110])).
% 3.52/0.95 thf(f113,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK2 @ X1)) = $true) | ((((~ (X2 @ (sK10 @ X2) @ (sK8 @ X2))) | (~ (X2 @ (sK8 @ X2) @ (sK7 @ X2))))) = $false) | (((sK3 @ sK4)) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | (((sK1 @ (sK6 @ X2) @ (sK9 @ X2))) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f111])).
% 3.52/0.95 thf(f114,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK2 @ X1)) = $true) | (((sK1 @ (sK6 @ X2) @ (sK9 @ X2))) = $true) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | (((sK3 @ sK4)) = $false) | (((~ (X2 @ (sK8 @ X2) @ (sK7 @ X2)))) = $false)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f113])).
% 3.52/0.95 thf(f117,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (sK8 @ X2) @ (sK7 @ X2)))) | (((sK1 @ (sK6 @ X2) @ (sK9 @ X2))) = $true) | (((sK3 @ sK4)) = $false) | (((sK2 @ X1)) = $true) | ($true = ((X2 @ X1 @ (sK5 @ X1))))) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f114])).
% 3.52/0.95 thf(f126,plain,(
% 3.52/0.95 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))))) = $true) | ((((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ X1 @ Y0)))) => (sK2 @ Y0)))) => (sK2 @ X1))) = $true)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f88])).
% 3.52/0.95 thf(f127,plain,(
% 3.52/0.95 ( ! [X2 : $i,X1 : $i] : (((((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ X1 @ Y0)))) => (sK2 @ Y0)))) => (sK2 @ X1))) = $true) | ($true = (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))) @ X2)))) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f126])).
% 3.52/0.95 thf(f128,plain,(
% 3.52/0.95 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))) @ X2))) | (((sK2 @ X1)) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ X1 @ Y0)))) => (sK2 @ Y0))))))) )),
% 3.52/0.95 inference(imp_proxy_clausification,[],[f127])).
% 3.52/0.95 thf(f129,plain,(
% 3.52/0.95 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))) @ X2))) | (((sK2 @ X1)) = $true) | ((((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ X1 @ Y0)))) => (sK2 @ Y0))) @ (sK12 @ X1))) = $false)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f128])).
% 3.52/0.95 thf(f130,plain,(
% 3.52/0.95 ( ! [X2 : $i,X1 : $i] : ((((sK2 @ X1)) = $true) | ($true = (((sK3 @ X2) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X2 @ Y0)))))))))))) | ($false = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ X1 @ (sK12 @ X1))))) => (sK2 @ (sK12 @ X1)))))) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f129])).
% 3.52/0.95 thf(f131,plain,(
% 3.52/0.95 ( ! [X2 : $i,X1 : $i] : ((((sK2 @ X1)) = $true) | ($true = ((sK3 @ X2))) | ($false = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ X1 @ (sK12 @ X1))))) => (sK2 @ (sK12 @ X1))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X2 @ Y0)))))))))))) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f130])).
% 3.52/0.95 thf(f133,plain,(
% 3.52/0.95 ( ! [X2 : $i,X1 : $i] : (($true = ((sK3 @ X2))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X2 @ Y0))))))))))) | ($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ X1 @ (sK12 @ X1))))))) | (((sK2 @ X1)) = $true)) )),
% 3.52/0.95 inference(imp_proxy_clausification,[],[f131])).
% 3.52/0.95 thf(f134,plain,(
% 3.52/0.95 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ X1 @ (sK12 @ X1))))))) | ($true = ((sK3 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X2 @ Y0))))))))) = $false) | (((sK2 @ X1)) = $true)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f133])).
% 3.52/0.95 thf(f135,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ X1 @ (sK12 @ X1)))) @ X3))) | (((sK2 @ X1)) = $true) | ($true = ((sK3 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X2 @ Y0))))))))) = $false)) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f134])).
% 3.52/0.95 thf(f136,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ X1 @ (sK12 @ X1)))) @ X3))) | ((((^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X2 @ Y0))))))) @ (sK13 @ X2))) = $false) | ($true = ((sK3 @ X2))) | (((sK2 @ X1)) = $true)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f135])).
% 3.52/0.95 thf(f137,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X3 @ Y0 @ Y1)))))))) | (X3 @ X1 @ (sK12 @ X1))))) | ((((sK3 @ (sK13 @ X2)) | (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK13 @ X2)))))))) = $false) | (((sK2 @ X1)) = $true) | ($true = ((sK3 @ X2)))) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f136])).
% 3.52/0.95 thf(f138,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X2))) | (((sK2 @ X1)) = $true) | ((((sK3 @ (sK13 @ X2)) | (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK13 @ X2)))))))) = $false) | ((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X3 @ Y0 @ Y1))))))))) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f137])).
% 3.52/0.95 thf(f139,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : ((((X3 @ X1 @ (sK12 @ X1))) = $true) | ($true = ((sK3 @ X2))) | ((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X3 @ Y0 @ Y1))))))))) = $true) | (((sK2 @ X1)) = $true) | (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK13 @ X2))))))) = $false)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f138])).
% 3.52/0.95 thf(f168,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : ((((sK2 @ X1)) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0)))))))))) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK13 @ X2))))))) = $false) | ($true = ((sK3 @ X2))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X3 @ Y0 @ Y1)))))))))) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f139])).
% 3.52/0.95 thf(f169,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0)))))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X3 @ Y0 @ Y1))))))))) | (((sK2 @ X1)) = $true) | ($true = ((sK3 @ X2))) | (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK13 @ X2))))))) = $false) | (((X3 @ X1 @ (sK12 @ X1))) = $true)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f168])).
% 3.52/0.95 thf(f170,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : ((((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK13 @ X2))))))) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0))))))) @ (sK19 @ X3)))) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | (((sK2 @ X1)) = $true) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X3 @ Y0 @ Y1))))))))) | ($true = ((sK3 @ X2)))) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f169])).
% 3.52/0.95 thf(f171,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK13 @ X2))))))) | (((sK2 @ X1)) = $true) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0))))))) @ (sK19 @ X3)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X3 @ Y0 @ Y1))))))))) | ($true = ((sK3 @ X2))) | (((X3 @ X1 @ (sK12 @ X1))) = $true)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f170])).
% 3.52/0.95 thf(f172,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK13 @ X2)))) @ X4))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0))))))) @ (sK19 @ X3)))) | (((sK2 @ X1)) = $true) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X3 @ Y0 @ Y1))))))))) | ($true = ((sK3 @ X2))) | (((X3 @ X1 @ (sK12 @ X1))) = $true)) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f171])).
% 3.52/0.95 thf(f173,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK13 @ X2)))) @ X4))) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | ($true = ((sK3 @ X2))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0))))))) @ (sK19 @ X3)))) | (((sK2 @ X1)) = $true) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X3 @ Y0 @ Y1))))))) = $false)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f172])).
% 3.52/0.95 thf(f174,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((sK2 @ X1)) = $true) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0))))))) @ (sK19 @ X3)))) | ($true = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK13 @ X2)))) @ X4))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (X3 @ Y0 @ Y1))))) @ (sK20 @ X3))) = $false) | ($true = ((sK3 @ X2))) | (((X3 @ X1 @ (sK12 @ X1))) = $true)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f173])).
% 3.52/0.95 thf(f175,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((sK2 @ X1)) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ (sK20 @ X3) @ Y0)) | (X3 @ (sK20 @ X3) @ Y0))))) = $false) | ($true = ((sK3 @ X2))) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | (((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y0 @ Y1)) | (X4 @ Y0 @ Y2)) | (~ (X4 @ Y1 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0)))))))) | (X4 @ X2 @ (sK13 @ X2)))) = $true) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X3 @ Y1 @ Y0)) | (~ (X3 @ Y0 @ (sK19 @ X3)))) | (X3 @ Y1 @ (sK19 @ X3)))))))) = $false)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f174])).
% 3.52/0.95 thf(f176,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((X3 @ X1 @ (sK12 @ X1))) = $true) | (((sK2 @ X1)) = $true) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X3 @ Y1 @ Y0)) | (~ (X3 @ Y0 @ (sK19 @ X3)))) | (X3 @ Y1 @ (sK19 @ X3)))))))) = $false) | (((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y0 @ Y1)) | (X4 @ Y0 @ Y2)) | (~ (X4 @ Y1 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0)))))))) | (X4 @ X2 @ (sK13 @ X2)))) = $true) | ($false = (((^[Y0 : $i]: ((~ (sK1 @ (sK20 @ X3) @ Y0)) | (X3 @ (sK20 @ X3) @ Y0))) @ (sK21 @ X3)))) | ($true = ((sK3 @ X2)))) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f175])).
% 3.52/0.95 thf(f177,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X3 @ Y1 @ Y0)) | (~ (X3 @ Y0 @ (sK19 @ X3)))) | (X3 @ Y1 @ (sK19 @ X3)))))) @ (sK22 @ X3))) = $false) | (((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y0 @ Y1)) | (X4 @ Y0 @ Y2)) | (~ (X4 @ Y1 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0)))))))) | (X4 @ X2 @ (sK13 @ X2)))) = $true) | ($false = (((^[Y0 : $i]: ((~ (sK1 @ (sK20 @ X3) @ Y0)) | (X3 @ (sK20 @ X3) @ Y0))) @ (sK21 @ X3)))) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | (((sK2 @ X1)) = $true)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f176])).
% 3.52/0.95 thf(f178,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((sK2 @ X1)) = $true) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y0 @ Y1)) | (X4 @ Y0 @ Y2)) | (~ (X4 @ Y1 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0)))))))))) | ($true = ((sK3 @ X2))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X3 @ Y1 @ Y0)) | (~ (X3 @ Y0 @ (sK19 @ X3)))) | (X3 @ Y1 @ (sK19 @ X3)))))) @ (sK22 @ X3))) = $false) | ($false = (((^[Y0 : $i]: ((~ (sK1 @ (sK20 @ X3) @ Y0)) | (X3 @ (sK20 @ X3) @ Y0))) @ (sK21 @ X3)))) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | (((X3 @ X1 @ (sK12 @ X1))) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f177])).
% 3.52/0.95 thf(f179,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($false = (((^[Y0 : $i]: ((~ (sK1 @ (sK20 @ X3) @ Y0)) | (X3 @ (sK20 @ X3) @ Y0))) @ (sK21 @ X3)))) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y0 @ Y1)) | (X4 @ Y0 @ Y2)) | (~ (X4 @ Y1 @ Y2)))))))))))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X3 @ Y1 @ Y0)) | (~ (X3 @ Y0 @ (sK19 @ X3)))) | (X3 @ Y1 @ (sK19 @ X3)))))) @ (sK22 @ X3))) = $false) | ($true = ((sK3 @ X2))) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0))))))))) | (((sK2 @ X1)) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f178])).
% 3.52/0.95 thf(f180,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X3 @ Y1 @ Y0)) | (~ (X3 @ Y0 @ (sK19 @ X3)))) | (X3 @ Y1 @ (sK19 @ X3)))))) @ (sK22 @ X3))) = $false) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0))))))))) | (((sK2 @ X1)) = $true) | ($true = ((sK3 @ X2))) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ($false = (((^[Y0 : $i]: ((~ (sK1 @ (sK20 @ X3) @ Y0)) | (X3 @ (sK20 @ X3) @ Y0))) @ (sK21 @ X3)))) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y0 @ Y1)) | (X4 @ Y0 @ Y2)) | (~ (X4 @ Y1 @ Y2)))))))))) = $false)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f179])).
% 3.52/0.95 thf(f181,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((sK2 @ X1)) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X3 @ Y1 @ Y0)) | (~ (X3 @ Y0 @ (sK19 @ X3)))) | (X3 @ Y1 @ (sK19 @ X3)))))) @ (sK22 @ X3))) = $false) | ($false = (((^[Y0 : $i]: ((~ (sK1 @ (sK20 @ X3) @ Y0)) | (X3 @ (sK20 @ X3) @ Y0))) @ (sK21 @ X3)))) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0))))))) = $false) | ($true = ((sK3 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y0 @ Y1)) | (X4 @ Y0 @ Y2)) | (~ (X4 @ Y1 @ Y2)))))))))) = $false)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f180])).
% 3.52/0.95 thf(f182,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ X2 @ (sK13 @ X2)))) | ($false = (((^[Y0 : $i]: ((~ (sK1 @ (sK20 @ X3) @ Y0)) | (X3 @ (sK20 @ X3) @ Y0))) @ (sK21 @ X3)))) | ($true = ((sK3 @ X2))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0))))) @ (sK23 @ X4))) = $false) | (((sK2 @ X1)) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y0 @ Y1)) | (X4 @ Y0 @ Y2)) | (~ (X4 @ Y1 @ Y2)))))))))) = $false) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X3 @ Y1 @ Y0)) | (~ (X3 @ Y0 @ (sK19 @ X3)))) | (X3 @ Y1 @ (sK19 @ X3)))))) @ (sK22 @ X3))) = $false)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f181])).
% 3.52/0.95 thf(f183,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($false = (((^[Y0 : $i]: ((~ (sK1 @ (sK20 @ X3) @ Y0)) | (X3 @ (sK20 @ X3) @ Y0))) @ (sK21 @ X3)))) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ($true = ((sK3 @ X2))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X3 @ Y1 @ Y0)) | (~ (X3 @ Y0 @ (sK19 @ X3)))) | (X3 @ Y1 @ (sK19 @ X3)))))) @ (sK22 @ X3))) = $false) | (((sK2 @ X1)) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y0 @ Y1)) | (X4 @ Y0 @ Y2)) | (~ (X4 @ Y1 @ Y2)))))))) @ (sK24 @ X4))) = $false) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0))))) @ (sK23 @ X4))) = $false) | (((X3 @ X1 @ (sK12 @ X1))) = $true)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f182])).
% 3.52/0.95 thf(f184,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ((((~ (sK1 @ (sK20 @ X3) @ (sK21 @ X3))) | (X3 @ (sK20 @ X3) @ (sK21 @ X3)))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK23 @ X4))) | (X4 @ Y0 @ (sK23 @ X4)))))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (X3 @ Y0 @ (sK22 @ X3))) | (~ (X3 @ (sK22 @ X3) @ (sK19 @ X3)))) | (X3 @ Y0 @ (sK19 @ X3))))))) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | (((sK2 @ X1)) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X4 @ (sK24 @ X4) @ Y0)) | (X4 @ (sK24 @ X4) @ Y1)) | (~ (X4 @ Y0 @ Y1)))))))) = $false)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f183])).
% 3.52/0.95 thf(f186,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X4 @ (sK24 @ X4) @ Y0)) | (X4 @ (sK24 @ X4) @ Y1)) | (~ (X4 @ Y0 @ Y1)))))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK23 @ X4))) | (X4 @ Y0 @ (sK23 @ X4)))))) = $false) | ($false = ((~ (sK1 @ (sK20 @ X3) @ (sK21 @ X3))))) | (((sK2 @ X1)) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (X3 @ Y0 @ (sK22 @ X3))) | (~ (X3 @ (sK22 @ X3) @ (sK19 @ X3)))) | (X3 @ Y0 @ (sK19 @ X3))))))) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | ($true = ((sK3 @ X2)))) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f184])).
% 3.52/0.95 thf(f187,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ($false = ((~ (sK1 @ (sK20 @ X3) @ (sK21 @ X3))))) | (((sK2 @ X1)) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (X3 @ Y0 @ (sK22 @ X3))) | (~ (X3 @ (sK22 @ X3) @ (sK19 @ X3)))) | (X3 @ Y0 @ (sK19 @ X3))))))) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X4 @ (sK24 @ X4) @ Y0)) | (X4 @ (sK24 @ X4) @ Y1)) | (~ (X4 @ Y0 @ Y1)))))) @ (sK25 @ X4)))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK23 @ X4))) | (X4 @ Y0 @ (sK23 @ X4)))))) = $false)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f186])).
% 3.52/0.95 thf(f188,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK23 @ X4))) | (X4 @ Y0 @ (sK23 @ X4)))))) = $false) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X4 @ (sK24 @ X4) @ Y0)) | (X4 @ (sK24 @ X4) @ Y1)) | (~ (X4 @ Y0 @ Y1)))))) @ (sK25 @ X4)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (X3 @ Y0 @ (sK22 @ X3))) | (~ (X3 @ (sK22 @ X3) @ (sK19 @ X3)))) | (X3 @ Y0 @ (sK19 @ X3))))))) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | (((sK2 @ X1)) = $true) | ($true = ((X4 @ X2 @ (sK13 @ X2))))) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f187])).
% 3.52/0.95 thf(f189,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X4 @ (sK24 @ X4) @ Y0)) | (X4 @ (sK24 @ X4) @ Y1)) | (~ (X4 @ Y0 @ Y1)))))) @ (sK25 @ X4)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (X3 @ Y0 @ (sK22 @ X3))) | (~ (X3 @ (sK22 @ X3) @ (sK19 @ X3)))) | (X3 @ Y0 @ (sK19 @ X3))))))) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ((((^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK23 @ X4))) | (X4 @ Y0 @ (sK23 @ X4)))) @ (sK26 @ X4))) = $false) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | ($true = ((sK3 @ X2))) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | (((sK2 @ X1)) = $true)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f188])).
% 3.52/0.95 thf(f190,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((sK2 @ X1)) = $true) | ((((^[Y0 : $i]: (((~ (X3 @ Y0 @ (sK22 @ X3))) | (~ (X3 @ (sK22 @ X3) @ (sK19 @ X3)))) | (X3 @ Y0 @ (sK19 @ X3)))) @ (sK27 @ X3))) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X4 @ (sK24 @ X4) @ Y0)) | (X4 @ (sK24 @ X4) @ Y1)) | (~ (X4 @ Y0 @ Y1)))))) @ (sK25 @ X4)))) | ((((^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK23 @ X4))) | (X4 @ Y0 @ (sK23 @ X4)))) @ (sK26 @ X4))) = $false) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ($true = ((sK3 @ X2))) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f189])).
% 3.52/0.95 thf(f191,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ X2 @ (sK13 @ X2)))) | (((sK2 @ X1)) = $true) | ($false = ((((~ (X3 @ (sK27 @ X3) @ (sK22 @ X3))) | (~ (X3 @ (sK22 @ X3) @ (sK19 @ X3)))) | (X3 @ (sK27 @ X3) @ (sK19 @ X3))))) | ((((~ (sK1 @ (sK26 @ X4) @ (sK23 @ X4))) | (X4 @ (sK26 @ X4) @ (sK23 @ X4)))) = $false) | (((!! @ $i @ (^[Y0 : $i]: (((~ (X4 @ (sK24 @ X4) @ (sK25 @ X4))) | (X4 @ (sK24 @ X4) @ Y0)) | (~ (X4 @ (sK25 @ X4) @ Y0)))))) = $false) | ($true = ((sK3 @ X2))) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f190])).
% 3.52/0.95 thf(f193,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((!! @ $i @ (^[Y0 : $i]: (((~ (X4 @ (sK24 @ X4) @ (sK25 @ X4))) | (X4 @ (sK24 @ X4) @ Y0)) | (~ (X4 @ (sK25 @ X4) @ Y0)))))) = $false) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | ((((~ (X3 @ (sK27 @ X3) @ (sK22 @ X3))) | (~ (X3 @ (sK22 @ X3) @ (sK19 @ X3))))) = $false) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ($true = ((sK3 @ X2))) | ((((~ (sK1 @ (sK26 @ X4) @ (sK23 @ X4))) | (X4 @ (sK26 @ X4) @ (sK23 @ X4)))) = $false) | (((sK2 @ X1)) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f191])).
% 3.52/0.95 thf(f194,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (((((~ (sK1 @ (sK26 @ X4) @ (sK23 @ X4))) | (X4 @ (sK26 @ X4) @ (sK23 @ X4)))) = $false) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | ((((^[Y0 : $i]: (((~ (X4 @ (sK24 @ X4) @ (sK25 @ X4))) | (X4 @ (sK24 @ X4) @ Y0)) | (~ (X4 @ (sK25 @ X4) @ Y0)))) @ (sK28 @ X4))) = $false) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ((((~ (X3 @ (sK27 @ X3) @ (sK22 @ X3))) | (~ (X3 @ (sK22 @ X3) @ (sK19 @ X3))))) = $false) | (((sK2 @ X1)) = $true) | ($true = ((sK3 @ X2)))) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f193])).
% 3.52/0.95 thf(f196,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (((((~ (X3 @ (sK27 @ X3) @ (sK22 @ X3))) | (~ (X3 @ (sK22 @ X3) @ (sK19 @ X3))))) = $false) | (((sK2 @ X1)) = $true) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | (((~ (sK1 @ (sK26 @ X4) @ (sK23 @ X4)))) = $false) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | ((((^[Y0 : $i]: (((~ (X4 @ (sK24 @ X4) @ (sK25 @ X4))) | (X4 @ (sK24 @ X4) @ Y0)) | (~ (X4 @ (sK25 @ X4) @ Y0)))) @ (sK28 @ X4))) = $false) | ($true = ((sK3 @ X2)))) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f194])).
% 3.52/0.95 thf(f197,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (((((^[Y0 : $i]: (((~ (X4 @ (sK24 @ X4) @ (sK25 @ X4))) | (X4 @ (sK24 @ X4) @ Y0)) | (~ (X4 @ (sK25 @ X4) @ Y0)))) @ (sK28 @ X4))) = $false) | (((~ (X3 @ (sK22 @ X3) @ (sK19 @ X3)))) = $false) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | (((sK2 @ X1)) = $true) | (((~ (sK1 @ (sK26 @ X4) @ (sK23 @ X4)))) = $false) | ($true = ((sK3 @ X2))) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | ($true = ((X4 @ X2 @ (sK13 @ X2))))) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f196])).
% 3.52/0.95 thf(f208,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((~ (sK1 @ (sK26 @ X4) @ (sK23 @ X4)))) = $false) | (((sK2 @ X1)) = $true) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ($true = ((X3 @ (sK22 @ X3) @ (sK19 @ X3)))) | ($true = ((sK3 @ X2))) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | ((((^[Y0 : $i]: (((~ (X4 @ (sK24 @ X4) @ (sK25 @ X4))) | (X4 @ (sK24 @ X4) @ Y0)) | (~ (X4 @ (sK25 @ X4) @ Y0)))) @ (sK28 @ X4))) = $false)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f197])).
% 3.52/0.95 thf(f209,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((sK2 @ X1)) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | ($true = ((sK1 @ (sK26 @ X4) @ (sK23 @ X4)))) | ($true = ((sK3 @ X2))) | ((((^[Y0 : $i]: (((~ (X4 @ (sK24 @ X4) @ (sK25 @ X4))) | (X4 @ (sK24 @ X4) @ Y0)) | (~ (X4 @ (sK25 @ X4) @ Y0)))) @ (sK28 @ X4))) = $false) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | ($true = ((X3 @ (sK22 @ X3) @ (sK19 @ X3)))) | ($true = ((X4 @ X2 @ (sK13 @ X2))))) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f208])).
% 3.52/0.95 thf(f210,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ X2 @ (sK13 @ X2)))) | ($true = ((sK1 @ (sK26 @ X4) @ (sK23 @ X4)))) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | ($false = ((((~ (X4 @ (sK24 @ X4) @ (sK25 @ X4))) | (X4 @ (sK24 @ X4) @ (sK28 @ X4))) | (~ (X4 @ (sK25 @ X4) @ (sK28 @ X4)))))) | ($true = ((X3 @ (sK22 @ X3) @ (sK19 @ X3)))) | ($true = ((sK3 @ X2))) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | (((sK2 @ X1)) = $true)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f209])).
% 3.52/0.95 thf(f211,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((sK2 @ X1)) = $true) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ($true = ((sK3 @ X2))) | ($true = ((X3 @ (sK22 @ X3) @ (sK19 @ X3)))) | ($true = ((sK1 @ (sK26 @ X4) @ (sK23 @ X4)))) | (((~ (X4 @ (sK25 @ X4) @ (sK28 @ X4)))) = $false) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f210])).
% 3.52/0.95 thf(f216,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK1 @ (sK26 @ X4) @ (sK23 @ X4)))) | ($true = ((sK3 @ X2))) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ($true = ((X3 @ (sK22 @ X3) @ (sK19 @ X3)))) | (((sK2 @ X1)) = $true) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | ($true = ((X4 @ (sK25 @ X4) @ (sK28 @ X4)))) | (((X3 @ X1 @ (sK12 @ X1))) = $true)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f211])).
% 3.52/0.95 thf(f357,plain,(
% 3.52/0.95 (((!! @ $i @ sK2)) = $false) | ((((^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))))))) @ sK44)) = $false)),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f83])).
% 3.52/0.95 thf(f358,plain,(
% 3.52/0.95 ((((^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))))))) @ sK44)) = $false) | (((sK2 @ sK45)) = $false)),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f357])).
% 3.52/0.95 thf(f359,plain,(
% 3.52/0.95 ((((sK3 @ sK44) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))))))) = $false) | (((sK2 @ sK45)) = $false)),
% 3.52/0.95 inference(beta-eta_normalization,[],[f358])).
% 3.52/0.95 thf(f360,plain,(
% 3.52/0.95 (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1)))))))))))))) = $false) | (((sK2 @ sK45)) = $false)),
% 3.52/0.95 inference(or_proxy_clausification,[],[f359])).
% 3.52/0.95 thf(f361,plain,(
% 3.52/0.95 (((sK2 @ sK45)) = $false) | (((sK3 @ sK44)) = $false)),
% 3.52/0.95 inference(or_proxy_clausification,[],[f359])).
% 3.52/0.95 thf(f362,plain,(
% 3.52/0.95 (((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))))) = $true) | (((sK2 @ sK45)) = $false)),
% 3.52/0.95 inference(not_proxy_clausification,[],[f360])).
% 3.52/0.95 thf(f363,plain,(
% 3.52/0.95 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))) @ X1))) | (((sK2 @ sK45)) = $false)) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f362])).
% 3.52/0.95 thf(f364,plain,(
% 3.52/0.95 ( ! [X1 : $i] : ((((sK2 @ sK45)) = $false) | ($true = (((sK3 @ X1) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X1 @ Y0))))))))))))) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f363])).
% 3.52/0.95 thf(f365,plain,(
% 3.52/0.95 ( ! [X1 : $i] : (($true = ((sK3 @ X1))) | (((sK2 @ sK45)) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X1 @ Y0)))))))))) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f364])).
% 3.52/0.95 thf(f366,plain,(
% 3.52/0.95 ( ! [X1 : $i] : ((((sK2 @ sK45)) = $false) | ($true = ((sK3 @ X1))) | (((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X1 @ Y0))))))))) = $false)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f365])).
% 3.52/0.95 thf(f367,plain,(
% 3.52/0.95 ( ! [X1 : $i] : (($true = ((sK3 @ X1))) | ($false = (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X1 @ Y0))))))) @ (sK46 @ X1)))) | (((sK2 @ sK45)) = $false)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f366])).
% 3.52/0.95 thf(f368,plain,(
% 3.52/0.95 ( ! [X1 : $i] : (((((sK3 @ (sK46 @ X1)) | (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X1 @ (sK46 @ X1)))))))) = $false) | ($true = ((sK3 @ X1))) | (((sK2 @ sK45)) = $false)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f367])).
% 3.52/0.95 thf(f369,plain,(
% 3.52/0.95 ( ! [X1 : $i] : ((((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X1 @ (sK46 @ X1))))))) = $false) | ($true = ((sK3 @ X1))) | (((sK2 @ sK45)) = $false)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f368])).
% 3.52/0.95 thf(f371,plain,(
% 3.52/0.95 ( ! [X1 : $i] : ((((sK2 @ sK45)) = $false) | ($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X1 @ (sK46 @ X1))))))) | ($true = ((sK3 @ X1)))) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f369])).
% 3.52/0.95 thf(f372,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X1))) | (((sK2 @ sK45)) = $false) | ((((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X1 @ (sK46 @ X1)))) @ X2)) = $true)) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f371])).
% 3.52/0.95 thf(f373,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK2 @ sK45)) = $false) | (((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y0 @ Y1)) | (X2 @ Y0 @ Y2)) | (~ (X2 @ Y1 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X2 @ Y1 @ Y0)))))))) | (X2 @ X1 @ (sK46 @ X1)))) = $true) | ($true = ((sK3 @ X1)))) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f372])).
% 3.52/0.95 thf(f374,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK46 @ X1)))) | ($true = ((sK3 @ X1))) | (((sK2 @ sK45)) = $false) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y0 @ Y1)) | (X2 @ Y0 @ Y2)) | (~ (X2 @ Y1 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X2 @ Y1 @ Y0))))))))))) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f373])).
% 3.52/0.95 thf(f375,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X2 @ Y1 @ Y0))))))))) | (((sK2 @ sK45)) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y0 @ Y1)) | (X2 @ Y0 @ Y2)) | (~ (X2 @ Y1 @ Y2))))))))))) = $true) | ($true = ((sK3 @ X1))) | ($true = ((X2 @ X1 @ (sK46 @ X1))))) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f374])).
% 3.52/0.95 thf(f376,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X1))) | (((sK2 @ sK45)) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y0 @ Y1)) | (X2 @ Y0 @ Y2)) | (~ (X2 @ Y1 @ Y2))))))))))) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X2 @ Y1 @ Y0)))))))) | ($true = ((X2 @ X1 @ (sK46 @ X1))))) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f375])).
% 3.52/0.95 thf(f377,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y0 @ Y1)) | (X2 @ Y0 @ Y2)) | (~ (X2 @ Y1 @ Y2)))))))))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X2 @ Y1 @ Y0)))))))) | ($true = ((sK3 @ X1))) | (((sK2 @ sK45)) = $false) | ($true = ((X2 @ X1 @ (sK46 @ X1))))) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f376])).
% 3.52/0.95 thf(f378,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X2 @ Y1 @ Y0)))))))) | ($true = ((sK3 @ X1))) | ($true = ((X2 @ X1 @ (sK46 @ X1)))) | (((sK2 @ sK45)) = $false) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y0 @ Y1)) | (X2 @ Y0 @ Y2)) | (~ (X2 @ Y1 @ Y2)))))))) @ (sK47 @ X2))) = $false)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f377])).
% 3.52/0.95 thf(f379,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK2 @ sK45)) = $false) | ($true = ((X2 @ X1 @ (sK46 @ X1)))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y0 @ Y1)) | (X2 @ Y0 @ Y2)) | (~ (X2 @ Y1 @ Y2)))))))) @ (sK47 @ X2))) = $false) | ($true = ((sK3 @ X1))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X2 @ Y1 @ Y0))))) @ (sK48 @ X2))))) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f378])).
% 3.52/0.95 thf(f380,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK2 @ sK45)) = $false) | ($true = ((X2 @ X1 @ (sK46 @ X1)))) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ (sK47 @ X2) @ Y0)) | (X2 @ (sK47 @ X2) @ Y1)) | (~ (X2 @ Y0 @ Y1)))))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK48 @ X2))) | (X2 @ Y0 @ (sK48 @ X2)))))) = $false) | ($true = ((sK3 @ X1)))) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f379])).
% 3.52/0.95 thf(f381,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ (sK47 @ X2) @ Y0)) | (X2 @ (sK47 @ X2) @ Y1)) | (~ (X2 @ Y0 @ Y1)))))) @ (sK49 @ X2))) = $false) | ($true = ((X2 @ X1 @ (sK46 @ X1)))) | ($true = ((sK3 @ X1))) | (((sK2 @ sK45)) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK48 @ X2))) | (X2 @ Y0 @ (sK48 @ X2)))))) = $false)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f380])).
% 3.52/0.95 thf(f382,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK46 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK48 @ X2))) | (X2 @ Y0 @ (sK48 @ X2)))) @ (sK50 @ X2)))) | (((sK2 @ sK45)) = $false) | ($true = ((sK3 @ X1))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ (sK47 @ X2) @ Y0)) | (X2 @ (sK47 @ X2) @ Y1)) | (~ (X2 @ Y0 @ Y1)))))) @ (sK49 @ X2))) = $false)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f381])).
% 3.52/0.95 thf(f383,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (((((~ (sK1 @ (sK50 @ X2) @ (sK48 @ X2))) | (X2 @ (sK50 @ X2) @ (sK48 @ X2)))) = $false) | ($true = ((sK3 @ X1))) | (((sK2 @ sK45)) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (X2 @ (sK47 @ X2) @ (sK49 @ X2))) | (X2 @ (sK47 @ X2) @ Y0)) | (~ (X2 @ (sK49 @ X2) @ Y0))))))) | ($true = ((X2 @ X1 @ (sK46 @ X1))))) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f382])).
% 3.52/0.95 thf(f385,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((~ (sK1 @ (sK50 @ X2) @ (sK48 @ X2)))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (X2 @ (sK47 @ X2) @ (sK49 @ X2))) | (X2 @ (sK47 @ X2) @ Y0)) | (~ (X2 @ (sK49 @ X2) @ Y0))))))) | ($true = ((X2 @ X1 @ (sK46 @ X1)))) | (((sK2 @ sK45)) = $false) | ($true = ((sK3 @ X1)))) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f383])).
% 3.52/0.95 thf(f386,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (X2 @ (sK47 @ X2) @ (sK49 @ X2))) | (X2 @ (sK47 @ X2) @ Y0)) | (~ (X2 @ (sK49 @ X2) @ Y0))))))) | ($true = ((sK1 @ (sK50 @ X2) @ (sK48 @ X2)))) | ($true = ((X2 @ X1 @ (sK46 @ X1)))) | ($true = ((sK3 @ X1))) | (((sK2 @ sK45)) = $false)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f385])).
% 3.52/0.95 thf(f387,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK46 @ X1)))) | ($true = ((sK3 @ X1))) | ((((^[Y0 : $i]: (((~ (X2 @ (sK47 @ X2) @ (sK49 @ X2))) | (X2 @ (sK47 @ X2) @ Y0)) | (~ (X2 @ (sK49 @ X2) @ Y0)))) @ (sK51 @ X2))) = $false) | ($true = ((sK1 @ (sK50 @ X2) @ (sK48 @ X2)))) | (((sK2 @ sK45)) = $false)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f386])).
% 3.52/0.95 thf(f388,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK46 @ X1)))) | ($false = ((((~ (X2 @ (sK47 @ X2) @ (sK49 @ X2))) | (X2 @ (sK47 @ X2) @ (sK51 @ X2))) | (~ (X2 @ (sK49 @ X2) @ (sK51 @ X2)))))) | (((sK2 @ sK45)) = $false) | ($true = ((sK3 @ X1))) | ($true = ((sK1 @ (sK50 @ X2) @ (sK48 @ X2))))) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f387])).
% 3.52/0.95 thf(f389,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK2 @ sK45)) = $false) | ($true = ((sK3 @ X1))) | ($true = ((sK1 @ (sK50 @ X2) @ (sK48 @ X2)))) | ($true = ((X2 @ X1 @ (sK46 @ X1)))) | (((~ (X2 @ (sK49 @ X2) @ (sK51 @ X2)))) = $false)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f388])).
% 3.52/0.95 thf(f394,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK2 @ sK45)) = $false) | ($true = ((sK1 @ (sK50 @ X2) @ (sK48 @ X2)))) | ($true = ((X2 @ X1 @ (sK46 @ X1)))) | ($true = ((sK3 @ X1))) | ($true = ((X2 @ (sK49 @ X2) @ (sK51 @ X2))))) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f389])).
% 3.52/0.95 thf(f403,plain,(
% 3.52/0.95 ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3)))))))))))))))))))) | ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))))))),
% 3.52/0.95 inference(beta-eta_normalization,[],[f77])).
% 3.52/0.95 thf(f404,plain,(
% 3.52/0.95 ( ! [X1 : ($i > $o)] : (((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3))))))))))))))))) @ X1)) = $true) | ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))))))) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f403])).
% 3.52/0.95 thf(f405,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X1 : ($i > $o)] : (($true = (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))) @ X2))) | ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3))))))))))))))))) @ X1)) = $true)) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f404])).
% 3.52/0.95 thf(f406,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X1 : ($i > $o)] : (((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0)))) => (!! @ $i @ X2))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((X1 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))))))))) = $true)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f405])).
% 3.52/0.95 thf(f407,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X1 : ($i > $o)] : ((((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((X1 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))))))))) = $true) | (((!! @ $i @ X2)) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0))))) = $false)) )),
% 3.52/0.95 inference(imp_proxy_clausification,[],[f406])).
% 3.52/0.95 thf(f408,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o)] : ((((!! @ $i @ X2)) = $true) | ($true = (((^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((X1 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))))))) @ X3))) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0))))) = $false)) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f407])).
% 3.52/0.95 thf(f409,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : (($true = (((^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((X1 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))))))) @ X3))) | (((X2 @ X4)) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0))))) = $false)) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f408])).
% 3.52/0.95 thf(f410,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : (((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0))) @ (sK53 @ X2))) = $false) | (((X2 @ X4)) = $true) | ($true = (((^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((X1 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))))))) @ X3)))) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f409])).
% 3.52/0.95 thf(f411,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : (($false = (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ (sK53 @ X2) @ Y0)))) => (X2 @ Y0)))) => (X2 @ (sK53 @ X2))))) | (((X2 @ X4)) = $true) | ((((X1 @ X3) | (~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))))))) = $true)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f410])).
% 3.52/0.95 thf(f412,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : ((((X2 @ X4)) = $true) | ((((X1 @ X3) | (~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))))))) = $true) | ($false = ((X2 @ (sK53 @ X2))))) )),
% 3.52/0.95 inference(imp_proxy_clausification,[],[f411])).
% 3.52/0.95 thf(f413,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ (sK53 @ X2) @ Y0)))) => (X2 @ Y0)))))) | ((((X1 @ X3) | (~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))))))) = $true) | (((X2 @ X4)) = $true)) )),
% 3.52/0.95 inference(imp_proxy_clausification,[],[f411])).
% 3.52/0.95 thf(f414,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ (sK53 @ X2) @ Y0)))) => (X2 @ Y0))) @ X5))) | ((((X1 @ X3) | (~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))))))) = $true) | (((X2 @ X4)) = $true)) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f413])).
% 3.52/0.95 thf(f415,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : ((((X1 @ X3)) = $true) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))))))) | ($true = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ (sK53 @ X2) @ Y0)))) => (X2 @ Y0))) @ X5))) | (((X2 @ X4)) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f414])).
% 3.52/0.95 thf(f416,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))))) = $false) | ($true = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ (sK53 @ X2) @ Y0)))) => (X2 @ Y0))) @ X5))) | (((X1 @ X3)) = $true) | (((X2 @ X4)) = $true)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f415])).
% 3.52/0.95 thf(f417,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : (((((^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))) @ (sK54 @ X1))) = $false) | (((X1 @ X3)) = $true) | (((X2 @ X4)) = $true) | ($true = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ (sK53 @ X2) @ Y0)))) => (X2 @ Y0))) @ X5)))) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f416])).
% 3.52/0.95 thf(f418,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : (((((X1 @ (sK54 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK54 @ X1) @ Y0))))))))))) = $false) | ((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ (sK53 @ X2) @ X5)))) => (X2 @ X5))) = $true) | (((X1 @ X3)) = $true) | (((X2 @ X4)) = $true)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f417])).
% 3.52/0.95 thf(f419,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : ((((X1 @ X3)) = $true) | (((X2 @ X4)) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK54 @ X1) @ Y0)))))))))) = $false) | ((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ (sK53 @ X2) @ X5)))) => (X2 @ X5))) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f418])).
% 3.52/0.95 thf(f446,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : ((((X1 @ X3)) = $true) | (((X2 @ X4)) = $true) | ((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ (sK53 @ X2) @ X5)))) => (X2 @ X5))) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK54 @ X1) @ Y0))))))))))) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f419])).
% 3.52/0.95 thf(f447,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK54 @ X1) @ Y0)))))))))) | ($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ (sK53 @ X2) @ X5))))) = $false) | (((X2 @ X4)) = $true)) )),
% 3.52/0.95 inference(imp_proxy_clausification,[],[f446])).
% 3.52/0.95 thf(f448,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : ((((X1 @ X3)) = $true) | (((X2 @ X4)) = $true) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ (sK53 @ X2) @ X5))))) = $false) | ($true = (((^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK54 @ X1) @ Y0))))))) @ X6))) | ($true = ((X2 @ X5)))) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f447])).
% 3.52/0.95 thf(f449,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK54 @ X1) @ Y0))))))) @ X6))) | (((X1 @ X3)) = $true) | ((((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ (sK53 @ X2) @ X5))) @ (sK56 @ X5 @ X2))) = $false) | (((X2 @ X4)) = $true) | ($true = ((X2 @ X5)))) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f448])).
% 3.52/0.95 thf(f450,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (((((X1 @ X6) | (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK54 @ X1) @ X6))))))) = $true) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5))) | (((X2 @ X4)) = $true) | (((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK56 @ X5 @ X2 @ Y2 @ Y1)) | (~ (sK56 @ X5 @ X2 @ Y1 @ Y0))) | (sK56 @ X5 @ X2 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (sK56 @ X5 @ X2 @ Y0 @ Y1)))))))) | (sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5))) = $false)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f449])).
% 3.52/0.95 thf(f451,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : ((((X2 @ X4)) = $true) | (((X1 @ X6)) = $true) | (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK54 @ X1) @ X6)))))) = $true) | ($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | (((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK56 @ X5 @ X2 @ Y2 @ Y1)) | (~ (sK56 @ X5 @ X2 @ Y1 @ Y0))) | (sK56 @ X5 @ X2 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (sK56 @ X5 @ X2 @ Y0 @ Y1)))))))) | (sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5))) = $false)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f450])).
% 3.52/0.95 thf(f452,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($false = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK54 @ X1) @ X6)))))) | (((X1 @ X6)) = $true) | (((X2 @ X4)) = $true) | (((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK56 @ X5 @ X2 @ Y2 @ Y1)) | (~ (sK56 @ X5 @ X2 @ Y1 @ Y0))) | (sK56 @ X5 @ X2 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (sK56 @ X5 @ X2 @ Y0 @ Y1)))))))) | (sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5))) = $false) | ($true = ((X2 @ X5))) | (((X1 @ X3)) = $true)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f451])).
% 3.52/0.95 thf(f453,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : ((((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK56 @ X5 @ X2 @ Y2 @ Y1)) | (~ (sK56 @ X5 @ X2 @ Y1 @ Y0))) | (sK56 @ X5 @ X2 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (sK56 @ X5 @ X2 @ Y0 @ Y1)))))))) | (sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5))) = $false) | (((X1 @ X6)) = $true) | ($true = ((X2 @ X5))) | ((((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK54 @ X1) @ X6))) @ (sK57 @ X1 @ X6))) = $false) | (((X1 @ X3)) = $true) | (((X2 @ X4)) = $true)) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f452])).
% 3.52/0.95 thf(f454,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($true = ((X2 @ X5))) | ((((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK54 @ X1) @ X6))) @ (sK57 @ X1 @ X6))) = $false) | ($false = ((sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5))) | (((X1 @ X3)) = $true) | (((X2 @ X4)) = $true) | (((X1 @ X6)) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f453])).
% 3.52/0.95 thf(f455,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : ((((X1 @ X3)) = $true) | (((X1 @ X6)) = $true) | ((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK56 @ X5 @ X2 @ Y2 @ Y1)) | (~ (sK56 @ X5 @ X2 @ Y1 @ Y0))) | (sK56 @ X5 @ X2 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (sK56 @ X5 @ X2 @ Y0 @ Y1))))))))) = $false) | ($true = ((X2 @ X5))) | (((X2 @ X4)) = $true) | ((((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK54 @ X1) @ X6))) @ (sK57 @ X1 @ X6))) = $false)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f453])).
% 3.52/0.95 thf(f456,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (((((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK54 @ X1) @ X6))) @ (sK57 @ X1 @ X6))) = $false) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (sK56 @ X5 @ X2 @ Y0 @ Y1))))))))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5))) | (((X1 @ X6)) = $true) | (((X2 @ X4)) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f455])).
% 3.52/0.95 thf(f501,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : ((((X2 @ X4)) = $true) | ($true = ((X2 @ X5))) | ((((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK54 @ X1) @ X6))) @ (sK57 @ X1 @ X6))) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (sK56 @ X5 @ X2 @ Y0 @ Y1)))))))) | (((X1 @ X3)) = $true) | (((X1 @ X6)) = $true)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f456])).
% 3.52/0.95 thf(f502,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X2 @ X4)) = $true) | ((((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK54 @ X1) @ X6))) @ (sK57 @ X1 @ X6))) = $false) | (((X1 @ X3)) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y0 @ Y1)) | (sK56 @ X5 @ X2 @ Y0 @ Y1))))) @ X7)) = $true) | (((X1 @ X6)) = $true) | ($true = ((X2 @ X5)))) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f501])).
% 3.52/0.95 thf(f503,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK57 @ X1 @ X6 @ Y0 @ Y1)) | (sK57 @ X1 @ X6 @ Y0 @ Y2)) | (~ (sK57 @ X1 @ X6 @ Y1 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK57 @ X1 @ X6 @ Y1 @ Y0)))))))) | (sK57 @ X1 @ X6 @ (sK54 @ X1) @ X6))) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ X7 @ Y0)) | (sK56 @ X5 @ X2 @ X7 @ Y0)))))) | (((X1 @ X6)) = $true) | (((X1 @ X3)) = $true) | (((X2 @ X4)) = $true) | ($true = ((X2 @ X5)))) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f502])).
% 3.52/0.95 thf(f504,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X1 @ X6)) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ X7 @ Y0)) | (sK56 @ X5 @ X2 @ X7 @ Y0)))))) | (((X1 @ X3)) = $true) | (((X2 @ X4)) = $true) | ($true = ((X2 @ X5))) | (((sK57 @ X1 @ X6 @ (sK54 @ X1) @ X6)) = $false)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f503])).
% 3.52/0.95 thf(f505,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK57 @ X1 @ X6 @ Y0 @ Y1)) | (sK57 @ X1 @ X6 @ Y0 @ Y2)) | (~ (sK57 @ X1 @ X6 @ Y1 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK57 @ X1 @ X6 @ Y1 @ Y0))))))))) = $false) | (((X1 @ X6)) = $true) | ($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ X7 @ Y0)) | (sK56 @ X5 @ X2 @ X7 @ Y0)))))) | (((X2 @ X4)) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f503])).
% 3.52/0.95 thf(f506,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X2 @ X4)) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ X7 @ Y0)) | (sK56 @ X5 @ X2 @ X7 @ Y0)))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK57 @ X1 @ X6 @ Y1 @ Y0))))))))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5))) | (((X1 @ X6)) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f505])).
% 3.52/0.95 thf(f522,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X2 @ X4)) = $true) | (((X1 @ X6)) = $true) | ($true = ((X2 @ X5))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK57 @ X1 @ X6 @ Y1 @ Y0))))))))) | (((X1 @ X3)) = $true) | ($true = (((^[Y0 : $i]: ((~ (sK1 @ X7 @ Y0)) | (sK56 @ X5 @ X2 @ X7 @ Y0))) @ X8)))) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f506])).
% 3.52/0.95 thf(f523,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X2 @ X4)) = $true) | ($true = ((X2 @ X5))) | (((X1 @ X6)) = $true) | (((X1 @ X3)) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK57 @ X1 @ X6 @ Y1 @ Y0)))))))) | ($true = (((^[Y0 : $i]: ((~ (sK1 @ X7 @ Y0)) | (sK56 @ X5 @ X2 @ X7 @ Y0))) @ X8)))) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f522])).
% 3.52/0.95 thf(f524,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK57 @ X1 @ X6 @ Y1 @ Y0))))) @ X9))) | (((X2 @ X4)) = $true) | ($true = (((^[Y0 : $i]: ((~ (sK1 @ X7 @ Y0)) | (sK56 @ X5 @ X2 @ X7 @ Y0))) @ X8))) | ($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | (((X1 @ X6)) = $true)) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f523])).
% 3.52/0.95 thf(f525,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ Y0 @ X9)) | (sK57 @ X1 @ X6 @ Y0 @ X9)))))) | (((X1 @ X3)) = $true) | (((X2 @ X4)) = $true) | (((X1 @ X6)) = $true) | ($true = ((X2 @ X5))) | ((((~ (sK1 @ X7 @ X8)) | (sK56 @ X5 @ X2 @ X7 @ X8))) = $true)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f524])).
% 3.52/0.95 thf(f526,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X10 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (((((~ (sK1 @ X7 @ X8)) | (sK56 @ X5 @ X2 @ X7 @ X8))) = $true) | ($true = (((^[Y0 : $i]: ((~ (sK1 @ Y0 @ X9)) | (sK57 @ X1 @ X6 @ Y0 @ X9))) @ X10))) | (((X1 @ X3)) = $true) | (((X1 @ X6)) = $true) | ($true = ((X2 @ X5))) | (((X2 @ X4)) = $true)) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f525])).
% 3.52/0.95 thf(f527,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X10 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK56 @ X5 @ X2 @ X7 @ X8)) = $true) | (((X2 @ X4)) = $true) | (((~ (sK1 @ X7 @ X8))) = $true) | ($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | (((X1 @ X6)) = $true) | ($true = (((^[Y0 : $i]: ((~ (sK1 @ Y0 @ X9)) | (sK57 @ X1 @ X6 @ Y0 @ X9))) @ X10)))) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f526])).
% 3.52/0.95 thf(f528,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X10 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | (((X2 @ X4)) = $true) | (((X1 @ X6)) = $true) | (((sK56 @ X5 @ X2 @ X7 @ X8)) = $true) | ($true = (((^[Y0 : $i]: ((~ (sK1 @ Y0 @ X9)) | (sK57 @ X1 @ X6 @ Y0 @ X9))) @ X10))) | ($false = ((sK1 @ X7 @ X8)))) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f527])).
% 3.52/0.95 thf(f529,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X10 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((sK1 @ X7 @ X8))) | (((sK56 @ X5 @ X2 @ X7 @ X8)) = $true) | ($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | (((X1 @ X6)) = $true) | (((X2 @ X4)) = $true) | ($true = (((~ (sK1 @ X10 @ X9)) | (sK57 @ X1 @ X6 @ X10 @ X9))))) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f528])).
% 3.52/0.95 thf(f530,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X10 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X1 @ X3)) = $true) | ($false = ((sK1 @ X7 @ X8))) | ($true = ((X2 @ X5))) | ($true = ((~ (sK1 @ X10 @ X9)))) | (((X2 @ X4)) = $true) | ($true = ((sK57 @ X1 @ X6 @ X10 @ X9))) | (((sK56 @ X5 @ X2 @ X7 @ X8)) = $true) | (((X1 @ X6)) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f529])).
% 3.52/0.95 thf(f531,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X10 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK1 @ X10 @ X9)) = $false) | ($true = ((sK57 @ X1 @ X6 @ X10 @ X9))) | (((X1 @ X6)) = $true) | ($false = ((sK1 @ X7 @ X8))) | (((X2 @ X4)) = $true) | ($true = ((X2 @ X5))) | (((sK56 @ X5 @ X2 @ X7 @ X8)) = $true) | (((X1 @ X3)) = $true)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f530])).
% 3.52/0.95 thf(f532,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X2 @ X4)) = $true) | (((sK57 @ X1 @ X6 @ (sK54 @ X1) @ X6)) = $false) | ($true = (((^[Y0 : $i]: ((~ (sK1 @ X7 @ Y0)) | (sK56 @ X5 @ X2 @ X7 @ Y0))) @ X8))) | (((X1 @ X6)) = $true) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5)))) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f504])).
% 3.52/0.95 thf(f533,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X1 @ X6)) = $true) | (((sK57 @ X1 @ X6 @ (sK54 @ X1) @ X6)) = $false) | (((X2 @ X4)) = $true) | ($true = ((X2 @ X5))) | ((((~ (sK1 @ X7 @ X8)) | (sK56 @ X5 @ X2 @ X7 @ X8))) = $true) | (((X1 @ X3)) = $true)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f532])).
% 3.52/0.95 thf(f534,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X1 @ X6)) = $true) | (((sK56 @ X5 @ X2 @ X7 @ X8)) = $true) | (((X2 @ X4)) = $true) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5))) | (((~ (sK1 @ X7 @ X8))) = $true) | (((sK57 @ X1 @ X6 @ (sK54 @ X1) @ X6)) = $false)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f533])).
% 3.52/0.95 thf(f535,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | ($false = ((sK1 @ X7 @ X8))) | (((X2 @ X4)) = $true) | (((sK57 @ X1 @ X6 @ (sK54 @ X1) @ X6)) = $false) | (((X1 @ X6)) = $true) | (((sK56 @ X5 @ X2 @ X7 @ X8)) = $true)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f534])).
% 3.52/0.95 thf(f536,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : ((((X1 @ X3)) = $true) | (((X1 @ X6)) = $true) | ($true = ((X2 @ X5))) | ($false = ((sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5))) | (((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK57 @ X1 @ X6 @ Y0 @ Y1)) | (sK57 @ X1 @ X6 @ Y0 @ Y2)) | (~ (sK57 @ X1 @ X6 @ Y1 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK57 @ X1 @ X6 @ Y1 @ Y0)))))))) | (sK57 @ X1 @ X6 @ (sK54 @ X1) @ X6))) = $false) | (((X2 @ X4)) = $true)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f454])).
% 3.52/0.95 thf(f537,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($false = ((sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5))) | (((X2 @ X4)) = $true) | (((sK57 @ X1 @ X6 @ (sK54 @ X1) @ X6)) = $false) | (((X1 @ X3)) = $true) | (((X1 @ X6)) = $true) | ($true = ((X2 @ X5)))) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f536])).
% 3.52/0.95 thf(f538,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : ((((X2 @ X4)) = $true) | (((X1 @ X3)) = $true) | (((X1 @ X6)) = $true) | ($true = ((X2 @ X5))) | ((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK57 @ X1 @ X6 @ Y0 @ Y1)) | (sK57 @ X1 @ X6 @ Y0 @ Y2)) | (~ (sK57 @ X1 @ X6 @ Y1 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK57 @ X1 @ X6 @ Y1 @ Y0))))))))) = $false) | ($false = ((sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5)))) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f536])).
% 3.52/0.95 thf(f539,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($false = ((sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5))) | (((X1 @ X6)) = $true) | ($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | (((X2 @ X4)) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK57 @ X1 @ X6 @ Y1 @ Y0)))))))))) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f538])).
% 3.52/0.95 thf(f552,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : ((((X2 @ X4)) = $true) | ($true = ((X2 @ X5))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK57 @ X1 @ X6 @ Y1 @ Y0)))))))) | ($false = ((sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5))) | (((X1 @ X3)) = $true) | (((X1 @ X6)) = $true)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f539])).
% 3.52/0.95 thf(f553,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | (((X1 @ X6)) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK57 @ X1 @ X6 @ Y1 @ Y0))))) @ X7)) = $true) | ($false = ((sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5))) | (((X2 @ X4)) = $true)) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f552])).
% 3.52/0.95 thf(f554,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X1 @ X6)) = $true) | (((X2 @ X4)) = $true) | ($false = ((sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ Y0 @ X7)) | (sK57 @ X1 @ X6 @ Y0 @ X7))))) = $true)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f553])).
% 3.52/0.95 thf(f555,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X1 @ X6)) = $true) | ((((^[Y0 : $i]: ((~ (sK1 @ Y0 @ X7)) | (sK57 @ X1 @ X6 @ Y0 @ X7))) @ X8)) = $true) | ($true = ((X2 @ X5))) | (((X2 @ X4)) = $true) | (((X1 @ X3)) = $true) | ($false = ((sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5)))) )),
% 3.52/0.95 inference(pi_proxy_clausification,[],[f554])).
% 3.52/0.95 thf(f556,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X1 @ X6)) = $true) | (((X2 @ X4)) = $true) | ((((~ (sK1 @ X8 @ X7)) | (sK57 @ X1 @ X6 @ X8 @ X7))) = $true) | (((X1 @ X3)) = $true) | ($false = ((sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5))) | ($true = ((X2 @ X5)))) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f555])).
% 3.52/0.95 thf(f557,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5))) | ($true = ((X2 @ X5))) | (((X2 @ X4)) = $true) | ($true = ((~ (sK1 @ X8 @ X7)))) | (((X1 @ X3)) = $true) | ($true = ((sK57 @ X1 @ X6 @ X8 @ X7))) | (((X1 @ X6)) = $true)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f556])).
% 3.52/0.95 thf(f558,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X2 @ X4)) = $true) | ($true = ((sK57 @ X1 @ X6 @ X8 @ X7))) | ($false = ((sK56 @ X5 @ X2 @ (sK53 @ X2) @ X5))) | (((X1 @ X6)) = $true) | (((X1 @ X3)) = $true) | (((sK1 @ X8 @ X7)) = $false) | ($true = ((X2 @ X5)))) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f557])).
% 3.52/0.95 thf(f559,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : ((((X2 @ X4)) = $true) | ($false = ((X2 @ (sK53 @ X2)))) | (((X1 @ X3)) = $true) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1)))))))))))))))) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f412])).
% 3.52/0.95 thf(f560,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : ((((X1 @ X3)) = $true) | ($false = ((X2 @ (sK53 @ X2)))) | (((X2 @ X4)) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))))) = $false)) )),
% 3.52/0.95 inference(not_proxy_clausification,[],[f559])).
% 3.52/0.95 thf(f561,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : ((((X2 @ X4)) = $true) | (((X1 @ X3)) = $true) | ($false = (((^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))))))))) @ (sK58 @ X1)))) | ($false = ((X2 @ (sK53 @ X2))))) )),
% 3.52/0.95 inference(sigma_proxy_clausification,[],[f560])).
% 3.52/0.95 thf(f562,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : ((((X2 @ X4)) = $true) | ($false = ((X2 @ (sK53 @ X2)))) | ((((X1 @ (sK58 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK58 @ X1) @ Y0))))))))))) = $false) | (((X1 @ X3)) = $true)) )),
% 3.52/0.95 inference(beta-eta_normalization,[],[f561])).
% 3.52/0.95 thf(f564,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : (($false = ((X2 @ (sK53 @ X2)))) | (((X2 @ X4)) = $true) | (((X1 @ X3)) = $true) | (((X1 @ (sK58 @ X1))) = $false)) )),
% 3.52/0.95 inference(or_proxy_clausification,[],[f562])).
% 3.52/0.95 thf(f595,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (sK7 @ X2)))) | (((sK3 @ sK4)) = $false) | (((sK1 @ (sK6 @ X2) @ (sK9 @ X2))) = $true) | (((sK2 @ X1)) = $true) | ($true = ((X2 @ X1 @ (sK5 @ X1))))) )),
% 3.52/0.95 inference(forward_demodulation,[],[f117,f50])).
% 3.52/0.95 thf(f601,definition,(
% 3.52/0.95 spl60_1 <=> (((sK3 @ sK4)) = $false)),
% 3.52/0.95 introduced(definition,[new_symbols(definition,[spl60_1])],[avatar_definition])).
% 3.52/0.95 thf(f603,plain,(
% 3.52/0.95 (((sK3 @ sK4)) = $false) | ~spl60_1),
% 3.52/0.95 inference(avatar_component_clause,[],[f601])).
% 3.52/0.95 thf(f619,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK23 @ X4)))) | ($true = ((X4 @ (sK25 @ X4) @ (sK28 @ X4)))) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | (((sK2 @ X1)) = $true) | ($true = ((X3 @ (sK22 @ X3) @ (sK19 @ X3))))) )),
% 3.52/0.95 inference(forward_demodulation,[],[f216,f50])).
% 3.52/0.95 thf(f664,definition,(
% 3.52/0.95 spl60_5 <=> (((sK2 @ sK45)) = $false)),
% 3.52/0.95 introduced(definition,[new_symbols(definition,[spl60_5])],[avatar_definition])).
% 3.52/0.95 thf(f666,plain,(
% 3.52/0.95 (((sK2 @ sK45)) = $false) | ~spl60_5),
% 3.52/0.95 inference(avatar_component_clause,[],[f664])).
% 3.52/0.95 thf(f668,definition,(
% 3.52/0.95 spl60_6 <=> (((sK3 @ sK44)) = $false)),
% 3.52/0.95 introduced(definition,[new_symbols(definition,[spl60_6])],[avatar_definition])).
% 3.52/0.95 thf(f670,plain,(
% 3.52/0.95 (((sK3 @ sK44)) = $false) | ~spl60_6),
% 3.52/0.95 inference(avatar_component_clause,[],[f668])).
% 3.52/0.95 thf(f671,plain,(
% 3.52/0.95 spl60_5 | spl60_6),
% 3.52/0.95 inference(avatar_split_clause,[],[f361,f668,f664])).
% 3.52/0.95 thf(f678,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK46 @ X1)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK48 @ X2)))) | (((sK2 @ sK45)) = $false) | ($true = ((X2 @ (sK49 @ X2) @ (sK51 @ X2)))) | ($true = ((sK3 @ X1)))) )),
% 3.52/0.95 inference(forward_demodulation,[],[f394,f50])).
% 3.52/0.95 thf(f693,definition,(
% 3.52/0.95 spl60_10 <=> ! [X3 : $i,X9 : $i,X11 : $i,X6 : $i,X1 : ($i > $o)] : ((((X1 @ X3)) = $true) | (((X1 @ X6)) = $true) | ($true = ((sK57 @ X1 @ X6 @ X11 @ X9))) | ($false = ((sK1 @ X11 @ X9))))),
% 3.52/0.95 introduced(definition,[new_symbols(definition,[spl60_10])],[avatar_definition])).
% 3.52/0.95 thf(f694,plain,(
% 3.52/0.95 ( ! [X3 : $i,X11 : $i,X1 : ($i > $o),X6 : $i,X9 : $i] : (($true = ((sK57 @ X1 @ X6 @ X11 @ X9))) | (((X1 @ X3)) = $true) | ($false = ((sK1 @ X11 @ X9))) | (((X1 @ X6)) = $true)) ) | ~spl60_10),
% 3.52/0.95 inference(avatar_component_clause,[],[f693])).
% 3.52/0.95 thf(f698,definition,(
% 3.52/0.95 spl60_11 <=> ! [X4 : $i,X7 : $i,X8 : $i,X5 : $i,X2 : ($i > $o)] : (($true = ((X2 @ X5))) | (((X2 @ X4)) = $true) | (((sK56 @ X5 @ X2 @ X7 @ X8)) = $true) | ($false = ((sK1 @ X7 @ X8))))),
% 3.52/0.95 introduced(definition,[new_symbols(definition,[spl60_11])],[avatar_definition])).
% 3.52/0.95 thf(f699,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X8 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK56 @ X5 @ X2 @ X7 @ X8)) = $true) | ($false = ((sK1 @ X7 @ X8))) | ($true = ((X2 @ X5))) | (((X2 @ X4)) = $true)) ) | ~spl60_11),
% 3.52/0.95 inference(avatar_component_clause,[],[f698])).
% 3.52/0.95 thf(f701,plain,(
% 3.52/0.95 spl60_11 | spl60_10),
% 3.52/0.95 inference(avatar_split_clause,[],[f531,f693,f698])).
% 3.52/0.95 thf(f702,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((sK1 @ X7 @ X8))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5))) | (((sK56 @ X5 @ X2 @ X7 @ X8)) = $true) | (((sK57 @ X1 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6)) = $false) | (((X2 @ X4)) = $true) | (((X1 @ X6)) = $true)) )),
% 3.52/0.95 inference(forward_demodulation,[],[f535,f50])).
% 3.52/0.95 thf(f704,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK1 @ X8 @ X7)) = $false) | (((X1 @ X6)) = $true) | ($true = ((X2 @ X5))) | ($false = ((sK56 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5))) | (((X2 @ X4)) = $true) | (((X1 @ X3)) = $true) | ($true = ((sK57 @ X1 @ X6 @ X8 @ X7)))) )),
% 3.52/0.95 inference(forward_demodulation,[],[f558,f50])).
% 3.52/0.95 thf(f705,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : ((((X1 @ X3)) = $true) | (((sK57 @ X1 @ X6 @ (sK54 @ X1) @ X6)) = $false) | ($false = ((sK56 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5))) | (((X1 @ X6)) = $true) | (((X2 @ X4)) = $true) | ($true = ((X2 @ X5)))) )),
% 3.52/0.95 inference(forward_demodulation,[],[f537,f50])).
% 3.52/0.95 thf(f706,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : ((((X2 @ X4)) = $true) | (((X1 @ X3)) = $true) | (((X1 @ (sK58 @ X1))) = $false) | (((X2 @ (d2unsorted @ d_unsorted_0))) = $false)) )),
% 3.52/0.95 inference(forward_demodulation,[],[f564,f50])).
% 3.52/0.95 thf(f711,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK5 @ X1)))) | (((sK3 @ sK4)) = $false) | (((sK1 @ (sK6 @ X2) @ (sK9 @ X2))) = $true) | (((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | (((sK2 @ X1)) = $true)) )),
% 3.52/0.95 inference(forward_demodulation,[],[f595,f50])).
% 3.52/0.95 thf(f727,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ (sK25 @ X4) @ (sK28 @ X4)))) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | (((sK2 @ X1)) = $true) | ($true = ((X3 @ (sK22 @ X3) @ (sK19 @ X3)))) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ($true = ((sK3 @ X2))) | (((X3 @ X1 @ (sK12 @ X1))) = $true)) )),
% 3.52/0.95 inference(forward_demodulation,[],[f619,f50])).
% 3.52/0.95 thf(f766,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ X1 @ (sK46 @ X1)))) | ($true = ((sK3 @ X1))) | ($true = ((X2 @ (sK49 @ X2) @ (sK51 @ X2)))) | (((sK2 @ sK45)) = $false)) )),
% 3.52/0.95 inference(forward_demodulation,[],[f678,f50])).
% 3.52/0.95 thf(f774,definition,(
% 3.52/0.95 spl60_13 <=> ! [X1 : ($i > $o),X3 : $i] : ((((X1 @ (d2unsorted @ d_unsorted_0))) = $false) | (((X1 @ X3)) = $true))),
% 3.52/0.95 introduced(definition,[new_symbols(definition,[spl60_13])],[avatar_definition])).
% 3.52/0.95 thf(f775,plain,(
% 3.52/0.95 ( ! [X3 : $i,X1 : ($i > $o)] : ((((X1 @ (d2unsorted @ d_unsorted_0))) = $false) | (((X1 @ X3)) = $true)) ) | ~spl60_13),
% 3.52/0.95 inference(avatar_component_clause,[],[f774])).
% 3.52/0.95 thf(f783,definition,(
% 3.52/0.95 spl60_15 <=> ! [X6 : $i,X1 : ($i > $o),X3 : $i] : ((((X1 @ X3)) = $true) | (((X1 @ X6)) = $true) | (((sK57 @ X1 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6)) = $false))),
% 3.52/0.95 introduced(definition,[new_symbols(definition,[spl60_15])],[avatar_definition])).
% 3.52/0.95 thf(f784,plain,(
% 3.52/0.95 ( ! [X3 : $i,X1 : ($i > $o),X6 : $i] : ((((sK57 @ X1 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6)) = $false) | (((X1 @ X6)) = $true) | (((X1 @ X3)) = $true)) ) | ~spl60_15),
% 3.52/0.95 inference(avatar_component_clause,[],[f783])).
% 3.52/0.95 thf(f786,plain,(
% 3.52/0.95 spl60_11 | spl60_15),
% 3.52/0.95 inference(avatar_split_clause,[],[f702,f783,f698])).
% 3.52/0.95 thf(f788,definition,(
% 3.52/0.95 spl60_16 <=> ! [X2 : ($i > $o),X5 : $i,X4 : $i] : (($false = ((sK56 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5))) | ($true = ((X2 @ X5))) | (((X2 @ X4)) = $true))),
% 3.52/0.95 introduced(definition,[new_symbols(definition,[spl60_16])],[avatar_definition])).
% 3.52/0.95 thf(f789,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X4 : $i,X5 : $i] : (($false = ((sK56 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5))) | (((X2 @ X4)) = $true) | ($true = ((X2 @ X5)))) ) | ~spl60_16),
% 3.52/0.95 inference(avatar_component_clause,[],[f788])).
% 3.52/0.95 thf(f791,plain,(
% 3.52/0.95 spl60_16 | spl60_10),
% 3.52/0.95 inference(avatar_split_clause,[],[f704,f693,f788])).
% 3.52/0.95 thf(f792,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($false = ((sK56 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5))) | (((X2 @ X4)) = $true) | (((X1 @ X3)) = $true) | (((X1 @ X6)) = $true) | ($true = ((X2 @ X5))) | (((sK57 @ X1 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6)) = $false)) )),
% 3.52/0.95 inference(forward_demodulation,[],[f705,f50])).
% 3.52/0.95 thf(f793,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : ((((X1 @ X3)) = $true) | (((X2 @ X4)) = $true) | (((X1 @ (d2unsorted @ d_unsorted_0))) = $false) | (((X2 @ (d2unsorted @ d_unsorted_0))) = $false)) )),
% 3.52/0.95 inference(forward_demodulation,[],[f706,f50])).
% 3.52/0.95 thf(f804,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK9 @ X2))) = $true) | (((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | (((sK3 @ sK4)) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | (((sK2 @ X1)) = $true)) )),
% 3.52/0.95 inference(forward_demodulation,[],[f711,f50])).
% 3.52/0.95 thf(f820,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((X3 @ X1 @ (sK12 @ X1))) = $true) | ($true = ((X3 @ (sK22 @ X3) @ (sK19 @ X3)))) | ($true = ((sK3 @ X2))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (sK28 @ X4)))) | (((sK2 @ X1)) = $true) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true)) )),
% 3.52/0.95 inference(forward_demodulation,[],[f727,f50])).
% 3.52/0.95 thf(f859,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X1))) | ($true = ((X2 @ X1 @ (sK46 @ X1)))) | (((sK2 @ sK45)) = $false) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (sK51 @ X2)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) )),
% 3.52/0.95 inference(forward_demodulation,[],[f766,f50])).
% 3.52/0.95 thf(f867,plain,(
% 3.52/0.95 spl60_15 | spl60_16),
% 3.52/0.95 inference(avatar_split_clause,[],[f792,f788,f783])).
% 3.52/0.95 thf(f868,plain,(
% 3.52/0.95 spl60_13 | spl60_13),
% 3.52/0.95 inference(avatar_split_clause,[],[f793,f774,f774])).
% 3.52/0.95 thf(f874,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK3 @ sK4)) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | (((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((sK2 @ X1)) = $true)) )),
% 3.52/0.95 inference(forward_demodulation,[],[f804,f50])).
% 3.52/0.95 thf(f892,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (sK28 @ X4)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | ($true = ((sK3 @ X2))) | (((sK2 @ X1)) = $true) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK19 @ X3))))) )),
% 3.52/0.95 inference(forward_demodulation,[],[f820,f50])).
% 3.52/0.95 thf(f932,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK3 @ X1))) | (((sK2 @ sK45)) = $false) | ($true = ((X2 @ X1 @ (sK46 @ X1))))) )),
% 3.52/0.95 inference(forward_demodulation,[],[f859,f50])).
% 3.52/0.95 thf(f938,definition,(
% 3.52/0.95 spl60_21 <=> ! [X2 : ($i > $i > $o),X1 : $i] : ((((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | (((sK2 @ X1)) = $true) | ($true = ((X2 @ X1 @ (sK5 @ X1)))))),
% 3.52/0.95 introduced(definition,[new_symbols(definition,[spl60_21])],[avatar_definition])).
% 3.52/0.95 thf(f939,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | (((sK2 @ X1)) = $true) | ($true = ((X2 @ X1 @ (sK5 @ X1))))) ) | ~spl60_21),
% 3.52/0.95 inference(avatar_component_clause,[],[f938])).
% 3.52/0.95 thf(f941,definition,(
% 3.52/0.95 spl60_22 <=> ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))),
% 3.52/0.95 introduced(definition,[new_symbols(definition,[spl60_22])],[avatar_definition])).
% 3.52/0.95 thf(f943,plain,(
% 3.52/0.95 ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ~spl60_22),
% 3.52/0.95 inference(avatar_component_clause,[],[f941])).
% 3.52/0.95 thf(f945,plain,(
% 3.52/0.95 spl60_21 | spl60_22 | spl60_1),
% 3.52/0.95 inference(avatar_split_clause,[],[f874,f601,f941,f938])).
% 3.52/0.95 thf(f955,definition,(
% 3.52/0.95 spl60_25 <=> ! [X1 : $i,X3 : ($i > $i > $o)] : ((((sK2 @ X1)) = $true) | (((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true))),
% 3.52/0.95 introduced(definition,[new_symbols(definition,[spl60_25])],[avatar_definition])).
% 3.52/0.95 thf(f956,plain,(
% 3.52/0.95 ( ! [X3 : ($i > $i > $o),X1 : $i] : ((((X3 @ X1 @ (sK12 @ X1))) = $true) | (((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | (((sK2 @ X1)) = $true)) ) | ~spl60_25),
% 3.52/0.95 inference(avatar_component_clause,[],[f955])).
% 3.52/0.95 thf(f969,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((X3 @ X1 @ (sK12 @ X1))) = $true) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((sK2 @ X1)) = $true) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK3 @ X2))) | (((sK1 @ (sK20 @ X3) @ (sK21 @ X3))) = $true) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK19 @ X3))))) )),
% 3.52/0.95 inference(forward_demodulation,[],[f892,f50])).
% 3.52/0.95 thf(f1011,definition,(
% 3.52/0.95 spl60_29 <=> ! [X2 : ($i > $i > $o),X1 : $i] : ((((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((X2 @ X1 @ (sK46 @ X1)))) | ($true = ((sK3 @ X1))))),
% 3.52/0.95 introduced(definition,[new_symbols(definition,[spl60_29])],[avatar_definition])).
% 3.52/0.95 thf(f1012,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK3 @ X1))) | ($true = ((X2 @ X1 @ (sK46 @ X1))))) ) | ~spl60_29),
% 3.52/0.95 inference(avatar_component_clause,[],[f1011])).
% 3.52/0.95 thf(f1018,plain,(
% 3.52/0.95 spl60_29 | spl60_5 | spl60_22),
% 3.52/0.95 inference(avatar_split_clause,[],[f932,f941,f664,f1011])).
% 3.52/0.95 thf(f1025,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK19 @ X3)))) | ($true = ((sK3 @ X2))) | (((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK21 @ X3))) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | (((sK2 @ X1)) = $true) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) )),
% 3.52/0.95 inference(forward_demodulation,[],[f969,f50])).
% 3.52/0.95 thf(f1060,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((sK2 @ X1)) = $true) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | (((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | (((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK21 @ X3))) = $true) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK3 @ X2))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) )),
% 3.52/0.95 inference(forward_demodulation,[],[f1025,f50])).
% 3.52/0.95 thf(f1100,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK3 @ X2))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | (((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((sK2 @ X1)) = $true)) )),
% 3.52/0.95 inference(forward_demodulation,[],[f1060,f50])).
% 3.52/0.95 thf(f1101,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((sK2 @ X1)) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ X2 @ (sK13 @ X2)))) | ($true = ((sK3 @ X2))) | (((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true)) )),
% 3.52/0.95 inference(duplicate_literal_removal,[],[f1100])).
% 3.52/0.95 thf(f1122,definition,(
% 3.52/0.95 spl60_31 <=> ! [X2 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ X2 @ (sK13 @ X2)))))),
% 3.52/0.95 introduced(definition,[new_symbols(definition,[spl60_31])],[avatar_definition])).
% 3.52/0.95 thf(f1123,plain,(
% 3.52/0.95 ( ! [X2 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK3 @ X2))) | ($true = ((X4 @ X2 @ (sK13 @ X2))))) ) | ~spl60_31),
% 3.52/0.95 inference(avatar_component_clause,[],[f1122])).
% 3.52/0.95 thf(f1132,plain,(
% 3.52/0.95 spl60_22 | spl60_31 | spl60_25),
% 3.52/0.95 inference(avatar_split_clause,[],[f1101,f955,f1122,f941])).
% 3.52/0.95 thf(f1143,plain,(
% 3.52/0.95 ( ! [X0 : $i] : ((((sK2 @ X0)) = $false)) ) | ~spl60_5),
% 3.52/0.95 inference(superposition,[],[f666,f64])).
% 3.52/0.95 thf(f1167,plain,(
% 3.52/0.95 ( ! [X2 : $i,X0 : $i,X1 : ($i > $o)] : (($false = ((X1 @ X0))) | (((X1 @ X2)) = $true)) ) | ~spl60_13),
% 3.52/0.95 inference(superposition,[],[f775,f50])).
% 3.52/0.95 thf(f1194,plain,(
% 3.52/0.95 ( ! [X0 : $i] : ((((sK1 @ X0 @ X0)) = $true)) ) | ~spl60_22),
% 3.52/0.95 inference(superposition,[],[f943,f50])).
% 3.52/0.95 thf(f1259,plain,(
% 3.52/0.95 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($true = ((sK1 @ X0 @ X1)))) ) | (~spl60_13 | ~spl60_22)),
% 3.52/0.95 inference(superposition,[],[f1167,f1194])).
% 3.52/0.95 thf(f1263,plain,(
% 3.52/0.95 ( ! [X0 : $i,X1 : $i] : (($true = ((sK1 @ X0 @ X1)))) ) | (~spl60_13 | ~spl60_22)),
% 3.52/0.95 inference(trivial_inequality_removal,[],[f1259])).
% 3.52/0.95 thf(f1269,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o)] : (($false = ((sK57 @ X1 @ X2 @ X0 @ X2))) | (((X1 @ X2)) = $true) | (((X1 @ X3)) = $true)) ) | ~spl60_15),
% 3.52/0.95 inference(superposition,[],[f784,f50])).
% 3.52/0.95 thf(f1621,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : $i,X0 : ($i > $o),X1 : $i,X4 : $i] : (($true = $false) | (((X0 @ X1)) = $true) | ($true = ((X0 @ X4))) | (((sK1 @ X2 @ X1)) = $false) | (((X0 @ X1)) = $true) | (((X0 @ X3)) = $true)) ) | (~spl60_10 | ~spl60_15)),
% 3.52/0.95 inference(superposition,[],[f1269,f694])).
% 3.52/0.95 thf(f1626,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : $i,X0 : ($i > $o),X1 : $i,X4 : $i] : (($true = ((X0 @ X4))) | (((X0 @ X3)) = $true) | (((sK1 @ X2 @ X1)) = $false) | ($true = $false) | (((X0 @ X1)) = $true)) ) | (~spl60_10 | ~spl60_15)),
% 3.52/0.95 inference(duplicate_literal_removal,[],[f1621])).
% 3.52/0.95 thf(f1627,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : $i,X0 : ($i > $o),X1 : $i,X4 : $i] : ((((sK1 @ X2 @ X1)) = $false) | (((X0 @ X3)) = $true) | (((X0 @ X1)) = $true) | ($true = ((X0 @ X4)))) ) | (~spl60_10 | ~spl60_15)),
% 3.52/0.95 inference(trivial_inequality_removal,[],[f1626])).
% 3.52/0.95 thf(f1646,plain,(
% 3.52/0.95 ( ! [X3 : $i,X0 : ($i > $o),X1 : $i,X4 : $i] : (($true = $false) | (((X0 @ X3)) = $true) | ($true = ((X0 @ X4))) | (((X0 @ X1)) = $true)) ) | (~spl60_10 | ~spl60_13 | ~spl60_15 | ~spl60_22)),
% 3.52/0.95 inference(forward_demodulation,[],[f1627,f1263])).
% 3.52/0.95 thf(f1647,plain,(
% 3.52/0.95 ( ! [X3 : $i,X0 : ($i > $o),X1 : $i,X4 : $i] : (($true = ((X0 @ X4))) | (((X0 @ X1)) = $true) | (((X0 @ X3)) = $true)) ) | (~spl60_10 | ~spl60_13 | ~spl60_15 | ~spl60_22)),
% 3.52/0.95 inference(trivial_inequality_removal,[],[f1646])).
% 3.52/0.95 thf(f1675,plain,(
% 3.52/0.95 ( ! [X3 : $i,X1 : $i,X4 : $i] : (((((^[Y0 : $i]: ($false)) @ X4)) = $true) | ($true = (((^[Y0 : $i]: ($false)) @ X1))) | ($true = (((^[Y0 : $i]: ($false)) @ X3)))) ) | (~spl60_10 | ~spl60_13 | ~spl60_15 | ~spl60_22)),
% 3.52/0.95 inference(primitive_instantiation,[],[f1647])).
% 3.52/0.95 thf(f1713,plain,(
% 3.52/0.95 ($true = $false) | ($true = $false) | ($true = $false) | (~spl60_10 | ~spl60_13 | ~spl60_15 | ~spl60_22)),
% 3.52/0.95 inference(beta-eta_normalization,[],[f1675])).
% 3.52/0.95 thf(f1714,plain,(
% 3.52/0.95 ($true = $false) | (~spl60_10 | ~spl60_13 | ~spl60_15 | ~spl60_22)),
% 3.52/0.95 inference(duplicate_literal_removal,[],[f1713])).
% 3.52/0.95 thf(f1715,plain,(
% 3.52/0.95 $false | (~spl60_10 | ~spl60_13 | ~spl60_15 | ~spl60_22)),
% 3.52/0.95 inference(trivial_inequality_removal,[],[f1714])).
% 3.52/0.95 thf(f1716,plain,(
% 3.52/0.95 ~spl60_10 | ~spl60_13 | ~spl60_15 | ~spl60_22),
% 3.52/0.95 inference(avatar_contradiction_clause,[],[f1715])).
% 3.52/0.95 thf(f1744,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X8 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X2 @ X5))) | (((X2 @ X4)) = $true) | (((sK56 @ X5 @ X2 @ X7 @ X8)) = $true) | ($true = $false)) ) | (~spl60_11 | ~spl60_13 | ~spl60_22)),
% 3.52/0.95 inference(forward_demodulation,[],[f699,f1263])).
% 3.52/0.95 thf(f1745,plain,(
% 3.52/0.95 ( ! [X2 : ($i > $o),X8 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK56 @ X5 @ X2 @ X7 @ X8)) = $true) | (((X2 @ X4)) = $true) | ($true = ((X2 @ X5)))) ) | (~spl60_11 | ~spl60_13 | ~spl60_22)),
% 3.52/0.95 inference(trivial_inequality_removal,[],[f1744])).
% 3.52/0.95 thf(f1834,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o)] : ((((X1 @ X3)) = $true) | (((X1 @ X2)) = $true) | ($true = ((X1 @ X0))) | ($true = $false) | ($true = ((X1 @ X0)))) ) | (~spl60_11 | ~spl60_13 | ~spl60_16 | ~spl60_22)),
% 3.52/0.95 inference(superposition,[],[f789,f1745])).
% 3.52/0.95 thf(f1844,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o)] : ((((X1 @ X3)) = $true) | ($true = ((X1 @ X0))) | (((X1 @ X2)) = $true) | ($true = $false)) ) | (~spl60_11 | ~spl60_13 | ~spl60_16 | ~spl60_22)),
% 3.52/0.95 inference(duplicate_literal_removal,[],[f1834])).
% 3.52/0.95 thf(f1845,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o)] : (($true = ((X1 @ X0))) | (((X1 @ X3)) = $true) | (((X1 @ X2)) = $true)) ) | (~spl60_11 | ~spl60_13 | ~spl60_16 | ~spl60_22)),
% 3.52/0.95 inference(trivial_inequality_removal,[],[f1844])).
% 3.52/0.95 thf(f1855,plain,(
% 3.52/0.95 ( ! [X2 : $i,X3 : $i,X0 : $i] : (($true = (((^[Y0 : $i]: ($false)) @ X2))) | ($true = (((^[Y0 : $i]: ($false)) @ X3))) | ($true = (((^[Y0 : $i]: ($false)) @ X0)))) ) | (~spl60_11 | ~spl60_13 | ~spl60_16 | ~spl60_22)),
% 3.52/0.95 inference(primitive_instantiation,[],[f1845])).
% 3.52/0.95 thf(f1887,plain,(
% 3.52/0.95 ($true = $false) | ($true = $false) | ($true = $false) | (~spl60_11 | ~spl60_13 | ~spl60_16 | ~spl60_22)),
% 3.52/0.95 inference(beta-eta_normalization,[],[f1855])).
% 3.52/0.95 thf(f1888,plain,(
% 3.52/0.95 ($true = $false) | (~spl60_11 | ~spl60_13 | ~spl60_16 | ~spl60_22)),
% 3.52/0.95 inference(duplicate_literal_removal,[],[f1887])).
% 3.52/0.95 thf(f1889,plain,(
% 3.52/0.95 $false | (~spl60_11 | ~spl60_13 | ~spl60_16 | ~spl60_22)),
% 3.52/0.95 inference(trivial_inequality_removal,[],[f1888])).
% 3.52/0.95 thf(f1890,plain,(
% 3.52/0.95 ~spl60_11 | ~spl60_13 | ~spl60_16 | ~spl60_22),
% 3.52/0.95 inference(avatar_contradiction_clause,[],[f1889])).
% 3.52/0.95 thf(f1940,plain,(
% 3.52/0.95 ( ! [X3 : ($i > $i > $o),X1 : $i] : (($true = $false) | (((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true)) ) | (~spl60_5 | ~spl60_25)),
% 3.52/0.95 inference(forward_demodulation,[],[f956,f1143])).
% 3.52/0.95 thf(f1941,plain,(
% 3.52/0.95 ( ! [X3 : ($i > $i > $o),X1 : $i] : ((((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | (((X3 @ X1 @ (sK12 @ X1))) = $true)) ) | (~spl60_5 | ~spl60_25)),
% 3.52/0.95 inference(trivial_inequality_removal,[],[f1940])).
% 3.52/0.95 thf(f1949,plain,(
% 3.52/0.95 ( ! [X0 : $i] : ((((sK3 @ X0)) = $false)) ) | ~spl60_1),
% 3.52/0.95 inference(superposition,[],[f603,f64])).
% 3.52/0.95 thf(f2332,plain,(
% 3.52/0.95 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))) @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))) @ X1 @ (sK12 @ X1))) = $true)) ) | (~spl60_5 | ~spl60_25)),
% 3.52/0.95 inference(primitive_instantiation,[],[f1941])).
% 3.52/0.95 thf(f2385,plain,(
% 3.52/0.95 ( ! [X1 : $i] : (($true = ((~ (X1 = (sK12 @ X1))))) | ($true = ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0)))))) ) | (~spl60_5 | ~spl60_25)),
% 3.52/0.95 inference(beta-eta_normalization,[],[f2332])).
% 3.52/0.95 thf(f2386,plain,(
% 3.52/0.95 ( ! [X1 : $i] : ((((X1 = (sK12 @ X1))) = $false) | ($true = ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0)))))) ) | (~spl60_5 | ~spl60_25)),
% 3.52/0.95 inference(not_proxy_clausification,[],[f2385])).
% 3.52/0.95 thf(f2387,plain,(
% 3.52/0.95 ( ! [X1 : $i] : ((((sK12 @ X1)) != X1) | ($true = ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0)))))) ) | (~spl60_5 | ~spl60_25)),
% 3.52/0.95 inference(equality_proxy_clausification,[],[f2386])).
% 3.52/0.95 thf(f2388,plain,(
% 3.52/0.95 ( ! [X1 : $i] : ((((sK12 @ X1)) != X1) | ($false = (((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0))))) ) | (~spl60_5 | ~spl60_25)),
% 3.52/0.95 inference(not_proxy_clausification,[],[f2387])).
% 3.52/0.95 thf(f2389,plain,(
% 3.52/0.95 ( ! [X1 : $i] : ((((sK12 @ X1)) != X1) | (((d2unsorted @ d_unsorted_0)) != ((d2unsorted @ d_unsorted_0)))) ) | (~spl60_5 | ~spl60_25)),
% 3.52/0.95 inference(equality_proxy_clausification,[],[f2388])).
% 3.52/0.95 thf(f2390,plain,(
% 3.52/0.95 ( ! [X1 : $i] : ((((sK12 @ X1)) != X1)) ) | (~spl60_5 | ~spl60_25)),
% 3.52/0.95 inference(trivial_inequality_removal,[],[f2389])).
% 3.52/0.95 thf(f2409,plain,(
% 3.52/0.95 $false | (~spl60_5 | ~spl60_25)),
% 3.52/0.95 inference(forward_subsumption_resolution,[],[f2390,f64])).
% 3.52/0.95 thf(f2410,plain,(
% 3.52/0.95 ~spl60_5 | ~spl60_25),
% 3.52/0.95 inference(avatar_contradiction_clause,[],[f2409])).
% 3.52/0.95 thf(f2439,plain,(
% 3.52/0.95 ( ! [X2 : $i] : (($true = (((^[Y0 : $i]: ((^[Y1 : $i]: ($false)))) @ X2 @ (sK13 @ X2)))) | ($true = ((sK3 @ X2))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: ($false)))) @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) ) | ~spl60_31),
% 3.52/0.95 inference(primitive_instantiation,[],[f1123])).
% 3.52/0.95 thf(f2477,plain,(
% 3.52/0.95 ( ! [X2 : $i] : (($true = $false) | ($true = ((sK3 @ X2))) | ($true = $false)) ) | ~spl60_31),
% 3.52/0.95 inference(beta-eta_normalization,[],[f2439])).
% 3.52/0.95 thf(f2478,plain,(
% 3.52/0.95 ( ! [X2 : $i] : (($true = $false) | ($true = ((sK3 @ X2)))) ) | ~spl60_31),
% 3.52/0.95 inference(duplicate_literal_removal,[],[f2477])).
% 3.52/0.95 thf(f2479,plain,(
% 3.52/0.95 ( ! [X2 : $i] : (($true = ((sK3 @ X2)))) ) | ~spl60_31),
% 3.52/0.96 inference(trivial_inequality_removal,[],[f2478])).
% 3.52/0.96 thf(f2518,plain,(
% 3.52/0.96 ($true = $false) | (~spl60_1 | ~spl60_31)),
% 3.52/0.96 inference(forward_demodulation,[],[f2479,f1949])).
% 3.52/0.96 thf(f2519,plain,(
% 3.52/0.96 $false | (~spl60_1 | ~spl60_31)),
% 3.52/0.96 inference(trivial_inequality_removal,[],[f2518])).
% 3.52/0.96 thf(f2520,plain,(
% 3.52/0.96 ~spl60_1 | ~spl60_31),
% 3.52/0.96 inference(avatar_contradiction_clause,[],[f2519])).
% 3.52/0.96 thf(f2573,plain,(
% 3.52/0.96 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = $false) | (((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((X2 @ X1 @ (sK5 @ X1))))) ) | (~spl60_5 | ~spl60_21)),
% 3.52/0.96 inference(forward_demodulation,[],[f939,f1143])).
% 3.52/0.96 thf(f2574,plain,(
% 3.52/0.96 ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((X2 @ X1 @ (sK5 @ X1))))) ) | (~spl60_5 | ~spl60_21)),
% 3.52/0.96 inference(trivial_inequality_removal,[],[f2573])).
% 3.52/0.96 thf(f2592,plain,(
% 3.52/0.96 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))) @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))) @ X1 @ (sK5 @ X1))))) ) | (~spl60_5 | ~spl60_21)),
% 3.52/0.96 inference(primitive_instantiation,[],[f2574])).
% 3.52/0.96 thf(f2650,plain,(
% 3.52/0.96 ( ! [X1 : $i] : (($true = ((~ (X1 = (sK5 @ X1))))) | ($true = ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0)))))) ) | (~spl60_5 | ~spl60_21)),
% 3.52/0.96 inference(beta-eta_normalization,[],[f2592])).
% 3.52/0.96 thf(f2651,plain,(
% 3.52/0.96 ( ! [X1 : $i] : ((((X1 = (sK5 @ X1))) = $false) | ($true = ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0)))))) ) | (~spl60_5 | ~spl60_21)),
% 3.52/0.96 inference(not_proxy_clausification,[],[f2650])).
% 3.52/0.96 thf(f2652,plain,(
% 3.52/0.96 ( ! [X1 : $i] : ((((sK5 @ X1)) != X1) | ($true = ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0)))))) ) | (~spl60_5 | ~spl60_21)),
% 3.52/0.96 inference(equality_proxy_clausification,[],[f2651])).
% 3.52/0.96 thf(f2653,plain,(
% 3.52/0.96 ( ! [X1 : $i] : ((((sK5 @ X1)) != X1) | ($false = (((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0))))) ) | (~spl60_5 | ~spl60_21)),
% 3.52/0.96 inference(not_proxy_clausification,[],[f2652])).
% 3.52/0.96 thf(f2654,plain,(
% 3.52/0.96 ( ! [X1 : $i] : ((((sK5 @ X1)) != X1) | (((d2unsorted @ d_unsorted_0)) != ((d2unsorted @ d_unsorted_0)))) ) | (~spl60_5 | ~spl60_21)),
% 3.52/0.96 inference(equality_proxy_clausification,[],[f2653])).
% 3.52/0.96 thf(f2655,plain,(
% 3.52/0.96 ( ! [X1 : $i] : ((((sK5 @ X1)) != X1)) ) | (~spl60_5 | ~spl60_21)),
% 3.52/0.96 inference(trivial_inequality_removal,[],[f2654])).
% 3.52/0.96 thf(f2672,plain,(
% 3.52/0.96 $false | (~spl60_5 | ~spl60_21)),
% 3.52/0.96 inference(forward_subsumption_resolution,[],[f2655,f64])).
% 3.52/0.96 thf(f2673,plain,(
% 3.52/0.96 ~spl60_5 | ~spl60_21),
% 3.52/0.96 inference(avatar_contradiction_clause,[],[f2672])).
% 3.52/0.96 thf(f2785,plain,(
% 3.52/0.96 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((^[Y1 : $i]: ($false)))) @ X1 @ (sK46 @ X1)))) | ($true = ((sK3 @ X1))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: ($false)))) @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) ) | ~spl60_29),
% 3.52/0.96 inference(primitive_instantiation,[],[f1012])).
% 3.52/0.96 thf(f2839,plain,(
% 3.52/0.96 ( ! [X1 : $i] : (($true = $false) | ($true = $false) | ($true = ((sK3 @ X1)))) ) | ~spl60_29),
% 3.52/0.96 inference(beta-eta_normalization,[],[f2785])).
% 3.52/0.96 thf(f2840,plain,(
% 3.52/0.96 ( ! [X1 : $i] : (($true = $false) | ($true = ((sK3 @ X1)))) ) | ~spl60_29),
% 3.52/0.96 inference(duplicate_literal_removal,[],[f2839])).
% 3.52/0.96 thf(f2841,plain,(
% 3.52/0.96 ( ! [X1 : $i] : (($true = ((sK3 @ X1)))) ) | ~spl60_29),
% 3.52/0.96 inference(trivial_inequality_removal,[],[f2840])).
% 3.52/0.96 thf(f2922,plain,(
% 3.52/0.96 ($true = $false) | (~spl60_6 | ~spl60_29)),
% 3.52/0.96 inference(forward_demodulation,[],[f670,f2841])).
% 3.52/0.96 thf(f2923,plain,(
% 3.52/0.96 $false | (~spl60_6 | ~spl60_29)),
% 3.52/0.96 inference(trivial_inequality_removal,[],[f2922])).
% 3.52/0.96 thf(f2924,plain,(
% 3.52/0.96 ~spl60_6 | ~spl60_29),
% 3.52/0.96 inference(avatar_contradiction_clause,[],[f2923])).
% 3.52/0.96 cnf(s3, plain, spl60_5 | spl60_6, inference(sat_conversion,[],[f671])).
% 3.52/0.96 cnf(s8, plain, spl60_10 | spl60_11, inference(sat_conversion,[],[f701])).
% 3.52/0.96 cnf(s12, plain, spl60_11 | spl60_15, inference(sat_conversion,[],[f786])).
% 3.52/0.96 cnf(s14, plain, spl60_10 | spl60_16, inference(sat_conversion,[],[f791])).
% 3.52/0.96 cnf(s18, plain, spl60_15 | spl60_16, inference(sat_conversion,[],[f867])).
% 3.52/0.96 cnf(s19, plain, spl60_13 | spl60_13, inference(sat_conversion,[],[f868])).
% 3.52/0.96 cnf(s20, plain, spl60_13, inference(rat,[],[s19])).
% 3.52/0.96 cnf(s23, plain, spl60_1 | spl60_21 | spl60_22, inference(sat_conversion,[],[f945])).
% 3.52/0.96 cnf(s36, plain, spl60_5 | spl60_22 | spl60_29, inference(sat_conversion,[],[f1018])).
% 3.52/0.96 cnf(s43, plain, spl60_22 | spl60_25 | spl60_31, inference(sat_conversion,[],[f1132])).
% 3.52/0.96 cnf(s54, plain, ~spl60_10 | ~spl60_13 | ~spl60_15 | ~spl60_22, inference(sat_conversion,[],[f1716])).
% 3.52/0.96 cnf(s56, plain, ~spl60_11 | ~spl60_13 | ~spl60_16 | ~spl60_22, inference(sat_conversion,[],[f1890])).
% 3.52/0.96 cnf(s69, plain, ~spl60_5 | ~spl60_25, inference(sat_conversion,[],[f2410])).
% 3.52/0.96 cnf(s72, plain, ~spl60_1 | ~spl60_31, inference(sat_conversion,[],[f2520])).
% 3.52/0.96 cnf(s83, plain, ~spl60_5 | ~spl60_21, inference(sat_conversion,[],[f2673])).
% 3.52/0.96 cnf(s92, plain, ~spl60_6 | ~spl60_29, inference(sat_conversion,[],[f2924])).
% 3.52/0.96 cnf(s94, plain, spl60_15 | ~spl60_22, inference(rat,[],[s56,s12,s18,s20])).
% 3.52/0.96 cnf(s95, plain, ~spl60_15 | ~spl60_22, inference(rat,[],[s56,s8,s14,s54,s20])).
% 3.52/0.96 cnf(s96, plain, ~spl60_22, inference(rat,[],[s95,s94])).
% 3.52/0.96 cnf(s98, plain, spl60_5, inference(rat,[],[s92,s36,s3,s96])).
% 3.52/0.96 cnf(s99, plain, ~spl60_21, inference(rat,[],[s83,s98])).
% 3.52/0.96 cnf(s100, plain, ~spl60_25, inference(rat,[],[s69,s98])).
% 3.52/0.96 cnf(s101, plain, spl60_1, inference(rat,[],[s23,s96,s99])).
% 3.52/0.96 cnf(s103, plain, spl60_31, inference(rat,[],[s43,s96,s100])).
% 3.52/0.96 cnf(s106, plain, $false, inference(rat,[],[s72,s103,s101])).
% 3.52/0.96 thf(f2926,plain,(
% 3.52/0.96 $false),
% 3.52/0.96 inference(avatar_sat_refutation,[],[s106])).
% 3.52/0.96 % SZS output end Proof for theBenchmark
% 3.52/0.96 % (3057735)------------------------------
% 3.52/0.96 % (3057735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.52/0.96 % (3057735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/0.96 % (3057735)CaDiCaL version: 2.1.3
% 3.52/0.96 % (3057735)Termination reason: Refutation
% 3.52/0.96 % (3057735)Time elapsed: 0.123 s
% 3.52/0.96 % (3057735)Peak memory usage: 14 MB
% 3.52/0.96 % (3057735)Instructions burned: 324 (million)
% 3.52/0.96 % (3057621)Success in time 0.683 s
% 3.52/0.96 % Vampire exiting
%------------------------------------------------------------------------------