%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP004^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:07:36 AM UTC 2026
% Result : Theorem 0.95s 0.40s
% Output : Refutation 0.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP004^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n002.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:23:08 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.37 % (1728818)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.37 % (1728827)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1058322613:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.37 % (1728829)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.37 % (1728829)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
% 0.20/0.37 % (1728827)Instruction limit reached!
% 0.20/0.37 % (1728827)------------------------------
% 0.20/0.37 % (1728827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.37 % (1728827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.37 % (1728827)CaDiCaL version: 2.1.3
% 0.20/0.37 % (1728827)Termination reason: Instruction limit
% 0.20/0.37 % (1728827)Termination phase: Saturation
% 0.20/0.37 % (1728827)Time elapsed: 0.006 s
% 0.20/0.37 % (1728827)Peak memory usage: 12 MB
% 0.20/0.37 % (1728827)Instructions burned: 26 (million)
% 0.20/0.37 % (1728823)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=314849889:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.37 % (1728824)lrs+10_16_si=on:nwc=1.5:random_seed=2386744985:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.37 % (1728828)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3966170324:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.37 % (1728825)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3245503272:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.37 % (1728826)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=2719387630: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)
% 0.20/0.37 % (1728829)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=802591458:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.37 % (1728825)Instruction limit reached!
% 0.20/0.37 % (1728825)------------------------------
% 0.20/0.37 % (1728825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.37 % (1728825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.37 % (1728825)CaDiCaL version: 2.1.3
% 0.20/0.37 % (1728825)Termination reason: Instruction limit
% 0.20/0.37 % (1728825)Termination phase: Property scanning
% 0.20/0.37 % (1728825)Time elapsed: 0.003 s
% 0.20/0.37 % (1728825)Peak memory usage: 9 MB
% 0.20/0.37 % (1728825)Instructions burned: 7 (million)
% 0.20/0.37 % (1728824)Instruction limit reached!
% 0.20/0.37 % (1728824)------------------------------
% 0.20/0.37 % (1728824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.37 % (1728824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.37 % (1728824)CaDiCaL version: 2.1.3
% 0.20/0.37 % (1728824)Termination reason: Instruction limit
% 0.20/0.37 % (1728824)Termination phase: Saturation
% 0.20/0.37 % (1728824)Time elapsed: 0.008 s
% 0.20/0.37 % (1728824)Peak memory usage: 11 MB
% 0.20/0.37 % (1728824)Instructions burned: 19 (million)
% 0.20/0.37 % (1728831)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2245904299:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (1728831)Instruction limit reached!
% 0.20/0.37 % (1728831)------------------------------
% 0.20/0.37 % (1728831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.37 % (1728831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.37 % (1728831)CaDiCaL version: 2.1.3
% 0.20/0.37 % (1728831)Termination reason: Instruction limit
% 0.20/0.37 % (1728831)Termination phase: Property scanning
% 0.20/0.37 % (1728831)Time elapsed: 0.001 s
% 0.20/0.37 % (1728831)Peak memory usage: 10 MB
% 0.20/0.37 % (1728831)Instructions burned: 4 (million)
% 0.20/0.37 % (1728841)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1507635607:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.95/0.40 % (1728838)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2101877897:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.95/0.40 % (1728841)Instruction limit reached!
% 0.95/0.40 % (1728841)------------------------------
% 0.95/0.40 % (1728841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728841)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728841)Termination reason: Instruction limit
% 0.95/0.40 % (1728841)Termination phase: Property scanning
% 0.95/0.40 % (1728841)Time elapsed: 0.003 s
% 0.95/0.40 % (1728841)Peak memory usage: 10 MB
% 0.95/0.40 % (1728841)Instructions burned: 14 (million)
% 0.95/0.40 % (1728838)Instruction limit reached!
% 0.95/0.40 % (1728838)------------------------------
% 0.95/0.40 % (1728838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728838)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728838)Termination reason: Instruction limit
% 0.95/0.40 % (1728838)Termination phase: Preprocessing 3
% 0.95/0.40 % (1728838)Time elapsed: 0.003 s
% 0.95/0.40 % (1728838)Peak memory usage: 10 MB
% 0.95/0.40 % (1728838)Instructions burned: 7 (million)
% 0.95/0.40 % (1728839)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.95/0.40 % (1728844)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
% 0.95/0.40 % (1728844)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.95/0.40 % (1728823)Instruction limit reached!
% 0.95/0.40 % (1728823)------------------------------
% 0.95/0.40 % (1728823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728823)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728823)Termination reason: Instruction limit
% 0.95/0.40 % (1728823)Termination phase: Saturation
% 0.95/0.40 % (1728823)Time elapsed: 0.041 s
% 0.95/0.40 % (1728823)Peak memory usage: 12 MB
% 0.95/0.40 % (1728823)Instructions burned: 87 (million)
% 0.95/0.40 % (1728844)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2108482239:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.95/0.40 % (1728839)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3302488758:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.95/0.40 % (1728845)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=1781854845:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.95/0.40 % (1728828)Instruction limit reached!
% 0.95/0.40 % (1728828)------------------------------
% 0.95/0.40 % (1728828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728828)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728828)Termination reason: Instruction limit
% 0.95/0.40 % (1728828)Termination phase: Saturation
% 0.95/0.40 % (1728828)Time elapsed: 0.049 s
% 0.95/0.40 % (1728828)Peak memory usage: 12 MB
% 0.95/0.40 % (1728828)Instructions burned: 77 (million)
% 0.95/0.40 % (1728839)Instruction limit reached!
% 0.95/0.40 % (1728839)------------------------------
% 0.95/0.40 % (1728839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728839)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728839)Termination reason: Instruction limit
% 0.95/0.40 % (1728839)Termination phase: Property scanning
% 0.95/0.40 % (1728839)Time elapsed: 0.006 s
% 0.95/0.40 % (1728839)Peak memory usage: 10 MB
% 0.95/0.40 % (1728839)Instructions burned: 7 (million)
% 0.95/0.40 % (1728846)lrs+10_1_si=on:cs=on:random_seed=3601914927:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.95/0.40 % (1728846)Instruction limit reached!
% 0.95/0.40 % (1728846)------------------------------
% 0.95/0.40 % (1728846)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728846)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728846)Termination reason: Instruction limit
% 0.95/0.40 % (1728846)Termination phase: Property scanning
% 0.95/0.40 % (1728846)Time elapsed: 0.003 s
% 0.95/0.40 % (1728846)Peak memory usage: 11 MB
% 0.95/0.40 % (1728846)Instructions burned: 14 (million)
% 0.95/0.40 % (1728844)Instruction limit reached!
% 0.95/0.40 % (1728844)------------------------------
% 0.95/0.40 % (1728844)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728844)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728844)Termination reason: Instruction limit
% 0.95/0.40 % (1728844)Termination phase: Saturation
% 0.95/0.40 % (1728844)Time elapsed: 0.016 s
% 0.95/0.40 % (1728844)Peak memory usage: 11 MB
% 0.95/0.40 % (1728844)Instructions burned: 31 (million)
% 0.95/0.40 % (1728850)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.95/0.40 % (1728854)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2295109460:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.95/0.40 % (1728850)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=3963887085:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.95/0.40 % (1728850)Instruction limit reached!
% 0.95/0.40 % (1728850)------------------------------
% 0.95/0.40 % (1728850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728850)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728850)Termination reason: Instruction limit
% 0.95/0.40 % (1728850)Termination phase: shuffling
% 0.95/0.40 % (1728850)Time elapsed: 0.002 s
% 0.95/0.40 % (1728850)Peak memory usage: 9 MB
% 0.95/0.40 % (1728850)Instructions burned: 4 (million)
% 0.95/0.40 % (1728853)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=739272702:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.95/0.40 % (1728854)Instruction limit reached!
% 0.95/0.40 % (1728854)------------------------------
% 0.95/0.40 % (1728854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728854)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728854)Termination reason: Instruction limit
% 0.95/0.40 % (1728854)Termination phase: Saturation
% 0.95/0.40 % (1728854)Time elapsed: 0.007 s
% 0.95/0.40 % (1728854)Peak memory usage: 12 MB
% 0.95/0.40 % (1728854)Instructions burned: 26 (million)
% 0.95/0.40 % (1728829)Instruction limit reached!
% 0.95/0.40 % (1728829)------------------------------
% 0.95/0.40 % (1728829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728829)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728829)Termination reason: Instruction limit
% 0.95/0.40 % (1728829)Termination phase: Saturation
% 0.95/0.40 % (1728829)Time elapsed: 0.077 s
% 0.95/0.40 % (1728829)Peak memory usage: 13 MB
% 0.95/0.40 % (1728829)Instructions burned: 158 (million)
% 0.95/0.40 % (1728853)Refutation not found, incomplete strategy
% 0.95/0.40 % (1728853)------------------------------
% 0.95/0.40 % (1728853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728853)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728853)Termination reason: Refutation not found, incomplete strategy
% 0.95/0.40 % (1728853)Time elapsed: 0.005 s
% 0.95/0.40 % (1728853)Peak memory usage: 12 MB
% 0.95/0.40 % (1728853)Instructions burned: 11 (million)
% 0.95/0.40 % (1728853)------------------------------
% 0.95/0.40 % (1728853)------------------------------
% 0.95/0.40 % (1728845)Instruction limit reached!
% 0.95/0.40 % (1728845)------------------------------
% 0.95/0.40 % (1728845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728845)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728845)Termination reason: Instruction limit
% 0.95/0.40 % (1728845)Termination phase: Saturation
% 0.95/0.40 % (1728845)Time elapsed: 0.042 s
% 0.95/0.40 % (1728845)Peak memory usage: 12 MB
% 0.95/0.40 % (1728845)Instructions burned: 86 (million)
% 0.95/0.40 % (1728859)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4114795498:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.95/0.40 % (1728851)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3894527928:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.95/0.40 % (1728857)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1943937193:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.95/0.40 % (1728860)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3754022059:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.95/0.40 % (1728857)Instruction limit reached!
% 0.95/0.40 % (1728857)------------------------------
% 0.95/0.40 % (1728857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728851)Refutation not found, incomplete strategy
% 0.95/0.40 % (1728851)------------------------------
% 0.95/0.40 % (1728851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728857)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728851)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728857)Termination reason: Instruction limit
% 0.95/0.40 % (1728857)Termination phase: Property scanning
% 0.95/0.40 % (1728851)Termination reason: Refutation not found, incomplete strategy
% 0.95/0.40 % (1728851)Time elapsed: 0.009 s
% 0.95/0.40 % (1728857)Time elapsed: 0.007 s
% 0.95/0.40 % (1728857)Peak memory usage: 10 MB
% 0.95/0.40 % (1728857)Instructions burned: 16 (million)
% 0.95/0.40 % (1728861)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3643322366: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)
% 0.95/0.40 % (1728861)Instruction limit reached!
% 0.95/0.40 % (1728861)------------------------------
% 0.95/0.40 % (1728861)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728861)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728861)Termination reason: Instruction limit
% 0.95/0.40 % (1728861)Termination phase: Property scanning
% 0.95/0.40 % (1728861)Time elapsed: 0.001 s
% 0.95/0.40 % (1728861)Peak memory usage: 10 MB
% 0.95/0.40 % (1728861)Instructions burned: 2 (million)
% 0.95/0.40 % (1728851)Peak memory usage: 12 MB
% 0.95/0.40 % (1728851)Instructions burned: 11 (million)
% 0.95/0.40 % (1728851)------------------------------
% 0.95/0.40 % (1728851)------------------------------
% 0.95/0.40 % (1728860)Instruction limit reached!
% 0.95/0.40 % (1728860)------------------------------
% 0.95/0.40 % (1728860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728860)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728860)Termination reason: Instruction limit
% 0.95/0.40 % (1728860)Termination phase: Property scanning
% 0.95/0.40 % (1728860)Time elapsed: 0.006 s
% 0.95/0.40 % (1728860)Peak memory usage: 10 MB
% 0.95/0.40 % (1728860)Instructions burned: 15 (million)
% 0.95/0.40 % (1728863)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1952313904:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.95/0.40 % (1728859) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1728818-1728859"...
% 0.95/0.40 % (1728871)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.95/0.40 % (1728863)Instruction limit reached!
% 0.95/0.40 % (1728863)------------------------------
% 0.95/0.40 % (1728863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.40 % (1728863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.40 % (1728863)CaDiCaL version: 2.1.3
% 0.95/0.40 % (1728863)Termination reason: Instruction limit
% 0.95/0.40 % (1728863)Termination phase: Saturation
% 0.95/0.40 % (1728863)Time elapsed: 0.013 s
% 0.95/0.40 % (1728863)Peak memory usage: 12 MB
% 0.95/0.40 % (1728863)Instructions burned: 27 (million)
% 0.95/0.40 % (1728869)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=570069571:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.95/0.40 % (1728859)...printing done.
% 0.95/0.40 % (1728859)Refutation found. Thanks to Tanya!
% 0.95/0.40 % SZS status Theorem for theBenchmark
% 0.95/0.40 % SZS output start Proof for theBenchmark
% 0.95/0.40 thf(type_def_5, type, u: $tType).
% 0.95/0.40 thf(type_def_6, type, d: $tType).
% 0.95/0.40 thf(type_def_7, type, du: $tType).
% 0.95/0.40 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 0.95/0.40 thf(func_def_0, type, tyop_2Emin_2Ebool: d).
% 0.95/0.40 thf(func_def_1, type, tyop_2Emin_2Efun: (d > d > d)).
% 0.95/0.40 thf(func_def_2, type, s: (d > u > du)).
% 0.95/0.40 thf(func_def_3, type, app_2E2: (du > du > u)).
% 0.95/0.40 thf(func_def_4, type, combin_i_2E0: u).
% 0.95/0.40 thf(func_def_5, type, combin_k_2E0: u).
% 0.95/0.40 thf(func_def_6, type, combin_s_2E0: u).
% 0.95/0.40 thf(func_def_7, type, c_2Ebool_2E_21_2E0: u).
% 0.95/0.40 thf(func_def_8, type, c_2Ebool_2E_21_2E1: (du > u)).
% 0.95/0.40 thf(func_def_9, type, c_2Ebool_2E_2F_5C_2E0: u).
% 0.95/0.40 thf(func_def_10, type, c_2Ebool_2E_2F_5C_2E2: (du > du > u)).
% 0.95/0.40 thf(func_def_11, type, c_2Emin_2E_3D_2E0: u).
% 0.95/0.40 thf(func_def_12, type, c_2Emin_2E_3D_2E2: (du > du > u)).
% 0.95/0.40 thf(func_def_13, type, c_2Emin_2E_3D_3D_3E_2E0: u).
% 0.95/0.40 thf(func_def_14, type, c_2Emin_2E_3D_3D_3E_2E2: (du > du > u)).
% 0.95/0.40 thf(func_def_15, type, c_2Ebool_2E_3F_2E0: u).
% 0.95/0.40 thf(func_def_16, type, c_2Ebool_2E_3F_2E1: (du > u)).
% 0.95/0.40 thf(func_def_17, type, c_2Epred__set_2ECHOICE_2E0: u).
% 0.95/0.40 thf(func_def_18, type, c_2Epred__set_2ECHOICE_2E1: (du > u)).
% 0.95/0.40 thf(func_def_19, type, c_2Epred__set_2EDELETE_2E0: u).
% 0.95/0.40 thf(func_def_20, type, c_2Epred__set_2EDELETE_2E2: (du > du > u)).
% 0.95/0.40 thf(func_def_21, type, c_2Ebool_2EF_2E0: u).
% 0.95/0.40 thf(func_def_22, type, c_2Ebool_2EIN_2E0: u).
% 0.95/0.40 thf(func_def_23, type, c_2Ebool_2EIN_2E2: (du > du > u)).
% 0.95/0.40 thf(func_def_24, type, c_2Epred__set_2EREST_2E0: u).
% 0.95/0.40 thf(func_def_25, type, c_2Epred__set_2EREST_2E1: (du > u)).
% 0.95/0.40 thf(func_def_26, type, c_2Epred__set_2ESUBSET_2E0: u).
% 0.95/0.40 thf(func_def_27, type, c_2Epred__set_2ESUBSET_2E2: (du > du > u)).
% 0.95/0.40 thf(func_def_28, type, c_2Ebool_2ET_2E0: u).
% 0.95/0.40 thf(func_def_29, type, c_2Ebool_2E_5C_2F_2E0: u).
% 0.95/0.40 thf(func_def_30, type, c_2Ebool_2E_5C_2F_2E2: (du > du > u)).
% 0.95/0.40 thf(func_def_31, type, c_2Ebool_2E_7E_2E0: u).
% 0.95/0.40 thf(func_def_32, type, c_2Ebool_2E_7E_2E1: (du > u)).
% 0.95/0.40 thf(func_def_33, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: (($o > $o) > $o > $o)).
% 0.95/0.40 thf(func_def_34, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (($o > $o > $o) > $o > $o > $o)).
% 0.95/0.40 thf(func_def_35, type, mono_2Ec_2Ebool_2E_2F_5C: ($o > $o > $o)).
% 0.95/0.40 thf(func_def_36, type, mono_2Ec_2Emin_2E_3D_3D_3E: ($o > $o > $o)).
% 0.95/0.40 thf(func_def_37, type, mono_2Ec_2Ebool_2EF: $o).
% 0.95/0.40 thf(func_def_38, type, mono_2Ec_2Ebool_2ET: $o).
% 0.95/0.40 thf(func_def_39, type, mono_2Ec_2Ebool_2E_5C_2F: ($o > $o > $o)).
% 0.95/0.40 thf(func_def_40, type, mono_2Ec_2Ebool_2E_7E: ($o > $o)).
% 0.95/0.41 thf(func_def_41, type, i_mono_2Etyop_2Emin_2Ebool: ($o > u)).
% 0.95/0.41 thf(func_def_42, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (($o > $o) > u)).
% 0.95/0.41 thf(func_def_43, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: (($o > $o > $o) > u)).
% 0.95/0.41 thf(func_def_44, type, j_mono_2Etyop_2Emin_2Ebool: (du > $o)).
% 0.95/0.41 thf(func_def_45, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (du > $o > $o)).
% 0.95/0.41 thf(func_def_46, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: (du > $o > $o > $o)).
% 0.95/0.41 thf(func_def_48, type, vNOT: ($o > $o)).
% 0.95/0.41 thf(func_def_51, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.95/0.41 thf(func_def_52, type, sK0: (u > d > u > d > u)).
% 0.95/0.41 thf(func_def_53, type, sK1: d).
% 0.95/0.41 thf(func_def_54, type, sK2: u).
% 0.95/0.41 thf(func_def_55, type, sK3: (u > u > d > u)).
% 0.95/0.41 thf(f30,axiom,(
% 0.95/0.41 ! [X1 : u,X0 : d,X2 : u] : (! [X3 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2))))) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2)))))),
% 0.95/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__DEF)).
% 0.95/0.41 thf(f31,axiom,(
% 0.95/0.41 ! [X2 : u,X3 : u,X0 : d,X1 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X2) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X3)))))) <=> ((~ (((s @ X0 @ X2)) = ((s @ X0 @ X3)))) & (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X2) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))))),
% 0.95/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__DELETE)).
% 0.95/0.41 thf(f32,axiom,(
% 0.95/0.41 ! [X0 : d,X1 : u] : (((s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))) = ((s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ (c_2Epred__set_2ECHOICE_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))))))),
% 0.95/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__DEF)).
% 0.95/0.41 thf(f33,conjecture,(
% 0.95/0.41 ! [X1 : u,X0 : d] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))),
% 0.95/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__SUBSET)).
% 0.95/0.41 thf(f34,negated_conjecture,(
% 0.95/0.41 ~ ! [X1 : u,X0 : d] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))),
% 0.95/0.41 inference(negated_conjecture,[status(cth)],[f33])).
% 0.95/0.41 thf(f35,plain,(
% 0.95/0.41 ! [X0 : u,X1 : u,X2 : d,X3 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3) @ (s @ X2 @ X1)))))) <=> ((~ (((s @ X2 @ X0)) = ((s @ X2 @ X1)))) & (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3))))))),
% 0.95/0.41 inference(rectify,[],[f31])).
% 0.95/0.41 thf(f36,plain,(
% 0.95/0.41 ! [X3 : u,X0 : u,X1 : u,X2 : d] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3) @ (s @ X2 @ X1)))))))) <=> ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3))))) = $true) & (((~ ((s @ X2 @ X0) = (s @ X2 @ X1)))) = $true)))),
% 0.95/0.41 inference(fool_elimination,[],[f35])).
% 0.95/0.41 thf(f43,plain,(
% 0.95/0.41 ! [X0 : u,X1 : d,X2 : u] : (! [X3 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X1 @ X3) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X1 @ X3) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X2))))) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X2)))))),
% 0.95/0.41 inference(rectify,[],[f30])).
% 0.95/0.41 thf(f44,plain,(
% 0.95/0.41 ! [X2 : u,X1 : d,X0 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X2))))) = $true) <=> ! [X3 : u] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X1 @ X3) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0)))))) => ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X1 @ X3) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X2))))))))),
% 0.95/0.41 inference(fool_elimination,[],[f43])).
% 0.95/0.41 thf(f47,plain,(
% 0.95/0.41 ~ ! [X0 : u,X1 : d] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0))) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0))))),
% 0.95/0.41 inference(rectify,[],[f34])).
% 0.95/0.41 thf(f48,plain,(
% 0.95/0.41 ~ ! [X0 : u,X1 : d] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0))) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0))))) = $true)),
% 0.95/0.41 inference(fool_elimination,[],[f47])).
% 0.95/0.41 thf(f64,plain,(
% 0.95/0.41 ? [X1 : d,X0 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0))) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0))))) != $true)),
% 0.95/0.41 inference(ennf_transformation,[],[f48])).
% 0.95/0.41 thf(f65,plain,(
% 0.95/0.41 ! [X1 : d,X2 : u,X0 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X2))))) = $true) <=> ! [X3 : u] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X1 @ X3) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X2)))))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X1 @ X3) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0))))))))),
% 0.95/0.41 inference(ennf_transformation,[],[f44])).
% 0.95/0.41 thf(f69,plain,(
% 0.95/0.41 ? [X0 : d,X1 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) != $true)),
% 0.95/0.41 inference(rectify,[],[f64])).
% 0.95/0.41 thf(f70,plain,(
% 0.95/0.41 ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK2))) @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK2))))))),
% 0.95/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f69])).
% 0.95/0.41 thf(f71,plain,(
% 0.95/0.41 ! [X3 : u,X0 : u,X1 : u,X2 : d] : ((($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3) @ (s @ X2 @ X1)))))))) | ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3))))) != $true) | (((~ ((s @ X2 @ X0) = (s @ X2 @ X1)))) != $true))) & (((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3))))) = $true) & (((~ ((s @ X2 @ X0) = (s @ X2 @ X1)))) = $true)) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3) @ (s @ X2 @ X1))))))))))),
% 0.95/0.41 inference(nnf_transformation,[],[f36])).
% 0.95/0.41 thf(f72,plain,(
% 0.95/0.41 ! [X3 : u,X0 : u,X1 : u,X2 : d] : ((($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3) @ (s @ X2 @ X1)))))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3))))) != $true) | (((~ ((s @ X2 @ X0) = (s @ X2 @ X1)))) != $true)) & (((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3))))) = $true) & (((~ ((s @ X2 @ X0) = (s @ X2 @ X1)))) = $true)) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3) @ (s @ X2 @ X1))))))))))),
% 0.95/0.41 inference(flattening,[],[f71])).
% 0.95/0.41 thf(f73,plain,(
% 0.95/0.41 ! [X0 : u,X1 : u,X2 : u,X3 : d] : ((($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X0) @ (s @ X3 @ X2)))))))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X0)))))) | ($true != ((~ ((s @ X3 @ X1) = (s @ X3 @ X2)))))) & ((($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X0)))))) & ($true = ((~ ((s @ X3 @ X1) = (s @ X3 @ X2)))))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X0) @ (s @ X3 @ X2))))))))))),
% 0.95/0.41 inference(rectify,[],[f72])).
% 0.95/0.41 thf(f76,plain,(
% 0.95/0.41 ! [X1 : d,X2 : u,X0 : u] : (((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X2))))) = $true) | ? [X3 : u] : (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X1 @ X3) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X2)))))) & ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X1 @ X3) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0)))))))) & (! [X3 : u] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X1 @ X3) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X2)))))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X1 @ X3) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0))))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X2))))) != $true)))),
% 0.95/0.41 inference(nnf_transformation,[],[f65])).
% 0.95/0.41 thf(f77,plain,(
% 0.95/0.41 ! [X0 : d,X1 : u,X2 : u] : (((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true) | ? [X3 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) != $true) & (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2))))) = $true))) & (! [X4 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2))))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) != $true)))),
% 0.95/0.41 inference(rectify,[],[f76])).
% 0.95/0.41 thf(f78,plain,(
% 0.95/0.41 ! [X0 : d,X1 : u,X2 : u] : (((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true) | (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ (sK3 @ X2 @ X1 @ X0)) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))))) & ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ (sK3 @ X2 @ X1 @ X0)) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2)))))))) & (! [X4 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2))))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) != $true)))),
% 0.95/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK0 @ X3 @ X2 @ X1 @ X0)],[f77])).
% 0.95/0.41 thf(f81,plain,(
% 0.95/0.41 ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK2))) @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK2))))))),
% 0.95/0.41 inference(cnf_transformation,[],[f70])).
% 0.95/0.41 thf(f84,plain,(
% 0.95/0.41 ( ! [X2 : u,X3 : d,X0 : u,X1 : u] : (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X0) @ (s @ X3 @ X2)))))))) | ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X0))))))) )),
% 0.95/0.41 inference(cnf_transformation,[],[f73])).
% 0.95/0.41 thf(f93,plain,(
% 0.95/0.41 ( ! [X2 : u,X0 : d,X1 : u] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ (sK3 @ X2 @ X1 @ X0)) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2)))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true)) )),
% 0.95/0.41 inference(cnf_transformation,[],[f78])).
% 0.95/0.41 thf(f94,plain,(
% 0.95/0.41 ( ! [X2 : u,X0 : d,X1 : u] : (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ (sK3 @ X2 @ X1 @ X0)) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true)) )),
% 0.95/0.41 inference(cnf_transformation,[],[f78])).
% 0.95/0.41 thf(f95,plain,(
% 0.95/0.41 ( ! [X0 : d,X1 : u] : ((((s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))) = ((s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ (c_2Epred__set_2ECHOICE_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))))))) )),
% 0.95/0.41 inference(cnf_transformation,[],[f32])).
% 0.95/0.41 thf(f98,definition,(
% 0.95/0.41 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.95/0.41 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.95/0.41 thf(f115,plain,(
% 0.95/0.41 ($false = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK2))) @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK2)))))) | ($true != $true)),
% 0.95/0.41 inference(superposition,[],[f81,f98])).
% 0.95/0.41 thf(f117,plain,(
% 0.95/0.41 ($false = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK2))) @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK2))))))),
% 0.95/0.41 inference(trivial_inequality_removal,[],[f115])).
% 0.95/0.41 thf(f207,plain,(
% 0.95/0.41 ( ! [X2 : u,X0 : d,X1 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X2) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))))) != $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X2) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true)) )),
% 0.95/0.41 inference(superposition,[],[f84,f95])).
% 0.95/0.41 thf(f264,plain,(
% 0.95/0.41 ( ! [X2 : u,X0 : d,X1 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ (sK3 @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)) @ X2 @ X0)) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true) | ($true != $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2))))) = $true)) )),
% 0.95/0.41 inference(superposition,[],[f207,f93])).
% 0.95/0.41 thf(f267,plain,(
% 0.95/0.41 ( ! [X2 : u,X0 : d,X1 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ (sK3 @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)) @ X2 @ X0)) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2))))) = $true)) )),
% 0.95/0.41 inference(trivial_inequality_removal,[],[f264])).
% 0.95/0.41 thf(f486,plain,(
% 0.95/0.41 ( ! [X0 : d,X1 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true) | ($true != $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true)) )),
% 0.95/0.41 inference(superposition,[],[f94,f267])).
% 0.95/0.41 thf(f496,plain,(
% 0.95/0.41 ( ! [X0 : d,X1 : u] : (($true != $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true)) )),
% 0.95/0.41 inference(duplicate_literal_removal,[],[f486])).
% 0.95/0.41 thf(f497,plain,(
% 0.95/0.41 ( ! [X0 : d,X1 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true)) )),
% 0.95/0.41 inference(trivial_inequality_removal,[],[f496])).
% 0.95/0.41 thf(f531,plain,(
% 0.95/0.41 ($false = $true)),
% 0.95/0.41 inference(superposition,[],[f117,f497])).
% 0.95/0.41 thf(f537,plain,(
% 0.95/0.41 $false),
% 0.95/0.41 inference(trivial_inequality_removal,[],[f531])).
% 0.95/0.41 % SZS output end Proof for theBenchmark
% 0.95/0.41 % (1728859)------------------------------
% 0.95/0.41 % (1728859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.41 % (1728859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.41 % (1728859)CaDiCaL version: 2.1.3
% 0.95/0.41 % (1728859)Termination reason: Refutation
% 0.95/0.41 % (1728859)Time elapsed: 0.031 s
% 0.95/0.41 % (1728859)Peak memory usage: 12 MB
% 0.95/0.41 % (1728859)Instructions burned: 122 (million)
% 0.95/0.41 % (1728818)Success in time 0.155 s
% 0.95/0.41 % Vampire exiting
%------------------------------------------------------------------------------