%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU815^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:39 AM UTC 2026
% Result : Theorem 0.67s 0.47s
% Output : Refutation 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU815^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n004.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:33:52 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 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
% 0.67/0.39 % (1369558)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.67/0.39 % (1369564)lrs+10_16_si=on:nwc=1.5:random_seed=4136949707:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.67/0.39 % (1369565)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2903492645:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.67/0.39 % (1369566)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=3954626109: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)
% 0.67/0.39 % (1369565)Refutation not found, incomplete strategy
% 0.67/0.39 % (1369565)------------------------------
% 0.67/0.39 % (1369565)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1369565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1369565)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1369565)Termination reason: Refutation not found, incomplete strategy
% 0.67/0.39 % (1369565)Time elapsed: 0.003 s
% 0.67/0.39 % (1369565)Peak memory usage: 12 MB
% 0.67/0.39 % (1369565)Instructions burned: 4 (million)
% 0.67/0.39 % (1369565)------------------------------
% 0.67/0.39 % (1369565)------------------------------
% 0.67/0.39 % (1369563)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2483652776:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.67/0.39 % (1369569)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.67/0.39 % (1369569)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
% 0.67/0.39 % (1369568)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3188596869:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.67/0.39 % (1369564)Instruction limit reached!
% 0.67/0.39 % (1369564)------------------------------
% 0.67/0.39 % (1369564)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1369564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1369564)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1369564)Termination reason: Instruction limit
% 0.67/0.39 % (1369564)Termination phase: Saturation
% 0.67/0.39 % (1369564)Time elapsed: 0.010 s
% 0.67/0.39 % (1369564)Peak memory usage: 12 MB
% 0.67/0.39 % (1369564)Instructions burned: 19 (million)
% 0.67/0.39 % (1369566)Refutation not found, incomplete strategy
% 0.67/0.39 % (1369566)------------------------------
% 0.67/0.39 % (1369566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1369566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1369566)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1369566)Termination reason: Refutation not found, incomplete strategy
% 0.67/0.39 % (1369566)Time elapsed: 0.012 s
% 0.67/0.39 % (1369566)Peak memory usage: 12 MB
% 0.67/0.39 % (1369566)Instructions burned: 19 (million)
% 0.67/0.39 % (1369566)------------------------------
% 0.67/0.39 % (1369566)------------------------------
% 0.67/0.39 % (1369569)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=25171090:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.67/0.39 % (1369567)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2698756491:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.67/0.39 % (1369573)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1367178221:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.67/0.39 % (1369573)Instruction limit reached!
% 0.67/0.39 % (1369573)------------------------------
% 0.67/0.39 % (1369573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1369573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1369573)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1369573)Termination reason: Instruction limit
% 0.67/0.39 % (1369573)Termination phase: Saturation
% 0.67/0.39 % (1369573)Time elapsed: 0.001 s
% 0.67/0.39 % (1369573)Peak memory usage: 11 MB
% 0.67/0.39 % (1369573)Instructions burned: 2 (million)
% 0.67/0.44 % (1369577)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.67/0.44 % (1369576)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4064697363:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.67/0.44 % (1369577)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2416754443:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.67/0.44 % (1369567)Instruction limit reached!
% 0.67/0.44 % (1369567)------------------------------
% 0.67/0.44 % (1369567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.44 % (1369567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.44 % (1369567)CaDiCaL version: 2.1.3
% 0.67/0.44 % (1369567)Termination reason: Instruction limit
% 0.67/0.44 % (1369567)Termination phase: Saturation
% 0.67/0.44 % (1369567)Time elapsed: 0.013 s
% 0.67/0.44 % (1369567)Peak memory usage: 12 MB
% 0.67/0.44 % (1369567)Instructions burned: 24 (million)
% 0.67/0.44 % (1369577)Instruction limit reached!
% 0.67/0.44 % (1369577)------------------------------
% 0.67/0.44 % (1369577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.44 % (1369577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.44 % (1369577)CaDiCaL version: 2.1.3
% 0.67/0.44 % (1369577)Termination reason: Instruction limit
% 0.67/0.44 % (1369577)Termination phase: Saturation
% 0.67/0.44 % (1369577)Time elapsed: 0.004 s
% 0.67/0.44 % (1369577)Peak memory usage: 12 MB
% 0.67/0.44 % (1369577)Instructions burned: 8 (million)
% 0.67/0.44 % (1369576)Instruction limit reached!
% 0.67/0.44 % (1369576)------------------------------
% 0.67/0.44 % (1369576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.44 % (1369576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.44 % (1369576)CaDiCaL version: 2.1.3
% 0.67/0.44 % (1369576)Termination reason: Instruction limit
% 0.67/0.44 % (1369576)Termination phase: Saturation
% 0.67/0.44 % (1369576)Time elapsed: 0.008 s
% 0.67/0.44 % (1369576)Peak memory usage: 12 MB
% 0.67/0.44 % (1369576)Instructions burned: 6 (million)
% 0.67/0.44 % (1369581)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3759813564:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.67/0.44 % (1369568)Instruction limit reached!
% 0.67/0.44 % (1369568)------------------------------
% 0.67/0.44 % (1369568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.44 % (1369568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.44 % (1369568)CaDiCaL version: 2.1.3
% 0.67/0.44 % (1369568)Termination reason: Instruction limit
% 0.67/0.44 % (1369568)Termination phase: Saturation
% 0.67/0.44 % (1369568)Time elapsed: 0.041 s
% 0.67/0.44 % (1369568)Peak memory usage: 12 MB
% 0.67/0.44 % (1369568)Instructions burned: 75 (million)
% 0.67/0.44 % (1369584)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
% 0.67/0.44 % (1369584)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.67/0.44 % (1369581)Instruction limit reached!
% 0.67/0.44 % (1369581)------------------------------
% 0.67/0.44 % (1369581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.44 % (1369581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.44 % (1369581)CaDiCaL version: 2.1.3
% 0.67/0.44 % (1369581)Termination reason: Instruction limit
% 0.67/0.44 % (1369581)Termination phase: Saturation
% 0.67/0.44 % (1369581)Time elapsed: 0.007 s
% 0.67/0.44 % (1369581)Peak memory usage: 12 MB
% 0.67/0.44 % (1369581)Instructions burned: 12 (million)
% 0.67/0.44 % (1369584)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2283504800:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.67/0.44 % (1369563)Instruction limit reached!
% 0.67/0.44 % (1369563)------------------------------
% 0.67/0.44 % (1369563)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.44 % (1369563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.47 % (1369563)CaDiCaL version: 2.1.3
% 0.67/0.47 % (1369563)Termination reason: Instruction limit
% 0.67/0.47 % (1369563)Termination phase: Saturation
% 0.67/0.47 % (1369563)Time elapsed: 0.047 s
% 0.67/0.47 % (1369563)Peak memory usage: 12 MB
% 0.67/0.47 % (1369563)Instructions burned: 88 (million)
% 0.67/0.47 % (1369586)lrs+10_1_si=on:cs=on:random_seed=1587886654:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.67/0.47 % (1369588)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.67/0.47 % (1369584)Instruction limit reached!
% 0.67/0.47 % (1369584)------------------------------
% 0.67/0.47 % (1369584)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.47 % (1369584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.47 % (1369584)CaDiCaL version: 2.1.3
% 0.67/0.47 % (1369584)Termination reason: Instruction limit
% 0.67/0.47 % (1369584)Termination phase: Saturation
% 0.67/0.47 % (1369584)Time elapsed: 0.015 s
% 0.67/0.47 % (1369584)Peak memory usage: 12 MB
% 0.67/0.47 % (1369584)Instructions burned: 28 (million)
% 0.67/0.47 % (1369586)Instruction limit reached!
% 0.67/0.47 % (1369586)------------------------------
% 0.67/0.47 % (1369586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.47 % (1369586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.47 % (1369586)CaDiCaL version: 2.1.3
% 0.67/0.47 % (1369586)Termination reason: Instruction limit
% 0.67/0.47 % (1369586)Termination phase: Saturation
% 0.67/0.47 % (1369586)Time elapsed: 0.006 s
% 0.67/0.47 % (1369586)Peak memory usage: 12 MB
% 0.67/0.47 % (1369586)Instructions burned: 9 (million)
% 0.67/0.47 % (1369589)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1365210513:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.67/0.47 % (1369588)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=3304995768:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.67/0.47 % (1369585)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=2334698813:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.67/0.47 % (1369588)Instruction limit reached!
% 0.67/0.47 % (1369588)------------------------------
% 0.67/0.47 % (1369588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.47 % (1369588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.47 % (1369588)CaDiCaL version: 2.1.3
% 0.67/0.47 % (1369588)Termination reason: Instruction limit
% 0.67/0.47 % (1369588)Termination phase: Property scanning
% 0.67/0.47 % (1369588)Time elapsed: 0.002 s
% 0.67/0.47 % (1369588)Peak memory usage: 10 MB
% 0.67/0.47 % (1369588)Instructions burned: 2 (million)
% 0.67/0.47 % (1369589)Refutation not found, incomplete strategy
% 0.67/0.47 % (1369589)------------------------------
% 0.67/0.47 % (1369589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.47 % (1369589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.47 % (1369589)CaDiCaL version: 2.1.3
% 0.67/0.47 % (1369589)Termination reason: Refutation not found, incomplete strategy
% 0.67/0.47 % (1369589)Time elapsed: 0.003 s
% 0.67/0.47 % (1369589)Peak memory usage: 12 MB
% 0.67/0.47 % (1369589)Instructions burned: 4 (million)
% 0.67/0.47 % (1369589)------------------------------
% 0.67/0.47 % (1369589)------------------------------
% 0.67/0.47 % (1369591)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3334507711:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.67/0.47 % (1369593)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=504577846:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.67/0.47 % (1369596)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1820860396:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.67/0.47 % (1369599)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=696294667:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.67/0.47 % (1369599)Instruction limit reached!
% 0.67/0.47 % (1369599)------------------------------
% 0.67/0.47 % (1369599)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.47 % (1369599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.47 % (1369599)CaDiCaL version: 2.1.3
% 0.67/0.47 % (1369599)Termination reason: Instruction limit
% 0.67/0.47 % (1369599)Termination phase: Saturation
% 0.67/0.47 % (1369599)Time elapsed: 0.008 s
% 0.67/0.47 % (1369599)Peak memory usage: 12 MB
% 0.67/0.47 % (1369599)Instructions burned: 15 (million)
% 0.67/0.47 % (1369593)Instruction limit reached!
% 0.67/0.47 % (1369593)------------------------------
% 0.67/0.47 % (1369593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.47 % (1369593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.47 % (1369593)CaDiCaL version: 2.1.3
% 0.67/0.47 % (1369593)Termination reason: Instruction limit
% 0.67/0.47 % (1369593)Termination phase: Saturation
% 0.67/0.47 % (1369593)Time elapsed: 0.016 s
% 0.67/0.47 % (1369593)Peak memory usage: 12 MB
% 0.67/0.47 % (1369593)Instructions burned: 26 (million)
% 0.67/0.47 % (1369596)Instruction limit reached!
% 0.67/0.47 % (1369596)------------------------------
% 0.67/0.47 % (1369596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.47 % (1369596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.47 % (1369596)CaDiCaL version: 2.1.3
% 0.67/0.47 % (1369596)Termination reason: Instruction limit
% 0.67/0.47 % (1369596)Termination phase: Saturation
% 0.67/0.47 % (1369596)Time elapsed: 0.015 s
% 0.67/0.47 % (1369596)Peak memory usage: 12 MB
% 0.67/0.47 % (1369596)Instructions burned: 15 (million)
% 0.67/0.47 % (1369598)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=376641821:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.67/0.47 % (1369585)Instruction limit reached!
% 0.67/0.47 % (1369585)------------------------------
% 0.67/0.47 % (1369585)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.47 % (1369585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.47 % (1369585)CaDiCaL version: 2.1.3
% 0.67/0.47 % (1369585)Termination reason: Instruction limit
% 0.67/0.47 % (1369585)Termination phase: Saturation
% 0.67/0.47 % (1369585)Time elapsed: 0.044 s
% 0.67/0.47 % (1369585)Peak memory usage: 12 MB
% 0.67/0.47 % (1369585)Instructions burned: 87 (million)
% 0.67/0.47 % (1369604)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3342857551: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)
% 0.67/0.47 % (1369605)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1098780931:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.67/0.47 % (1369604)Instruction limit reached!
% 0.67/0.47 % (1369604)------------------------------
% 0.67/0.47 % (1369604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.47 % (1369604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.47 % (1369604)CaDiCaL version: 2.1.3
% 0.67/0.47 % (1369604)Termination reason: Instruction limit
% 0.67/0.47 % (1369604)Termination phase: Saturation
% 0.67/0.47 % (1369604)Time elapsed: 0.002 s
% 0.67/0.47 % (1369604)Peak memory usage: 11 MB
% 0.67/0.47 % (1369604)Instructions burned: 4 (million)
% 0.67/0.47 % (1369606)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=4096345288:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.67/0.47 % (1369608)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=549961567:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.67/0.47 % (1369606)Instruction limit reached!
% 0.67/0.47 % (1369606)------------------------------
% 0.67/0.47 % (1369606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.47 % (1369606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.47 % (1369606)CaDiCaL version: 2.1.3
% 0.67/0.47 % (1369606)Termination reason: Instruction limit
% 0.67/0.47 % (1369606)Termination phase: Saturation
% 0.67/0.47 % (1369606)Time elapsed: 0.013 s
% 0.67/0.47 % (1369606)Peak memory usage: 12 MB
% 0.67/0.47 % (1369606)Instructions burned: 25 (million)
% 0.67/0.47 % (1369605)Instruction limit reached!
% 0.67/0.47 % (1369605)------------------------------
% 0.67/0.47 % (1369605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.47 % (1369605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.47 % (1369605)CaDiCaL version: 2.1.3
% 0.67/0.47 % (1369605)Termination reason: Instruction limit
% 0.67/0.47 % (1369605)Termination phase: Saturation
% 0.67/0.47 % (1369605)Time elapsed: 0.015 s
% 0.67/0.47 % (1369605)Peak memory usage: 12 MB
% 0.67/0.47 % (1369605)Instructions burned: 26 (million)
% 0.67/0.47 % (1369611)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
% 0.67/0.47 % (1369611)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.67/0.47 % (1369611)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=3897988215:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.67/0.47 % (1369569)Instruction limit reached!
% 0.67/0.47 % (1369569)------------------------------
% 0.67/0.47 % (1369569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.47 % (1369569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.47 % (1369569)CaDiCaL version: 2.1.3
% 0.67/0.47 % (1369569)Termination reason: Instruction limit
% 0.67/0.47 % (1369569)Termination phase: Saturation
% 0.67/0.47 % (1369569)Time elapsed: 0.126 s
% 0.67/0.47 % (1369569)Peak memory usage: 13 MB
% 0.67/0.47 % (1369569)Instructions burned: 159 (million)
% 0.67/0.47 % (1369611)Instruction limit reached!
% 0.67/0.47 % (1369611)------------------------------
% 0.67/0.47 % (1369611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.47 % (1369611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.47 % (1369611)CaDiCaL version: 2.1.3
% 0.67/0.47 % (1369611)Termination reason: Instruction limit
% 0.67/0.47 % (1369611)Termination phase: Saturation
% 0.67/0.47 % (1369611)Time elapsed: 0.008 s
% 0.67/0.47 % (1369611)Peak memory usage: 12 MB
% 0.67/0.47 % (1369611)Instructions burned: 14 (million)
% 0.67/0.47 % (1369615)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=3574112045:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 0.67/0.47 % (1369617)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=4094617276:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 0.67/0.47 % (1369608) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1369558-1369608"...
% 0.67/0.47 % (1369614)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.67/0.47 % (1369614)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=3278426912:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.67/0.47 % (1369617)Instruction limit reached!
% 0.67/0.47 % (1369617)------------------------------
% 0.67/0.47 % (1369617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.47 % (1369617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.47 % (1369617)CaDiCaL version: 2.1.3
% 0.67/0.47 % (1369617)Termination reason: Instruction limit
% 0.67/0.47 % (1369617)Termination phase: Saturation
% 0.67/0.47 % (1369617)Time elapsed: 0.005 s
% 0.67/0.47 % (1369617)Peak memory usage: 12 MB
% 0.67/0.47 % (1369617)Instructions burned: 8 (million)
% 0.67/0.47 % (1369608)...printing done.
% 0.67/0.47 % (1369608)Refutation found. Thanks to Tanya!
% 0.67/0.47 % SZS status Theorem for theBenchmark
% 0.67/0.47 % SZS output start Proof for theBenchmark
% 0.67/0.47 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.67/0.47 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.67/0.47 thf(func_def_1, type, setunion: ($i > $i)).
% 0.67/0.47 thf(func_def_2, type, setunionI: $o).
% 0.67/0.47 thf(func_def_4, type, setunionE: $o).
% 0.67/0.47 thf(func_def_5, type, subset: ($i > $i > $o)).
% 0.67/0.47 thf(func_def_6, type, subsetI1: $o).
% 0.67/0.47 thf(func_def_7, type, transitiveset: ($i > $o)).
% 0.67/0.47 thf(func_def_8, type, transitivesetOp2: $o).
% 0.67/0.47 thf(func_def_11, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.67/0.47 thf(func_def_12, type, vIMP: ($o > $o > $o)).
% 0.67/0.47 thf(func_def_13, type, db0: !>[X0: $tType]:(X0)).
% 0.67/0.47 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 0.67/0.47 thf(func_def_15, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.67/0.47 thf(func_def_19, type, sK3: ($i > $i > $i)).
% 0.67/0.47 thf(func_def_28, type, sK12: $o).
% 0.67/0.47 thf(func_def_29, type, sK13: ($o > $i > $i > $i)).
% 0.67/0.47 thf(func_def_31, type, sF15: $o).
% 0.67/0.47 thf(func_def_32, type, vNOT: ($o > $o)).
% 0.67/0.47 thf(func_def_34, type, sK17: ($i > $i)).
% 0.67/0.47 thf(f1,axiom,(
% 0.67/0.47 (setunionI = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0)))))),
% 0.67/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI)).
% 0.67/0.47 thf(f2,axiom,(
% 0.67/0.47 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)) = setunionE)),
% 0.67/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE)).
% 0.67/0.47 thf(f3,axiom,(
% 0.67/0.47 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.67/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
% 0.67/0.47 thf(f4,axiom,(
% 0.67/0.47 (transitiveset = (^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))))),
% 0.67/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitiveset)).
% 0.67/0.47 thf(f5,axiom,(
% 0.67/0.47 (transitivesetOp2 = ! [X0 : $i] : ((transitiveset @ X0) => ! [X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0)))))),
% 0.67/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivesetOp2)).
% 0.67/0.47 thf(f6,conjecture,(
% 0.67/0.47 setunionI => (setunionE => (subsetI1 => (transitivesetOp2 => ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (transitiveset @ X1)) => (transitiveset @ (setunion @ X0))))))),
% 0.67/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionTransitive)).
% 0.67/0.47 thf(f7,negated_conjecture,(
% 0.67/0.47 ~(setunionI => (setunionE => (subsetI1 => (transitivesetOp2 => ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (transitiveset @ X1)) => (transitiveset @ (setunion @ X0)))))))),
% 0.67/0.47 inference(negated_conjecture,[status(cth)],[f6])).
% 0.67/0.47 thf(f8,plain,(
% 0.67/0.47 (transitivesetOp2 = ! [X0 : $i] : ((transitiveset @ X0) => ! [X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0)))))),
% 0.67/0.47 inference(rectify,[],[f5])).
% 0.67/0.47 thf(f9,plain,(
% 0.67/0.47 ! [X0 : $i] : ((((transitiveset @ X0)) = $true) => ! [X2 : $i,X1 : $i] : ((((in @ X1 @ X0)) = $true) => ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)))) <=> (transitivesetOp2 = $true)),
% 0.67/0.47 inference(fool_elimination,[],[f8])).
% 0.67/0.47 thf(f10,plain,(
% 0.67/0.47 (setunionI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ((in @ X1 @ X2) => (in @ X0 @ (setunion @ X2)))))),
% 0.67/0.47 inference(rectify,[],[f1])).
% 0.67/0.47 thf(f11,plain,(
% 0.67/0.47 ! [X1 : $i,X2 : $i,X0 : $i] : (($true = ((in @ X0 @ X1))) => ((((in @ X1 @ X2)) = $true) => ($true = ((in @ X0 @ (setunion @ X2)))))) <=> (setunionI = $true)),
% 0.67/0.47 inference(fool_elimination,[],[f10])).
% 0.67/0.47 thf(f12,plain,(
% 0.67/0.47 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.67/0.47 inference(rectify,[],[f3])).
% 0.67/0.47 thf(f13,plain,(
% 0.67/0.47 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true)) <=> (subsetI1 = $true)),
% 0.67/0.47 inference(fool_elimination,[],[f12])).
% 0.67/0.47 thf(f14,plain,(
% 0.67/0.47 ~(setunionI => (setunionE => (subsetI1 => (transitivesetOp2 => ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (transitiveset @ X1)) => (transitiveset @ (setunion @ X0)))))))),
% 0.67/0.47 inference(rectify,[],[f7])).
% 0.67/0.47 thf(f15,plain,(
% 0.67/0.47 ~((setunionI = $true) => ((setunionE = $true) => ((subsetI1 = $true) => ((transitivesetOp2 = $true) => ! [X0 : $i] : (! [X1 : $i] : ((((in @ X1 @ X0)) = $true) => (((transitiveset @ X1)) = $true)) => (((transitiveset @ (setunion @ X0))) = $true))))))),
% 0.67/0.47 inference(fool_elimination,[],[f14])).
% 0.67/0.47 thf(f16,plain,(
% 0.67/0.47 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setunion @ X1)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X0 @ X3) => ((in @ X3 @ X1) => X2)) => X2)) = setunionE)),
% 0.67/0.47 inference(rectify,[],[f2])).
% 0.67/0.47 thf(f17,plain,(
% 0.67/0.47 ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (setunion @ X1)))) => ! [X2 : $o] : (! [X3 : $i] : ((((in @ X0 @ X3)) = $true) => (($true = ((in @ X3 @ X1))) => ($true = X2))) => ($true = X2))) <=> (setunionE = $true)),
% 0.67/0.48 inference(fool_elimination,[],[f16])).
% 0.67/0.48 thf(f18,plain,(
% 0.67/0.48 (transitiveset = (^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))))),
% 0.67/0.48 inference(rectify,[],[f4])).
% 0.67/0.48 thf(f19,plain,(
% 0.67/0.48 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 0.67/0.48 inference(fool_elimination,[],[f18])).
% 0.67/0.48 thf(f20,plain,(
% 0.67/0.48 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) <=> (subsetI1 = $true)),
% 0.67/0.48 inference(ennf_transformation,[],[f13])).
% 0.67/0.48 thf(f21,plain,(
% 0.67/0.48 ! [X0 : $i,X1 : $i] : (! [X2 : $o] : (($true = X2) | ? [X3 : $i] : ((($true != X2) & ($true = ((in @ X3 @ X1)))) & (((in @ X0 @ X3)) = $true))) | ($true != ((in @ X0 @ (setunion @ X1))))) <=> (setunionE = $true)),
% 0.67/0.48 inference(ennf_transformation,[],[f17])).
% 0.67/0.48 thf(f22,plain,(
% 0.67/0.48 (setunionE = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $o] : (? [X3 : $i] : ((((in @ X0 @ X3)) = $true) & ($true != X2) & ($true = ((in @ X3 @ X1)))) | ($true = X2)) | ($true != ((in @ X0 @ (setunion @ X1)))))),
% 0.67/0.48 inference(flattening,[],[f21])).
% 0.67/0.48 thf(f23,plain,(
% 0.67/0.48 ! [X1 : $i,X2 : $i,X0 : $i] : ((($true = ((in @ X0 @ (setunion @ X2)))) | (((in @ X1 @ X2)) != $true)) | ($true != ((in @ X0 @ X1)))) <=> (setunionI = $true)),
% 0.67/0.48 inference(ennf_transformation,[],[f11])).
% 0.67/0.48 thf(f24,plain,(
% 0.67/0.48 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ (setunion @ X2)))) | ($true != ((in @ X0 @ X1))) | (((in @ X1 @ X2)) != $true)) <=> (setunionI = $true)),
% 0.67/0.48 inference(flattening,[],[f23])).
% 0.67/0.48 thf(f25,plain,(
% 0.67/0.48 (((? [X0 : $i] : (! [X1 : $i] : ((((transitiveset @ X1)) = $true) | (((in @ X1 @ X0)) != $true)) & (((transitiveset @ (setunion @ X0))) != $true)) & (transitivesetOp2 = $true)) & (subsetI1 = $true)) & (setunionE = $true)) & (setunionI = $true)),
% 0.67/0.48 inference(ennf_transformation,[],[f15])).
% 0.67/0.48 thf(f26,plain,(
% 0.67/0.48 (subsetI1 = $true) & (setunionE = $true) & ? [X0 : $i] : (! [X1 : $i] : ((((transitiveset @ X1)) = $true) | (((in @ X1 @ X0)) != $true)) & (((transitiveset @ (setunion @ X0))) != $true)) & (setunionI = $true) & (transitivesetOp2 = $true)),
% 0.67/0.48 inference(flattening,[],[f25])).
% 0.67/0.48 thf(f27,plain,(
% 0.67/0.48 ! [X0 : $i] : (! [X2 : $i,X1 : $i] : (((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) | (((in @ X1 @ X0)) != $true)) | (((transitiveset @ X0)) != $true)) <=> (transitivesetOp2 = $true)),
% 0.67/0.48 inference(ennf_transformation,[],[f9])).
% 0.67/0.48 thf(f28,plain,(
% 0.67/0.48 (transitivesetOp2 = $true) <=> ! [X0 : $i] : (! [X2 : $i,X1 : $i] : ((((in @ X1 @ X0)) != $true) | (((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) | (((transitiveset @ X0)) != $true))),
% 0.67/0.48 inference(flattening,[],[f27])).
% 0.67/0.48 thf(f29,plain,(
% 0.67/0.48 ((transitivesetOp2 = $true) | ? [X0 : $i] : (? [X2 : $i,X1 : $i] : ((((in @ X1 @ X0)) = $true) & (((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true)) & (((transitiveset @ X0)) = $true))) & (! [X0 : $i] : (! [X2 : $i,X1 : $i] : ((((in @ X1 @ X0)) != $true) | (((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) | (((transitiveset @ X0)) != $true)) | (transitivesetOp2 != $true))),
% 0.67/0.48 inference(nnf_transformation,[],[f28])).
% 0.67/0.48 thf(f30,plain,(
% 0.67/0.48 ((transitivesetOp2 = $true) | ? [X0 : $i] : (? [X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X1 @ X2)) = $true) & (((in @ X1 @ X0)) != $true)) & (((transitiveset @ X0)) = $true))) & (! [X3 : $i] : (! [X4 : $i,X5 : $i] : ((((in @ X5 @ X3)) != $true) | (((in @ X4 @ X5)) != $true) | (((in @ X4 @ X3)) = $true)) | ($true != ((transitiveset @ X3)))) | (transitivesetOp2 != $true))),
% 0.67/0.48 inference(rectify,[],[f29])).
% 0.67/0.48 thf(f31,plain,(
% 0.67/0.48 ((transitivesetOp2 = $true) | ((($true = ((in @ sK2 @ sK0))) & (((in @ sK1 @ sK2)) = $true) & ($true != ((in @ sK1 @ sK0)))) & ($true = ((transitiveset @ sK0))))) & (! [X3 : $i] : (! [X4 : $i,X5 : $i] : ((((in @ X5 @ X3)) != $true) | (((in @ X4 @ X5)) != $true) | (((in @ X4 @ X3)) = $true)) | ($true != ((transitiveset @ X3)))) | (transitivesetOp2 != $true))),
% 0.67/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f30])).
% 0.67/0.48 thf(f32,plain,(
% 0.67/0.48 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) & (((subset @ X0 @ X1)) != $true)))),
% 0.67/0.48 inference(nnf_transformation,[],[f20])).
% 0.67/0.48 thf(f33,plain,(
% 0.67/0.48 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (($true = ((in @ X5 @ X4))) | (((in @ X5 @ X3)) != $true)) & (((subset @ X3 @ X4)) != $true)))),
% 0.67/0.48 inference(rectify,[],[f32])).
% 0.67/0.48 thf(f34,plain,(
% 0.67/0.48 (! [X0 : $i,X1 : $i] : ((($true != ((in @ (sK3 @ X1 @ X0) @ X1))) & ($true = ((in @ (sK3 @ X1 @ X0) @ X0)))) | (((subset @ X0 @ X1)) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | (! [X5 : $i] : (($true = ((in @ X5 @ sK5))) | (((in @ X5 @ sK4)) != $true)) & ($true != ((subset @ sK4 @ sK5)))))),
% 0.67/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK4,sK5]),skolemize(X2,sK3 @ X1 @ X0),skolemize(X3,sK4),skolemize(X4,sK5)],[f33])).
% 0.67/0.48 thf(f35,plain,(
% 0.67/0.48 (subsetI1 = $true) & (setunionE = $true) & (! [X1 : $i] : ((((transitiveset @ X1)) = $true) | (((in @ X1 @ sK6)) != $true)) & ($true != ((transitiveset @ (setunion @ sK6))))) & (setunionI = $true) & (transitivesetOp2 = $true)),
% 0.67/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f26])).
% 0.67/0.48 thf(f36,plain,(
% 0.67/0.48 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ (setunion @ X2)))) | ($true != ((in @ X0 @ X1))) | (((in @ X1 @ X2)) != $true)) | (setunionI != $true)) & ((setunionI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ (setunion @ X2)))) & ($true = ((in @ X0 @ X1))) & (((in @ X1 @ X2)) = $true)))),
% 0.67/0.48 inference(nnf_transformation,[],[f24])).
% 0.67/0.48 thf(f37,plain,(
% 0.67/0.48 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ (setunion @ X2)))) | ($true != ((in @ X0 @ X1))) | (((in @ X1 @ X2)) != $true)) | (setunionI != $true)) & ((setunionI = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X3 @ (setunion @ X5)))) & (((in @ X3 @ X4)) = $true) & (((in @ X4 @ X5)) = $true)))),
% 0.67/0.48 inference(rectify,[],[f36])).
% 0.67/0.48 thf(f38,plain,(
% 0.67/0.48 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ (setunion @ X2)))) | ($true != ((in @ X0 @ X1))) | (((in @ X1 @ X2)) != $true)) | (setunionI != $true)) & ((setunionI = $true) | (($true != ((in @ sK7 @ (setunion @ sK9)))) & ($true = ((in @ sK7 @ sK8))) & ($true = ((in @ sK8 @ sK9)))))),
% 0.67/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X3,sK7),skolemize(X4,sK8),skolemize(X5,sK9)],[f37])).
% 0.67/0.48 thf(f39,plain,(
% 0.67/0.48 ((setunionE = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $o] : (! [X3 : $i] : ((((in @ X0 @ X3)) != $true) | ($true = X2) | ($true != ((in @ X3 @ X1)))) & ($true != X2)) & ($true = ((in @ X0 @ (setunion @ X1)))))) & (! [X1 : $i,X0 : $i] : (! [X2 : $o] : (? [X3 : $i] : ((((in @ X0 @ X3)) = $true) & ($true != X2) & ($true = ((in @ X3 @ X1)))) | ($true = X2)) | ($true != ((in @ X0 @ (setunion @ X1))))) | (setunionE != $true))),
% 0.67/0.48 inference(nnf_transformation,[],[f22])).
% 0.67/0.48 thf(f40,plain,(
% 0.67/0.48 ((setunionE = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $o] : (! [X3 : $i] : ((((in @ X1 @ X3)) != $true) | ($true = X2) | (((in @ X3 @ X0)) != $true)) & ($true != X2)) & (((in @ X1 @ (setunion @ X0))) = $true))) & (! [X4 : $i,X5 : $i] : (! [X6 : $o] : (? [X7 : $i] : (($true = ((in @ X5 @ X7))) & ($true != X6) & ($true = ((in @ X7 @ X4)))) | ($true = X6)) | ($true != ((in @ X5 @ (setunion @ X4))))) | (setunionE != $true))),
% 0.67/0.48 inference(rectify,[],[f39])).
% 0.67/0.48 thf(f41,plain,(
% 0.67/0.48 ((setunionE = $true) | ((! [X3 : $i] : ((((in @ sK11 @ X3)) != $true) | ($true = sK12) | ($true != ((in @ X3 @ sK10)))) & ($true != sK12)) & ($true = ((in @ sK11 @ (setunion @ sK10)))))) & (! [X4 : $i,X5 : $i] : (! [X6 : $o] : ((($true = ((in @ X5 @ (sK13 @ X6 @ X5 @ X4)))) & ($true != X6) & ($true = ((in @ (sK13 @ X6 @ X5 @ X4) @ X4)))) | ($true = X6)) | ($true != ((in @ X5 @ (setunion @ X4))))) | (setunionE != $true))),
% 0.67/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,vAPP]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X2,sK3 @ X1 @ X0)],[f40])).
% 0.67/0.48 thf(f42,plain,(
% 0.67/0.48 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X3)) = $true) | (((in @ X5 @ X3)) != $true) | (transitivesetOp2 != $true) | (((in @ X4 @ X5)) != $true) | ($true != ((transitiveset @ X3)))) )),
% 0.67/0.48 inference(cnf_transformation,[],[f31])).
% 0.67/0.48 thf(f49,plain,(
% 0.67/0.48 ( ! [X0 : $i,X1 : $i] : ((subsetI1 != $true) | ($true = ((in @ (sK3 @ X1 @ X0) @ X0))) | (((subset @ X0 @ X1)) = $true)) )),
% 0.67/0.48 inference(cnf_transformation,[],[f34])).
% 0.67/0.48 thf(f50,plain,(
% 0.67/0.48 ( ! [X0 : $i,X1 : $i] : ((subsetI1 != $true) | ($true != ((in @ (sK3 @ X1 @ X0) @ X1))) | (((subset @ X0 @ X1)) = $true)) )),
% 0.67/0.48 inference(cnf_transformation,[],[f34])).
% 0.67/0.48 thf(f51,plain,(
% 0.67/0.48 (transitivesetOp2 = $true)),
% 0.67/0.48 inference(cnf_transformation,[],[f35])).
% 0.67/0.48 thf(f52,plain,(
% 0.67/0.48 (setunionI = $true)),
% 0.67/0.48 inference(cnf_transformation,[],[f35])).
% 0.67/0.48 thf(f53,plain,(
% 0.67/0.48 ($true != ((transitiveset @ (setunion @ sK6))))),
% 0.67/0.48 inference(cnf_transformation,[],[f35])).
% 0.67/0.48 thf(f54,plain,(
% 0.67/0.48 ( ! [X1 : $i] : ((((in @ X1 @ sK6)) != $true) | (((transitiveset @ X1)) = $true)) )),
% 0.67/0.48 inference(cnf_transformation,[],[f35])).
% 0.67/0.48 thf(f55,plain,(
% 0.67/0.48 (setunionE = $true)),
% 0.67/0.48 inference(cnf_transformation,[],[f35])).
% 0.67/0.48 thf(f56,plain,(
% 0.67/0.48 (subsetI1 = $true)),
% 0.67/0.48 inference(cnf_transformation,[],[f35])).
% 0.67/0.48 thf(f60,plain,(
% 0.67/0.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X2)) != $true) | ($true = ((in @ X0 @ (setunion @ X2)))) | (setunionI != $true) | ($true != ((in @ X0 @ X1)))) )),
% 0.67/0.48 inference(cnf_transformation,[],[f38])).
% 0.67/0.48 thf(f61,plain,(
% 0.67/0.48 ( ! [X6 : $o,X4 : $i,X5 : $i] : (($true != ((in @ X5 @ (setunion @ X4)))) | ($true = X6) | ($true = ((in @ (sK13 @ X6 @ X5 @ X4) @ X4))) | (setunionE != $true)) )),
% 0.67/0.48 inference(cnf_transformation,[],[f41])).
% 0.67/0.48 thf(f63,plain,(
% 0.67/0.48 ( ! [X6 : $o,X4 : $i,X5 : $i] : (($true = ((in @ X5 @ (sK13 @ X6 @ X5 @ X4)))) | ($true != ((in @ X5 @ (setunion @ X4)))) | ($true = X6) | (setunionE != $true)) )),
% 0.67/0.48 inference(cnf_transformation,[],[f41])).
% 0.67/0.48 thf(f67,plain,(
% 0.67/0.48 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 0.67/0.48 inference(cnf_transformation,[],[f19])).
% 0.67/0.48 thf(f71,definition,(
% 0.67/0.48 (sF14 = ((setunion @ sK6)))),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[sF14])],[function_definition])).
% 0.67/0.48 thf(f72,definition,(
% 0.67/0.48 (sF15 = ((transitiveset @ sF14)))),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[sF15])],[function_definition])).
% 0.67/0.48 thf(f73,plain,(
% 0.67/0.48 (((transitiveset @ sF14)) = sF15)),
% 0.67/0.48 inference(reorient_equations,[],[f72])).
% 0.67/0.48 thf(f74,plain,(
% 0.67/0.48 ($true != sF15)),
% 0.67/0.48 inference(definition_folding,[],[f53,f73,f71])).
% 0.67/0.48 thf(f76,plain,(
% 0.67/0.48 ($true = sF15) | (((transitiveset @ sF14)) = $false)),
% 0.67/0.48 inference(iff_proxy_clausification,[],[f73])).
% 0.67/0.48 thf(f78,definition,(
% 0.67/0.48 spl16_1 <=> ($true = sF15)),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition])).
% 0.67/0.48 thf(f79,plain,(
% 0.67/0.48 ($true != sF15) | spl16_1),
% 0.67/0.48 inference(avatar_component_clause,[],[f78])).
% 0.67/0.48 thf(f82,definition,(
% 0.67/0.48 spl16_2 <=> (((transitiveset @ sF14)) = $false)),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition])).
% 0.67/0.48 thf(f84,plain,(
% 0.67/0.48 (((transitiveset @ sF14)) = $false) | ~spl16_2),
% 0.67/0.48 inference(avatar_component_clause,[],[f82])).
% 0.67/0.48 thf(f85,plain,(
% 0.67/0.48 spl16_1 | spl16_2),
% 0.67/0.48 inference(avatar_split_clause,[],[f76,f82,f78])).
% 0.67/0.48 thf(f96,definition,(
% 0.67/0.48 spl16_5 <=> (setunionI = $true)),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[spl16_5])],[avatar_definition])).
% 0.67/0.48 thf(f105,definition,(
% 0.67/0.48 spl16_7 <=> (transitivesetOp2 = $true)),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[spl16_7])],[avatar_definition])).
% 0.67/0.48 thf(f117,definition,(
% 0.67/0.48 spl16_10 <=> (subsetI1 = $true)),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition])).
% 0.67/0.48 thf(f121,plain,(
% 0.67/0.48 ~spl16_1),
% 0.67/0.48 inference(avatar_split_clause,[],[f74,f78])).
% 0.67/0.48 thf(f123,definition,(
% 0.67/0.48 spl16_11 <=> ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK3 @ X1 @ X0) @ X1))) | (((subset @ X0 @ X1)) = $true))),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[spl16_11])],[avatar_definition])).
% 0.67/0.48 thf(f124,plain,(
% 0.67/0.48 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK3 @ X1 @ X0) @ X1))) | (((subset @ X0 @ X1)) = $true)) ) | ~spl16_11),
% 0.67/0.48 inference(avatar_component_clause,[],[f123])).
% 0.67/0.48 thf(f125,plain,(
% 0.67/0.48 ~spl16_10 | spl16_11),
% 0.67/0.48 inference(avatar_split_clause,[],[f50,f123,f117])).
% 0.67/0.48 thf(f137,definition,(
% 0.67/0.48 spl16_14 <=> (setunionE = $true)),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[spl16_14])],[avatar_definition])).
% 0.67/0.48 thf(f151,definition,(
% 0.67/0.48 spl16_17 <=> ! [X6 : $o,X4 : $i,X5 : $i] : (($true != ((in @ X5 @ (setunion @ X4)))) | ($true = ((in @ (sK13 @ X6 @ X5 @ X4) @ X4))) | ($true = X6))),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[spl16_17])],[avatar_definition])).
% 0.67/0.48 thf(f152,plain,(
% 0.67/0.48 ( ! [X6 : $o,X4 : $i,X5 : $i] : (($true = ((in @ (sK13 @ X6 @ X5 @ X4) @ X4))) | ($true = X6) | ($true != ((in @ X5 @ (setunion @ X4))))) ) | ~spl16_17),
% 0.67/0.48 inference(avatar_component_clause,[],[f151])).
% 0.67/0.48 thf(f153,plain,(
% 0.67/0.48 spl16_17 | ~spl16_14),
% 0.67/0.48 inference(avatar_split_clause,[],[f61,f137,f151])).
% 0.67/0.48 thf(f154,plain,(
% 0.67/0.48 spl16_7),
% 0.67/0.48 inference(avatar_split_clause,[],[f51,f105])).
% 0.67/0.48 thf(f161,definition,(
% 0.67/0.48 spl16_19 <=> ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X1 @ X0) @ X0))) | (((subset @ X0 @ X1)) = $true))),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[spl16_19])],[avatar_definition])).
% 0.67/0.48 thf(f162,plain,(
% 0.67/0.48 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X1 @ X0) @ X0))) | (((subset @ X0 @ X1)) = $true)) ) | ~spl16_19),
% 0.67/0.48 inference(avatar_component_clause,[],[f161])).
% 0.67/0.48 thf(f163,plain,(
% 0.67/0.48 ~spl16_10 | spl16_19),
% 0.67/0.48 inference(avatar_split_clause,[],[f49,f161,f117])).
% 0.67/0.48 thf(f165,definition,(
% 0.67/0.48 spl16_20 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X2)) != $true) | ($true != ((in @ X0 @ X1))) | ($true = ((in @ X0 @ (setunion @ X2)))))),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[spl16_20])],[avatar_definition])).
% 0.67/0.48 thf(f166,plain,(
% 0.67/0.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (setunion @ X2)))) | ($true != ((in @ X0 @ X1))) | (((in @ X1 @ X2)) != $true)) ) | ~spl16_20),
% 0.67/0.48 inference(avatar_component_clause,[],[f165])).
% 0.67/0.48 thf(f167,plain,(
% 0.67/0.48 spl16_20 | ~spl16_5),
% 0.67/0.48 inference(avatar_split_clause,[],[f60,f96,f165])).
% 0.67/0.48 thf(f173,plain,(
% 0.67/0.48 spl16_10),
% 0.67/0.48 inference(avatar_split_clause,[],[f56,f117])).
% 0.67/0.48 thf(f189,definition,(
% 0.67/0.48 spl16_25 <=> ! [X6 : $o,X4 : $i,X5 : $i] : (($true = ((in @ X5 @ (sK13 @ X6 @ X5 @ X4)))) | ($true = X6) | ($true != ((in @ X5 @ (setunion @ X4)))))),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[spl16_25])],[avatar_definition])).
% 0.67/0.48 thf(f190,plain,(
% 0.67/0.48 ( ! [X6 : $o,X4 : $i,X5 : $i] : (($true = ((in @ X5 @ (sK13 @ X6 @ X5 @ X4)))) | ($true != ((in @ X5 @ (setunion @ X4)))) | ($true = X6)) ) | ~spl16_25),
% 0.67/0.48 inference(avatar_component_clause,[],[f189])).
% 0.67/0.48 thf(f191,plain,(
% 0.67/0.48 ~spl16_14 | spl16_25),
% 0.67/0.48 inference(avatar_split_clause,[],[f63,f189,f137])).
% 0.67/0.48 thf(f193,definition,(
% 0.67/0.48 spl16_26 <=> ! [X4 : $i,X5 : $i,X3 : $i] : ((((in @ X4 @ X3)) = $true) | ($true != ((transitiveset @ X3))) | (((in @ X4 @ X5)) != $true) | (((in @ X5 @ X3)) != $true))),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[spl16_26])],[avatar_definition])).
% 0.67/0.48 thf(f194,plain,(
% 0.67/0.48 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X3)) = $true) | (((in @ X5 @ X3)) != $true) | ($true != ((transitiveset @ X3))) | (((in @ X4 @ X5)) != $true)) ) | ~spl16_26),
% 0.67/0.48 inference(avatar_component_clause,[],[f193])).
% 0.67/0.48 thf(f195,plain,(
% 0.67/0.48 spl16_26 | ~spl16_7),
% 0.67/0.48 inference(avatar_split_clause,[],[f42,f105,f193])).
% 0.67/0.48 thf(f196,plain,(
% 0.67/0.48 spl16_5),
% 0.67/0.48 inference(avatar_split_clause,[],[f52,f96])).
% 0.67/0.48 thf(f197,plain,(
% 0.67/0.48 spl16_14),
% 0.67/0.48 inference(avatar_split_clause,[],[f55,f137])).
% 0.67/0.48 thf(f204,plain,(
% 0.67/0.48 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ sF14))) | (((in @ X1 @ sK6)) != $true) | ($true != ((in @ X0 @ X1)))) ) | ~spl16_20),
% 0.67/0.48 inference(superposition,[],[f166,f71])).
% 0.67/0.48 thf(f207,plain,(
% 0.67/0.48 ( ! [X0 : $i,X1 : $i] : ((((in @ X1 @ sK6)) != $true) | (((in @ (sK3 @ sF14 @ X0) @ X1)) != $true) | (((subset @ X0 @ sF14)) = $true) | ($true != $true)) ) | (~spl16_11 | ~spl16_20)),
% 0.67/0.48 inference(superposition,[],[f124,f204])).
% 0.67/0.48 thf(f208,plain,(
% 0.67/0.48 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK3 @ sF14 @ X0) @ X1)) != $true) | (((in @ X1 @ sK6)) != $true) | (((subset @ X0 @ sF14)) = $true)) ) | (~spl16_11 | ~spl16_20)),
% 0.67/0.48 inference(trivial_inequality_removal,[],[f207])).
% 0.67/0.48 thf(f222,plain,(
% 0.67/0.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X0 @ sF14)) = $true) | (((transitiveset @ X1)) != $true) | ($true != $true) | (((in @ (sK3 @ sF14 @ X0) @ X2)) != $true) | (((in @ X1 @ sK6)) != $true) | (((in @ X2 @ X1)) != $true)) ) | (~spl16_11 | ~spl16_20 | ~spl16_26)),
% 0.67/0.48 inference(superposition,[],[f208,f194])).
% 0.67/0.48 thf(f228,plain,(
% 0.67/0.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ sK6)) != $true) | (((in @ X2 @ X1)) != $true) | (((in @ (sK3 @ sF14 @ X0) @ X2)) != $true) | (((transitiveset @ X1)) != $true) | (((subset @ X0 @ sF14)) = $true)) ) | (~spl16_11 | ~spl16_20 | ~spl16_26)),
% 0.67/0.48 inference(trivial_inequality_removal,[],[f222])).
% 0.67/0.48 thf(f230,plain,(
% 0.67/0.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK3 @ sF14 @ X0) @ X2)) != $true) | (((in @ X2 @ X1)) != $true) | (((subset @ X0 @ sF14)) = $true) | (((in @ X1 @ sK6)) != $true)) ) | (~spl16_11 | ~spl16_20 | ~spl16_26)),
% 0.67/0.48 inference(forward_subsumption_resolution,[],[f228,f54])).
% 0.67/0.48 thf(f236,plain,(
% 0.67/0.48 ( ! [X1 : $i] : ((((transitiveset @ X1)) = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))) @ X1)))) )),
% 0.67/0.48 inference(argument_congruence,[],[f67])).
% 0.67/0.48 thf(f237,plain,(
% 0.67/0.48 ( ! [X1 : $i] : ((((transitiveset @ X1)) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))) @ X1)) = $false)) )),
% 0.67/0.48 inference(iff_proxy_clausification,[],[f236])).
% 0.67/0.48 thf(f243,plain,(
% 0.67/0.48 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (subset @ Y0 @ X1))))) = $false) | (((transitiveset @ X1)) = $true)) )),
% 0.67/0.48 inference(beta-eta_normalization,[],[f237])).
% 0.67/0.48 thf(f244,plain,(
% 0.67/0.48 ( ! [X1 : $i] : ((((transitiveset @ X1)) = $true) | ((((^[Y0 : $i]: ((in @ Y0 @ X1) => (subset @ Y0 @ X1))) @ (sK17 @ X1))) = $false)) )),
% 0.67/0.48 inference(sigma_proxy_clausification,[],[f243])).
% 0.67/0.48 thf(f245,plain,(
% 0.67/0.48 ( ! [X1 : $i] : (((((in @ (sK17 @ X1) @ X1) => (subset @ (sK17 @ X1) @ X1))) = $false) | (((transitiveset @ X1)) = $true)) )),
% 0.67/0.48 inference(beta-eta_normalization,[],[f244])).
% 0.67/0.48 thf(f246,plain,(
% 0.67/0.48 ( ! [X1 : $i] : ((((subset @ (sK17 @ X1) @ X1)) = $false) | (((transitiveset @ X1)) = $true)) )),
% 0.67/0.48 inference(imp_proxy_clausification,[],[f245])).
% 0.67/0.48 thf(f247,plain,(
% 0.67/0.48 ( ! [X1 : $i] : ((((in @ (sK17 @ X1) @ X1)) = $true) | (((transitiveset @ X1)) = $true)) )),
% 0.67/0.48 inference(imp_proxy_clausification,[],[f245])).
% 0.67/0.48 thf(f426,plain,(
% 0.67/0.48 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ X1))) | ($true != $true) | (((in @ X1 @ sK6)) != $true) | (((subset @ X0 @ sF14)) = $true) | (((subset @ X0 @ sF14)) = $true)) ) | (~spl16_11 | ~spl16_19 | ~spl16_20 | ~spl16_26)),
% 0.67/0.48 inference(superposition,[],[f230,f162])).
% 0.67/0.48 thf(f435,plain,(
% 0.67/0.48 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ X1))) | (((subset @ X0 @ sF14)) = $true) | (((in @ X1 @ sK6)) != $true) | ($true != $true)) ) | (~spl16_11 | ~spl16_19 | ~spl16_20 | ~spl16_26)),
% 0.67/0.48 inference(duplicate_literal_removal,[],[f426])).
% 0.67/0.48 thf(f436,plain,(
% 0.67/0.48 ( ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ sF14)) = $true) | ($true != ((in @ X0 @ X1))) | (((in @ X1 @ sK6)) != $true)) ) | (~spl16_11 | ~spl16_19 | ~spl16_20 | ~spl16_26)),
% 0.67/0.48 inference(trivial_inequality_removal,[],[f435])).
% 0.67/0.48 thf(f438,plain,(
% 0.67/0.48 ( ! [X0 : $i] : (($true = ((transitiveset @ sF14))) | ($true != ((in @ X0 @ sK6))) | ($true = $false) | (((in @ (sK17 @ sF14) @ X0)) != $true)) ) | (~spl16_11 | ~spl16_19 | ~spl16_20 | ~spl16_26)),
% 0.67/0.48 inference(superposition,[],[f246,f436])).
% 0.67/0.48 thf(f439,plain,(
% 0.67/0.48 ( ! [X0 : $i] : (($true = ((transitiveset @ sF14))) | (((in @ (sK17 @ sF14) @ X0)) != $true) | ($true != ((in @ X0 @ sK6)))) ) | (~spl16_11 | ~spl16_19 | ~spl16_20 | ~spl16_26)),
% 0.67/0.48 inference(trivial_inequality_removal,[],[f438])).
% 0.67/0.48 thf(f441,plain,(
% 0.67/0.48 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK6))) | (((in @ (sK17 @ sF14) @ X0)) != $true) | ($true = $false)) ) | (~spl16_2 | ~spl16_11 | ~spl16_19 | ~spl16_20 | ~spl16_26)),
% 0.67/0.48 inference(forward_demodulation,[],[f439,f84])).
% 0.67/0.48 thf(f442,plain,(
% 0.67/0.48 ( ! [X0 : $i] : ((((in @ (sK17 @ sF14) @ X0)) != $true) | ($true != ((in @ X0 @ sK6)))) ) | (~spl16_2 | ~spl16_11 | ~spl16_19 | ~spl16_20 | ~spl16_26)),
% 0.67/0.48 inference(trivial_inequality_removal,[],[f441])).
% 0.67/0.48 thf(f448,plain,(
% 0.67/0.48 ( ! [X0 : $o,X1 : $i] : (($true = X0) | ($true != $true) | (((in @ (sK17 @ sF14) @ (setunion @ X1))) != $true) | (((in @ (sK13 @ X0 @ (sK17 @ sF14) @ X1) @ sK6)) != $true)) ) | (~spl16_2 | ~spl16_11 | ~spl16_19 | ~spl16_20 | ~spl16_25 | ~spl16_26)),
% 0.67/0.48 inference(superposition,[],[f442,f190])).
% 0.67/0.48 thf(f450,plain,(
% 0.67/0.48 ( ! [X0 : $o,X1 : $i] : ((((in @ (sK13 @ X0 @ (sK17 @ sF14) @ X1) @ sK6)) != $true) | (((in @ (sK17 @ sF14) @ (setunion @ X1))) != $true) | ($true = X0)) ) | (~spl16_2 | ~spl16_11 | ~spl16_19 | ~spl16_20 | ~spl16_25 | ~spl16_26)),
% 0.67/0.48 inference(trivial_inequality_removal,[],[f448])).
% 0.67/0.48 thf(f519,definition,(
% 0.67/0.48 spl16_35 <=> ! [X0 : $o] : ($true = X0)),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[spl16_35])],[avatar_definition])).
% 0.67/0.48 thf(f520,plain,(
% 0.67/0.48 ( ! [X0 : $o] : (($true = X0)) ) | ~spl16_35),
% 0.67/0.48 inference(avatar_component_clause,[],[f519])).
% 0.67/0.48 thf(f540,plain,(
% 0.67/0.48 ( ! [X0 : $o] : (($true = X0) | ($true != $true) | ($true != ((in @ (sK17 @ sF14) @ (setunion @ sK6)))) | ($true = X0) | ($true != ((in @ (sK17 @ sF14) @ (setunion @ sK6))))) ) | (~spl16_2 | ~spl16_11 | ~spl16_17 | ~spl16_19 | ~spl16_20 | ~spl16_25 | ~spl16_26)),
% 0.67/0.48 inference(superposition,[],[f450,f152])).
% 0.67/0.48 thf(f541,plain,(
% 0.67/0.48 ( ! [X0 : $o] : (($true = X0) | ($true != ((in @ (sK17 @ sF14) @ (setunion @ sK6)))) | ($true != $true)) ) | (~spl16_2 | ~spl16_11 | ~spl16_17 | ~spl16_19 | ~spl16_20 | ~spl16_25 | ~spl16_26)),
% 0.67/0.48 inference(duplicate_literal_removal,[],[f540])).
% 0.67/0.48 thf(f542,plain,(
% 0.67/0.48 ( ! [X0 : $o] : (($true != ((in @ (sK17 @ sF14) @ (setunion @ sK6)))) | ($true = X0)) ) | (~spl16_2 | ~spl16_11 | ~spl16_17 | ~spl16_19 | ~spl16_20 | ~spl16_25 | ~spl16_26)),
% 0.67/0.48 inference(trivial_inequality_removal,[],[f541])).
% 0.67/0.48 thf(f544,plain,(
% 0.67/0.48 ( ! [X0 : $o] : ((((in @ (sK17 @ sF14) @ sF14)) != $true) | ($true = X0)) ) | (~spl16_2 | ~spl16_11 | ~spl16_17 | ~spl16_19 | ~spl16_20 | ~spl16_25 | ~spl16_26)),
% 0.67/0.48 inference(forward_demodulation,[],[f542,f71])).
% 0.67/0.48 thf(f546,definition,(
% 0.67/0.48 spl16_36 <=> (((in @ (sK17 @ sF14) @ sF14)) = $true)),
% 0.67/0.48 introduced(definition,[new_symbols(definition,[spl16_36])],[avatar_definition])).
% 0.67/0.48 thf(f548,plain,(
% 0.67/0.48 (((in @ (sK17 @ sF14) @ sF14)) != $true) | spl16_36),
% 0.67/0.48 inference(avatar_component_clause,[],[f546])).
% 0.67/0.48 thf(f549,plain,(
% 0.67/0.48 spl16_35 | ~spl16_36 | ~spl16_2 | ~spl16_11 | ~spl16_17 | ~spl16_19 | ~spl16_20 | ~spl16_25 | ~spl16_26),
% 0.67/0.48 inference(avatar_split_clause,[],[f544,f193,f189,f165,f161,f151,f123,f82,f546,f519])).
% 0.67/0.48 thf(f551,plain,(
% 0.67/0.48 ($true != $true) | ($true = ((transitiveset @ sF14))) | spl16_36),
% 0.67/0.48 inference(superposition,[],[f548,f247])).
% 0.67/0.48 thf(f554,plain,(
% 0.67/0.48 ($true = ((transitiveset @ sF14))) | spl16_36),
% 0.67/0.48 inference(trivial_inequality_removal,[],[f551])).
% 0.67/0.48 thf(f557,plain,(
% 0.67/0.48 ($true = $false) | (~spl16_2 | spl16_36)),
% 0.67/0.48 inference(forward_demodulation,[],[f554,f84])).
% 0.67/0.48 thf(f558,plain,(
% 0.67/0.48 $false | (~spl16_2 | spl16_36)),
% 0.67/0.48 inference(trivial_inequality_removal,[],[f557])).
% 0.67/0.48 thf(f559,plain,(
% 0.67/0.48 ~spl16_2 | spl16_36),
% 0.67/0.48 inference(avatar_contradiction_clause,[],[f558])).
% 0.67/0.48 thf(f594,plain,(
% 0.67/0.48 ($true != $true) | (spl16_1 | ~spl16_35)),
% 0.67/0.48 inference(superposition,[],[f79,f520])).
% 0.67/0.48 thf(f614,plain,(
% 0.67/0.48 $false | (spl16_1 | ~spl16_35)),
% 0.67/0.48 inference(trivial_inequality_removal,[],[f594])).
% 0.67/0.48 thf(f615,plain,(
% 0.67/0.48 spl16_1 | ~spl16_35),
% 0.67/0.48 inference(avatar_contradiction_clause,[],[f614])).
% 0.67/0.48 cnf(s1, plain, spl16_1 | spl16_2, inference(sat_conversion,[],[f85])).
% 0.67/0.48 cnf(s6, plain, ~spl16_1, inference(sat_conversion,[],[f121])).
% 0.67/0.48 cnf(s7, plain, ~spl16_10 | spl16_11, inference(sat_conversion,[],[f125])).
% 0.67/0.48 cnf(s12, plain, ~spl16_14 | spl16_17, inference(sat_conversion,[],[f153])).
% 0.67/0.48 cnf(s13, plain, spl16_7, inference(sat_conversion,[],[f154])).
% 0.67/0.48 cnf(s15, plain, ~spl16_10 | spl16_19, inference(sat_conversion,[],[f163])).
% 0.67/0.48 cnf(s16, plain, ~spl16_5 | spl16_20, inference(sat_conversion,[],[f167])).
% 0.67/0.48 cnf(s18, plain, spl16_10, inference(sat_conversion,[],[f173])).
% 0.67/0.48 cnf(s22, plain, ~spl16_14 | spl16_25, inference(sat_conversion,[],[f191])).
% 0.67/0.48 cnf(s23, plain, ~spl16_7 | spl16_26, inference(sat_conversion,[],[f195])).
% 0.67/0.48 cnf(s24, plain, spl16_5, inference(sat_conversion,[],[f196])).
% 0.67/0.48 cnf(s25, plain, spl16_14, inference(sat_conversion,[],[f197])).
% 0.67/0.48 cnf(s31, plain, ~spl16_2 | ~spl16_11 | ~spl16_17 | ~spl16_19 | ~spl16_20 | ~spl16_25 | ~spl16_26 | spl16_35 | ~spl16_36, inference(sat_conversion,[],[f549])).
% 0.67/0.48 cnf(s32, plain, ~spl16_2 | spl16_36, inference(sat_conversion,[],[f559])).
% 0.67/0.48 cnf(s36, plain, spl16_1 | ~spl16_35, inference(sat_conversion,[],[f615])).
% 0.67/0.48 cnf(s48, plain, spl16_25, inference(rat,[],[s22,s25])).
% 0.67/0.48 cnf(s49, plain, spl16_20, inference(rat,[],[s16,s24])).
% 0.67/0.48 cnf(s50, plain, spl16_19, inference(rat,[],[s15,s18])).
% 0.67/0.48 cnf(s51, plain, spl16_26, inference(rat,[],[s23,s13])).
% 0.67/0.48 cnf(s52, plain, spl16_17, inference(rat,[],[s12,s25])).
% 0.67/0.48 cnf(s53, plain, spl16_11, inference(rat,[],[s7,s18])).
% 0.67/0.48 cnf(s54, plain, ~spl16_35, inference(rat,[],[s36,s6])).
% 0.67/0.48 cnf(s55, plain, spl16_2, inference(rat,[],[s1,s6])).
% 0.67/0.48 cnf(s56, plain, spl16_36, inference(rat,[],[s32,s55])).
% 0.67/0.48 cnf(s57, plain, $false, inference(rat,[],[s31,s54,s53,s51,s48,s49,s50,s52,s56,s55])).
% 0.67/0.48 thf(f660,plain,(
% 0.67/0.48 $false),
% 0.67/0.48 inference(avatar_sat_refutation,[],[s57])).
% 0.67/0.48 % SZS output end Proof for theBenchmark
% 0.67/0.48 % (1369608)------------------------------
% 0.67/0.48 % (1369608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.48 % (1369608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.48 % (1369608)CaDiCaL version: 2.1.3
% 0.67/0.48 % (1369608)Termination reason: Refutation
% 0.67/0.48 % (1369608)Time elapsed: 0.034 s
% 0.67/0.48 % (1369608)Peak memory usage: 13 MB
% 0.67/0.48 % (1369608)Instructions burned: 56 (million)
% 0.67/0.48 % (1369558)Success in time 0.212 s
% 0.67/0.48 % Vampire exiting
%------------------------------------------------------------------------------