%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP076^2 : TPTP v9.3.1. Released v7.5.0.
% 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 08:08:14 AM UTC 2026
% Result : Theorem 0.66s 0.41s
% Output : Refutation 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP076^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n004.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 19:47:52 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.26 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
% 0.66/0.38 % (1748292)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.66/0.38 % (1748303)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.66/0.38 % (1748303)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
% 0.66/0.38 % (1748303)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=3948645477:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.66/0.38 % (1748299)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1457662399:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.66/0.38 % (1748300)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=1623955418: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)
% 0.66/0.38 % (1748297)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=417541519:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.66/0.38 % (1748298)lrs+10_16_si=on:nwc=1.5:random_seed=758174024:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.66/0.38 % (1748301)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1739517517:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.66/0.38 % (1748302)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=654279948:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.66/0.38 % (1748299)Instruction limit reached!
% 0.66/0.38 % (1748299)------------------------------
% 0.66/0.38 % (1748299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (1748299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (1748299)CaDiCaL version: 2.1.3
% 0.66/0.38 % (1748299)Termination reason: Instruction limit
% 0.66/0.38 % (1748299)Termination phase: shuffling
% 0.66/0.38 % (1748299)Time elapsed: 0.003 s
% 0.66/0.38 % (1748299)Peak memory usage: 10 MB
% 0.66/0.38 % (1748299)Instructions burned: 5 (million)
% 0.66/0.38 % (1748298)Instruction limit reached!
% 0.66/0.38 % (1748298)------------------------------
% 0.66/0.38 % (1748298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (1748298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (1748298)CaDiCaL version: 2.1.3
% 0.66/0.38 % (1748298)Termination reason: Instruction limit
% 0.66/0.38 % (1748298)Termination phase: Property scanning
% 0.66/0.38 % (1748298)Time elapsed: 0.010 s
% 0.66/0.38 % (1748298)Peak memory usage: 10 MB
% 0.66/0.38 % (1748298)Instructions burned: 20 (million)
% 0.66/0.38 % (1748301)Instruction limit reached!
% 0.66/0.38 % (1748301)------------------------------
% 0.66/0.38 % (1748301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (1748301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (1748301)CaDiCaL version: 2.1.3
% 0.66/0.39 % (1748301)Termination reason: Instruction limit
% 0.66/0.39 % (1748301)Termination phase: shuffling
% 0.66/0.39 % (1748301)Time elapsed: 0.012 s
% 0.66/0.39 % (1748301)Peak memory usage: 10 MB
% 0.66/0.39 % (1748301)Instructions burned: 25 (million)
% 0.66/0.39 % (1748311)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1798927754:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.66/0.39 % (1748311)Instruction limit reached!
% 0.66/0.39 % (1748311)------------------------------
% 0.66/0.39 % (1748311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.39 % (1748311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.39 % (1748311)CaDiCaL version: 2.1.3
% 0.66/0.39 % (1748311)Termination reason: Instruction limit
% 0.66/0.39 % (1748311)Termination phase: shuffling
% 0.66/0.39 % (1748311)Time elapsed: 0.003 s
% 0.66/0.39 % (1748311)Peak memory usage: 10 MB
% 0.66/0.39 % (1748311)Instructions burned: 5 (million)
% 0.66/0.39 % (1748313)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.66/0.41 % (1748312)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3350602925:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.66/0.41 % (1748313)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3109333469:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.66/0.41 % (1748312)Instruction limit reached!
% 0.66/0.41 % (1748312)------------------------------
% 0.66/0.41 % (1748312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748312)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748312)Termination reason: Instruction limit
% 0.66/0.41 % (1748312)Termination phase: shuffling
% 0.66/0.41 % (1748312)Time elapsed: 0.003 s
% 0.66/0.41 % (1748312)Peak memory usage: 10 MB
% 0.66/0.41 % (1748312)Instructions burned: 6 (million)
% 0.66/0.41 % (1748303)Instruction limit reached!
% 0.66/0.41 % (1748303)------------------------------
% 0.66/0.41 % (1748303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748303)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748303)Termination reason: Instruction limit
% 0.66/0.41 % (1748303)Termination phase: Saturation
% 0.66/0.41 % (1748303)Time elapsed: 0.041 s
% 0.66/0.41 % (1748303)Peak memory usage: 14 MB
% 0.66/0.41 % (1748303)Instructions burned: 160 (million)
% 0.66/0.41 % (1748313)Instruction limit reached!
% 0.66/0.41 % (1748313)------------------------------
% 0.66/0.41 % (1748313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748313)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748313)Termination reason: Instruction limit
% 0.66/0.41 % (1748313)Termination phase: shuffling
% 0.66/0.41 % (1748313)Time elapsed: 0.003 s
% 0.66/0.41 % (1748313)Peak memory usage: 10 MB
% 0.66/0.41 % (1748313)Instructions burned: 7 (million)
% 0.66/0.41 % (1748302)Instruction limit reached!
% 0.66/0.41 % (1748302)------------------------------
% 0.66/0.41 % (1748302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748302)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748302)Termination reason: Instruction limit
% 0.66/0.41 % (1748302)Termination phase: Property scanning
% 0.66/0.41 % (1748302)Time elapsed: 0.038 s
% 0.66/0.41 % (1748302)Peak memory usage: 12 MB
% 0.66/0.41 % (1748302)Instructions burned: 82 (million)
% 0.66/0.41 % (1748319)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=4123629568:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.66/0.41 % (1748315)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3483122644:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.66/0.41 % (1748318)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
% 0.66/0.41 % (1748318)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.66/0.41 % (1748318)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=24690968:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.66/0.41 % (1748315)Instruction limit reached!
% 0.66/0.41 % (1748315)------------------------------
% 0.66/0.41 % (1748315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748315)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748315)Termination reason: Instruction limit
% 0.66/0.41 % (1748315)Termination phase: shuffling
% 0.66/0.41 % (1748315)Time elapsed: 0.006 s
% 0.66/0.41 % (1748315)Peak memory usage: 10 MB
% 0.66/0.41 % (1748315)Instructions burned: 13 (million)
% 0.66/0.41 % (1748321)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.66/0.41 % (1748297)Instruction limit reached!
% 0.66/0.41 % (1748297)------------------------------
% 0.66/0.41 % (1748297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748297)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748297)Termination reason: Instruction limit
% 0.66/0.41 % (1748297)Termination phase: Property scanning
% 0.66/0.41 % (1748297)Time elapsed: 0.055 s
% 0.66/0.41 % (1748297)Peak memory usage: 12 MB
% 0.66/0.41 % (1748297)Instructions burned: 88 (million)
% 0.66/0.41 % (1748320)lrs+10_1_si=on:cs=on:random_seed=2284959676:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.66/0.41 % (1748321)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=1248472423:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.66/0.41 % (1748321)Instruction limit reached!
% 0.66/0.41 % (1748321)------------------------------
% 0.66/0.41 % (1748321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748321)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748321)Termination reason: Instruction limit
% 0.66/0.41 % (1748321)Termination phase: shuffling
% 0.66/0.41 % (1748321)Time elapsed: 0.003 s
% 0.66/0.41 % (1748321)Peak memory usage: 10 MB
% 0.66/0.41 % (1748321)Instructions burned: 6 (million)
% 0.66/0.41 % (1748319)Instruction limit reached!
% 0.66/0.41 % (1748319)------------------------------
% 0.66/0.41 % (1748319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748319)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748319)Termination reason: Instruction limit
% 0.66/0.41 % (1748319)Termination phase: Function definition elimination
% 0.66/0.41 % (1748319)Time elapsed: 0.021 s
% 0.66/0.41 % (1748319)Peak memory usage: 11 MB
% 0.66/0.41 % (1748319)Instructions burned: 90 (million)
% 0.66/0.41 % (1748318)Instruction limit reached!
% 0.66/0.41 % (1748318)------------------------------
% 0.66/0.41 % (1748318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748318)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748318)Termination reason: Instruction limit
% 0.66/0.41 % (1748318)Termination phase: Property scanning
% 0.66/0.41 % (1748318)Time elapsed: 0.014 s
% 0.66/0.41 % (1748318)Peak memory usage: 10 MB
% 0.66/0.41 % (1748318)Instructions burned: 30 (million)
% 0.66/0.41 % (1748320)Instruction limit reached!
% 0.66/0.41 % (1748320)------------------------------
% 0.66/0.41 % (1748320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748320)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748320)Termination reason: Instruction limit
% 0.66/0.41 % (1748320)Termination phase: shuffling
% 0.66/0.41 % (1748320)Time elapsed: 0.010 s
% 0.66/0.41 % (1748320)Peak memory usage: 10 MB
% 0.66/0.41 % (1748320)Instructions burned: 9 (million)
% 0.66/0.41 % (1748325)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1381808339:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.66/0.41 % (1748327)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3595780816:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.66/0.41 % (1748330)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3496097850:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.66/0.41 % (1748330)Instruction limit reached!
% 0.66/0.41 % (1748330)------------------------------
% 0.66/0.41 % (1748330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748330)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748330)Termination reason: Instruction limit
% 0.66/0.41 % (1748330)Termination phase: Property scanning
% 0.66/0.41 % (1748330)Time elapsed: 0.004 s
% 0.66/0.41 % (1748330)Peak memory usage: 10 MB
% 0.66/0.41 % (1748330)Instructions burned: 16 (million)
% 0.66/0.41 % (1748329)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1795975526:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.66/0.41 % (1748331)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3421029906:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.66/0.41 % (1748332)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1081546506:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.66/0.41 % (1748325)Instruction limit reached!
% 0.66/0.41 % (1748325)------------------------------
% 0.66/0.41 % (1748325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748325)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748325)Termination reason: Instruction limit
% 0.66/0.41 % (1748325)Termination phase: Property scanning
% 0.66/0.41 % (1748325)Time elapsed: 0.019 s
% 0.66/0.41 % (1748325)Peak memory usage: 11 MB
% 0.66/0.41 % (1748325)Instructions burned: 39 (million)
% 0.66/0.41 % (1748336)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1510737696: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)
% 0.66/0.41 % (1748336)Instruction limit reached!
% 0.66/0.41 % (1748336)------------------------------
% 0.66/0.41 % (1748336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748336)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748336)Termination reason: Instruction limit
% 0.66/0.41 % (1748336)Termination phase: shuffling
% 0.66/0.41 % (1748336)Time elapsed: 0.001 s
% 0.66/0.41 % (1748336)Peak memory usage: 10 MB
% 0.66/0.41 % (1748336)Instructions burned: 2 (million)
% 0.66/0.41 % (1748332)Instruction limit reached!
% 0.66/0.41 % (1748332)------------------------------
% 0.66/0.41 % (1748332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748332)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748332)Termination reason: Instruction limit
% 0.66/0.41 % (1748332)Termination phase: Property scanning
% 0.66/0.41 % (1748332)Time elapsed: 0.007 s
% 0.66/0.41 % (1748332)Peak memory usage: 10 MB
% 0.66/0.41 % (1748332)Instructions burned: 14 (million)
% 0.66/0.41 % (1748329)Instruction limit reached!
% 0.66/0.41 % (1748329)------------------------------
% 0.66/0.41 % (1748329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748329)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748329)Termination reason: Instruction limit
% 0.66/0.41 % (1748329)Termination phase: SInE selection
% 0.66/0.41 % (1748329)Time elapsed: 0.013 s
% 0.66/0.41 % (1748329)Peak memory usage: 11 MB
% 0.66/0.41 % (1748329)Instructions burned: 26 (million)
% 0.66/0.41 % (1748327) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1748292-1748327"...
% 0.66/0.41 % (1748342)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2504852851:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.66/0.41 % (1748327)...printing done.
% 0.66/0.41 % (1748327)Refutation found. Thanks to Tanya!
% 0.66/0.41 % SZS status Theorem for theBenchmark
% 0.66/0.41 % SZS output start Proof for theBenchmark
% 0.66/0.41 thf(type_def_5, type, hF_Mirabelle_hf: $tType).
% 0.66/0.41 thf(type_def_6, type, set: $tType > $tType).
% 0.66/0.41 thf(type_def_7, type, nat: $tType).
% 0.66/0.41 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 0.66/0.41 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_2, type, zero: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_3, type, top: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_4, type, group_add: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_5, type, lattice: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_6, type, monoid_add: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_7, type, semigroup_add: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_8, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_9, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_10, type, distrib_lattice: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_11, type, semilattice_inf: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_12, type, semilattice_sup: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_13, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_14, type, bounded_lattice_top: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_15, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_16, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_17, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_18, type, bounde1561333602nf_top: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_19, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.66/0.41 thf(func_def_20, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.66/0.41 thf(func_def_21, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.66/0.41 thf(func_def_22, type, hF_Mir1687042746ollect: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_23, type, hF_Mirabelle_HF: (set @ hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_24, type, hF_Mirabelle_HInter: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_25, type, hF_Mirabelle_HUnion: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_26, type, hF_Mir569462966eplace: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_27, type, hF_Mirabelle_RepFun: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_28, type, hF_Mirabelle_Replace: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_29, type, hF_Mirabelle_hcard: (hF_Mirabelle_hf > nat)).
% 0.66/0.41 thf(func_def_30, type, hF_Mirabelle_Abs_hf: (nat > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_31, type, hF_Mirabelle_Rep_hf: (hF_Mirabelle_hf > nat)).
% 0.66/0.41 thf(func_def_32, type, hF_Mirabelle_hfset: (hF_Mirabelle_hf > set @ hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_33, type, hF_Mirabelle_hfst: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_34, type, hF_Mir859708136nction: (hF_Mirabelle_hf > $o)).
% 0.66/0.41 thf(func_def_35, type, hF_Mirabelle_hinsert: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_36, type, hF_Mirabelle_hmem: (hF_Mirabelle_hf > hF_Mirabelle_hf > $o)).
% 0.66/0.41 thf(func_def_37, type, hF_Mirabelle_hpair: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_38, type, hF_Mir1093797708lation: (hF_Mirabelle_hf > $o)).
% 0.66/0.41 thf(func_def_39, type, hF_Mir165288108strict: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_40, type, hF_Mirabelle_hsnd: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_41, type, hF_Mirabelle_hsplit: !>[X0: $tType]:(((hF_Mirabelle_hf > hF_Mirabelle_hf > X0) > hF_Mirabelle_hf > X0))).
% 0.66/0.41 thf(func_def_42, type, hF_Mir796903520_hpair: (hF_Mirabelle_hf > $o)).
% 0.66/0.41 thf(func_def_43, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.66/0.41 thf(func_def_44, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.66/0.41 thf(func_def_45, type, suc: (nat > nat)).
% 0.66/0.41 thf(func_def_46, type, top_top: !>[X0: $tType]:(X0)).
% 0.66/0.41 thf(func_def_47, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.66/0.41 thf(func_def_48, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.66/0.41 thf(func_def_49, type, type_definition: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > set @ X1 > $o))).
% 0.66/0.41 thf(func_def_50, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.66/0.41 thf(func_def_51, type, r: hF_Mirabelle_hf).
% 0.66/0.41 thf(func_def_52, type, x: hF_Mirabelle_hf).
% 0.66/0.41 thf(func_def_56, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.66/0.41 thf(func_def_57, type, db0: !>[X0: $tType]:(X0)).
% 0.66/0.41 thf(func_def_58, type, db1: !>[X0: $tType]:(X0)).
% 0.66/0.41 thf(func_def_59, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.66/0.41 thf(func_def_60, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.66/0.41 thf(func_def_61, type, vAND: ($o > $o > $o)).
% 0.66/0.41 thf(func_def_62, type, vOR: ($o > $o > $o)).
% 0.66/0.41 thf(func_def_63, type, db2: !>[X0: $tType]:(X0)).
% 0.66/0.41 thf(func_def_64, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.66/0.41 thf(func_def_65, type, vIMP: ($o > $o > $o)).
% 0.66/0.41 thf(func_def_66, type, vNOT: ($o > $o)).
% 0.66/0.41 thf(func_def_67, type, db3: !>[X0: $tType]:(X0)).
% 0.66/0.41 thf(func_def_68, type, sK0: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.66/0.41 thf(func_def_69, type, sK1: hF_Mirabelle_hf).
% 0.66/0.41 thf(func_def_70, type, sK2: hF_Mirabelle_hf).
% 0.66/0.41 thf(func_def_71, type, sK3: hF_Mirabelle_hf).
% 0.66/0.41 thf(func_def_72, type, sK4: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_73, type, sK5: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_74, type, sK6: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_75, type, sK7: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_76, type, sK8: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_77, type, sK9: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_78, type, sK10: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_79, type, sK11: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_80, type, sK12: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_81, type, sK13: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_82, type, sK14: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_83, type, sK15: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_84, type, sK16: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_85, type, sK17: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_86, type, sK18: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_87, type, sK19: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_88, type, sK20: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_89, type, sK21: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_90, type, sK22: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_91, type, sK23: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_92, type, sK24: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(func_def_93, type, sK25: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.66/0.41 thf(f2,axiom,(
% 0.66/0.41 (hF_Mir859708136nction = (^[X0 : hF_Mirabelle_hf] : (! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ X2) @ X0) => ! [X3 : hF_Mirabelle_hf] : ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ X3) @ X0) => (X2 = X3))))))),
% 0.66/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_hfunction__def)).
% 0.66/0.41 thf(f3,axiom,(
% 0.66/0.41 ! [X2 : hF_Mirabelle_hf,X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (((hF_Mirabelle_hmem @ X0 @ (hF_Mir165288108strict @ X1 @ X2))) = ? [X3 : hF_Mirabelle_hf,X4 : hF_Mirabelle_hf] : ((hF_Mirabelle_hmem @ X3 @ X2) & (X0 = ((hF_Mirabelle_hpair @ X3 @ X4)))) & (hF_Mirabelle_hmem @ X0 @ X1))),
% 0.66/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_hrestrict__iff)).
% 0.66/0.41 thf(f298,axiom,(
% 0.66/0.41 (hF_Mir859708136nction @ r)),
% 0.66/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.66/0.41 thf(f299,conjecture,(
% 0.66/0.41 (hF_Mir859708136nction @ (hF_Mir165288108strict @ r @ x))),
% 0.66/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.66/0.41 thf(f300,negated_conjecture,(
% 0.66/0.41 ~(hF_Mir859708136nction @ (hF_Mir165288108strict @ r @ x))),
% 0.66/0.41 inference(negated_conjecture,[status(cth)],[f299])).
% 0.66/0.41 thf(f446,plain,(
% 0.66/0.41 ~(hF_Mir859708136nction @ (hF_Mir165288108strict @ r @ x))),
% 0.66/0.41 inference(rectify,[],[f300])).
% 0.66/0.41 thf(f447,plain,(
% 0.66/0.41 ~ (((hF_Mir859708136nction @ (hF_Mir165288108strict @ r @ x))) = $true)),
% 0.66/0.41 inference(fool_elimination,[],[f446])).
% 0.66/0.41 thf(f450,plain,(
% 0.66/0.41 (hF_Mir859708136nction = (^[X0 : hF_Mirabelle_hf] : (! [X1 : hF_Mirabelle_hf,X2 : hF_Mirabelle_hf] : ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X2 @ X1) @ X0) => ! [X3 : hF_Mirabelle_hf] : ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X2 @ X3) @ X0) => (X1 = X3))))))),
% 0.66/0.41 inference(rectify,[],[f2])).
% 0.66/0.41 thf(f451,plain,(
% 0.66/0.41 (hF_Mir859708136nction = (^[Y0 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y1 @ Y2) @ Y0) => (!! @ hF_Mirabelle_hf @ (^[Y3 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y1 @ Y3) @ Y0) => (Y2 = Y3)))))))))))),
% 0.66/0.41 inference(fool_elimination,[],[f450])).
% 0.66/0.41 thf(f452,plain,(
% 0.66/0.41 ! [X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf,X2 : hF_Mirabelle_hf] : (((hF_Mirabelle_hmem @ X1 @ (hF_Mir165288108strict @ X2 @ X0))) = ? [X3 : hF_Mirabelle_hf,X4 : hF_Mirabelle_hf] : ((hF_Mirabelle_hmem @ X3 @ X0) & (((hF_Mirabelle_hpair @ X3 @ X4)) = X1)) & (hF_Mirabelle_hmem @ X1 @ X2))),
% 0.66/0.41 inference(rectify,[],[f3])).
% 0.66/0.41 thf(f453,plain,(
% 0.66/0.41 ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf,X0 : hF_Mirabelle_hf] : (((hF_Mirabelle_hmem @ X1 @ (hF_Mir165288108strict @ X2 @ X0))) = (((hF_Mirabelle_hmem @ X1 @ X2) & (?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (?? @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: (((hF_Mirabelle_hpair @ Y1 @ Y0) = X1) & (hF_Mirabelle_hmem @ Y1 @ X0)))))))))),
% 0.66/0.41 inference(fool_elimination,[],[f452])).
% 0.66/0.41 thf(f648,plain,(
% 0.66/0.41 (hF_Mir859708136nction @ r)),
% 0.66/0.41 inference(rectify,[],[f298])).
% 0.66/0.41 thf(f649,plain,(
% 0.66/0.41 (((hF_Mir859708136nction @ r)) = $true)),
% 0.66/0.41 inference(fool_elimination,[],[f648])).
% 0.66/0.41 thf(f751,plain,(
% 0.66/0.41 (((hF_Mir859708136nction @ (hF_Mir165288108strict @ r @ x))) != $true)),
% 0.66/0.41 inference(flattening,[],[f447])).
% 0.66/0.41 thf(f754,plain,(
% 0.66/0.41 ! [X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf,X2 : hF_Mirabelle_hf] : (((hF_Mirabelle_hmem @ X1 @ (hF_Mir165288108strict @ X0 @ X2))) = (((hF_Mirabelle_hmem @ X1 @ X0) & (?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (?? @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: (((hF_Mirabelle_hpair @ Y1 @ Y0) = X1) & (hF_Mirabelle_hmem @ Y1 @ X2)))))))))),
% 0.66/0.41 inference(rectify,[],[f453])).
% 0.66/0.41 thf(f758,plain,(
% 0.66/0.41 (hF_Mir859708136nction = (^[Y0 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y1 @ Y2) @ Y0) => (!! @ hF_Mirabelle_hf @ (^[Y3 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y1 @ Y3) @ Y0) => (Y2 = Y3)))))))))))),
% 0.66/0.41 inference(cnf_transformation,[],[f451])).
% 0.66/0.41 thf(f759,plain,(
% 0.66/0.41 ( ! [X2 : hF_Mirabelle_hf,X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((((hF_Mirabelle_hmem @ X1 @ (hF_Mir165288108strict @ X0 @ X2))) = (((hF_Mirabelle_hmem @ X1 @ X0) & (?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (?? @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: (((hF_Mirabelle_hpair @ Y1 @ Y0) = X1) & (hF_Mirabelle_hmem @ Y1 @ X2)))))))))) )),
% 0.66/0.41 inference(cnf_transformation,[],[f754])).
% 0.66/0.41 thf(f760,plain,(
% 0.66/0.41 (((hF_Mir859708136nction @ r)) = $true)),
% 0.66/0.41 inference(cnf_transformation,[],[f649])).
% 0.66/0.41 thf(f761,plain,(
% 0.66/0.41 (((hF_Mir859708136nction @ (hF_Mir165288108strict @ r @ x))) != $true)),
% 0.66/0.41 inference(cnf_transformation,[],[f751])).
% 0.66/0.41 thf(f766,plain,(
% 0.66/0.41 ($true = (((^[Y0 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y1 @ Y2) @ Y0) => (!! @ hF_Mirabelle_hf @ (^[Y3 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y1 @ Y3) @ Y0) => (Y2 = Y3)))))))))) @ r)))),
% 0.66/0.41 inference(definition_unfolding,[],[f760,f758])).
% 0.66/0.41 thf(f767,plain,(
% 0.66/0.41 ((((^[Y0 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y1 @ Y2) @ Y0) => (!! @ hF_Mirabelle_hf @ (^[Y3 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y1 @ Y3) @ Y0) => (Y2 = Y3)))))))))) @ (hF_Mir165288108strict @ r @ x))) != $true)),
% 0.66/0.41 inference(definition_unfolding,[],[f761,f758])).
% 0.66/0.41 thf(f768,plain,(
% 0.66/0.41 (((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y0 @ Y1) @ r) => (!! @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y0 @ Y2) @ r) => (Y1 = Y2)))))))))) = $true)),
% 0.66/0.41 inference(beta-eta_normalization,[],[f766])).
% 0.66/0.41 thf(f769,plain,(
% 0.66/0.41 ( ! [X1 : hF_Mirabelle_hf] : (((((^[Y0 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y0 @ Y1) @ r) => (!! @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y0 @ Y2) @ r) => (Y1 = Y2)))))))) @ X1)) = $true)) )),
% 0.66/0.41 inference(pi_proxy_clausification,[],[f768])).
% 0.66/0.41 thf(f770,plain,(
% 0.66/0.41 ( ! [X1 : hF_Mirabelle_hf] : ((((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ Y0) @ r) => (!! @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ Y1) @ r) => (Y0 = Y1)))))))) = $true)) )),
% 0.66/0.41 inference(beta-eta_normalization,[],[f769])).
% 0.66/0.41 thf(f771,plain,(
% 0.66/0.41 ( ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (($true = (((^[Y0 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ Y0) @ r) => (!! @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ Y1) @ r) => (Y0 = Y1)))))) @ X2)))) )),
% 0.66/0.41 inference(pi_proxy_clausification,[],[f770])).
% 0.66/0.41 thf(f772,plain,(
% 0.66/0.41 ( ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (($true = (((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ X2) @ r) => (!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ Y0) @ r) => (X2 = Y0)))))))) )),
% 0.66/0.41 inference(beta-eta_normalization,[],[f771])).
% 0.66/0.41 thf(f773,plain,(
% 0.66/0.41 ( ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (($false = ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ X2) @ r))) | (((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ Y0) @ r) => (X2 = Y0))))) = $true)) )),
% 0.66/0.41 inference(imp_proxy_clausification,[],[f772])).
% 0.66/0.41 thf(f774,plain,(
% 0.66/0.41 ( ! [X2 : hF_Mirabelle_hf,X3 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (($false = ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ X2) @ r))) | ((((^[Y0 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ Y0) @ r) => (X2 = Y0))) @ X3)) = $true)) )),
% 0.66/0.41 inference(pi_proxy_clausification,[],[f773])).
% 0.66/0.41 thf(f775,plain,(
% 0.66/0.41 ( ! [X2 : hF_Mirabelle_hf,X3 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (($false = ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ X2) @ r))) | ((((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ X3) @ r) => (X2 = X3))) = $true)) )),
% 0.66/0.41 inference(beta-eta_normalization,[],[f774])).
% 0.66/0.41 thf(f776,plain,(
% 0.66/0.41 ( ! [X2 : hF_Mirabelle_hf,X3 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (($false = ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ X2) @ r))) | ($true = ((X2 = X3))) | ($false = ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ X3) @ r)))) )),
% 0.66/0.41 inference(imp_proxy_clausification,[],[f775])).
% 0.66/0.41 thf(f777,plain,(
% 0.66/0.41 ( ! [X2 : hF_Mirabelle_hf,X3 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (($false = ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ X3) @ r))) | (X2 = X3) | ($false = ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X1 @ X2) @ r)))) )),
% 0.66/0.41 inference(equality_proxy_clausification,[],[f776])).
% 0.66/0.41 thf(f778,plain,(
% 0.66/0.41 (((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y0 @ Y1) @ (hF_Mir165288108strict @ r @ x)) => (!! @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y0 @ Y2) @ (hF_Mir165288108strict @ r @ x)) => (Y1 = Y2)))))))))) != $true)),
% 0.66/0.41 inference(beta-eta_normalization,[],[f767])).
% 0.66/0.41 thf(f779,plain,(
% 0.66/0.41 ($false = (((^[Y0 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y0 @ Y1) @ (hF_Mir165288108strict @ r @ x)) => (!! @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ Y0 @ Y2) @ (hF_Mir165288108strict @ r @ x)) => (Y1 = Y2)))))))) @ sK1)))),
% 0.66/0.41 inference(sigma_proxy_clausification,[],[f778])).
% 0.66/0.41 thf(f780,plain,(
% 0.66/0.41 ($false = ((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ Y0) @ (hF_Mir165288108strict @ r @ x)) => (!! @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ Y1) @ (hF_Mir165288108strict @ r @ x)) => (Y0 = Y1)))))))))),
% 0.66/0.41 inference(beta-eta_normalization,[],[f779])).
% 0.66/0.41 thf(f781,plain,(
% 0.66/0.41 ($false = (((^[Y0 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ Y0) @ (hF_Mir165288108strict @ r @ x)) => (!! @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ Y1) @ (hF_Mir165288108strict @ r @ x)) => (Y0 = Y1)))))) @ sK2)))),
% 0.66/0.41 inference(sigma_proxy_clausification,[],[f780])).
% 0.66/0.41 thf(f782,plain,(
% 0.66/0.41 ($false = (((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ sK2) @ (hF_Mir165288108strict @ r @ x)) => (!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ Y0) @ (hF_Mir165288108strict @ r @ x)) => (sK2 = Y0)))))))),
% 0.66/0.41 inference(beta-eta_normalization,[],[f781])).
% 0.66/0.41 thf(f783,plain,(
% 0.66/0.41 ($false = ((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ Y0) @ (hF_Mir165288108strict @ r @ x)) => (sK2 = Y0))))))),
% 0.66/0.41 inference(imp_proxy_clausification,[],[f782])).
% 0.66/0.41 thf(f784,plain,(
% 0.66/0.41 (((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ sK2) @ (hF_Mir165288108strict @ r @ x))) = $true)),
% 0.66/0.41 inference(imp_proxy_clausification,[],[f782])).
% 0.66/0.41 thf(f785,plain,(
% 0.66/0.41 ($false = (((^[Y0 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ Y0) @ (hF_Mir165288108strict @ r @ x)) => (sK2 = Y0))) @ sK3)))),
% 0.66/0.41 inference(sigma_proxy_clausification,[],[f783])).
% 0.66/0.41 thf(f786,plain,(
% 0.66/0.41 ((((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ sK3) @ (hF_Mir165288108strict @ r @ x)) => (sK2 = sK3))) = $false)),
% 0.66/0.41 inference(beta-eta_normalization,[],[f785])).
% 0.66/0.41 thf(f787,plain,(
% 0.66/0.41 ($false = ((sK2 = sK3)))),
% 0.66/0.41 inference(imp_proxy_clausification,[],[f786])).
% 0.66/0.41 thf(f788,plain,(
% 0.66/0.41 ($true = ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ sK3) @ (hF_Mir165288108strict @ r @ x))))),
% 0.66/0.41 inference(imp_proxy_clausification,[],[f786])).
% 0.66/0.41 thf(f789,plain,(
% 0.66/0.41 (sK3 != sK2)),
% 0.66/0.41 inference(equality_proxy_clausification,[],[f787])).
% 0.66/0.41 thf(f791,plain,(
% 0.66/0.41 ( ! [X2 : hF_Mirabelle_hf,X3 : hF_Mirabelle_hf,X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X0 @ X1) @ (hF_Mir165288108strict @ r @ X2))) = (($false & (?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (?? @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: (((hF_Mirabelle_hpair @ Y1 @ Y0) = (hF_Mirabelle_hpair @ X0 @ X1)) & (hF_Mirabelle_hmem @ Y1 @ X2))))))))) | (X1 = X3) | (((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X0 @ X3) @ r)) = $false)) )),
% 0.66/0.41 inference(superposition,[],[f759,f777])).
% 0.66/0.41 thf(f794,plain,(
% 0.66/0.41 ( ! [X2 : hF_Mirabelle_hf,X3 : hF_Mirabelle_hf,X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((X1 = X3) | ($true = (($false & (?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (?? @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: (((hF_Mirabelle_hpair @ Y1 @ Y0) = (hF_Mirabelle_hpair @ X0 @ X1)) & (hF_Mirabelle_hmem @ Y1 @ X2))))))))) | ($false = ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X0 @ X1) @ (hF_Mir165288108strict @ r @ X2)))) | (((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X0 @ X3) @ r)) = $false)) )),
% 0.66/0.41 inference(iff_proxy_clausification,[],[f791])).
% 0.66/0.41 thf(f796,plain,(
% 0.66/0.41 ( ! [X2 : hF_Mirabelle_hf,X3 : hF_Mirabelle_hf,X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (($false = ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X0 @ X1) @ (hF_Mir165288108strict @ r @ X2)))) | ($false = $true) | (X1 = X3) | (((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X0 @ X3) @ r)) = $false)) )),
% 0.66/0.41 inference(and_proxy_clausification,[],[f794])).
% 0.66/0.41 thf(f797,plain,(
% 0.66/0.41 ( ! [X2 : hF_Mirabelle_hf,X3 : hF_Mirabelle_hf,X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (($false = ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X0 @ X1) @ (hF_Mir165288108strict @ r @ X2)))) | (X1 = X3) | (((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ X0 @ X3) @ r)) = $false)) )),
% 0.66/0.41 inference(trivial_inequality_removal,[],[f796])).
% 0.66/0.41 thf(f891,plain,(
% 0.66/0.41 ( ! [X0 : hF_Mirabelle_hf] : (($false = $true) | ($false = ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ X0) @ r))) | (sK3 = X0)) )),
% 0.66/0.41 inference(superposition,[],[f797,f788])).
% 0.66/0.41 thf(f919,plain,(
% 0.66/0.41 ( ! [X0 : hF_Mirabelle_hf] : (($false = ((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ X0) @ r))) | (sK3 = X0)) )),
% 0.66/0.41 inference(trivial_inequality_removal,[],[f891])).
% 0.66/0.41 thf(f932,plain,(
% 0.66/0.41 ( ! [X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((sK3 = X0) | (((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ X0) @ (hF_Mir165288108strict @ r @ X1))) = (($false & (?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (?? @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: (((hF_Mirabelle_hpair @ Y1 @ Y0) = (hF_Mirabelle_hpair @ sK1 @ X0)) & (hF_Mirabelle_hmem @ Y1 @ X1)))))))))) )),
% 0.66/0.41 inference(superposition,[],[f759,f919])).
% 0.66/0.41 thf(f935,plain,(
% 0.66/0.41 ( ! [X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((sK3 = X0) | (((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ X0) @ (hF_Mir165288108strict @ r @ X1))) = $false) | ($true = (($false & (?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (?? @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: (((hF_Mirabelle_hpair @ Y1 @ Y0) = (hF_Mirabelle_hpair @ sK1 @ X0)) & (hF_Mirabelle_hmem @ Y1 @ X1)))))))))) )),
% 0.66/0.41 inference(iff_proxy_clausification,[],[f932])).
% 0.66/0.41 thf(f937,plain,(
% 0.66/0.41 ( ! [X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ X0) @ (hF_Mir165288108strict @ r @ X1))) = $false) | ($false = $true) | (sK3 = X0)) )),
% 0.66/0.41 inference(and_proxy_clausification,[],[f935])).
% 0.66/0.41 thf(f938,plain,(
% 0.66/0.41 ( ! [X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((((hF_Mirabelle_hmem @ (hF_Mirabelle_hpair @ sK1 @ X0) @ (hF_Mir165288108strict @ r @ X1))) = $false) | (sK3 = X0)) )),
% 0.66/0.41 inference(trivial_inequality_removal,[],[f937])).
% 0.66/0.41 thf(f1007,plain,(
% 0.66/0.41 (sK3 = sK2) | ($false = $true)),
% 0.66/0.41 inference(superposition,[],[f784,f938])).
% 0.66/0.41 thf(f1009,plain,(
% 0.66/0.41 (sK3 = sK2)),
% 0.66/0.41 inference(trivial_inequality_removal,[],[f1007])).
% 0.66/0.41 thf(f1026,plain,(
% 0.66/0.41 $false),
% 0.66/0.41 inference(forward_subsumption_resolution,[],[f1009,f789])).
% 0.66/0.41 % SZS output end Proof for theBenchmark
% 0.66/0.41 % (1748327)------------------------------
% 0.66/0.41 % (1748327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.41 % (1748327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.41 % (1748327)CaDiCaL version: 2.1.3
% 0.66/0.41 % (1748327)Termination reason: Refutation
% 0.66/0.41 % (1748327)Time elapsed: 0.026 s
% 0.66/0.41 % (1748327)Peak memory usage: 13 MB
% 0.66/0.41 % (1748327)Instructions burned: 49 (million)
% 0.66/0.41 % (1748292)Success in time 0.146 s
% 0.66/0.41 % Vampire exiting
%------------------------------------------------------------------------------