%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT123^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 07:48:22 AM UTC 2026
% Result : Theorem 0.64s 0.40s
% Output : Refutation 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT123^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n003.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 18:00:29 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.39 % (2853406)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.64/0.39 % (2853430)lrs+10_16_si=on:nwc=1.5:random_seed=3672205137:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.64/0.39 % (2853435)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.64/0.39 % (2853435)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
% 0.64/0.39 % (2853430)Instruction limit reached!
% 0.64/0.39 % (2853430)------------------------------
% 0.64/0.39 % (2853430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.39 % (2853430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.39 % (2853430)CaDiCaL version: 2.1.3
% 0.64/0.39 % (2853430)Termination reason: Instruction limit
% 0.64/0.39 % (2853430)Termination phase: Property scanning
% 0.64/0.39 % (2853430)Time elapsed: 0.005 s
% 0.64/0.39 % (2853430)Peak memory usage: 10 MB
% 0.64/0.39 % (2853430)Instructions burned: 20 (million)
% 0.64/0.39 % (2853429)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1675911332:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.64/0.39 % (2853431)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3964678024:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.64/0.39 % (2853433)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=235038218:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.64/0.39 % (2853434)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2199147119:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.64/0.39 % (2853435)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=883825994:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.64/0.39 % (2853432)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=3508568820: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)
% 0.64/0.39 % (2853431)Instruction limit reached!
% 0.64/0.39 % (2853431)------------------------------
% 0.64/0.39 % (2853431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.39 % (2853431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.39 % (2853431)CaDiCaL version: 2.1.3
% 0.64/0.39 % (2853431)Termination reason: Instruction limit
% 0.64/0.39 % (2853431)Termination phase: shuffling
% 0.64/0.39 % (2853431)Time elapsed: 0.002 s
% 0.64/0.39 % (2853431)Peak memory usage: 10 MB
% 0.64/0.39 % (2853431)Instructions burned: 3 (million)
% 0.64/0.39 % (2853443)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1179654928:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.64/0.39 % (2853443)Instruction limit reached!
% 0.64/0.39 % (2853443)------------------------------
% 0.64/0.39 % (2853443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.39 % (2853443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.39 % (2853443)CaDiCaL version: 2.1.3
% 0.64/0.39 % (2853443)Termination reason: Instruction limit
% 0.64/0.39 % (2853443)Termination phase: shuffling
% 0.64/0.39 % (2853443)Time elapsed: 0.001 s
% 0.64/0.39 % (2853443)Peak memory usage: 10 MB
% 0.64/0.39 % (2853443)Instructions burned: 3 (million)
% 0.64/0.39 % (2853433)Instruction limit reached!
% 0.64/0.39 % (2853433)------------------------------
% 0.64/0.39 % (2853433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.39 % (2853433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.39 % (2853433)CaDiCaL version: 2.1.3
% 0.64/0.39 % (2853433)Termination reason: Instruction limit
% 0.64/0.39 % (2853433)Termination phase: Preprocessing 1
% 0.64/0.39 % (2853433)Time elapsed: 0.012 s
% 0.64/0.39 % (2853433)Peak memory usage: 10 MB
% 0.64/0.39 % (2853433)Instructions burned: 26 (million)
% 0.64/0.39 % (2853457)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.64/0.40 % (2853457)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=910013750:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.64/0.40 % (2853451)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2722268541:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.64/0.40 % (2853457)Instruction limit reached!
% 0.64/0.40 % (2853457)------------------------------
% 0.64/0.40 % (2853457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.40 % (2853457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.40 % (2853457)CaDiCaL version: 2.1.3
% 0.64/0.40 % (2853457)Termination reason: Instruction limit
% 0.64/0.40 % (2853457)Termination phase: shuffling
% 0.64/0.40 % (2853457)Time elapsed: 0.003 s
% 0.64/0.40 % (2853457)Peak memory usage: 10 MB
% 0.64/0.40 % (2853457)Instructions burned: 14 (million)
% 0.64/0.40 % (2853451)Instruction limit reached!
% 0.64/0.40 % (2853451)------------------------------
% 0.64/0.40 % (2853451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.40 % (2853451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.40 % (2853451)CaDiCaL version: 2.1.3
% 0.64/0.40 % (2853451)Termination reason: Instruction limit
% 0.64/0.40 % (2853451)Termination phase: shuffling
% 0.64/0.40 % (2853451)Time elapsed: 0.005 s
% 0.64/0.40 % (2853451)Peak memory usage: 10 MB
% 0.64/0.40 % (2853451)Instructions burned: 9 (million)
% 0.64/0.40 % (2853459)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2084258506:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.64/0.40 % (2853467)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
% 0.64/0.40 % (2853467)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.64/0.40 % (2853467)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1544480670:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.64/0.40 % (2853434)Instruction limit reached!
% 0.64/0.40 % (2853434)------------------------------
% 0.64/0.40 % (2853434)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.40 % (2853434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.40 % (2853434)CaDiCaL version: 2.1.3
% 0.64/0.40 % (2853434)Termination reason: Instruction limit
% 0.64/0.40 % (2853434)Termination phase: Property scanning
% 0.64/0.40 % (2853434)Time elapsed: 0.036 s
% 0.64/0.40 % (2853434)Peak memory usage: 12 MB
% 0.64/0.40 % (2853434)Instructions burned: 77 (million)
% 0.64/0.40 % (2853459)Instruction limit reached!
% 0.64/0.40 % (2853459)------------------------------
% 0.64/0.40 % (2853459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.40 % (2853459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.40 % (2853459)CaDiCaL version: 2.1.3
% 0.64/0.40 % (2853459)Termination reason: Instruction limit
% 0.64/0.40 % (2853459)Termination phase: shuffling
% 0.64/0.40 % (2853459)Time elapsed: 0.006 s
% 0.64/0.40 % (2853459)Peak memory usage: 10 MB
% 0.64/0.40 % (2853459)Instructions burned: 12 (million)
% 0.64/0.40 % (2853429)Instruction limit reached!
% 0.64/0.40 % (2853429)------------------------------
% 0.64/0.40 % (2853429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.40 % (2853429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.40 % (2853429)CaDiCaL version: 2.1.3
% 0.64/0.40 % (2853429)Termination reason: Instruction limit
% 0.64/0.40 % (2853429)Termination phase: Saturation
% 0.64/0.40 % (2853429)Time elapsed: 0.041 s
% 0.64/0.40 % (2853429)Peak memory usage: 13 MB
% 0.64/0.40 % (2853429)Instructions burned: 89 (million)
% 0.64/0.40 % (2853467)Instruction limit reached!
% 0.64/0.40 % (2853467)------------------------------
% 0.64/0.40 % (2853467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.40 % (2853467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.40 % (2853467)CaDiCaL version: 2.1.3
% 0.64/0.40 % (2853467)Termination reason: Instruction limit
% 0.64/0.40 % (2853467)Termination phase: Property scanning
% 0.64/0.40 % (2853467)Time elapsed: 0.010 s
% 0.64/0.40 % (2853467)Peak memory usage: 10 MB
% 0.64/0.40 % (2853467)Instructions burned: 44 (million)
% 0.64/0.40 % (2853471)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=2776880332:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.64/0.40 % (2853481)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.64/0.40 % (2853481)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=1191158625:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.64/0.40 % (2853479)lrs+10_1_si=on:cs=on:random_seed=3871352614:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.64/0.40 % (2853485)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=7189883:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.64/0.40 % (2853481)Instruction limit reached!
% 0.64/0.40 % (2853481)------------------------------
% 0.64/0.40 % (2853481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.40 % (2853481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.40 % (2853481)CaDiCaL version: 2.1.3
% 0.64/0.40 % (2853481)Termination reason: Instruction limit
% 0.64/0.40 % (2853481)Termination phase: shuffling
% 0.64/0.40 % (2853481)Time elapsed: 0.002 s
% 0.64/0.40 % (2853481)Peak memory usage: 10 MB
% 0.64/0.40 % (2853481)Instructions burned: 3 (million)
% 0.64/0.40 % (2853483)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=575691939:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.64/0.40 % (2853479)Instruction limit reached!
% 0.64/0.40 % (2853479)------------------------------
% 0.64/0.40 % (2853479)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.40 % (2853479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.40 % (2853479)CaDiCaL version: 2.1.3
% 0.64/0.40 % (2853479)Termination reason: Instruction limit
% 0.64/0.40 % (2853479)Termination phase: shuffling
% 0.64/0.40 % (2853479)Time elapsed: 0.004 s
% 0.64/0.40 % (2853479)Peak memory usage: 10 MB
% 0.64/0.40 % (2853479)Instructions burned: 8 (million)
% 0.64/0.40 % (2853485)Refutation not found, incomplete strategy
% 0.64/0.40 % (2853485)------------------------------
% 0.64/0.40 % (2853485)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.40 % (2853485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.40 % (2853485)CaDiCaL version: 2.1.3
% 0.64/0.40 % (2853485)Termination reason: Refutation not found, incomplete strategy
% 0.64/0.40 % (2853485)Time elapsed: 0.010 s
% 0.64/0.40 % (2853485)Peak memory usage: 13 MB
% 0.64/0.40 % (2853485)Instructions burned: 39 (million)
% 0.64/0.40 % (2853485)------------------------------
% 0.64/0.40 % (2853485)------------------------------
% 0.64/0.40 % (2853435)Instruction limit reached!
% 0.64/0.40 % (2853435)------------------------------
% 0.64/0.40 % (2853435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.40 % (2853435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.40 % (2853435)CaDiCaL version: 2.1.3
% 0.64/0.40 % (2853435)Termination reason: Instruction limit
% 0.64/0.40 % (2853435)Termination phase: Saturation
% 0.64/0.40 % (2853435)Time elapsed: 0.075 s
% 0.64/0.40 % (2853435)Peak memory usage: 13 MB
% 0.64/0.40 % (2853435)Instructions burned: 157 (million)
% 0.64/0.40 % (2853494)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2663300340:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.64/0.40 % (2853483)Instruction limit reached!
% 0.64/0.40 % (2853483)------------------------------
% 0.64/0.40 % (2853483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.40 % (2853483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.40 % (2853483)CaDiCaL version: 2.1.3
% 0.64/0.40 % (2853483)Termination reason: Instruction limit
% 0.64/0.40 % (2853483)Termination phase: Property scanning
% 0.64/0.40 % (2853483)Time elapsed: 0.019 s
% 0.64/0.40 % (2853483)Peak memory usage: 11 MB
% 0.64/0.40 % (2853483)Instructions burned: 39 (million)
% 0.64/0.40 % (2853497)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3346313474:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.64/0.40 % (2853499)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=105641860:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.64/0.40 % (2853497)Instruction limit reached!
% 0.64/0.40 % (2853497)------------------------------
% 0.64/0.40 % (2853497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.40 % (2853497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.40 % (2853497)CaDiCaL version: 2.1.3
% 0.64/0.40 % (2853497)Termination reason: Instruction limit
% 0.64/0.40 % (2853497)Termination phase: shuffling
% 0.64/0.40 % (2853497)Time elapsed: 0.007 s
% 0.64/0.40 % (2853497)Peak memory usage: 10 MB
% 0.64/0.40 % (2853497)Instructions burned: 15 (million)
% 0.64/0.40 % (2853432) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2853406-2853432"...
% 0.64/0.40 % (2853471)Instruction limit reached!
% 0.64/0.40 % (2853471)------------------------------
% 0.64/0.40 % (2853471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.40 % (2853471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.40 % (2853471)CaDiCaL version: 2.1.3
% 0.64/0.40 % (2853471)Termination reason: Instruction limit
% 0.64/0.40 % (2853471)Termination phase: Property scanning
% 0.64/0.40 % (2853471)Time elapsed: 0.037 s
% 0.64/0.40 % (2853471)Peak memory usage: 11 MB
% 0.64/0.40 % (2853471)Instructions burned: 87 (million)
% 0.64/0.40 % (2853494)Instruction limit reached!
% 0.64/0.40 % (2853494)------------------------------
% 0.64/0.40 % (2853494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.40 % (2853494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.40 % (2853494)CaDiCaL version: 2.1.3
% 0.64/0.40 % (2853494)Termination reason: Instruction limit
% 0.64/0.40 % (2853494)Termination phase: Property scanning
% 0.64/0.40 % (2853494)Time elapsed: 0.011 s
% 0.64/0.40 % (2853494)Peak memory usage: 10 MB
% 0.64/0.40 % (2853494)Instructions burned: 25 (million)
% 0.64/0.40 % (2853432)...printing done.
% 0.64/0.40 % (2853432)Refutation found. Thanks to Tanya!
% 0.64/0.40 % SZS status Theorem for theBenchmark
% 0.64/0.40 % SZS output start Proof for theBenchmark
% 0.64/0.40 thf(type_def_5, type, coindu1593790203_llist: $tType > $tType).
% 0.64/0.40 thf(type_def_6, type, extended_enat: $tType).
% 0.64/0.40 thf(type_def_7, type, set: $tType > $tType).
% 0.64/0.40 thf(type_def_8, type, nat: $tType).
% 0.64/0.40 thf(type_def_9, type, itself: $tType > $tType).
% 0.64/0.40 thf(type_def_10, type, a: $tType).
% 0.64/0.40 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 0.64/0.40 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.64/0.40 thf(func_def_1, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.64/0.40 thf(func_def_2, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.64/0.40 thf(func_def_3, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.64/0.40 thf(func_def_4, type, no_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.64/0.40 thf(func_def_5, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.64/0.40 thf(func_def_6, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.64/0.40 thf(func_def_7, type, wellorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.64/0.40 thf(func_def_8, type, dense_order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.64/0.40 thf(func_def_9, type, linordered_idom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.64/0.40 thf(func_def_10, type, dense_linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.64/0.40 thf(func_def_11, type, cancel_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.64/0.40 thf(func_def_12, type, ordere236663937imp_le: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.64/0.40 thf(func_def_13, type, condit1656338222tinuum: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.64/0.40 thf(func_def_14, type, condit1037483654norder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.64/0.40 thf(func_def_15, type, coindu749330388e_lnth: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat > X0))).
% 0.64/0.40 thf(func_def_16, type, coindu1802687541_ltake: !>[X0: $tType]:((extended_enat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.64/0.40 thf(func_def_17, type, coindu440805660e_enat: !>[X0: $tType]:((X0 > (extended_enat > X0) > extended_enat > X0))).
% 0.64/0.40 thf(func_def_18, type, coinductive_enat_set: set @ extended_enat).
% 0.64/0.40 thf(func_def_19, type, coindu530039314t_setp: (extended_enat > $o)).
% 0.64/0.40 thf(func_def_20, type, coindu1491768222unfold: !>[X0: $tType]:(((X0 > $o) > (X0 > X0) > X0 > extended_enat))).
% 0.64/0.40 thf(func_def_21, type, extended_eSuc: (extended_enat > extended_enat)).
% 0.64/0.40 thf(func_def_22, type, extended_enat2: (nat > extended_enat)).
% 0.64/0.40 thf(func_def_23, type, extended_case_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 0.64/0.40 thf(func_def_24, type, extended_rec_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 0.64/0.40 thf(func_def_25, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.64/0.40 thf(func_def_26, type, suc: (nat > nat)).
% 0.64/0.40 thf(func_def_27, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.64/0.40 thf(func_def_28, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.64/0.40 thf(func_def_29, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.64/0.40 thf(func_def_30, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.64/0.40 thf(func_def_31, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.64/0.40 thf(func_def_32, type, ma: nat).
% 0.64/0.40 thf(func_def_33, type, na: extended_enat).
% 0.64/0.40 thf(func_def_34, type, thesis: $o).
% 0.64/0.40 thf(func_def_38, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.64/0.40 thf(func_def_39, type, db2: !>[X0: $tType]:(X0)).
% 0.64/0.40 thf(func_def_40, type, db0: !>[X0: $tType]:(X0)).
% 0.64/0.40 thf(func_def_41, type, db1: !>[X0: $tType]:(X0)).
% 0.64/0.40 thf(func_def_42, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.64/0.40 thf(func_def_43, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.64/0.40 thf(func_def_44, type, vOR: ($o > $o > $o)).
% 0.64/0.40 thf(func_def_45, type, vAND: ($o > $o > $o)).
% 0.64/0.40 thf(func_def_46, type, vNOT: ($o > $o)).
% 0.64/0.40 thf(func_def_47, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.64/0.40 thf(func_def_48, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.64/0.40 thf(func_def_49, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.64/0.40 thf(func_def_50, type, sK2: !>[X0: $tType]:((X0 > X0))).
% 0.64/0.40 thf(func_def_51, type, sK3: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.64/0.40 thf(func_def_52, type, sK4: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.64/0.40 thf(func_def_53, type, sK5: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.64/0.40 thf(func_def_54, type, sK6: !>[X0: $tType]:((X0 > X0))).
% 0.64/0.40 thf(func_def_55, type, sK7: (nat > (nat > $o) > nat)).
% 0.64/0.40 thf(func_def_56, type, sK8: (nat > (nat > $o) > nat)).
% 0.64/0.40 thf(func_def_57, type, sK9: !>[X0: $tType]:((X0 > X0))).
% 0.64/0.40 thf(func_def_58, type, sK10: !>[X0: $tType]:((X0 > X0))).
% 0.64/0.40 thf(func_def_59, type, sK11: (extended_enat > nat > nat)).
% 0.64/0.40 thf(func_def_60, type, sK12: !>[X0: $tType]:(((X0 > extended_enat) > nat > X0))).
% 0.64/0.40 thf(func_def_61, type, sK13: !>[X0: $tType]:(((X0 > extended_enat) > X0))).
% 0.64/0.40 thf(func_def_62, type, sK14: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_63, type, sK15: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_64, type, sK16: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_65, type, sK17: !>[X0: $tType]:((X0 > X0))).
% 0.64/0.40 thf(func_def_66, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_67, type, sK19: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_68, type, sK20: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_69, type, sK21: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_70, type, sK22: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_71, type, sK23: ((nat > $o) > nat)).
% 0.64/0.40 thf(func_def_72, type, sK24: !>[X0: $tType]:((X0 > X0))).
% 0.64/0.40 thf(func_def_73, type, sK25: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_74, type, sK26: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.64/0.40 thf(func_def_75, type, sK27: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_76, type, sK28: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.64/0.40 thf(func_def_77, type, sK29: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.64/0.40 thf(func_def_78, type, sK30: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.64/0.40 thf(func_def_79, type, sK31: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_80, type, sK32: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_81, type, sK33: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_82, type, sK34: !>[X0: $tType]:((X0 > X0))).
% 0.64/0.40 thf(func_def_83, type, sK35: ((nat > $o) > nat > nat > nat)).
% 0.64/0.40 thf(func_def_84, type, sK36: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.64/0.40 thf(func_def_85, type, sK37: !>[X0: $tType]:((nat > (X0 > $o) > (X0 > nat) > X0))).
% 0.64/0.40 thf(func_def_86, type, sK38: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_87, type, sK39: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.64/0.40 thf(func_def_88, type, sK40: ((extended_enat > $o) > extended_enat)).
% 0.64/0.40 thf(func_def_89, type, sK41: !>[X0: $tType, X1: $tType]:((X0 > X1))).
% 0.64/0.40 thf(func_def_90, type, sK42: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_91, type, sK43: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_92, type, sK44: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_93, type, sK45: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_94, type, sK46: (nat > nat > nat)).
% 0.64/0.40 thf(func_def_95, type, sK47: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_96, type, sK48: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_97, type, sK49: !>[X0: $tType]:((X0 > X0))).
% 0.64/0.40 thf(func_def_98, type, sK50: ((nat > $o) > nat)).
% 0.64/0.40 thf(func_def_99, type, sK51: !>[X0: $tType]:((X0 > X0))).
% 0.64/0.40 thf(func_def_100, type, sK52: (nat > nat > nat)).
% 0.64/0.40 thf(func_def_101, type, sK53: (nat > nat)).
% 0.64/0.40 thf(func_def_102, type, sK54: (nat > nat > nat)).
% 0.64/0.40 thf(func_def_103, type, sK55: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_104, type, sK56: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.64/0.40 thf(func_def_105, type, sK57: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.64/0.40 thf(func_def_106, type, sK58: !>[X0: $tType]:((X0 > X0))).
% 0.64/0.40 thf(func_def_107, type, sK59: (extended_enat > nat)).
% 0.64/0.40 thf(func_def_108, type, sK60: ((nat > nat) > nat)).
% 0.64/0.40 thf(func_def_109, type, sK61: ((nat > nat) > nat)).
% 0.64/0.40 thf(func_def_110, type, sK62: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.64/0.40 thf(func_def_111, type, sK63: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.64/0.40 thf(func_def_112, type, sK64: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_113, type, sK65: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_114, type, sK66: (extended_enat > nat > nat)).
% 0.64/0.40 thf(func_def_115, type, sK67: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.64/0.40 thf(func_def_116, type, sK68: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.64/0.40 thf(func_def_117, type, sK69: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_118, type, sK70: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_119, type, sK71: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_120, type, sK72: (extended_enat > nat)).
% 0.64/0.40 thf(func_def_121, type, sK73: ((nat > nat > $o) > nat)).
% 0.64/0.40 thf(func_def_122, type, sK74: ((nat > nat > $o) > nat)).
% 0.64/0.40 thf(func_def_123, type, sK75: ((nat > nat > $o) > nat)).
% 0.64/0.40 thf(func_def_124, type, sK76: ((nat > nat > $o) > nat)).
% 0.64/0.40 thf(func_def_125, type, sK77: ((nat > $o) > nat)).
% 0.64/0.40 thf(func_def_126, type, sK78: !>[X0: $tType]:((X0 > X0))).
% 0.64/0.40 thf(func_def_127, type, sK79: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.64/0.40 thf(func_def_128, type, sK80: !>[X0: $tType]:((X0 > X0))).
% 0.64/0.40 thf(func_def_129, type, sK81: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_130, type, sK82: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_131, type, sK83: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_132, type, sK84: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_133, type, sK85: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.64/0.40 thf(func_def_134, type, sK86: (nat > nat > nat)).
% 0.64/0.40 thf(func_def_135, type, sK87: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_136, type, sK88: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_137, type, sK89: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.64/0.40 thf(func_def_138, type, sK90: (extended_enat > extended_enat > extended_enat)).
% 0.64/0.40 thf(func_def_139, type, sK91: ((nat > $o) > nat > nat > nat)).
% 0.64/0.40 thf(func_def_140, type, sK92: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.64/0.40 thf(func_def_141, type, sK93: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_142, type, sK94: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_143, type, sK95: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.64/0.40 thf(func_def_144, type, sK96: !>[X0: $tType]:((X0 > X0))).
% 0.64/0.40 thf(func_def_145, type, sK97: (nat > extended_enat > nat)).
% 0.64/0.40 thf(func_def_146, type, sK98: (extended_enat > extended_enat > nat)).
% 0.64/0.40 thf(func_def_147, type, sK99: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.64/0.40 thf(func_def_148, type, sK100: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.64/0.40 thf(func_def_149, type, sK101: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_150, type, sK102: !>[X0: $tType]:((X0 > X0))).
% 0.64/0.40 thf(func_def_151, type, sK103: !>[X0: $tType]:((X0 > X0))).
% 0.64/0.40 thf(func_def_152, type, sK104: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.64/0.40 thf(func_def_153, type, sK105: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_154, type, sK106: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_155, type, sK107: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_156, type, sK108: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.64/0.40 thf(func_def_157, type, sK109: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.64/0.40 thf(func_def_159, type, inv_extended_eSuc_111: (extended_enat > extended_enat)).
% 0.64/0.40 thf(func_def_160, type, inv_suc_112: (nat > nat)).
% 0.64/0.40 thf(func_def_161, type, inv_extended_enat2_113: (extended_enat > nat)).
% 0.64/0.40 thf(f1,axiom,(
% 0.64/0.40 (ord_less @ extended_enat @ (extended_enat2 @ (suc @ ma)) @ na)),
% 0.64/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Suc_Oprems)).
% 0.64/0.40 thf(f24,axiom,(
% 0.64/0.40 ! [X0 : extended_enat,X1 : extended_enat] : ((ord_less @ extended_enat @ X0 @ X1) => (ord_less_eq @ extended_enat @ (extended_eSuc @ X0) @ X1))),
% 0.64/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_ileI1)).
% 0.64/0.40 thf(f25,axiom,(
% 0.64/0.40 ! [X0 : extended_enat,X1 : extended_enat] : (((ord_less_eq @ extended_enat @ (extended_eSuc @ X0) @ X1)) = ? [X2 : extended_enat] : ((ord_less_eq @ extended_enat @ X0 @ X2) & (X1 = ((extended_eSuc @ X2)))))),
% 0.64/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_eSuc__le__iff)).
% 0.64/0.40 thf(f281,axiom,(
% 0.64/0.40 ! [X0 : extended_enat] : ((na = ((extended_eSuc @ X0))) => thesis)),
% 0.64/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.64/0.40 thf(f282,conjecture,(
% 0.64/0.40 thesis),
% 0.64/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 0.64/0.40 thf(f283,negated_conjecture,(
% 0.64/0.40 ~thesis),
% 0.64/0.40 inference(negated_conjecture,[status(cth)],[f282])).
% 0.64/0.40 thf(f339,plain,(
% 0.64/0.40 ! [X0 : extended_enat,X1 : extended_enat] : ((ord_less @ extended_enat @ X0 @ X1) => (ord_less_eq @ extended_enat @ (extended_eSuc @ X0) @ X1))),
% 0.64/0.40 inference(rectify,[],[f24])).
% 0.64/0.40 thf(f340,plain,(
% 0.64/0.40 ! [X0 : extended_enat,X1 : extended_enat] : ((((ord_less @ extended_enat @ X0 @ X1)) = $true) => (((ord_less_eq @ extended_enat @ (extended_eSuc @ X0) @ X1)) = $true))),
% 0.64/0.40 inference(fool_elimination,[],[f339])).
% 0.64/0.40 thf(f410,plain,(
% 0.64/0.40 ~thesis),
% 0.64/0.40 inference(rectify,[],[f283])).
% 0.64/0.40 thf(f411,plain,(
% 0.64/0.40 ~ (thesis = $true)),
% 0.64/0.40 inference(fool_elimination,[],[f410])).
% 0.64/0.40 thf(f609,plain,(
% 0.64/0.40 ! [X0 : extended_enat,X1 : extended_enat] : (((ord_less_eq @ extended_enat @ (extended_eSuc @ X0) @ X1)) = ? [X2 : extended_enat] : ((ord_less_eq @ extended_enat @ X0 @ X2) & (X1 = ((extended_eSuc @ X2)))))),
% 0.64/0.40 inference(rectify,[],[f25])).
% 0.64/0.40 thf(f610,plain,(
% 0.64/0.40 ! [X1 : extended_enat,X0 : extended_enat] : ((((ord_less_eq @ extended_enat @ (extended_eSuc @ X0) @ X1)) = $true) <=> ? [X2 : extended_enat] : ((((ord_less_eq @ extended_enat @ X0 @ X2)) = $true) & (((extended_eSuc @ X2)) = X1)))),
% 0.64/0.40 inference(fool_elimination,[],[f609])).
% 0.64/0.40 thf(f619,plain,(
% 0.64/0.40 ! [X0 : extended_enat] : ((na = ((extended_eSuc @ X0))) => thesis)),
% 0.64/0.40 inference(rectify,[],[f281])).
% 0.64/0.40 thf(f620,plain,(
% 0.64/0.40 ! [X0 : extended_enat] : ((na = ((extended_eSuc @ X0))) => (thesis = $true))),
% 0.64/0.40 inference(fool_elimination,[],[f619])).
% 0.64/0.40 thf(f743,plain,(
% 0.64/0.40 (ord_less @ extended_enat @ (extended_enat2 @ (suc @ ma)) @ na)),
% 0.64/0.40 inference(rectify,[],[f1])).
% 0.64/0.40 thf(f744,plain,(
% 0.64/0.40 (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ ma)) @ na)) = $true)),
% 0.64/0.40 inference(fool_elimination,[],[f743])).
% 0.64/0.40 thf(f799,plain,(
% 0.64/0.40 (thesis != $true)),
% 0.64/0.40 inference(flattening,[],[f411])).
% 0.64/0.40 thf(f991,plain,(
% 0.64/0.40 ! [X0 : extended_enat] : ((na != ((extended_eSuc @ X0))) | (thesis = $true))),
% 0.64/0.40 inference(ennf_transformation,[],[f620])).
% 0.64/0.40 thf(f1065,plain,(
% 0.64/0.40 ! [X1 : extended_enat,X0 : extended_enat] : ((((ord_less @ extended_enat @ X0 @ X1)) != $true) | (((ord_less_eq @ extended_enat @ (extended_eSuc @ X0) @ X1)) = $true))),
% 0.64/0.40 inference(ennf_transformation,[],[f340])).
% 0.64/0.40 thf(f1303,plain,(
% 0.64/0.40 ! [X0 : extended_enat,X1 : extended_enat] : ((((ord_less @ extended_enat @ X1 @ X0)) != $true) | (((ord_less_eq @ extended_enat @ (extended_eSuc @ X1) @ X0)) = $true))),
% 0.64/0.40 inference(rectify,[],[f1065])).
% 0.64/0.40 thf(f1314,plain,(
% 0.64/0.40 ! [X1 : extended_enat,X0 : extended_enat] : (((((ord_less_eq @ extended_enat @ (extended_eSuc @ X0) @ X1)) = $true) | ! [X2 : extended_enat] : ((((ord_less_eq @ extended_enat @ X0 @ X2)) != $true) | (((extended_eSuc @ X2)) != X1))) & (? [X2 : extended_enat] : ((((ord_less_eq @ extended_enat @ X0 @ X2)) = $true) & (((extended_eSuc @ X2)) = X1)) | (((ord_less_eq @ extended_enat @ (extended_eSuc @ X0) @ X1)) != $true)))),
% 0.64/0.40 inference(nnf_transformation,[],[f610])).
% 0.64/0.40 thf(f1315,plain,(
% 0.64/0.40 ! [X0 : extended_enat,X1 : extended_enat] : (((((ord_less_eq @ extended_enat @ (extended_eSuc @ X1) @ X0)) = $true) | ! [X2 : extended_enat] : ((((ord_less_eq @ extended_enat @ X1 @ X2)) != $true) | (((extended_eSuc @ X2)) != X0))) & (? [X3 : extended_enat] : ((((ord_less_eq @ extended_enat @ X1 @ X3)) = $true) & (((extended_eSuc @ X3)) = X0)) | (((ord_less_eq @ extended_enat @ (extended_eSuc @ X1) @ X0)) != $true)))),
% 0.64/0.40 inference(rectify,[],[f1314])).
% 0.64/0.40 thf(f1316,plain,(
% 0.64/0.40 ! [X0 : extended_enat,X1 : extended_enat] : (((((ord_less_eq @ extended_enat @ (extended_eSuc @ X1) @ X0)) = $true) | ! [X2 : extended_enat] : ((((ord_less_eq @ extended_enat @ X1 @ X2)) != $true) | (((extended_eSuc @ X2)) != X0))) & (((((ord_less_eq @ extended_enat @ X1 @ (sK90 @ X1 @ X0))) = $true) & (((extended_eSuc @ (sK90 @ X1 @ X0))) = X0)) | (((ord_less_eq @ extended_enat @ (extended_eSuc @ X1) @ X0)) != $true)))),
% 0.64/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK2 @ X0 @ X1)],[f1315])).
% 0.64/0.40 thf(f1493,plain,(
% 0.64/0.40 (thesis != $true)),
% 0.64/0.40 inference(cnf_transformation,[],[f799])).
% 0.64/0.40 thf(f1646,plain,(
% 0.64/0.40 (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ ma)) @ na)) = $true)),
% 0.64/0.40 inference(cnf_transformation,[],[f744])).
% 0.64/0.40 thf(f1713,plain,(
% 0.64/0.40 ( ! [X0 : extended_enat,X1 : extended_enat] : ((((ord_less_eq @ extended_enat @ (extended_eSuc @ X1) @ X0)) = $true) | (((ord_less @ extended_enat @ X1 @ X0)) != $true)) )),
% 0.64/0.40 inference(cnf_transformation,[],[f1303])).
% 0.64/0.40 thf(f1735,plain,(
% 0.64/0.40 ( ! [X0 : extended_enat,X1 : extended_enat] : ((((ord_less_eq @ extended_enat @ (extended_eSuc @ X1) @ X0)) != $true) | (((extended_eSuc @ (sK90 @ X1 @ X0))) = X0)) )),
% 0.64/0.40 inference(cnf_transformation,[],[f1316])).
% 0.64/0.40 thf(f1803,plain,(
% 0.64/0.40 ( ! [X0 : extended_enat] : ((na != ((extended_eSuc @ X0))) | (thesis = $true)) )),
% 0.64/0.40 inference(cnf_transformation,[],[f991])).
% 0.64/0.40 thf(f2126,definition,(
% 0.64/0.40 spl110_7 <=> (thesis = $true)),
% 0.64/0.40 introduced(definition,[new_symbols(definition,[spl110_7])],[avatar_definition])).
% 0.64/0.40 thf(f2130,definition,(
% 0.64/0.40 spl110_8 <=> ! [X0 : extended_enat] : (na != ((extended_eSuc @ X0)))),
% 0.64/0.40 introduced(definition,[new_symbols(definition,[spl110_8])],[avatar_definition])).
% 0.64/0.40 thf(f2131,plain,(
% 0.64/0.40 ( ! [X0 : extended_enat] : ((na != ((extended_eSuc @ X0)))) ) | ~spl110_8),
% 0.64/0.40 inference(avatar_component_clause,[],[f2130])).
% 0.64/0.40 thf(f2132,plain,(
% 0.64/0.40 spl110_7 | spl110_8),
% 0.64/0.40 inference(avatar_split_clause,[],[f1803,f2130,f2126])).
% 0.64/0.40 thf(f2158,plain,(
% 0.64/0.40 ~spl110_7),
% 0.64/0.40 inference(avatar_split_clause,[],[f1493,f2126])).
% 0.64/0.40 thf(f2185,definition,(
% 0.64/0.40 spl110_19 <=> (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ ma)) @ na)) = $true)),
% 0.64/0.40 introduced(definition,[new_symbols(definition,[spl110_19])],[avatar_definition])).
% 0.64/0.40 thf(f2187,plain,(
% 0.64/0.40 (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ ma)) @ na)) = $true) | ~spl110_19),
% 0.64/0.40 inference(avatar_component_clause,[],[f2185])).
% 0.64/0.40 thf(f2188,plain,(
% 0.64/0.40 spl110_19),
% 0.64/0.40 inference(avatar_split_clause,[],[f1646,f2185])).
% 0.64/0.40 thf(f2282,plain,(
% 0.64/0.40 ( ! [X0 : extended_enat,X1 : extended_enat] : ((((ord_less @ extended_enat @ X0 @ X1)) != $true) | (((extended_eSuc @ (sK90 @ X0 @ X1))) = X1) | ($true != $true)) )),
% 0.64/0.40 inference(superposition,[],[f1735,f1713])).
% 0.64/0.40 thf(f2284,plain,(
% 0.64/0.40 ( ! [X0 : extended_enat,X1 : extended_enat] : ((((extended_eSuc @ (sK90 @ X0 @ X1))) = X1) | (((ord_less @ extended_enat @ X0 @ X1)) != $true)) )),
% 0.64/0.40 inference(trivial_inequality_removal,[],[f2282])).
% 0.64/0.40 thf(f2410,plain,(
% 0.64/0.40 ( ! [X0 : extended_enat,X1 : extended_enat] : ((((ord_less @ extended_enat @ X1 @ X0)) != $true) | (na != X0)) ) | ~spl110_8),
% 0.64/0.40 inference(superposition,[],[f2131,f2284])).
% 0.64/0.40 thf(f2505,plain,(
% 0.64/0.40 (na != na) | ($true != $true) | (~spl110_8 | ~spl110_19)),
% 0.64/0.40 inference(superposition,[],[f2410,f2187])).
% 0.64/0.40 thf(f2506,plain,(
% 0.64/0.40 $false | (~spl110_8 | ~spl110_19)),
% 0.64/0.40 inference(trivial_inequality_removal,[],[f2505])).
% 0.64/0.40 thf(f2507,plain,(
% 0.64/0.40 ~spl110_8 | ~spl110_19),
% 0.64/0.40 inference(avatar_contradiction_clause,[],[f2506])).
% 0.64/0.40 cnf(s7, plain, spl110_7 | spl110_8, inference(sat_conversion,[],[f2132])).
% 0.64/0.40 cnf(s13, plain, ~spl110_7, inference(sat_conversion,[],[f2158])).
% 0.64/0.40 cnf(s19, plain, spl110_19, inference(sat_conversion,[],[f2188])).
% 0.64/0.40 cnf(s31, plain, ~spl110_8 | ~spl110_19, inference(sat_conversion,[],[f2507])).
% 0.64/0.40 cnf(s33, plain, ~spl110_8, inference(rat,[],[s31,s19])).
% 0.64/0.40 cnf(s35, plain, $false, inference(rat,[],[s7,s33,s13])).
% 0.64/0.40 thf(f2508,plain,(
% 0.64/0.40 $false),
% 0.64/0.40 inference(avatar_sat_refutation,[],[s35])).
% 0.64/0.40 % SZS output end Proof for theBenchmark
% 0.64/0.40 % (2853432)------------------------------
% 0.64/0.40 % (2853432)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.40 % (2853432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.40 % (2853432)CaDiCaL version: 2.1.3
% 0.64/0.40 % (2853432)Termination reason: Refutation
% 0.64/0.40 % (2853432)Time elapsed: 0.090 s
% 0.64/0.40 % (2853432)Peak memory usage: 14 MB
% 0.64/0.40 % (2853432)Instructions burned: 183 (million)
% 0.64/0.40 % (2853406)Success in time 0.148 s
% 0.64/0.40 % Vampire exiting
%------------------------------------------------------------------------------