%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP095^2 : 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 : n008.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 08:08:19 AM UTC 2026
% Result : Theorem 0.50s 0.46s
% Output : Refutation 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP095^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 19:53:39 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.21/0.28 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
% 0.50/0.42 % (3647281)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.50/0.42 % (3647292)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.50/0.42 % (3647292)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
% 0.50/0.42 % (3647292)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=721992022:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.50/0.42 % (3647286)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3709364190:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.50/0.42 % (3647288)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4162128858:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.50/0.42 % (3647289)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=2449984510: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)
% 0.50/0.42 % (3647290)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3245362827:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.50/0.42 % (3647291)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1818173434:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.50/0.42 % (3647287)lrs+10_16_si=on:nwc=1.5:random_seed=1331522445:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.50/0.42 % (3647288)Instruction limit reached!
% 0.50/0.42 % (3647288)------------------------------
% 0.50/0.42 % (3647288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.42 % (3647288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.42 % (3647288)CaDiCaL version: 2.1.3
% 0.50/0.42 % (3647288)Termination reason: Instruction limit
% 0.50/0.42 % (3647288)Termination phase: shuffling
% 0.50/0.42 % (3647288)Time elapsed: 0.002 s
% 0.50/0.42 % (3647288)Peak memory usage: 10 MB
% 0.50/0.42 % (3647288)Instructions burned: 4 (million)
% 0.50/0.42 % (3647287)Instruction limit reached!
% 0.50/0.42 % (3647287)------------------------------
% 0.50/0.42 % (3647287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.42 % (3647287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.42 % (3647287)CaDiCaL version: 2.1.3
% 0.50/0.42 % (3647287)Termination reason: Instruction limit
% 0.50/0.42 % (3647287)Termination phase: Property scanning
% 0.50/0.42 % (3647287)Time elapsed: 0.010 s
% 0.50/0.42 % (3647287)Peak memory usage: 10 MB
% 0.50/0.42 % (3647287)Instructions burned: 20 (million)
% 0.50/0.42 % (3647290)Instruction limit reached!
% 0.50/0.42 % (3647290)------------------------------
% 0.50/0.42 % (3647290)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.42 % (3647290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.42 % (3647290)CaDiCaL version: 2.1.3
% 0.50/0.42 % (3647290)Termination reason: Instruction limit
% 0.50/0.42 % (3647290)Termination phase: Property scanning
% 0.50/0.42 % (3647290)Time elapsed: 0.012 s
% 0.50/0.42 % (3647290)Peak memory usage: 10 MB
% 0.50/0.42 % (3647290)Instructions burned: 24 (million)
% 0.50/0.42 % (3647300)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2481340326:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.50/0.42 % (3647300)Instruction limit reached!
% 0.50/0.42 % (3647300)------------------------------
% 0.50/0.42 % (3647300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.42 % (3647300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.42 % (3647300)CaDiCaL version: 2.1.3
% 0.50/0.42 % (3647300)Termination reason: Instruction limit
% 0.50/0.42 % (3647300)Termination phase: shuffling
% 0.50/0.42 % (3647300)Time elapsed: 0.002 s
% 0.50/0.42 % (3647300)Peak memory usage: 10 MB
% 0.50/0.42 % (3647300)Instructions burned: 3 (million)
% 0.50/0.42 % (3647302)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.50/0.45 % (3647301)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2975700836:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.50/0.45 % (3647302)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=476052525:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.50/0.45 % (3647301)Instruction limit reached!
% 0.50/0.45 % (3647301)------------------------------
% 0.50/0.45 % (3647301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (3647301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (3647301)CaDiCaL version: 2.1.3
% 0.50/0.45 % (3647301)Termination reason: Instruction limit
% 0.50/0.45 % (3647301)Termination phase: shuffling
% 0.50/0.45 % (3647301)Time elapsed: 0.003 s
% 0.50/0.45 % (3647301)Peak memory usage: 10 MB
% 0.50/0.45 % (3647301)Instructions burned: 5 (million)
% 0.50/0.45 % (3647291)Instruction limit reached!
% 0.50/0.45 % (3647291)------------------------------
% 0.50/0.45 % (3647291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (3647291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (3647291)CaDiCaL version: 2.1.3
% 0.50/0.45 % (3647291)Termination reason: Instruction limit
% 0.50/0.45 % (3647291)Termination phase: Property scanning
% 0.50/0.45 % (3647291)Time elapsed: 0.035 s
% 0.50/0.45 % (3647291)Peak memory usage: 12 MB
% 0.50/0.45 % (3647291)Instructions burned: 75 (million)
% 0.50/0.45 % (3647302)Instruction limit reached!
% 0.50/0.45 % (3647302)------------------------------
% 0.50/0.45 % (3647302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (3647302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (3647302)CaDiCaL version: 2.1.3
% 0.50/0.45 % (3647302)Termination reason: Instruction limit
% 0.50/0.45 % (3647302)Termination phase: shuffling
% 0.50/0.45 % (3647302)Time elapsed: 0.004 s
% 0.50/0.45 % (3647302)Peak memory usage: 10 MB
% 0.50/0.45 % (3647302)Instructions burned: 8 (million)
% 0.50/0.45 % (3647292)Instruction limit reached!
% 0.50/0.45 % (3647292)------------------------------
% 0.50/0.45 % (3647292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (3647292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (3647292)CaDiCaL version: 2.1.3
% 0.50/0.45 % (3647292)Termination reason: Instruction limit
% 0.50/0.45 % (3647292)Termination phase: Saturation
% 0.50/0.45 % (3647292)Time elapsed: 0.045 s
% 0.50/0.45 % (3647292)Peak memory usage: 13 MB
% 0.50/0.45 % (3647292)Instructions burned: 158 (million)
% 0.50/0.45 % (3647286)Instruction limit reached!
% 0.50/0.45 % (3647286)------------------------------
% 0.50/0.45 % (3647286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (3647286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (3647286)CaDiCaL version: 2.1.3
% 0.50/0.45 % (3647286)Termination reason: Instruction limit
% 0.50/0.45 % (3647286)Termination phase: Saturation
% 0.50/0.45 % (3647286)Time elapsed: 0.041 s
% 0.50/0.45 % (3647286)Peak memory usage: 13 MB
% 0.50/0.45 % (3647286)Instructions burned: 88 (million)
% 0.50/0.45 % (3647304)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=746540160:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.50/0.45 % (3647310)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.50/0.45 % (3647310)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=1126305643:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.50/0.45 % (3647307)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
% 0.50/0.45 % (3647307)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.50/0.45 % (3647310)Instruction limit reached!
% 0.50/0.45 % (3647310)------------------------------
% 0.50/0.45 % (3647310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (3647310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.46 % (3647310)CaDiCaL version: 2.1.3
% 0.50/0.46 % (3647310)Termination reason: Instruction limit
% 0.50/0.46 % (3647310)Termination phase: shuffling
% 0.50/0.46 % (3647310)Time elapsed: 0.001 s
% 0.50/0.46 % (3647310)Peak memory usage: 10 MB
% 0.50/0.46 % (3647310)Instructions burned: 3 (million)
% 0.50/0.46 % (3647304)Instruction limit reached!
% 0.50/0.46 % (3647304)------------------------------
% 0.50/0.46 % (3647304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.46 % (3647304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.46 % (3647307)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3460285865:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.50/0.46 % (3647304)CaDiCaL version: 2.1.3
% 0.50/0.46 % (3647304)Termination reason: Instruction limit
% 0.50/0.46 % (3647304)Termination phase: shuffling
% 0.50/0.46 % (3647304)Time elapsed: 0.006 s
% 0.50/0.46 % (3647304)Peak memory usage: 10 MB
% 0.50/0.46 % (3647304)Instructions burned: 13 (million)
% 0.50/0.46 % (3647308)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=2057447964:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.50/0.46 % (3647309)lrs+10_1_si=on:cs=on:random_seed=4135900001:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.50/0.46 % (3647309)Instruction limit reached!
% 0.50/0.46 % (3647309)------------------------------
% 0.50/0.46 % (3647309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.46 % (3647309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.46 % (3647309)CaDiCaL version: 2.1.3
% 0.50/0.46 % (3647309)Termination reason: Instruction limit
% 0.50/0.46 % (3647309)Termination phase: shuffling
% 0.50/0.46 % (3647309)Time elapsed: 0.004 s
% 0.50/0.46 % (3647309)Peak memory usage: 10 MB
% 0.50/0.46 % (3647309)Instructions burned: 8 (million)
% 0.50/0.46 % (3647311)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3618875904:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.50/0.46 % (3647314)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3211217114:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.50/0.46 % (3647307)Instruction limit reached!
% 0.50/0.46 % (3647307)------------------------------
% 0.50/0.46 % (3647307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.46 % (3647307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.46 % (3647307)CaDiCaL version: 2.1.3
% 0.50/0.46 % (3647307)Termination reason: Instruction limit
% 0.50/0.46 % (3647307)Termination phase: Property scanning
% 0.50/0.46 % (3647307)Time elapsed: 0.014 s
% 0.50/0.46 % (3647307)Peak memory usage: 10 MB
% 0.50/0.46 % (3647307)Instructions burned: 30 (million)
% 0.50/0.46 % (3647316)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2398450307:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.50/0.46 % (3647311)Instruction limit reached!
% 0.50/0.46 % (3647311)------------------------------
% 0.50/0.46 % (3647311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.46 % (3647311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.46 % (3647311)CaDiCaL version: 2.1.3
% 0.50/0.46 % (3647311)Termination reason: Instruction limit
% 0.50/0.46 % (3647311)Termination phase: Preprocessing 3
% 0.50/0.46 % (3647311)Time elapsed: 0.018 s
% 0.50/0.46 % (3647311)Peak memory usage: 11 MB
% 0.50/0.46 % (3647311)Instructions burned: 38 (million)
% 0.50/0.46 % (3647321)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=765254637:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.50/0.46 % (3647316)Instruction limit reached!
% 0.50/0.46 % (3647316)------------------------------
% 0.50/0.46 % (3647316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.46 % (3647316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.46 % (3647316)CaDiCaL version: 2.1.3
% 0.50/0.46 % (3647316)Termination reason: Instruction limit
% 0.50/0.46 % (3647316)Termination phase: Property scanning
% 0.50/0.46 % (3647316)Time elapsed: 0.012 s
% 0.50/0.46 % (3647316)Peak memory usage: 10 MB
% 0.50/0.46 % (3647316)Instructions burned: 25 (million)
% 0.50/0.46 % (3647314)Refutation not found, incomplete strategy
% 0.50/0.46 % (3647314)------------------------------
% 0.50/0.46 % (3647314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.46 % (3647314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.46 % (3647314)CaDiCaL version: 2.1.3
% 0.50/0.46 % (3647314)Termination reason: Refutation not found, incomplete strategy
% 0.50/0.46 % (3647314)Time elapsed: 0.024 s
% 0.50/0.46 % (3647314)Peak memory usage: 13 MB
% 0.50/0.46 % (3647314)Instructions burned: 87 (million)
% 0.50/0.46 % (3647314)------------------------------
% 0.50/0.46 % (3647314)------------------------------
% 0.50/0.46 % (3647322)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2929077789:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.50/0.46 % (3647321)Instruction limit reached!
% 0.50/0.46 % (3647321)------------------------------
% 0.50/0.46 % (3647321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.46 % (3647321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.46 % (3647321)CaDiCaL version: 2.1.3
% 0.50/0.46 % (3647321)Termination reason: Instruction limit
% 0.50/0.46 % (3647321)Termination phase: shuffling
% 0.50/0.46 % (3647321)Time elapsed: 0.007 s
% 0.50/0.46 % (3647321)Peak memory usage: 10 MB
% 0.50/0.46 % (3647321)Instructions burned: 15 (million)
% 0.50/0.46 % (3647308)Instruction limit reached!
% 0.50/0.46 % (3647308)------------------------------
% 0.50/0.46 % (3647308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.46 % (3647308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.46 % (3647308)CaDiCaL version: 2.1.3
% 0.50/0.46 % (3647308)Termination reason: Instruction limit
% 0.50/0.46 % (3647308)Termination phase: Property scanning
% 0.50/0.46 % (3647308)Time elapsed: 0.037 s
% 0.50/0.46 % (3647308)Peak memory usage: 11 MB
% 0.50/0.46 % (3647308)Instructions burned: 86 (million)
% 0.50/0.46 % (3647324)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=906622687:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.50/0.46 % (3647326)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=386378720: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)
% 0.50/0.46 % (3647328)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2735401992:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.50/0.46 % (3647326)Instruction limit reached!
% 0.50/0.46 % (3647326)------------------------------
% 0.50/0.46 % (3647326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.46 % (3647326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.46 % (3647326)CaDiCaL version: 2.1.3
% 0.50/0.46 % (3647326)Termination reason: Instruction limit
% 0.50/0.46 % (3647326)Termination phase: shuffling
% 0.50/0.46 % (3647326)Time elapsed: 0.001 s
% 0.50/0.46 % (3647326)Peak memory usage: 10 MB
% 0.50/0.46 % (3647326)Instructions burned: 5 (million)
% 0.50/0.46 % (3647324)Instruction limit reached!
% 0.50/0.46 % (3647324)------------------------------
% 0.50/0.46 % (3647324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.46 % (3647324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.46 % (3647324)CaDiCaL version: 2.1.3
% 0.50/0.46 % (3647324)Termination reason: Instruction limit
% 0.50/0.46 % (3647324)Termination phase: shuffling
% 0.50/0.46 % (3647324)Time elapsed: 0.008 s
% 0.50/0.46 % (3647324)Peak memory usage: 10 MB
% 0.50/0.46 % (3647324)Instructions burned: 15 (million)
% 0.50/0.46 % (3647329)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2036303551:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.50/0.46 % (3647330)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3122550889:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.50/0.46 % (3647334)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
% 0.50/0.46 % (3647334)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.50/0.46 % (3647289) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3647281-3647289"...
% 0.50/0.46 % (3647334)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=3119901572:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.50/0.46 % (3647289)...printing done.
% 0.50/0.46 % (3647328)Instruction limit reached!
% 0.50/0.46 % (3647328)------------------------------
% 0.50/0.46 % (3647328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.46 % (3647328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.46 % (3647328)CaDiCaL version: 2.1.3
% 0.50/0.46 % (3647328)Termination reason: Instruction limit
% 0.50/0.46 % (3647328)Termination phase: Property scanning
% 0.50/0.46 % (3647328)Time elapsed: 0.013 s
% 0.50/0.46 % (3647328)Peak memory usage: 10 MB
% 0.50/0.46 % (3647328)Instructions burned: 28 (million)
% 0.50/0.46 % (3647329)Instruction limit reached!
% 0.50/0.46 % (3647329)------------------------------
% 0.50/0.46 % (3647329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.46 % (3647329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.46 % (3647329)CaDiCaL version: 2.1.3
% 0.50/0.46 % (3647329)Termination reason: Instruction limit
% 0.50/0.46 % (3647329)Termination phase: Property scanning
% 0.50/0.46 % (3647329)Time elapsed: 0.011 s
% 0.50/0.46 % (3647329)Peak memory usage: 10 MB
% 0.50/0.46 % (3647329)Instructions burned: 24 (million)
% 0.50/0.46 % (3647334)Instruction limit reached!
% 0.50/0.46 % (3647334)------------------------------
% 0.50/0.46 % (3647334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.46 % (3647334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.46 % (3647334)CaDiCaL version: 2.1.3
% 0.50/0.46 % (3647334)Termination reason: Instruction limit
% 0.50/0.46 % (3647334)Termination phase: shuffling
% 0.50/0.46 % (3647334)Time elapsed: 0.003 s
% 0.50/0.46 % (3647334)Peak memory usage: 10 MB
% 0.50/0.46 % (3647334)Instructions burned: 15 (million)
% 0.50/0.46 % (3647289)Refutation found. Thanks to Tanya!
% 0.50/0.46 % SZS status Theorem for theBenchmark
% 0.50/0.46 % SZS output start Proof for theBenchmark
% 0.50/0.46 thf(type_def_5, type, poly: $tType > $tType).
% 0.50/0.46 thf(type_def_6, type, real: $tType).
% 0.50/0.46 thf(type_def_7, type, set: $tType > $tType).
% 0.50/0.46 thf(type_def_8, type, nat: $tType).
% 0.50/0.46 thf(type_def_9, type, int: $tType).
% 0.50/0.46 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.50/0.46 thf(func_def_0, type, ab_group_add: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_1, type, idom: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_2, type, one: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_3, type, zero: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_4, type, power: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_5, type, field: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_6, type, ring_1: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_7, type, ring_char_0: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_8, type, comm_ring: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_9, type, group_add: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_10, type, semiring_1: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_11, type, comm_ring_1: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_12, type, idom_divide: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_13, type, monoid_mult: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_14, type, field_char_0: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_15, type, division_ring: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_16, type, field_abs_sgn: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_17, type, comm_semiring_0: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_18, type, comm_semiring_1: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_19, type, linordered_idom: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_20, type, linordered_field: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_21, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_22, type, linordered_semidom: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_23, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_24, type, ring_n68954251visors: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_25, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_26, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_27, type, ordere142940540dd_abs: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_28, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_29, type, semiri134348788visors: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_30, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.50/0.46 thf(func_def_31, type, abs_abs: !>[X0: $tType]:((X0 > X0))).
% 0.50/0.46 thf(func_def_32, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.50/0.46 thf(func_def_33, type, one_one: !>[X0: $tType]:(X0)).
% 0.50/0.46 thf(func_def_34, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.50/0.46 thf(func_def_35, type, ring_1_Ints: !>[X0: $tType]:(set @ X0)).
% 0.50/0.46 thf(func_def_36, type, ring_1_of_int: !>[X0: $tType]:((int > X0))).
% 0.50/0.46 thf(func_def_37, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.50/0.46 thf(func_def_38, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.50/0.46 thf(func_def_39, type, algebraic: !>[X0: $tType]:((X0 > $o))).
% 0.50/0.46 thf(func_def_40, type, degree: !>[X0: $tType]:((poly @ X0 > nat))).
% 0.50/0.46 thf(func_def_41, type, poly2: !>[X0: $tType]:((poly @ X0 > X0 > X0))).
% 0.50/0.46 thf(func_def_42, type, coeff: !>[X0: $tType]:((poly @ X0 > nat > X0))).
% 0.50/0.46 thf(func_def_43, type, power_power: !>[X0: $tType]:((X0 > nat > X0))).
% 0.50/0.46 thf(func_def_44, type, field_char_0_Rats: !>[X0: $tType]:(set @ X0)).
% 0.50/0.46 thf(func_def_45, type, divide_divide: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.50/0.46 thf(func_def_46, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.50/0.46 thf(func_def_47, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.50/0.46 thf(func_def_48, type, a: real).
% 0.50/0.46 thf(func_def_49, type, m: real).
% 0.50/0.46 thf(func_def_50, type, a2: int).
% 0.50/0.46 thf(func_def_51, type, b: int).
% 0.50/0.46 thf(func_def_52, type, n: nat).
% 0.50/0.46 thf(func_def_53, type, p: poly @ real).
% 0.50/0.46 thf(func_def_54, type, roots: set @ real).
% 0.50/0.46 thf(func_def_55, type, thesis: $o).
% 0.50/0.46 thf(func_def_56, type, x: real).
% 0.50/0.46 thf(func_def_60, type, db0: !>[X0: $tType]:(X0)).
% 0.50/0.46 thf(func_def_61, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.50/0.46 thf(func_def_62, type, db1: !>[X0: $tType]:(X0)).
% 0.50/0.46 thf(func_def_63, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.50/0.46 thf(func_def_64, type, vAND: ($o > $o > $o)).
% 0.50/0.46 thf(func_def_65, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.50/0.46 thf(func_def_66, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.50/0.46 thf(func_def_67, type, vNOT: ($o > $o)).
% 0.50/0.46 thf(func_def_68, type, db2: !>[X0: $tType]:(X0)).
% 0.50/0.46 thf(func_def_69, type, sK0: (poly @ real > real > real > real)).
% 0.50/0.46 thf(func_def_70, type, sK1: !>[X0: $tType]:((X0 > X0))).
% 0.50/0.46 thf(func_def_71, type, sK2: !>[X0: $tType]:((poly @ X0 > poly @ X0 > nat))).
% 0.50/0.46 thf(func_def_72, type, sK3: !>[X0: $tType]:((poly @ X0 > nat > nat))).
% 0.50/0.46 thf(func_def_73, type, sK4: !>[X0: $tType]:((X0 > int))).
% 0.50/0.46 thf(func_def_74, type, sK5: !>[X0: $tType]:((poly @ X0 > X0))).
% 0.50/0.46 thf(func_def_75, type, sK6: (poly @ real > real)).
% 0.50/0.46 thf(func_def_76, type, sK7: !>[X0: $tType]:((X0 > X0))).
% 0.50/0.46 thf(func_def_77, type, sK8: !>[X0: $tType]:((X0 > poly @ X0))).
% 0.50/0.46 thf(func_def_78, type, sK9: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.50/0.46 thf(func_def_79, type, sK10: !>[X0: $tType]:((nat > poly @ X0 > nat))).
% 0.50/0.46 thf(func_def_80, type, sK11: (poly @ real > nat)).
% 0.50/0.46 thf(func_def_81, type, sK12: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.50/0.46 thf(func_def_82, type, sK13: !>[X0: $tType]:(((X0 > $o) > int))).
% 0.50/0.46 thf(func_def_83, type, sK14: (real > poly @ real > real > real)).
% 0.50/0.46 thf(func_def_84, type, sK15: !>[X0: $tType]:((poly @ X0 > nat))).
% 0.50/0.46 thf(func_def_85, type, sK16: (real > nat > int)).
% 0.50/0.46 thf(func_def_86, type, sK17: (real > nat > int)).
% 0.50/0.46 thf(func_def_87, type, sK18: poly @ real).
% 0.50/0.46 thf(func_def_88, type, sK19: (real > int)).
% 0.50/0.46 thf(func_def_89, type, sK20: (real > int)).
% 0.50/0.46 thf(func_def_91, type, sK22: !>[X0: $tType]:((poly @ X0 > poly @ X0 > X0))).
% 0.50/0.46 thf(f3,axiom,(
% 0.50/0.46 ! [X0 : nat] : (member @ real @ (coeff @ real @ p @ X0) @ ring_1_Ints @ real)),
% 0.50/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_p_I1_J)).
% 0.50/0.46 thf(f4,axiom,(
% 0.50/0.46 (ord_less @ int @ zero_zero @ int @ b)),
% 0.50/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_b)).
% 0.50/0.46 thf(f6,axiom,(
% 0.50/0.46 (((poly2 @ real @ p @ (divide_divide @ real @ (ring_1_of_int @ real @ a2) @ (ring_1_of_int @ real @ b)))) != zero_zero @ real)),
% 0.50/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_no__root)).
% 0.50/0.46 thf(f76,axiom,(
% 0.50/0.46 ! [X0 : poly @ real,X2 : int,X1 : int] : (! [X3 : nat] : (member @ real @ (coeff @ real @ X0 @ X3) @ ring_1_Ints @ real) => ((ord_less @ int @ zero_zero @ int @ X1) => ((((poly2 @ real @ X0 @ (divide_divide @ real @ (ring_1_of_int @ real @ X2) @ (ring_1_of_int @ real @ X1)))) != zero_zero @ real) => (ord_less_eq @ real @ (divide_divide @ real @ one_one @ real @ (power_power @ real @ (ring_1_of_int @ real @ X1) @ (degree @ real @ X0))) @ (abs_abs @ real @ (poly2 @ real @ X0 @ (divide_divide @ real @ (ring_1_of_int @ real @ X2) @ (ring_1_of_int @ real @ X1))))))))),
% 0.50/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_int__poly__rat__no__root__ge)).
% 0.50/0.46 thf(f346,conjecture,(
% 0.50/0.46 (ord_less_eq @ real @ (divide_divide @ real @ one_one @ real @ (power_power @ real @ (ring_1_of_int @ real @ b) @ (degree @ real @ p))) @ (abs_abs @ real @ (poly2 @ real @ p @ (divide_divide @ real @ (ring_1_of_int @ real @ a2) @ (ring_1_of_int @ real @ b)))))),
% 0.50/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.50/0.46 thf(f347,negated_conjecture,(
% 0.50/0.46 ~(ord_less_eq @ real @ (divide_divide @ real @ one_one @ real @ (power_power @ real @ (ring_1_of_int @ real @ b) @ (degree @ real @ p))) @ (abs_abs @ real @ (poly2 @ real @ p @ (divide_divide @ real @ (ring_1_of_int @ real @ a2) @ (ring_1_of_int @ real @ b)))))),
% 0.50/0.46 inference(negated_conjecture,[status(cth)],[f346])).
% 0.50/0.46 thf(f410,plain,(
% 0.50/0.46 (ord_less @ int @ zero_zero @ int @ b)),
% 0.50/0.46 inference(rectify,[],[f4])).
% 0.50/0.46 thf(f411,plain,(
% 0.50/0.46 (((ord_less @ int @ zero_zero @ int @ b)) = $true)),
% 0.50/0.46 inference(fool_elimination,[],[f410])).
% 0.50/0.46 thf(f693,plain,(
% 0.50/0.46 ! [X0 : nat] : (member @ real @ (coeff @ real @ p @ X0) @ ring_1_Ints @ real)),
% 0.50/0.46 inference(rectify,[],[f3])).
% 0.50/0.46 thf(f694,plain,(
% 0.50/0.46 ! [X0 : nat] : (((member @ real @ (coeff @ real @ p @ X0) @ ring_1_Ints @ real)) = $true)),
% 0.50/0.46 inference(fool_elimination,[],[f693])).
% 0.50/0.46 thf(f899,plain,(
% 0.50/0.46 ~(ord_less_eq @ real @ (divide_divide @ real @ one_one @ real @ (power_power @ real @ (ring_1_of_int @ real @ b) @ (degree @ real @ p))) @ (abs_abs @ real @ (poly2 @ real @ p @ (divide_divide @ real @ (ring_1_of_int @ real @ a2) @ (ring_1_of_int @ real @ b)))))),
% 0.50/0.46 inference(rectify,[],[f347])).
% 0.50/0.46 thf(f900,plain,(
% 0.50/0.46 ~ (((ord_less_eq @ real @ (divide_divide @ real @ one_one @ real @ (power_power @ real @ (ring_1_of_int @ real @ b) @ (degree @ real @ p))) @ (abs_abs @ real @ (poly2 @ real @ p @ (divide_divide @ real @ (ring_1_of_int @ real @ a2) @ (ring_1_of_int @ real @ b)))))) = $true)),
% 0.50/0.46 inference(fool_elimination,[],[f899])).
% 0.50/0.46 thf(f927,plain,(
% 0.50/0.46 ! [X0 : poly @ real,X1 : int,X2 : int] : (! [X3 : nat] : (member @ real @ (coeff @ real @ X0 @ X3) @ ring_1_Ints @ real) => ((ord_less @ int @ zero_zero @ int @ X2) => ((zero_zero @ real != ((poly2 @ real @ X0 @ (divide_divide @ real @ (ring_1_of_int @ real @ X1) @ (ring_1_of_int @ real @ X2))))) => (ord_less_eq @ real @ (divide_divide @ real @ one_one @ real @ (power_power @ real @ (ring_1_of_int @ real @ X2) @ (degree @ real @ X0))) @ (abs_abs @ real @ (poly2 @ real @ X0 @ (divide_divide @ real @ (ring_1_of_int @ real @ X1) @ (ring_1_of_int @ real @ X2))))))))),
% 0.50/0.46 inference(rectify,[],[f76])).
% 0.50/0.46 thf(f928,plain,(
% 0.50/0.46 ! [X2 : int,X0 : poly @ real,X1 : int] : (! [X3 : nat] : (((member @ real @ (coeff @ real @ X0 @ X3) @ ring_1_Ints @ real)) = $true) => ((((ord_less @ int @ zero_zero @ int @ X2)) = $true) => ((zero_zero @ real != ((poly2 @ real @ X0 @ (divide_divide @ real @ (ring_1_of_int @ real @ X1) @ (ring_1_of_int @ real @ X2))))) => ($true = ((ord_less_eq @ real @ (divide_divide @ real @ one_one @ real @ (power_power @ real @ (ring_1_of_int @ real @ X2) @ (degree @ real @ X0))) @ (abs_abs @ real @ (poly2 @ real @ X0 @ (divide_divide @ real @ (ring_1_of_int @ real @ X1) @ (ring_1_of_int @ real @ X2))))))))))),
% 0.50/0.46 inference(fool_elimination,[],[f927])).
% 0.50/0.46 thf(f1032,plain,(
% 0.50/0.46 (((ord_less_eq @ real @ (divide_divide @ real @ one_one @ real @ (power_power @ real @ (ring_1_of_int @ real @ b) @ (degree @ real @ p))) @ (abs_abs @ real @ (poly2 @ real @ p @ (divide_divide @ real @ (ring_1_of_int @ real @ a2) @ (ring_1_of_int @ real @ b)))))) != $true)),
% 0.50/0.46 inference(flattening,[],[f900])).
% 0.50/0.46 thf(f1252,plain,(
% 0.50/0.46 ! [X2 : int,X0 : poly @ real,X1 : int] : (((($true = ((ord_less_eq @ real @ (divide_divide @ real @ one_one @ real @ (power_power @ real @ (ring_1_of_int @ real @ X2) @ (degree @ real @ X0))) @ (abs_abs @ real @ (poly2 @ real @ X0 @ (divide_divide @ real @ (ring_1_of_int @ real @ X1) @ (ring_1_of_int @ real @ X2))))))) | (zero_zero @ real = ((poly2 @ real @ X0 @ (divide_divide @ real @ (ring_1_of_int @ real @ X1) @ (ring_1_of_int @ real @ X2)))))) | (((ord_less @ int @ zero_zero @ int @ X2)) != $true)) | ? [X3 : nat] : (((member @ real @ (coeff @ real @ X0 @ X3) @ ring_1_Ints @ real)) != $true))),
% 0.50/0.46 inference(ennf_transformation,[],[f928])).
% 0.50/0.46 thf(f1253,plain,(
% 0.50/0.46 ! [X0 : poly @ real,X1 : int,X2 : int] : ((zero_zero @ real = ((poly2 @ real @ X0 @ (divide_divide @ real @ (ring_1_of_int @ real @ X1) @ (ring_1_of_int @ real @ X2))))) | ? [X3 : nat] : (((member @ real @ (coeff @ real @ X0 @ X3) @ ring_1_Ints @ real)) != $true) | ($true = ((ord_less_eq @ real @ (divide_divide @ real @ one_one @ real @ (power_power @ real @ (ring_1_of_int @ real @ X2) @ (degree @ real @ X0))) @ (abs_abs @ real @ (poly2 @ real @ X0 @ (divide_divide @ real @ (ring_1_of_int @ real @ X1) @ (ring_1_of_int @ real @ X2))))))) | (((ord_less @ int @ zero_zero @ int @ X2)) != $true))),
% 0.50/0.46 inference(flattening,[],[f1252])).
% 0.50/0.46 thf(f1460,plain,(
% 0.50/0.46 ! [X0 : poly @ real,X1 : int,X2 : int] : ((zero_zero @ real = ((poly2 @ real @ X0 @ (divide_divide @ real @ (ring_1_of_int @ real @ X1) @ (ring_1_of_int @ real @ X2))))) | ($true != ((member @ real @ (coeff @ real @ X0 @ (sK11 @ X0)) @ ring_1_Ints @ real))) | ($true = ((ord_less_eq @ real @ (divide_divide @ real @ one_one @ real @ (power_power @ real @ (ring_1_of_int @ real @ X2) @ (degree @ real @ X0))) @ (abs_abs @ real @ (poly2 @ real @ X0 @ (divide_divide @ real @ (ring_1_of_int @ real @ X1) @ (ring_1_of_int @ real @ X2))))))) | (((ord_less @ int @ zero_zero @ int @ X2)) != $true))),
% 0.50/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X2 @ X1 @ X0)],[f1253])).
% 0.50/0.46 thf(f1682,plain,(
% 0.50/0.46 (zero_zero @ real != ((poly2 @ real @ p @ (divide_divide @ real @ (ring_1_of_int @ real @ a2) @ (ring_1_of_int @ real @ b)))))),
% 0.50/0.46 inference(cnf_transformation,[],[f6])).
% 0.50/0.46 thf(f1790,plain,(
% 0.50/0.46 ( ! [X2 : int,X0 : poly @ real,X1 : int] : (($true = ((ord_less_eq @ real @ (divide_divide @ real @ one_one @ real @ (power_power @ real @ (ring_1_of_int @ real @ X2) @ (degree @ real @ X0))) @ (abs_abs @ real @ (poly2 @ real @ X0 @ (divide_divide @ real @ (ring_1_of_int @ real @ X1) @ (ring_1_of_int @ real @ X2))))))) | (((ord_less @ int @ zero_zero @ int @ X2)) != $true) | (zero_zero @ real = ((poly2 @ real @ X0 @ (divide_divide @ real @ (ring_1_of_int @ real @ X1) @ (ring_1_of_int @ real @ X2))))) | ($true != ((member @ real @ (coeff @ real @ X0 @ (sK11 @ X0)) @ ring_1_Ints @ real)))) )),
% 0.50/0.46 inference(cnf_transformation,[],[f1460])).
% 0.50/0.46 thf(f1803,plain,(
% 0.50/0.46 ( ! [X0 : nat] : ((((member @ real @ (coeff @ real @ p @ X0) @ ring_1_Ints @ real)) = $true)) )),
% 0.50/0.46 inference(cnf_transformation,[],[f694])).
% 0.50/0.46 thf(f1948,plain,(
% 0.50/0.46 (((ord_less_eq @ real @ (divide_divide @ real @ one_one @ real @ (power_power @ real @ (ring_1_of_int @ real @ b) @ (degree @ real @ p))) @ (abs_abs @ real @ (poly2 @ real @ p @ (divide_divide @ real @ (ring_1_of_int @ real @ a2) @ (ring_1_of_int @ real @ b)))))) != $true)),
% 0.50/0.46 inference(cnf_transformation,[],[f1032])).
% 0.50/0.46 thf(f1996,plain,(
% 0.50/0.46 (((ord_less @ int @ zero_zero @ int @ b)) = $true)),
% 0.50/0.46 inference(cnf_transformation,[],[f411])).
% 0.50/0.46 thf(f2254,definition,(
% 0.50/0.46 spl21_23 <=> (((ord_less_eq @ real @ (divide_divide @ real @ one_one @ real @ (power_power @ real @ (ring_1_of_int @ real @ b) @ (degree @ real @ p))) @ (abs_abs @ real @ (poly2 @ real @ p @ (divide_divide @ real @ (ring_1_of_int @ real @ a2) @ (ring_1_of_int @ real @ b)))))) = $true)),
% 0.50/0.46 introduced(definition,[new_symbols(definition,[spl21_23])],[avatar_definition])).
% 0.50/0.46 thf(f2256,plain,(
% 0.50/0.46 (((ord_less_eq @ real @ (divide_divide @ real @ one_one @ real @ (power_power @ real @ (ring_1_of_int @ real @ b) @ (degree @ real @ p))) @ (abs_abs @ real @ (poly2 @ real @ p @ (divide_divide @ real @ (ring_1_of_int @ real @ a2) @ (ring_1_of_int @ real @ b)))))) != $true) | spl21_23),
% 0.50/0.46 inference(avatar_component_clause,[],[f2254])).
% 0.50/0.46 thf(f2257,plain,(
% 0.50/0.46 ~spl21_23),
% 0.50/0.46 inference(avatar_split_clause,[],[f1948,f2254])).
% 0.50/0.46 thf(f2309,definition,(
% 0.50/0.46 spl21_34 <=> (zero_zero @ real = ((poly2 @ real @ p @ (divide_divide @ real @ (ring_1_of_int @ real @ a2) @ (ring_1_of_int @ real @ b)))))),
% 0.50/0.46 introduced(definition,[new_symbols(definition,[spl21_34])],[avatar_definition])).
% 0.50/0.46 thf(f2311,plain,(
% 0.50/0.46 (zero_zero @ real != ((poly2 @ real @ p @ (divide_divide @ real @ (ring_1_of_int @ real @ a2) @ (ring_1_of_int @ real @ b))))) | spl21_34),
% 0.50/0.46 inference(avatar_component_clause,[],[f2309])).
% 0.50/0.46 thf(f2312,plain,(
% 0.50/0.46 ~spl21_34),
% 0.50/0.46 inference(avatar_split_clause,[],[f1682,f2309])).
% 0.50/0.46 thf(f2369,definition,(
% 0.50/0.46 spl21_46 <=> (((ord_less @ int @ zero_zero @ int @ b)) = $true)),
% 0.50/0.46 introduced(definition,[new_symbols(definition,[spl21_46])],[avatar_definition])).
% 0.50/0.46 thf(f2371,plain,(
% 0.50/0.46 (((ord_less @ int @ zero_zero @ int @ b)) = $true) | ~spl21_46),
% 0.50/0.46 inference(avatar_component_clause,[],[f2369])).
% 0.50/0.46 thf(f2372,plain,(
% 0.50/0.46 spl21_46),
% 0.50/0.46 inference(avatar_split_clause,[],[f1996,f2369])).
% 0.50/0.46 thf(f3348,plain,(
% 0.50/0.46 (((ord_less @ int @ zero_zero @ int @ b)) != $true) | (zero_zero @ real = ((poly2 @ real @ p @ (divide_divide @ real @ (ring_1_of_int @ real @ a2) @ (ring_1_of_int @ real @ b))))) | ($true != $true) | ($true != ((member @ real @ (coeff @ real @ p @ (sK11 @ p)) @ ring_1_Ints @ real))) | spl21_23),
% 0.50/0.46 inference(superposition,[],[f2256,f1790])).
% 0.50/0.46 thf(f3349,plain,(
% 0.50/0.46 (((ord_less @ int @ zero_zero @ int @ b)) != $true) | ($true != ((member @ real @ (coeff @ real @ p @ (sK11 @ p)) @ ring_1_Ints @ real))) | (zero_zero @ real = ((poly2 @ real @ p @ (divide_divide @ real @ (ring_1_of_int @ real @ a2) @ (ring_1_of_int @ real @ b))))) | spl21_23),
% 0.50/0.46 inference(trivial_inequality_removal,[],[f3348])).
% 0.50/0.46 thf(f3355,plain,(
% 0.50/0.46 (zero_zero @ real = ((poly2 @ real @ p @ (divide_divide @ real @ (ring_1_of_int @ real @ a2) @ (ring_1_of_int @ real @ b))))) | ($true != ((member @ real @ (coeff @ real @ p @ (sK11 @ p)) @ ring_1_Ints @ real))) | (spl21_23 | ~spl21_46)),
% 0.50/0.46 inference(forward_subsumption_resolution,[],[f3349,f2371])).
% 0.50/0.46 thf(f3384,plain,(
% 0.50/0.46 ($true != ((member @ real @ (coeff @ real @ p @ (sK11 @ p)) @ ring_1_Ints @ real))) | (spl21_23 | spl21_34 | ~spl21_46)),
% 0.50/0.46 inference(forward_subsumption_resolution,[],[f3355,f2311])).
% 0.50/0.46 thf(f3385,plain,(
% 0.50/0.46 $false | (spl21_23 | spl21_34 | ~spl21_46)),
% 0.50/0.46 inference(forward_subsumption_resolution,[],[f3384,f1803])).
% 0.50/0.46 thf(f3386,plain,(
% 0.50/0.46 spl21_23 | spl21_34 | ~spl21_46),
% 0.50/0.46 inference(avatar_contradiction_clause,[],[f3385])).
% 0.50/0.46 cnf(s22, plain, ~spl21_23, inference(sat_conversion,[],[f2257])).
% 0.50/0.46 cnf(s33, plain, ~spl21_34, inference(sat_conversion,[],[f2312])).
% 0.50/0.46 cnf(s45, plain, spl21_46, inference(sat_conversion,[],[f2372])).
% 0.50/0.46 cnf(s181, plain, spl21_23 | spl21_34 | ~spl21_46, inference(sat_conversion,[],[f3386])).
% 0.50/0.46 cnf(s211, plain, spl21_23, inference(rat,[],[s181,s45,s33])).
% 0.50/0.46 cnf(s212, plain, $false, inference(rat,[],[s22,s211])).
% 0.50/0.46 thf(f3387,plain,(
% 0.50/0.46 $false),
% 0.50/0.46 inference(avatar_sat_refutation,[],[s212])).
% 0.50/0.46 % SZS output end Proof for theBenchmark
% 0.50/0.46 % (3647289)------------------------------
% 0.50/0.46 % (3647289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.46 % (3647289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.46 % (3647289)CaDiCaL version: 2.1.3
% 0.50/0.46 % (3647289)Termination reason: Refutation
% 0.50/0.46 % (3647289)Time elapsed: 0.117 s
% 0.50/0.46 % (3647289)Peak memory usage: 15 MB
% 0.50/0.46 % (3647289)Instructions burned: 214 (million)
% 0.50/0.46 % (3647281)Success in time 0.17 s
% 0.50/0.46 % Vampire exiting
%------------------------------------------------------------------------------