%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP196^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:08:46 AM UTC 2026
% Result : Theorem 0.31s 0.45s
% Output : Refutation 0.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP196^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n001.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 20:16:21 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.21/0.28 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
% 0.31/0.45 % (1758634)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.31/0.45 % (1758641)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=644808521:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.31/0.45 % (1758641)Instruction limit reached!
% 0.31/0.45 % (1758641)------------------------------
% 0.31/0.45 % (1758641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (1758641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (1758641)CaDiCaL version: 2.1.3
% 0.31/0.45 % (1758641)Termination reason: Instruction limit
% 0.31/0.45 % (1758641)Termination phase: shuffling
% 0.31/0.45 % (1758641)Time elapsed: 0.002 s
% 0.31/0.45 % (1758641)Peak memory usage: 10 MB
% 0.31/0.45 % (1758641)Instructions burned: 7 (million)
% 0.31/0.45 % (1758640)lrs+10_16_si=on:nwc=1.5:random_seed=4023460876:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.31/0.45 % (1758639)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3536712425:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.31/0.45 % (1758642)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=2620084399: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)
% 0.31/0.45 % (1758647)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2740106404:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.31/0.45 % (1758640)Instruction limit reached!
% 0.31/0.45 % (1758640)------------------------------
% 0.31/0.45 % (1758640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (1758640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (1758640)CaDiCaL version: 2.1.3
% 0.31/0.45 % (1758640)Termination reason: Instruction limit
% 0.31/0.45 % (1758640)Termination phase: shuffling
% 0.31/0.45 % (1758640)Time elapsed: 0.009 s
% 0.31/0.45 % (1758640)Peak memory usage: 10 MB
% 0.31/0.45 % (1758640)Instructions burned: 19 (million)
% 0.31/0.45 % (1758647)Instruction limit reached!
% 0.31/0.45 % (1758647)------------------------------
% 0.31/0.45 % (1758647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (1758647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (1758647)CaDiCaL version: 2.1.3
% 0.31/0.45 % (1758647)Termination reason: Instruction limit
% 0.31/0.45 % (1758647)Termination phase: shuffling
% 0.31/0.45 % (1758647)Time elapsed: 0.003 s
% 0.31/0.45 % (1758647)Peak memory usage: 10 MB
% 0.31/0.45 % (1758647)Instructions burned: 11 (million)
% 0.31/0.45 % (1758643)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2371226686:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.31/0.45 % (1758645)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.31/0.45 % (1758645)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
% 0.31/0.45 % (1758644)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=378029158:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.31/0.45 % (1758645)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=2468796092:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.31/0.45 % (1758653)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.31/0.45 % (1758652)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2529143003:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.31/0.45 % (1758653)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2753983405:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.31/0.45 % (1758652)Instruction limit reached!
% 0.31/0.45 % (1758652)------------------------------
% 0.31/0.45 % (1758652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (1758652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (1758652)CaDiCaL version: 2.1.3
% 0.31/0.45 % (1758652)Termination reason: Instruction limit
% 0.31/0.45 % (1758652)Termination phase: shuffling
% 0.31/0.45 % (1758652)Time elapsed: 0.003 s
% 0.31/0.45 % (1758652)Peak memory usage: 10 MB
% 0.31/0.45 % (1758652)Instructions burned: 5 (million)
% 0.31/0.45 % (1758643)Instruction limit reached!
% 0.31/0.45 % (1758643)------------------------------
% 0.31/0.45 % (1758643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (1758643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (1758643)CaDiCaL version: 2.1.3
% 0.31/0.45 % (1758643)Termination reason: Instruction limit
% 0.31/0.45 % (1758643)Termination phase: shuffling
% 0.31/0.45 % (1758643)Time elapsed: 0.020 s
% 0.31/0.45 % (1758643)Peak memory usage: 10 MB
% 0.31/0.45 % (1758643)Instructions burned: 24 (million)
% 0.31/0.45 % (1758653)Instruction limit reached!
% 0.31/0.45 % (1758653)------------------------------
% 0.31/0.45 % (1758653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (1758653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (1758653)CaDiCaL version: 2.1.3
% 0.31/0.45 % (1758653)Termination reason: Instruction limit
% 0.31/0.45 % (1758653)Termination phase: shuffling
% 0.31/0.45 % (1758653)Time elapsed: 0.004 s
% 0.31/0.45 % (1758653)Peak memory usage: 10 MB
% 0.31/0.45 % (1758653)Instructions burned: 8 (million)
% 0.31/0.45 % (1758660)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
% 0.31/0.45 % (1758639)Instruction limit reached!
% 0.31/0.45 % (1758639)------------------------------
% 0.31/0.45 % (1758639)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (1758639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (1758660)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.31/0.45 % (1758639)CaDiCaL version: 2.1.3
% 0.31/0.45 % (1758639)Termination reason: Instruction limit
% 0.31/0.45 % (1758639)Termination phase: Property scanning
% 0.31/0.45 % (1758639)Time elapsed: 0.043 s
% 0.31/0.45 % (1758639)Peak memory usage: 12 MB
% 0.31/0.45 % (1758639)Instructions burned: 89 (million)
% 0.31/0.45 % (1758660)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2080980997:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.31/0.45 % (1758659)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=74615016:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.31/0.45 % (1758660)Instruction limit reached!
% 0.31/0.45 % (1758660)------------------------------
% 0.31/0.45 % (1758660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (1758660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (1758660)CaDiCaL version: 2.1.3
% 0.31/0.45 % (1758660)Termination reason: Instruction limit
% 0.31/0.45 % (1758660)Termination phase: shuffling
% 0.31/0.45 % (1758660)Time elapsed: 0.007 s
% 0.31/0.45 % (1758660)Peak memory usage: 10 MB
% 0.31/0.45 % (1758660)Instructions burned: 29 (million)
% 0.31/0.45 % (1758661)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=862531031:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.31/0.45 % (1758659)Instruction limit reached!
% 0.31/0.45 % (1758659)------------------------------
% 0.31/0.45 % (1758659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (1758659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (1758659)CaDiCaL version: 2.1.3
% 0.31/0.45 % (1758659)Termination reason: Instruction limit
% 0.31/0.45 % (1758659)Termination phase: shuffling
% 0.31/0.45 % (1758659)Time elapsed: 0.007 s
% 0.31/0.45 % (1758659)Peak memory usage: 10 MB
% 0.31/0.45 % (1758659)Instructions burned: 13 (million)
% 0.31/0.45 % (1758665)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.31/0.45 % (1758662)lrs+10_1_si=on:cs=on:random_seed=2564151167:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.31/0.45 % (1758665)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=3658538243:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.31/0.45 % (1758665)Instruction limit reached!
% 0.31/0.45 % (1758665)------------------------------
% 0.31/0.45 % (1758665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (1758665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (1758665)CaDiCaL version: 2.1.3
% 0.31/0.45 % (1758665)Termination reason: Instruction limit
% 0.31/0.45 % (1758665)Termination phase: shuffling
% 0.31/0.45 % (1758665)Time elapsed: 0.001 s
% 0.31/0.45 % (1758665)Peak memory usage: 10 MB
% 0.31/0.45 % (1758665)Instructions burned: 6 (million)
% 0.31/0.45 % (1758662)Instruction limit reached!
% 0.31/0.45 % (1758662)------------------------------
% 0.31/0.45 % (1758662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (1758662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (1758662)CaDiCaL version: 2.1.3
% 0.31/0.45 % (1758662)Termination reason: Instruction limit
% 0.31/0.45 % (1758662)Termination phase: shuffling
% 0.31/0.45 % (1758662)Time elapsed: 0.004 s
% 0.31/0.45 % (1758662)Peak memory usage: 10 MB
% 0.31/0.45 % (1758662)Instructions burned: 8 (million)
% 0.31/0.45 % (1758644)Instruction limit reached!
% 0.31/0.45 % (1758644)------------------------------
% 0.31/0.45 % (1758644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (1758644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (1758644)CaDiCaL version: 2.1.3
% 0.31/0.45 % (1758644)Termination reason: Instruction limit
% 0.31/0.45 % (1758644)Termination phase: Preprocessing 3
% 0.31/0.45 % (1758644)Time elapsed: 0.053 s
% 0.31/0.45 % (1758644)Peak memory usage: 12 MB
% 0.31/0.45 % (1758644)Instructions burned: 76 (million)
% 0.31/0.45 % (1758670)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4118762810:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.31/0.45 % (1758667)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2076982914:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.31/0.45 % (1758671)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3131149741:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.31/0.45 % (1758642) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1758634-1758642"...
% 0.31/0.45 % (1758670) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1758634-1758670"...
% 0.31/0.45 % (1758670)...printing done.
% 0.31/0.45 % (1758672)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3868568089:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.31/0.45 % (1758642)...printing done.
% 0.31/0.45 % (1758670)Refutation found. Thanks to Tanya!
% 0.31/0.45 % SZS status Theorem for theBenchmark
% 0.31/0.45 % SZS output start Proof for theBenchmark
% 0.31/0.45 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.31/0.45 thf(type_def_6, type, poly: $tType > $tType).
% 0.31/0.45 thf(type_def_7, type, option: $tType > $tType).
% 0.31/0.45 thf(type_def_8, type, real: $tType).
% 0.31/0.45 thf(type_def_9, type, list: $tType > $tType).
% 0.31/0.45 thf(type_def_10, type, set: $tType > $tType).
% 0.31/0.45 thf(type_def_11, type, nat: $tType).
% 0.31/0.45 thf(type_def_12, type, sTfun: ($tType * $tType) > $tType).
% 0.31/0.45 thf(func_def_0, type, ab_group_add: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_1, type, linordered_idom: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_2, type, comm_semiring_0: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_3, type, type: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_4, type, size: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_5, type, ord: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_6, type, group_add: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_7, type, linorder: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_8, type, comm_semiring_1: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_9, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_10, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_11, type, bNF_Greatest_Shift: !>[X0: $tType]:((set @ list @ X0 > X0 > set @ list @ X0))).
% 0.31/0.45 thf(func_def_12, type, bNF_Greatest_Succ: !>[X0: $tType]:((set @ list @ X0 > list @ X0 > set @ X0))).
% 0.31/0.45 thf(func_def_13, type, bNF_Greatest_shift: !>[X0: $tType, X1: $tType]:(((list @ X0 > X1) > X0 > list @ X0 > X1))).
% 0.31/0.45 thf(func_def_14, type, times_times: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.31/0.45 thf(func_def_15, type, append: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 0.31/0.45 thf(func_def_16, type, arg_min_list: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > X0))).
% 0.31/0.45 thf(func_def_17, type, bind: !>[X0: $tType, X1: $tType]:((list @ X0 > (X0 > list @ X1) > list @ X1))).
% 0.31/0.45 thf(func_def_18, type, butlast: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.31/0.45 thf(func_def_19, type, concat: !>[X0: $tType]:((list @ list @ X0 > list @ X0))).
% 0.31/0.45 thf(func_def_20, type, enumerate: !>[X0: $tType]:((nat > list @ X0 > list @ product_prod @ nat @ X0))).
% 0.31/0.45 thf(func_def_21, type, foldr: !>[X0: $tType, X1: $tType]:(((X0 > X1 > X1) > list @ X0 > X1 > X1))).
% 0.31/0.45 thf(func_def_22, type, gen_length: !>[X0: $tType]:((nat > list @ X0 > nat))).
% 0.31/0.45 thf(func_def_23, type, insert: !>[X0: $tType]:((X0 > list @ X0 > list @ X0))).
% 0.31/0.45 thf(func_def_24, type, last: !>[X0: $tType]:((list @ X0 > X0))).
% 0.31/0.45 thf(func_def_25, type, lenlex: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0))).
% 0.31/0.45 thf(func_def_26, type, lex: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0))).
% 0.31/0.45 thf(func_def_27, type, lexord: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0))).
% 0.31/0.45 thf(func_def_28, type, cons: !>[X0: $tType]:((X0 > list @ X0 > list @ X0))).
% 0.31/0.45 thf(func_def_29, type, nil: !>[X0: $tType]:(list @ X0)).
% 0.31/0.45 thf(func_def_30, type, map: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1))).
% 0.31/0.45 thf(func_def_31, type, rec_list: !>[X0: $tType, X1: $tType]:((X0 > (X1 > list @ X1 > X0 > X0) > list @ X1 > X0))).
% 0.31/0.45 thf(func_def_32, type, list_ex: !>[X0: $tType]:(((X0 > $o) > list @ X0 > $o))).
% 0.31/0.45 thf(func_def_33, type, list_ex1: !>[X0: $tType]:(((X0 > $o) > list @ X0 > $o))).
% 0.31/0.45 thf(func_def_34, type, listrel: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ list @ X0 @ list @ X1))).
% 0.31/0.45 thf(func_def_35, type, listrel1: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0))).
% 0.31/0.45 thf(func_def_36, type, listrelp: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o))).
% 0.31/0.45 thf(func_def_37, type, map_filter: !>[X0: $tType, X1: $tType]:(((X0 > option @ X1) > list @ X0 > list @ X1))).
% 0.31/0.45 thf(func_def_38, type, map_tailrec_rev: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > list @ X1))).
% 0.31/0.45 thf(func_def_39, type, map_tailrec_rev_rel: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > $o))).
% 0.31/0.45 thf(func_def_40, type, maps: !>[X0: $tType, X1: $tType]:(((X0 > list @ X1) > list @ X0 > list @ X1))).
% 0.31/0.45 thf(func_def_41, type, member: !>[X0: $tType]:((list @ X0 > X0 > $o))).
% 0.31/0.45 thf(func_def_42, type, null: !>[X0: $tType]:((list @ X0 > $o))).
% 0.31/0.45 thf(func_def_43, type, lexordp_eq: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o))).
% 0.31/0.45 thf(func_def_44, type, ord_lexordp_eq: !>[X0: $tType]:((list @ X0 > list @ X0 > $o))).
% 0.31/0.45 thf(func_def_45, type, product: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > list @ product_prod @ X0 @ X1))).
% 0.31/0.45 thf(func_def_46, type, product_lists: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 0.31/0.45 thf(func_def_47, type, rotate: !>[X0: $tType]:((nat > list @ X0 > list @ X0))).
% 0.31/0.45 thf(func_def_48, type, rotate1: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.31/0.45 thf(func_def_49, type, splice: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 0.31/0.45 thf(func_def_50, type, subseqs: !>[X0: $tType]:((list @ X0 > list @ list @ X0))).
% 0.31/0.45 thf(func_def_51, type, zip: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > list @ product_prod @ X0 @ X1))).
% 0.31/0.45 thf(func_def_52, type, linorder_part: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1 > list @ X0 > product_prod @ list @ X0 @ product_prod @ list @ X0 @ list @ X0))).
% 0.31/0.45 thf(func_def_53, type, suc: (nat > nat)).
% 0.31/0.45 thf(func_def_54, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 0.31/0.45 thf(func_def_55, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.31/0.45 thf(func_def_56, type, plus_coeffs: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 0.31/0.45 thf(func_def_57, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.31/0.45 thf(func_def_58, type, irrefl: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 0.31/0.45 thf(func_def_59, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.31/0.45 thf(func_def_60, type, sturm_2060350619rm_seq: (list @ poly @ real > $o)).
% 0.31/0.45 thf(func_def_61, type, sturm_801371416rm_seq: (list @ poly @ real > poly @ real > $o)).
% 0.31/0.45 thf(func_def_62, type, sturm_1585582267axioms: (list @ poly @ real > poly @ real > $o)).
% 0.31/0.45 thf(func_def_63, type, accp: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > $o))).
% 0.31/0.45 thf(func_def_64, type, member2: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.31/0.45 thf(func_def_68, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.31/0.45 thf(func_def_69, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.31/0.45 thf(func_def_70, type, vAND: ($o > $o > $o)).
% 0.31/0.45 thf(func_def_71, type, db1: !>[X0: $tType]:(X0)).
% 0.31/0.45 thf(func_def_72, type, db0: !>[X0: $tType]:(X0)).
% 0.31/0.45 thf(func_def_73, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.31/0.45 thf(func_def_74, type, vOR: ($o > $o > $o)).
% 0.31/0.45 thf(func_def_75, type, vNOT: ($o > $o)).
% 0.31/0.45 thf(func_def_76, type, db2: !>[X0: $tType]:(X0)).
% 0.31/0.45 thf(func_def_77, type, db3: !>[X0: $tType]:(X0)).
% 0.31/0.45 thf(func_def_78, type, vIMP: ($o > $o > $o)).
% 0.31/0.45 thf(func_def_79, type, db6: !>[X0: $tType]:(X0)).
% 0.31/0.45 thf(func_def_80, type, db4: !>[X0: $tType]:(X0)).
% 0.31/0.45 thf(func_def_81, type, db5: !>[X0: $tType]:(X0)).
% 0.31/0.45 thf(func_def_82, type, sK0: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 0.31/0.45 thf(func_def_83, type, sK1: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_84, type, sK2: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 0.31/0.45 thf(func_def_85, type, sK3: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_86, type, sK4: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X0))).
% 0.31/0.45 thf(func_def_87, type, sK5: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_88, type, sK6: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X1))).
% 0.31/0.45 thf(func_def_89, type, sK7: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X1))).
% 0.31/0.45 thf(func_def_90, type, sK8: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X1))).
% 0.31/0.45 thf(func_def_91, type, sK9: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_92, type, sK10: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X0))).
% 0.31/0.45 thf(func_def_93, type, sK11: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X1))).
% 0.31/0.45 thf(func_def_94, type, sK12: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_95, type, sK13: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_96, type, sK14: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_97, type, sK15: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_98, type, sK16: !>[X0: $tType]:((list @ X0 > X0))).
% 0.31/0.45 thf(func_def_99, type, sK17: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.31/0.45 thf(func_def_100, type, sK18: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_101, type, sK19: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_102, type, sK20: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_103, type, sK21: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_104, type, sK22: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_105, type, sK23: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_106, type, sK24: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_107, type, sK25: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_108, type, sK26: !>[X0: $tType]:((list @ X0 > X0))).
% 0.31/0.45 thf(func_def_109, type, sK27: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.31/0.45 thf(func_def_110, type, sK28: !>[X0: $tType]:((list @ X0 > X0))).
% 0.31/0.45 thf(func_def_111, type, sK29: !>[X0: $tType]:((list @ X0 > X0))).
% 0.31/0.45 thf(func_def_112, type, sK30: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_113, type, sK31: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 0.31/0.45 thf(func_def_114, type, sK32: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_115, type, sK33: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_116, type, sK34: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_117, type, sK35: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 0.31/0.45 thf(func_def_118, type, sK36: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 0.31/0.45 thf(func_def_119, type, sK37: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.31/0.45 thf(func_def_120, type, sK38: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 0.31/0.45 thf(func_def_121, type, sK39: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 0.31/0.45 thf(func_def_122, type, sK40: !>[X0: $tType]:((list @ list @ X0 > X0))).
% 0.31/0.45 thf(func_def_123, type, sK41: !>[X0: $tType]:((list @ list @ X0 > list @ X0))).
% 0.31/0.45 thf(func_def_124, type, sK42: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_125, type, sK43: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_126, type, sK44: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_127, type, sK45: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_128, type, sK46: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > X1 > X0))).
% 0.31/0.45 thf(func_def_129, type, sK47: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > list @ X1))).
% 0.31/0.45 thf(func_def_130, type, sK48: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > X1))).
% 0.31/0.45 thf(func_def_131, type, sK49: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > X1 > X0))).
% 0.31/0.45 thf(func_def_132, type, sK50: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_133, type, sK51: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_134, type, sK52: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_135, type, sK53: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_136, type, sK54: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_137, type, sK55: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_138, type, sK56: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_139, type, sK57: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.31/0.45 thf(func_def_140, type, sK58: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.31/0.45 thf(f1,axiom,(
% 0.31/0.45 ! [X4 : list @ poly @ real] : ((sturm_2060350619rm_seq @ X4) => (X4 != nil @ poly @ real))),
% 0.31/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_quasi__sturm__seq_Ops__not__Nil)).
% 0.31/0.45 thf(f286,conjecture,(
% 0.31/0.45 ~(sturm_2060350619rm_seq @ nil @ poly @ real)),
% 0.31/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.31/0.45 thf(f287,negated_conjecture,(
% 0.31/0.45 ~ ~(sturm_2060350619rm_seq @ nil @ poly @ real)),
% 0.31/0.45 inference(negated_conjecture,[status(cth)],[f286])).
% 0.31/0.45 thf(f532,plain,(
% 0.31/0.45 ~ ~(sturm_2060350619rm_seq @ nil @ poly @ real)),
% 0.31/0.45 inference(rectify,[],[f287])).
% 0.31/0.45 thf(f533,plain,(
% 0.31/0.45 ~ ~ (((sturm_2060350619rm_seq @ nil @ poly @ real)) = $true)),
% 0.31/0.45 inference(fool_elimination,[],[f532])).
% 0.31/0.45 thf(f621,plain,(
% 0.31/0.45 ! [X0 : list @ poly @ real] : ((sturm_2060350619rm_seq @ X0) => (nil @ poly @ real != X0))),
% 0.31/0.45 inference(rectify,[],[f1])).
% 0.31/0.45 thf(f622,plain,(
% 0.31/0.45 ! [X0 : list @ poly @ real] : ((((sturm_2060350619rm_seq @ X0)) = $true) => (nil @ poly @ real != X0))),
% 0.31/0.45 inference(fool_elimination,[],[f621])).
% 0.31/0.45 thf(f665,plain,(
% 0.31/0.45 (((sturm_2060350619rm_seq @ nil @ poly @ real)) = $true)),
% 0.31/0.45 inference(flattening,[],[f533])).
% 0.31/0.45 thf(f680,plain,(
% 0.31/0.45 ! [X0 : list @ poly @ real] : ((((sturm_2060350619rm_seq @ X0)) != $true) | (nil @ poly @ real != X0))),
% 0.31/0.45 inference(ennf_transformation,[],[f622])).
% 0.31/0.45 thf(f738,plain,(
% 0.31/0.45 ( ! [X0 : list @ poly @ real] : ((((sturm_2060350619rm_seq @ X0)) != $true) | (nil @ poly @ real != X0)) )),
% 0.31/0.45 inference(cnf_transformation,[],[f680])).
% 0.31/0.45 thf(f758,plain,(
% 0.31/0.45 (((sturm_2060350619rm_seq @ nil @ poly @ real)) = $true)),
% 0.31/0.45 inference(cnf_transformation,[],[f665])).
% 0.31/0.45 thf(f771,plain,(
% 0.31/0.45 (((sturm_2060350619rm_seq @ nil @ poly @ real)) != $true)),
% 0.31/0.45 inference(equality_resolution,[],[f738])).
% 0.31/0.45 thf(f775,plain,(
% 0.31/0.45 $false),
% 0.31/0.45 inference(forward_subsumption_resolution,[],[f758,f771])).
% 0.31/0.45 % SZS output end Proof for theBenchmark
% 0.31/0.45 % (1758670)------------------------------
% 0.31/0.45 % (1758670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (1758670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (1758670)CaDiCaL version: 2.1.3
% 0.31/0.45 % (1758670)Termination reason: Refutation
% 0.31/0.45 % (1758670)Time elapsed: 0.016 s
% 0.31/0.45 % (1758670)Peak memory usage: 13 MB
% 0.31/0.45 % (1758670)Instructions burned: 64 (million)
% 0.31/0.45 % (1758634)Success in time 0.152 s
% 0.31/0.45 % Vampire exiting
%------------------------------------------------------------------------------