%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL006-6 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 : Tue Sep 29 09:37:37 AM UTC 2026
% Result : Unsatisfiable 4.75s 1.64s
% Output : Refutation 5.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 24
% Syntax : Number of formulae : 82 ( 82 unt; 20 def)
% Number of atoms : 82 ( 81 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 18 con; 0-3 aty)
% Number of variables : 87 ( 87 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
fof(f2,negated_conjecture,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
fof(f3,negated_conjecture,
strong_fixed_point = apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f5,definition,
! [X0] : sF0(X0) = apply(s,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
! [X0] : apply(s,X0) = sF0(X0),
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
! [X0,X1] : sF1(X0,X1) = apply(sF0(X0),X1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
! [X0,X1] : apply(sF0(X0),X1) = sF1(X0,X1),
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = apply(sF1(X0,X1),X2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f10,plain,
! [X2,X0,X1] : apply(sF1(X0,X1),X2) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
! [X2,X0,X1] : sF3(X0,X2,X1) = apply(apply(X0,X2),apply(X1,X2)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f12,plain,
! [X2,X0,X1] : apply(apply(X0,X2),apply(X1,X2)) = sF3(X0,X2,X1),
inference(reorient_equations,[],[f11]) ).
fof(f13,plain,
! [X2,X0,X1] : sF2(X0,X1,X2) = sF3(X0,X2,X1),
inference(definition_folding,[],[f1,f12,f10,f8,f6]) ).
fof(f14,definition,
! [X0] : sF4(X0) = apply(k,X0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f15,plain,
! [X0] : apply(k,X0) = sF4(X0),
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
! [X0,X1] : sF5(X0,X1) = apply(sF4(X0),X1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f17,plain,
! [X0,X1] : apply(sF4(X0),X1) = sF5(X0,X1),
inference(reorient_equations,[],[f16]) ).
fof(f18,plain,
! [X0,X1] : sF5(X0,X1) = X0,
inference(definition_folding,[],[f2,f17,f15]) ).
fof(f19,definition,
sF6 = apply(s,k),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f20,plain,
apply(s,k) = sF6,
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
sF7 = apply(sF6,k),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f22,plain,
apply(sF6,k) = sF7,
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
sF8 = apply(s,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f24,plain,
apply(s,sF7) = sF8,
inference(reorient_equations,[],[f23]) ).
fof(f25,definition,
sF9 = apply(sF8,sF7),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f26,plain,
apply(sF8,sF7) = sF9,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF10 = apply(k,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f28,plain,
apply(k,sF9) = sF10,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF11 = apply(s,sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f30,plain,
apply(s,sF10) = sF11,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF12 = apply(k,s),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f32,plain,
apply(k,s) = sF12,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF13 = apply(s,sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f34,plain,
apply(s,sF12) = sF13,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF14 = apply(sF13,k),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f36,plain,
apply(sF13,k) = sF14,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF15 = apply(s,sF14),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f38,plain,
apply(s,sF14) = sF15,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF16 = apply(sF15,sF10),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f40,plain,
apply(sF15,sF10) = sF16,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF17 = apply(sF11,sF16),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f42,plain,
apply(sF11,sF16) = sF17,
inference(reorient_equations,[],[f41]) ).
fof(f43,plain,
strong_fixed_point = sF17,
inference(definition_folding,[],[f3,f42,f40,f28,f26,f22,f20,f24,f22,f20,f38,f36,f34,f32,f30,f28,f26,f22,f20,f24,f22,f20]) ).
fof(f44,definition,
sF18 = apply(strong_fixed_point,fixed_pt),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f45,plain,
apply(strong_fixed_point,fixed_pt) = sF18,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF19 = apply(fixed_pt,sF18),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f47,plain,
apply(fixed_pt,sF18) = sF19,
inference(reorient_equations,[],[f46]) ).
fof(f48,plain,
sF18 != sF19,
inference(definition_folding,[],[f4,f47,f45,f45]) ).
fof(f49,plain,
! [X0,X1] : apply(sF4(X0),X1) = X0,
inference(forward_demodulation,[],[f18,f17]) ).
fof(f50,plain,
! [X2,X0,X1] : apply(apply(X0,X2),apply(X1,X2)) = sF2(X0,X1,X2),
inference(forward_demodulation,[],[f13,f12]) ).
fof(f51,plain,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
inference(forward_demodulation,[],[f49,f15]) ).
fof(f52,plain,
! [X2,X0,X1] : apply(apply(X0,X2),apply(X1,X2)) = apply(sF1(X0,X1),X2),
inference(forward_demodulation,[],[f50,f10]) ).
fof(f53,plain,
! [X2,X0,X1] : apply(apply(X0,X2),apply(X1,X2)) = apply(apply(sF0(X0),X1),X2),
inference(forward_demodulation,[],[f52,f8]) ).
fof(f54,plain,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(forward_demodulation,[],[f53,f6]) ).
fof(f55,plain,
! [X0] : s = apply(sF12,X0),
inference(superposition,[],[f51,f32]) ).
fof(f56,plain,
! [X0] : sF9 = apply(sF10,X0),
inference(superposition,[],[f51,f28]) ).
fof(f58,plain,
! [X0,X1] : apply(apply(sF7,X1),apply(X0,X1)) = apply(apply(sF8,X0),X1),
inference(superposition,[],[f54,f24]) ).
fof(f59,plain,
! [X0,X1] : apply(apply(sF10,X1),apply(X0,X1)) = apply(apply(sF11,X0),X1),
inference(superposition,[],[f54,f30]) ).
fof(f60,plain,
! [X0,X1] : apply(apply(sF12,X1),apply(X0,X1)) = apply(apply(sF13,X0),X1),
inference(superposition,[],[f54,f34]) ).
fof(f61,plain,
! [X0,X1] : apply(apply(sF14,X1),apply(X0,X1)) = apply(apply(sF15,X0),X1),
inference(superposition,[],[f54,f38]) ).
fof(f64,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(apply(apply(s,apply(k,X0)),X1),X2),
inference(superposition,[],[f54,f51]) ).
fof(f76,plain,
! [X0,X1] : apply(apply(apply(s,k),X0),X1) = X1,
inference(superposition,[],[f51,f54]) ).
fof(f77,plain,
! [X0,X1] : apply(apply(sF6,X0),X1) = X1,
inference(forward_demodulation,[],[f76,f20]) ).
fof(f81,plain,
! [X0,X1] : apply(apply(sF13,X0),X1) = apply(s,apply(X0,X1)),
inference(forward_demodulation,[],[f60,f55]) ).
fof(f82,plain,
! [X0,X1] : apply(apply(sF11,X0),X1) = apply(sF9,apply(X0,X1)),
inference(forward_demodulation,[],[f59,f56]) ).
fof(f84,plain,
! [X0] : apply(sF7,X0) = X0,
inference(superposition,[],[f77,f22]) ).
fof(f92,plain,
! [X0] : apply(s,apply(k,X0)) = apply(sF14,X0),
inference(superposition,[],[f81,f36]) ).
fof(f100,plain,
! [X0] : apply(sF9,apply(sF16,X0)) = apply(sF17,X0),
inference(superposition,[],[f82,f42]) ).
fof(f105,plain,
! [X0] : apply(sF9,apply(sF16,X0)) = apply(strong_fixed_point,X0),
inference(forward_demodulation,[],[f100,f43]) ).
fof(f108,plain,
! [X0,X1] : apply(apply(sF8,X0),X1) = apply(X1,apply(X0,X1)),
inference(forward_demodulation,[],[f58,f84]) ).
fof(f109,plain,
! [X0] : apply(X0,apply(sF7,X0)) = apply(sF9,X0),
inference(superposition,[],[f108,f26]) ).
fof(f139,plain,
! [X0] : apply(sF9,X0) = apply(X0,X0),
inference(forward_demodulation,[],[f109,f84]) ).
fof(f246,plain,
! [X0,X1] : apply(apply(sF15,X0),X1) = apply(apply(s,apply(k,X1)),apply(X0,X1)),
inference(forward_demodulation,[],[f61,f92]) ).
fof(f873,plain,
! [X0] : apply(apply(s,apply(k,X0)),sF9) = apply(apply(sF15,sF10),X0),
inference(superposition,[],[f246,f56]) ).
fof(f899,plain,
! [X0] : apply(sF16,X0) = apply(apply(s,apply(k,X0)),sF9),
inference(forward_demodulation,[],[f873,f40]) ).
fof(f916,plain,
! [X0,X1] : apply(X0,apply(sF9,X1)) = apply(apply(sF16,X0),X1),
inference(superposition,[],[f64,f899]) ).
fof(f997,plain,
! [X0] : apply(sF9,apply(sF16,X0)) = apply(X0,apply(sF9,apply(sF16,X0))),
inference(superposition,[],[f139,f916]) ).
fof(f1010,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(forward_demodulation,[],[f997,f105]) ).
fof(f1025,plain,
sF18 = apply(fixed_pt,sF18),
inference(superposition,[],[f1010,f45]) ).
fof(f1092,plain,
sF18 = sF19,
inference(forward_demodulation,[],[f1025,f47]) ).
fof(f1096,plain,
sF18 != sF18,
inference(superposition,[],[f48,f1092]) ).
fof(f1097,plain,
$false,
inference(trivial_inequality_removal,[],[f1096]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL006-6 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.27 % Computer : n009.cluster.edu
% 0.12/0.27 % Model : x86_64 x86_64
% 0.12/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.27 % Memory : 8046.5625MB
% 0.12/0.27 % OS : Linux 6.8.0-71-generic
% 0.12/0.27 % CPULimit : 300
% 0.12/0.27 % WCLimit : 300
% 0.12/0.27 % DateTime : Mon Sep 28 21:29:30 UTC 2026
% 0.12/0.27 % CPUTime :
% 0.12/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.32 Running first-order theorem proving
% 0.26/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.75/1.64 % (3504108)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.75/1.64 % (3504129)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4247926089:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.75/1.64 % (3504132)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3970460476:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.75/1.64 % (3504131)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=998034528:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.75/1.64 % (3504130)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=812414962:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.75/1.64 % (3504127)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3578204125:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.75/1.64 % (3504126)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3590789778:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.75/1.64 % (3504129)Instruction limit reached!
% 4.75/1.64 % (3504129)------------------------------
% 4.75/1.64 % (3504129)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.75/1.64 % (3504129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.75/1.64 % (3504129)CaDiCaL version: 2.1.3
% 4.75/1.64 % (3504129)Termination reason: Instruction limit
% 4.75/1.64 % (3504129)Termination phase: Saturation
% 4.75/1.64 % (3504129)Time elapsed: 0.072 s
% 4.75/1.64 % (3504129)Peak memory usage: 89 MB
% 4.75/1.64 % (3504129)Instructions burned: 137 (million)
% 4.75/1.64 % (3504130)First to succeed.
% 4.75/1.64 % (3504130)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3504108"
% 4.75/1.64 % (3504128)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=522007930:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.75/1.64 % (3504140)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2655533631:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 4.75/1.64 % (3504131)Instruction limit reached!
% 4.75/1.64 % (3504131)------------------------------
% 4.75/1.64 % (3504131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.75/1.64 % (3504131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.75/1.64 % (3504131)CaDiCaL version: 2.1.3
% 4.75/1.64 % (3504131)Termination reason: Instruction limit
% 4.75/1.64 % (3504131)Termination phase: Saturation
% 4.75/1.64 % (3504131)Time elapsed: 0.255 s
% 4.75/1.64 % (3504131)Peak memory usage: 90 MB
% 4.75/1.64 % (3504131)Instructions burned: 258 (million)
% 4.75/1.64 % (3504130)Refutation found. Thanks to Tanya!
% 4.75/1.64 % SZS status Unsatisfiable for theBenchmark
% 4.75/1.64 % SZS output start Proof for theBenchmark
% See solution above
% 5.85/1.83 % (3504130)------------------------------
% 5.85/1.83 % (3504130)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.85/1.83 % (3504130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.83 % (3504130)CaDiCaL version: 2.1.3
% 5.85/1.83 % (3504130)Termination reason: Refutation
% 5.85/1.83 % (3504130)Time elapsed: 0.066 s
% 5.85/1.83 % (3504130)Peak memory usage: 89 MB
% 5.85/1.83 % (3504130)Instructions burned: 69 (million)
% 5.85/1.83 % (3504130)------------------------------
% 5.85/1.83 % (3504130)------------------------------
% 5.85/1.83 % (3504108)Success in time 0.694 s
% 5.85/1.83 % Vampire exiting
%------------------------------------------------------------------------------