%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL031-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 09:37:40 AM UTC 2026
% Result : Unsatisfiable 2.69s 1.15s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 37 ( 37 unt; 9 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0,X1] : apply(apply(l,X0),X1) = apply(X0,apply(X1,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_definition) ).
fof(f2,negated_conjecture,
! [X0,X1] : apply(apply(o,X0),X1) = apply(X1,apply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',o_definition) ).
fof(f3,negated_conjecture,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).
fof(f4,definition,
! [X0] : sF0(X0) = apply(l,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f5,plain,
! [X0] : apply(l,X0) = sF0(X0),
inference(reorient_equations,[],[f4]) ).
fof(f6,definition,
! [X0,X1] : sF1(X0,X1) = apply(sF0(X0),X1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f7,plain,
! [X0,X1] : apply(sF0(X0),X1) = sF1(X0,X1),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
! [X1] : sF2(X1) = apply(X1,X1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f9,plain,
! [X1] : apply(X1,X1) = sF2(X1),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X0,X1] : sF3(X0,X1) = apply(X0,sF2(X1)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f11,plain,
! [X0,X1] : apply(X0,sF2(X1)) = sF3(X0,X1),
inference(reorient_equations,[],[f10]) ).
fof(f12,plain,
! [X0,X1] : sF1(X0,X1) = sF3(X0,X1),
inference(definition_folding,[],[f1,f11,f9,f7,f5]) ).
fof(f13,definition,
! [X0] : sF4(X0) = apply(o,X0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f14,plain,
! [X0] : apply(o,X0) = sF4(X0),
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
! [X0,X1] : sF5(X0,X1) = apply(sF4(X0),X1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f16,plain,
! [X0,X1] : apply(sF4(X0),X1) = sF5(X0,X1),
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
! [X0,X1] : sF6(X1,X0) = apply(X1,apply(X0,X1)),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f18,plain,
! [X0,X1] : apply(X1,apply(X0,X1)) = sF6(X1,X0),
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
! [X0,X1] : sF5(X0,X1) = sF6(X1,X0),
inference(definition_folding,[],[f2,f18,f16,f14]) ).
fof(f20,definition,
! [X0] : sF7(X0) = apply(X0,f(X0)),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f21,plain,
! [X0] : apply(X0,f(X0)) = sF7(X0),
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
! [X0] : sF8(X0) = apply(f(X0),sF7(X0)),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f23,plain,
! [X0] : apply(f(X0),sF7(X0)) = sF8(X0),
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
! [X0] : sF7(X0) != sF8(X0),
inference(definition_folding,[],[f3,f23,f21,f21]) ).
fof(f25,plain,
! [X0] : sF7(X0) != apply(f(X0),sF7(X0)),
inference(forward_demodulation,[],[f24,f23]) ).
fof(f26,plain,
! [X0,X1] : apply(X1,apply(X0,X1)) = sF5(X0,X1),
inference(forward_demodulation,[],[f19,f18]) ).
fof(f27,plain,
! [X0,X1] : sF1(X0,X1) = apply(X0,sF2(X1)),
inference(forward_demodulation,[],[f12,f11]) ).
fof(f28,plain,
! [X0,X1] : apply(X1,apply(X0,X1)) = apply(sF4(X0),X1),
inference(forward_demodulation,[],[f26,f16]) ).
fof(f29,plain,
! [X0,X1] : apply(X0,apply(X1,X1)) = sF1(X0,X1),
inference(forward_demodulation,[],[f27,f9]) ).
fof(f30,plain,
! [X0,X1] : apply(apply(o,X0),X1) = apply(X1,apply(X0,X1)),
inference(forward_demodulation,[],[f28,f14]) ).
fof(f31,plain,
! [X0,X1] : apply(X0,apply(X1,X1)) = apply(sF0(X0),X1),
inference(forward_demodulation,[],[f29,f7]) ).
fof(f32,plain,
! [X0,X1] : apply(apply(l,X0),X1) = apply(X0,apply(X1,X1)),
inference(forward_demodulation,[],[f31,f5]) ).
fof(f34,plain,
! [X0] : apply(f(X0),sF7(X0)) = apply(apply(o,X0),f(X0)),
inference(superposition,[],[f30,f21]) ).
fof(f59,plain,
! [X0] : sF7(X0) != apply(apply(o,X0),f(X0)),
inference(superposition,[],[f25,f34]) ).
fof(f62,plain,
! [X0] : sF7(apply(X0,X0)) != apply(apply(apply(l,o),X0),f(apply(X0,X0))),
inference(superposition,[],[f59,f32]) ).
fof(f635,plain,
sF7(apply(apply(l,o),apply(l,o))) != sF7(apply(apply(l,o),apply(l,o))),
inference(superposition,[],[f62,f21]) ).
fof(f636,plain,
$false,
inference(trivial_inequality_removal,[],[f635]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL031-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n026.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 21:32:57 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 2.69/1.15 % (94215)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.69/1.15 % (94224)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2517259511:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.69/1.15 % (94224)First to succeed.
% 2.69/1.15 % (94224)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-94215"
% 2.69/1.15 % (94226)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3410163706:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.69/1.15 % (94223)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2472460123:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.69/1.15 % (94221)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=3890822492:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.69/1.15 % (94225)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3018595137:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.69/1.15 % (94222)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1714276736:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.69/1.15 % (94220)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=2172094949:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.69/1.15 % (94226)Also succeeded, but the first one will report.
% 2.69/1.15 % (94223)Also succeeded, but the first one will report.
% 2.69/1.15 % (94224)Refutation found. Thanks to Tanya!
% 2.69/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.69/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.15 % (94224)------------------------------
% 2.69/1.15 % (94224)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.15 % (94224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.15 % (94224)CaDiCaL version: 2.1.3
% 2.69/1.15 % (94224)Termination reason: Refutation
% 2.69/1.15 % (94224)Time elapsed: 0.016 s
% 2.69/1.15 % (94224)Peak memory usage: 88 MB
% 2.69/1.15 % (94224)Instructions burned: 49 (million)
% 2.69/1.15 % (94224)------------------------------
% 2.69/1.15 % (94224)------------------------------
% 2.69/1.15 % (94215)Success in time 0.285 s
% 2.69/1.15 % Vampire exiting
%------------------------------------------------------------------------------