%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL021-1 : 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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:37:39 AM UTC 2026
% Result : Unsatisfiable 0.25s 1.13s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 31 unt; 7 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 53 ( 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f2,negated_conjecture,
! [X0] : apply(m,X0) = apply(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_definition) ).
fof(f4,negated_conjecture,
! [X0] : X0 != apply(combinator,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).
fof(f5,plain,
! [X0] : apply(combinator,X0) != X0,
inference(reorient_equations,[],[f4]) ).
fof(f6,definition,
! [X0] : sF0(X0) = apply(b,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f7,plain,
! [X0] : apply(b,X0) = sF0(X0),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
! [X0,X1] : sF1(X0,X1) = apply(sF0(X0),X1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f9,plain,
! [X0,X1] : apply(sF0(X0),X1) = sF1(X0,X1),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = apply(sF1(X0,X1),X2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f11,plain,
! [X2,X0,X1] : apply(sF1(X0,X1),X2) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
! [X2,X0,X1] : sF3(X0,X1,X2) = apply(X0,apply(X1,X2)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f13,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = sF3(X0,X1,X2),
inference(reorient_equations,[],[f12]) ).
fof(f14,plain,
! [X2,X0,X1] : sF2(X0,X1,X2) = sF3(X0,X1,X2),
inference(definition_folding,[],[f1,f13,f11,f9,f7]) ).
fof(f15,definition,
! [X0] : sF4(X0) = apply(m,X0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f16,plain,
! [X0] : apply(m,X0) = sF4(X0),
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
! [X0] : sF5(X0) = apply(X0,X0),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f18,plain,
! [X0] : apply(X0,X0) = sF5(X0),
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
! [X0] : sF4(X0) = sF5(X0),
inference(definition_folding,[],[f2,f18,f16]) ).
fof(f29,definition,
! [X0] : sF10(X0) = apply(combinator,X0),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f30,plain,
! [X0] : apply(combinator,X0) = sF10(X0),
inference(reorient_equations,[],[f29]) ).
fof(f31,plain,
! [X0] : sF10(X0) != X0,
inference(definition_folding,[],[f5,f30]) ).
fof(f32,plain,
! [X0] : apply(combinator,X0) != X0,
inference(forward_demodulation,[],[f31,f30]) ).
fof(f34,plain,
! [X0] : apply(X0,X0) = sF4(X0),
inference(forward_demodulation,[],[f19,f18]) ).
fof(f35,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = sF2(X0,X1,X2),
inference(forward_demodulation,[],[f14,f13]) ).
fof(f37,plain,
! [X0] : apply(m,X0) = apply(X0,X0),
inference(forward_demodulation,[],[f34,f16]) ).
fof(f38,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(sF1(X0,X1),X2),
inference(forward_demodulation,[],[f35,f11]) ).
fof(f40,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(apply(sF0(X0),X1),X2),
inference(forward_demodulation,[],[f38,f9]) ).
fof(f42,plain,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(forward_demodulation,[],[f40,f7]) ).
fof(f51,plain,
! [X0,X1] : apply(m,apply(apply(b,X0),X1)) = apply(X0,apply(X1,apply(apply(b,X0),X1))),
inference(superposition,[],[f42,f37]) ).
fof(f545,plain,
! [X0] : apply(m,apply(apply(b,combinator),X0)) != apply(X0,apply(apply(b,combinator),X0)),
inference(superposition,[],[f32,f51]) ).
fof(f1851,plain,
$false,
inference(equality_resolution,[],[f545]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL021-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n003.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Mon Sep 28 21:31:43 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 Running first-order theorem proving
% 0.10/0.27 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
% 0.25/1.13 % (2047004)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.25/1.13 % (2047056)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3059189154:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 0.25/1.13 % (2047054)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3506757439:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 0.25/1.13 % (2047051)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=1238920256:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 0.25/1.13 % (2047053)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1007012193:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 0.25/1.13 % (2047049)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=465724838:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 0.25/1.13 % (2047056)First to succeed.
% 0.25/1.13 % (2047056)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2047004"
% 0.25/1.13 % (2047057)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4052066485:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 0.25/1.13 % (2047059)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1907052209:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 0.25/1.13 % (2047054)Also succeeded, but the first one will report.
% 0.25/1.13 % (2047059)Also succeeded, but the first one will report.
% 0.25/1.13 % (2047057)Also succeeded, but the first one will report.
% 0.25/1.13 % (2047056)Refutation found. Thanks to Tanya!
% 0.25/1.13 % SZS status Unsatisfiable for theBenchmark
% 0.25/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/1.13 % (2047056)------------------------------
% 0.25/1.13 % (2047056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.25/1.13 % (2047056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/1.13 % (2047056)CaDiCaL version: 2.1.3
% 0.25/1.13 % (2047056)Termination reason: Refutation
% 0.25/1.13 % (2047056)Time elapsed: 0.039 s
% 0.25/1.13 % (2047056)Peak memory usage: 89 MB
% 0.25/1.13 % (2047056)Instructions burned: 124 (million)
% 0.25/1.13 % (2047056)------------------------------
% 0.25/1.13 % (2047056)------------------------------
% 0.25/1.13 % (2047004)Success in time 0.299 s
% 0.25/1.13 % Vampire exiting
%------------------------------------------------------------------------------