%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL008-1 : 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 : n005.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 2.73s 1.19s
% Output : Refutation 2.73s
% 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(f3,negated_conjecture,
! [X0] : X0 != apply(combinator,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).
fof(f4,plain,
! [X0] : apply(combinator,X0) != X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,definition,
! [X0] : sF0(X0) = apply(b,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
! [X0] : apply(b,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,X1,X2) = apply(X0,apply(X1,X2)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f12,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = sF3(X0,X1,X2),
inference(reorient_equations,[],[f11]) ).
fof(f13,plain,
! [X2,X0,X1] : sF2(X0,X1,X2) = sF3(X0,X1,X2),
inference(definition_folding,[],[f1,f12,f10,f8,f6]) ).
fof(f14,definition,
! [X0] : sF4(X0) = apply(m,X0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f15,plain,
! [X0] : apply(m,X0) = sF4(X0),
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
! [X0] : sF5(X0) = apply(X0,X0),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f17,plain,
! [X0] : apply(X0,X0) = sF5(X0),
inference(reorient_equations,[],[f16]) ).
fof(f18,plain,
! [X0] : sF4(X0) = sF5(X0),
inference(definition_folding,[],[f2,f17,f15]) ).
fof(f19,definition,
! [X0] : sF6(X0) = apply(combinator,X0),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f20,plain,
! [X0] : apply(combinator,X0) = sF6(X0),
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
! [X0] : sF6(X0) != X0,
inference(definition_folding,[],[f4,f20]) ).
fof(f22,plain,
! [X0] : apply(combinator,X0) != X0,
inference(forward_demodulation,[],[f21,f20]) ).
fof(f23,plain,
! [X0] : apply(X0,X0) = sF4(X0),
inference(forward_demodulation,[],[f18,f17]) ).
fof(f24,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = sF2(X0,X1,X2),
inference(forward_demodulation,[],[f13,f12]) ).
fof(f25,plain,
! [X0] : apply(m,X0) = apply(X0,X0),
inference(forward_demodulation,[],[f23,f15]) ).
fof(f26,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(sF1(X0,X1),X2),
inference(forward_demodulation,[],[f24,f10]) ).
fof(f27,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(apply(sF0(X0),X1),X2),
inference(forward_demodulation,[],[f26,f8]) ).
fof(f28,plain,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(forward_demodulation,[],[f27,f6]) ).
fof(f31,plain,
! [X0,X1] : apply(m,apply(apply(b,X0),X1)) = apply(X0,apply(X1,apply(apply(b,X0),X1))),
inference(superposition,[],[f28,f25]) ).
fof(f45,plain,
! [X0] : apply(m,apply(apply(b,combinator),X0)) != apply(X0,apply(apply(b,combinator),X0)),
inference(superposition,[],[f22,f31]) ).
fof(f54,plain,
$false,
inference(equality_resolution,[],[f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:29:16 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 2.73/1.19 % (1202906)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.73/1.19 % (1202985)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4292509131:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.73/1.19 % (1202985)First to succeed.
% 2.73/1.19 % (1202985)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1202906"
% 2.73/1.19 % (1202983)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3631893385:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.73/1.19 % (1202981)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=1221066985:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.73/1.19 % (1202982)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=3531333938:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.73/1.19 % (1202984)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1897596713:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.73/1.19 % (1202984)Also succeeded, but the first one will report.
% 2.73/1.19 % (1202986)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4007325756:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.73/1.19 % (1202987)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2476059566:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.73/1.19 % (1202987)Also succeeded, but the first one will report.
% 2.73/1.19 % (1202986)Also succeeded, but the first one will report.
% 2.73/1.19 % (1202985)Refutation found. Thanks to Tanya!
% 2.73/1.19 % SZS status Unsatisfiable for theBenchmark
% 2.73/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.19 % (1202985)------------------------------
% 2.73/1.19 % (1202985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.19 % (1202985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.19 % (1202985)CaDiCaL version: 2.1.3
% 2.73/1.19 % (1202985)Termination reason: Refutation
% 2.73/1.19 % (1202985)Time elapsed: 0.002 s
% 2.73/1.19 % (1202985)Peak memory usage: 88 MB
% 2.73/1.19 % (1202985)Instructions burned: 4 (million)
% 2.73/1.19 % (1202985)------------------------------
% 2.73/1.19 % (1202985)------------------------------
% 2.73/1.19 % (1202906)Success in time 0.298 s
% 2.73/1.19 % Vampire exiting
%------------------------------------------------------------------------------