%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL032-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 4.72s 1.45s
% Output : Refutation 4.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 7 ( 7 unt; 0 def)
% Number of atoms : 7 ( 6 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : apply(m,X0) = apply(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_definition) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(q,X0),X1),X2) = apply(X1,apply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',q_definition) ).
fof(f3,negated_conjecture,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
fof(f7,plain,
! [X0,X1] : apply(X0,apply(X1,f(apply(apply(q,X1),X0)))) != apply(f(apply(apply(q,X1),X0)),apply(X0,apply(X1,f(apply(apply(q,X1),X0))))),
inference(superposition,[],[f3,f2]) ).
fof(f8,plain,
! [X0,X1] : apply(X0,apply(X1,apply(apply(q,X1),X0))) = apply(m,apply(apply(q,X1),X0)),
inference(superposition,[],[f1,f2]) ).
fof(f57,plain,
! [X0] : apply(m,apply(apply(q,X0),f(apply(apply(q,apply(q,X0)),X0)))) != apply(X0,apply(apply(q,X0),f(apply(apply(q,apply(q,X0)),X0)))),
inference(superposition,[],[f7,f8]) ).
fof(f68,plain,
$false,
inference(equality_resolution,[],[f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL032-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 21:30:07 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.72/1.45 % (807527)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.72/1.45 % (807620)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2733682965:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.72/1.45 % (807618)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=405570722:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.72/1.45 % (807613)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=1902779293:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.72/1.45 % (807612)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=1441344971:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.72/1.45 % (807614)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=577858385:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.72/1.45 % (807617)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3610144525:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.72/1.45 % (807617)First to succeed.
% 4.72/1.45 % (807617)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-807527"
% 4.72/1.45 % (807621)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3390360365:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.72/1.45 % (807621)Also succeeded, but the first one will report.
% 4.72/1.45 % (807620)Instruction limit reached!
% 4.72/1.45 % (807620)------------------------------
% 4.72/1.45 % (807620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.45 % (807620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.45 % (807620)CaDiCaL version: 2.1.3
% 4.72/1.45 % (807620)Termination reason: Instruction limit
% 4.72/1.45 % (807620)Termination phase: Saturation
% 4.72/1.45 % (807620)Time elapsed: 0.097 s
% 4.72/1.45 % (807620)Peak memory usage: 92 MB
% 4.72/1.45 % (807620)Instructions burned: 259 (million)
% 4.72/1.45 % (807618)Instruction limit reached!
% 4.72/1.45 % (807618)------------------------------
% 4.72/1.45 % (807618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.45 % (807618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.45 % (807618)CaDiCaL version: 2.1.3
% 4.72/1.45 % (807618)Termination reason: Instruction limit
% 4.72/1.45 % (807618)Termination phase: Saturation
% 4.72/1.45 % (807618)Time elapsed: 0.100 s
% 4.72/1.45 % (807618)Peak memory usage: 89 MB
% 4.72/1.45 % (807618)Instructions burned: 183 (million)
% 4.72/1.45 % (807676)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1779717604:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 4.72/1.45 % (807677)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2333679689:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 4.72/1.45 % (807617)Refutation found. Thanks to Tanya!
% 4.72/1.45 % SZS status Unsatisfiable for theBenchmark
% 4.72/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 4.72/1.45 % (807617)------------------------------
% 4.72/1.45 % (807617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.45 % (807617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.45 % (807617)CaDiCaL version: 2.1.3
% 4.72/1.45 % (807617)Termination reason: Refutation
% 4.72/1.45 % (807617)Time elapsed: 0.007 s
% 4.72/1.45 % (807617)Peak memory usage: 87 MB
% 4.72/1.45 % (807617)Instructions burned: 9 (million)
% 4.72/1.45 % (807617)------------------------------
% 4.72/1.45 % (807617)------------------------------
% 4.72/1.45 % (807527)Success in time 0.591 s
% 4.72/1.45 % Vampire exiting
%------------------------------------------------------------------------------