%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL002-5 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 09:37:33 AM UTC 2026
% Result : Unsatisfiable 0.20s 1.13s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 12 unt; 1 def)
% Number of atoms : 12 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [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,axiom,
! [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(f3,axiom,
! [X2,X0,X1] : apply(apply(apply(c,X0),X1),X2) = apply(apply(X0,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_definition) ).
fof(f5,axiom,
! [X0] : weak_fixed_point(X0) = apply(apply(apply(s,apply(c,apply(b,X0))),apply(s,apply(c,apply(b,X0)))),apply(s,apply(c,apply(b,X0)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',weak_fixed_point) ).
fof(f6,negated_conjecture,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
fof(f7,plain,
apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))),
inference(definition_unfolding,[],[f6,f5,f5]) ).
fof(f8,definition,
~ sP0(apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f9,plain,
sP0(apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt)))))),
inference(inequality_splitting,[],[f7,f8]) ).
fof(f19,plain,
! [X2,X0,X1] : apply(apply(apply(c,apply(b,X0)),X1),X2) = apply(X0,apply(X2,X1)),
inference(superposition,[],[f2,f3]) ).
fof(f40,plain,
~ sP0(apply(apply(apply(c,apply(b,fixed_pt)),apply(s,apply(c,apply(b,fixed_pt)))),apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))))),
inference(superposition,[],[f8,f1]) ).
fof(f517,plain,
sP0(apply(apply(apply(c,apply(b,fixed_pt)),apply(s,apply(c,apply(b,fixed_pt)))),apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))))),
inference(superposition,[],[f9,f19]) ).
fof(f518,plain,
$false,
inference(forward_subsumption_resolution,[],[f517,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-5 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n008.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:29:25 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 0.20/1.13 % (2670834)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.20/1.13 % (2670842)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2831883728:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.20/1.13 % (2670842)First to succeed.
% 0.20/1.13 % (2670842)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2670834"
% 0.20/1.13 % (2670841)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=279481942:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.20/1.13 % (2670839)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=3072961261:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.20/1.13 % (2670845)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3241615130:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.20/1.13 % (2670844)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=738848503:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.20/1.13 % (2670840)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=4260218634:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.20/1.13 % (2670843)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1681831442:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.20/1.13 % (2670843)Also succeeded, but the first one will report.
% 0.20/1.13 % (2670844)Also succeeded, but the first one will report.
% 0.20/1.13 % (2670842)Refutation found. Thanks to Tanya!
% 0.20/1.13 % SZS status Unsatisfiable for theBenchmark
% 0.20/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.13 % (2670842)------------------------------
% 0.20/1.13 % (2670842)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.13 % (2670842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.13 % (2670842)CaDiCaL version: 2.1.3
% 0.20/1.13 % (2670842)Termination reason: Refutation
% 0.20/1.13 % (2670842)Time elapsed: 0.013 s
% 0.20/1.13 % (2670842)Peak memory usage: 88 MB
% 0.20/1.13 % (2670842)Instructions burned: 40 (million)
% 0.20/1.13 % (2670842)------------------------------
% 0.20/1.13 % (2670842)------------------------------
% 0.20/1.13 % (2670834)Success in time 0.274 s
% 0.20/1.13 % Vampire exiting
%------------------------------------------------------------------------------