%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL002-1 : 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 : n018.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 09:37:32 AM UTC 2026
% Result : Unsatisfiable 0.19s 1.31s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 9 ( 9 unt; 0 def)
% Number of atoms : 9 ( 8 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 : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 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(f4,axiom,
! [X0] : apply(i,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_definition) ).
fof(f5,negated_conjecture,
! [X0] : X0 != apply(fixed_pt,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).
fof(f6,plain,
! [X0] : apply(fixed_pt,X0) != X0,
inference(reorient_equations,[],[f5]) ).
fof(f13,plain,
! [X0,X1] : apply(apply(apply(s,X1),i),X0) = apply(apply(X1,X0),X0),
inference(superposition,[],[f1,f4]) ).
fof(f79,plain,
! [X0,X1] : apply(X0,apply(X1,X1)) = apply(apply(apply(s,apply(b,X0)),i),X1),
inference(superposition,[],[f13,f2]) ).
fof(f130,plain,
! [X0] : apply(X0,X0) != apply(apply(apply(s,apply(b,fixed_pt)),i),X0),
inference(superposition,[],[f6,f79]) ).
fof(f247,plain,
$false,
inference(equality_resolution,[],[f130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n018.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 21:30:40 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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
% 0.19/1.31 % (3804378)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.19/1.31 % (3804384)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=441925773:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.19/1.31 % (3804388)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1315044418:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.19/1.31 % (3804389)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1012720938:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.19/1.31 % (3804383)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=3250881452:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.19/1.31 % (3804385)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2038585613:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.19/1.31 % (3804386)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3103202659:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.19/1.31 % (3804387)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1258920597:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.19/1.31 % (3804389)First to succeed.
% 0.19/1.31 % (3804389)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3804378"
% 0.19/1.31 % (3804386)Instruction limit reached!
% 0.19/1.31 % (3804386)------------------------------
% 0.19/1.31 % (3804386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (3804386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (3804386)CaDiCaL version: 2.1.3
% 0.19/1.31 % (3804386)Termination reason: Instruction limit
% 0.19/1.31 % (3804386)Termination phase: Saturation
% 0.19/1.31 % (3804386)Time elapsed: 0.080 s
% 0.19/1.31 % (3804386)Peak memory usage: 88 MB
% 0.19/1.31 % (3804386)Instructions burned: 137 (million)
% 0.19/1.31 % (3804387)Also succeeded, but the first one will report.
% 0.19/1.31 % (3804388)Instruction limit reached!
% 0.19/1.31 % (3804388)------------------------------
% 0.19/1.31 % (3804388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (3804388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (3804388)CaDiCaL version: 2.1.3
% 0.19/1.31 % (3804388)Termination reason: Instruction limit
% 0.19/1.31 % (3804388)Termination phase: Saturation
% 0.19/1.31 % (3804388)Time elapsed: 0.161 s
% 0.19/1.31 % (3804388)Peak memory usage: 90 MB
% 0.19/1.31 % (3804388)Instructions burned: 258 (million)
% 0.19/1.31 % (3804397)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1831508689:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 0.19/1.31 % (3804389)Refutation found. Thanks to Tanya!
% 0.19/1.31 % SZS status Unsatisfiable for theBenchmark
% 0.19/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.31 % (3804389)------------------------------
% 0.19/1.31 % (3804389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (3804389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (3804389)CaDiCaL version: 2.1.3
% 0.19/1.31 % (3804389)Termination reason: Refutation
% 0.19/1.31 % (3804389)Time elapsed: 0.011 s
% 0.19/1.31 % (3804389)Peak memory usage: 88 MB
% 0.19/1.31 % (3804389)Instructions burned: 17 (million)
% 0.19/1.31 % (3804389)------------------------------
% 0.19/1.31 % (3804389)------------------------------
% 0.19/1.31 % (3804378)Success in time 0.437 s
% 0.19/1.31 % Vampire exiting
%------------------------------------------------------------------------------