%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 09:38:05 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.27s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 10 ( 10 unt; 0 def)
% Number of atoms : 10 ( 9 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 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,axiom,
! [X0] : weak_fixed_point(X0) = apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i)),
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(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i)) != apply(fixed_pt,apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i))),
inference(definition_unfolding,[],[f6,f5,f5]) ).
fof(f14,plain,
! [X0,X1] : apply(apply(apply(s,X1),i),X0) = apply(apply(X1,X0),X0),
inference(superposition,[],[f1,f4]) ).
fof(f81,plain,
! [X0,X1] : apply(X0,apply(X1,X1)) = apply(apply(apply(s,apply(b,X0)),i),X1),
inference(superposition,[],[f14,f2]) ).
fof(f144,plain,
apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i)) != apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i)),
inference(superposition,[],[f7,f81]) ).
fof(f151,plain,
$false,
inference(trivial_inequality_removal,[],[f144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n003.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:30:28 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.27 % (2042698)Will run a generic schedule for satisfiability detection.
% 0.17/0.27 % (2042707)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2442426320:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.27 % (2042704)% WARNING: option uhcvi not known.
% 0.17/0.27 % (2042703)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2208901540_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.27 % (2042704)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=17666549:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.27 % (2042705)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4067812413:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.27 % (2042706)dis+10_1_sil=32000:sp=arity:random_seed=1749867619:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.27 % (2042708)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4284736158:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.27 % (2042709)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1502689115:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.27 % TRYING [1]
% 0.17/0.27 % TRYING [2]
% 0.17/0.27 % TRYING [3]
% 0.17/0.27 % (2042705) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2042698-2042705"...
% 0.17/0.27 % TRYING [4]
% 0.17/0.27 % (2042705)...printing done.
% 0.17/0.27 % (2042705)Refutation found. Thanks to Tanya!
% 0.17/0.27 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.27 % (2042705)------------------------------
% 0.17/0.27 % (2042705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.27 % (2042705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.27 % (2042705)CaDiCaL version: 2.1.3
% 0.17/0.27 % (2042705)Termination reason: Refutation
% 0.17/0.27 % (2042705)Time elapsed: 0.008 s
% 0.17/0.27 % (2042705)Peak memory usage: 11 MB
% 0.17/0.27 % (2042705)Instructions burned: 11 (million)
% 0.17/0.27 % (2042698)Success in time 0.045 s
% 0.17/0.27 % Vampire exiting
%------------------------------------------------------------------------------