%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL062-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 09:38:19 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,axiom,
! [X0,X1] : apply(apply(t,X0),X1) = apply(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_definition) ).
fof(f3,negated_conjecture,
apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)),x),y),z) != apply(apply(x,z),y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_combinator) ).
fof(f42,plain,
! [X2,X0,X1] : apply(X1,apply(X0,X2)) = apply(apply(apply(t,X0),apply(b,X1)),X2),
inference(superposition,[],[f1,f2]) ).
fof(f48,plain,
apply(apply(x,z),y) != apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),t),x)),y),z),
inference(superposition,[],[f3,f1]) ).
fof(f50,plain,
apply(apply(x,z),y) != apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(t,x))),y),z),
inference(superposition,[],[f48,f1]) ).
fof(f53,plain,
apply(apply(x,z),y) != apply(apply(apply(apply(b,apply(t,x)),apply(apply(b,b),t)),y),z),
inference(superposition,[],[f50,f2]) ).
fof(f58,plain,
apply(apply(x,z),y) != apply(apply(apply(t,x),apply(apply(apply(b,b),t),y)),z),
inference(superposition,[],[f53,f1]) ).
fof(f61,plain,
apply(apply(x,z),y) != apply(apply(apply(t,x),apply(b,apply(t,y))),z),
inference(superposition,[],[f58,f1]) ).
fof(f92,plain,
apply(apply(x,z),y) != apply(apply(t,y),apply(x,z)),
inference(superposition,[],[f61,f42]) ).
fof(f93,plain,
apply(apply(t,y),apply(x,z)) != apply(apply(t,y),apply(x,z)),
inference(superposition,[],[f92,f2]) ).
fof(f94,plain,
$false,
inference(trivial_inequality_removal,[],[f93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL062-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n020.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 21:33:16 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.09/0.26 % (591934)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (591945)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1721454529:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.26 % (591940)% WARNING: option uhcvi not known.
% 0.09/0.26 % (591945) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-591934-591945"...
% 0.09/0.26 % (591945)...printing done.
% 0.09/0.26 % (591945)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.26 % (591945)------------------------------
% 0.09/0.26 % (591945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (591945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (591945)CaDiCaL version: 2.1.3
% 0.09/0.26 % (591945)Termination reason: Refutation
% 0.09/0.26 % (591945)Time elapsed: 0.004 s
% 0.09/0.26 % (591945)Peak memory usage: 11 MB
% 0.09/0.26 % (591945)Instructions burned: 12 (million)
% 0.09/0.26 % (591934)Success in time 0.029 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------