%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL064-8 : 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 : n015.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 09:38:21 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.25s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 11 ( 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 : 5 ( 5 !; 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(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,t),t)),x),y),z) != apply(apply(z,x),y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_combinator) ).
fof(f68,plain,
apply(apply(z,x),y) != apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(apply(apply(b,t),t),x)),y),z),
inference(superposition,[],[f3,f1]) ).
fof(f75,plain,
apply(apply(z,x),y) != apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,apply(t,x))),y),z),
inference(superposition,[],[f68,f1]) ).
fof(f81,plain,
apply(apply(z,x),y) != apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(t,apply(t,x)))),y),z),
inference(superposition,[],[f75,f1]) ).
fof(f84,plain,
apply(apply(z,x),y) != apply(apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y),z),
inference(superposition,[],[f81,f2]) ).
fof(f89,plain,
apply(apply(z,x),y) != apply(apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)),z),
inference(superposition,[],[f84,f1]) ).
fof(f92,plain,
apply(apply(z,x),y) != apply(apply(apply(t,apply(t,x)),apply(b,apply(t,y))),z),
inference(superposition,[],[f89,f1]) ).
fof(f94,plain,
apply(apply(z,x),y) != apply(apply(apply(b,apply(t,y)),apply(t,x)),z),
inference(superposition,[],[f92,f2]) ).
fof(f97,plain,
apply(apply(z,x),y) != apply(apply(t,y),apply(apply(t,x),z)),
inference(superposition,[],[f94,f1]) ).
fof(f98,plain,
apply(apply(t,y),apply(apply(t,x),z)) != apply(apply(t,y),apply(z,x)),
inference(superposition,[],[f97,f2]) ).
fof(f99,plain,
apply(apply(t,y),apply(z,x)) != apply(apply(t,y),apply(z,x)),
inference(superposition,[],[f98,f2]) ).
fof(f100,plain,
$false,
inference(trivial_inequality_removal,[],[f99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL064-8 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.19 % Computer : n015.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Mon Sep 28 21:35:47 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.23 Running first-order model finding
% 0.11/0.23 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
% 0.11/0.25 % (3058933)Will run a generic schedule for satisfiability detection.
% 0.11/0.25 % (3058946)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3016739765:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.11/0.25 % (3058940)% WARNING: option uhcvi not known.
% 0.11/0.25 % (3058946) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3058933-3058946"...
% 0.11/0.25 % (3058946)...printing done.
% 0.11/0.25 % (3058946)Refutation found. Thanks to Tanya!
% 0.11/0.25 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.25 % (3058946)------------------------------
% 0.11/0.25 % (3058946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.25 % (3058946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.25 % (3058946)CaDiCaL version: 2.1.3
% 0.11/0.25 % (3058946)Termination reason: Refutation
% 0.11/0.25 % (3058946)Time elapsed: 0.004 s
% 0.11/0.25 % (3058946)Peak memory usage: 11 MB
% 0.11/0.25 % (3058946)Instructions burned: 13 (million)
% 0.11/0.25 % (3058933)Success in time 0.018 s
% 0.11/0.25 % Vampire exiting
%------------------------------------------------------------------------------