%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL060-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 01:01:54 PM UTC 2026
% Result : Unsatisfiable 3.85s 1.03s
% Output : CNFRefutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 8 RR)
% Number of literals : 12 ( 11 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t13,plain,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
inference(orient,[status(thm)],[t1]) ).
cnf(t0,axiom,
apply(apply(t,X1),X2) = apply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t12,plain,
apply(apply(t,X1),X2) = apply(X2,X1),
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
apply(apply(apply(apply(apply(b,apply(t,b)),apply(apply(b,b),t)),x),y),z) != apply(y,apply(x,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
apply(apply(apply(apply(t,b),apply(apply(apply(b,b),t),x)),y),z) != apply(y,apply(x,z)),
inference(rw,[status(thm)],[goal_0,t13]) ).
cnf(g0_1,plain,
apply(apply(apply(apply(apply(apply(b,b),t),x),b),y),z) != apply(y,apply(x,z)),
inference(rw,[status(thm)],[g0_0,t12]) ).
cnf(g0_2,plain,
apply(apply(apply(apply(b,apply(t,x)),b),y),z) != apply(y,apply(x,z)),
inference(rw,[status(thm)],[g0_1,t13]) ).
cnf(g0_3,plain,
apply(apply(apply(t,x),apply(b,y)),z) != apply(y,apply(x,z)),
inference(rw,[status(thm)],[g0_2,t13]) ).
cnf(g0_4,plain,
apply(apply(apply(b,y),x),z) != apply(y,apply(x,z)),
inference(rw,[status(thm)],[g0_3,t12]) ).
cnf(g0_5,plain,
apply(y,apply(x,z)) != apply(y,apply(x,z)),
inference(rw,[status(thm)],[g0_4,t13]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL060-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 07:24:36 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.85/1.03 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.85/1.03 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------