%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL062-3 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 01:01:55 PM UTC 2026
% Result : Unsatisfiable 2.58s 0.76s
% Output : CNFRefutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 10 RR)
% Number of literals : 14 ( 13 equ; 9 neg)
% Maximal clause size : 1 ( 1 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 : 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(t15,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(t14,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(apply(b,apply(t,apply(apply(b,b),t))),b)),t),x),y),z) != apply(apply(x,z),y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,x)),y),z) != apply(apply(x,z),y),
inference(rw,[status(thm)],[goal_0,t15]) ).
cnf(g0_1,plain,
apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(t,x))),y),z) != apply(apply(x,z),y),
inference(rw,[status(thm)],[g0_0,t15]) ).
cnf(g0_2,plain,
apply(apply(apply(apply(b,apply(t,x)),apply(apply(b,b),t)),y),z) != apply(apply(x,z),y),
inference(rw,[status(thm)],[g0_1,t14]) ).
cnf(g0_3,plain,
apply(apply(apply(t,x),apply(apply(apply(b,b),t),y)),z) != apply(apply(x,z),y),
inference(rw,[status(thm)],[g0_2,t15]) ).
cnf(g0_4,plain,
apply(apply(apply(apply(apply(b,b),t),y),x),z) != apply(apply(x,z),y),
inference(rw,[status(thm)],[g0_3,t14]) ).
cnf(g0_5,plain,
apply(apply(apply(b,apply(t,y)),x),z) != apply(apply(x,z),y),
inference(rw,[status(thm)],[g0_4,t15]) ).
cnf(g0_6,plain,
apply(apply(t,y),apply(x,z)) != apply(apply(x,z),y),
inference(rw,[status(thm)],[g0_5,t15]) ).
cnf(g0_7,plain,
apply(apply(x,z),y) != apply(apply(x,z),y),
inference(rw,[status(thm)],[g0_6,t14]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL062-3 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Fri Sep 25 07:23:48 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.58/0.76 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.58/0.76 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------