%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL066-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 01:01:58 PM UTC 2026
% Result : Unsatisfiable 5.08s 1.11s
% Output : CNFRefutation 5.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 9 RR)
% Number of literals : 13 ( 12 equ; 8 neg)
% Maximal clause size : 1 ( 1 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 : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t14,plain,
apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
inference(orient,[status(thm)],[t2]) ).
cnf(t0,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t16,plain,
apply(apply(X1,X2),X2) = apply(apply(w,X1),X2),
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
apply(apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(rw,[status(thm)],[goal_0,t14]) ).
cnf(g0_1,plain,
apply(apply(apply(apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(rw,[status(thm)],[g0_0,t16]) ).
cnf(g0_2,plain,
apply(apply(apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(rw,[status(thm)],[g0_1,t14]) ).
cnf(g0_3,plain,
apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(rw,[status(thm)],[g0_2,t14]) ).
cnf(g0_4,plain,
apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(rw,[status(thm)],[g0_3,t14]) ).
cnf(g0_5,plain,
apply(apply(apply(q,apply(x,y)),apply(x,y)),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(rw,[status(thm)],[g0_4,t14]) ).
cnf(g0_6,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(x,y),apply(apply(x,y),z)),
inference(rw,[status(thm)],[g0_5,t14]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL066-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n013.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 07:26:36 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.08/1.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.08/1.11 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------