%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL063-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 103.52s 31.71s
% Output : CNFRefutation 103.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 7 RR)
% Number of literals : 29 ( 28 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eg0,negated_conjecture,
apply(apply(apply(X,f(X)),g(X)),h(X)) != apply(apply(h(X),g(X)),f(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t3,plain,
eq(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),apply(apply(h(X1),g(X1)),f(X1))) = efalse,
inference(equality_encoding,[status(esa)],[eg0]) ).
cnf(t7,plain,
eq(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),apply(apply(h(X1),g(X1)),f(X1))) = efalse,
inference(orient,[status(thm)],[t3]) ).
cnf(t2,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t5,plain,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
inference(orient,[status(thm)],[t2]) ).
cnf(t12,plain,
efalse = eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),g(apply(apply(b,X1),X2))),h(apply(apply(b,X1),X2))),apply(apply(h(apply(apply(b,X1),X2)),g(apply(apply(b,X1),X2))),f(apply(apply(b,X1),X2)))),
inference(cp,[status(thm)],[t7,t5]) ).
cnf(t26,plain,
eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),g(apply(apply(b,X1),X2))),h(apply(apply(b,X1),X2))),apply(apply(h(apply(apply(b,X1),X2)),g(apply(apply(b,X1),X2))),f(apply(apply(b,X1),X2)))) = efalse,
inference(orient,[status(thm)],[t12]) ).
cnf(t1,axiom,
apply(apply(t,X1),X2) = apply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t4,plain,
apply(apply(t,X1),X2) = apply(X2,X1),
inference(orient,[status(thm)],[t1]) ).
cnf(t30,plain,
efalse = eq(apply(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2),g(apply(apply(b,apply(t,X2)),X1))),h(apply(apply(b,apply(t,X2)),X1))),apply(apply(h(apply(apply(b,apply(t,X2)),X1)),g(apply(apply(b,apply(t,X2)),X1))),f(apply(apply(b,apply(t,X2)),X1)))),
inference(cp,[status(thm)],[t26,t4]) ).
cnf(t79,plain,
eq(apply(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2),g(apply(apply(b,apply(t,X2)),X1))),h(apply(apply(b,apply(t,X2)),X1))),apply(apply(h(apply(apply(b,apply(t,X2)),X1)),g(apply(apply(b,apply(t,X2)),X1))),f(apply(apply(b,apply(t,X2)),X1)))) = efalse,
inference(orient,[status(thm)],[t30]) ).
cnf(t84,plain,
efalse = eq(apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),apply(apply(h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),
inference(cp,[status(thm)],[t79,t5]) ).
cnf(t532,plain,
eq(apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),apply(apply(h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))) = efalse,
inference(orient,[status(thm)],[t84]) ).
cnf(t533,plain,
efalse = eq(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(X2,g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(apply(h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),
inference(cp,[status(thm)],[t532,t5]) ).
cnf(t540,plain,
eq(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(X2,g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(apply(h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))) = efalse,
inference(orient,[status(thm)],[t533]) ).
cnf(t545,plain,
efalse = eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))))),apply(X3,g(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))))),h(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2))))),apply(apply(h(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))),g(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2))))),f(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))))),
inference(cp,[status(thm)],[t540,t5]) ).
cnf(t3939,plain,
eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))))),apply(X3,g(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))))),h(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2))))),apply(apply(h(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))),g(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2))))),f(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))))) = efalse,
inference(orient,[status(thm)],[t545]) ).
cnf(t3940,plain,
efalse = eq(apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1))))),apply(apply(X2,g(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1)))))),apply(apply(h(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1)))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1))))),f(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1)))))),
inference(cp,[status(thm)],[t3939,t5]) ).
cnf(t3949,plain,
eq(apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1))))),apply(apply(X2,g(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1)))))),apply(apply(h(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1)))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1))))),f(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1)))))) = efalse,
inference(orient,[status(thm)],[t3940]) ).
cnf(t3950,plain,
efalse = eq(apply(apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t)))))),
inference(cp,[status(thm)],[t3949,t4]) ).
cnf(t3958,plain,
eq(apply(apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t)))))) = efalse,
inference(orient,[status(thm)],[t3950]) ).
cnf(t3960,plain,
efalse = eq(apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))))),
inference(cp,[status(thm)],[t3958,t4]) ).
cnf(t0,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t6,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t0]) ).
cnf(t5884,plain,
efalse = etrue,
inference(step,[status(thm)],[t3960,t6]) ).
cnf(t3965,plain,
efalse = etrue,
inference(orient,[status(thm)],[t5884]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t3965]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL063-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 07:27:26 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 103.52/31.71 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 103.52/31.71 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------