%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL062-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 27.16s 6.11s
% Output : CNFRefutation 27.16s
% 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 : 12 ( 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 : 41 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eg0,negated_conjecture,
apply(apply(apply(X,f(X)),g(X)),h(X)) != apply(apply(f(X),h(X)),g(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t3,plain,
eq(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),apply(apply(f(X1),h(X1)),g(X1))) = efalse,
inference(equality_encoding,[status(esa)],[eg0]) ).
cnf(t7,plain,
eq(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),apply(apply(f(X1),h(X1)),g(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/sandbox2/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(f(apply(apply(b,X1),X2)),h(apply(apply(b,X1),X2))),g(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(f(apply(apply(b,X1),X2)),h(apply(apply(b,X1),X2))),g(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/sandbox2/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(f(apply(apply(b,apply(t,X2)),X1)),h(apply(apply(b,apply(t,X2)),X1))),g(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(f(apply(apply(b,apply(t,X2)),X1)),h(apply(apply(b,apply(t,X2)),X1))),g(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(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),g(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(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),g(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(f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),g(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(f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))) = efalse,
inference(orient,[status(thm)],[t533]) ).
cnf(t542,plain,
efalse = eq(apply(apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))),
inference(cp,[status(thm)],[t540,t4]) ).
cnf(t554,plain,
eq(apply(apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))) = efalse,
inference(orient,[status(thm)],[t542]) ).
cnf(t559,plain,
efalse = eq(apply(apply(apply(X1,apply(X2,g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),
inference(cp,[status(thm)],[t554,t5]) ).
cnf(t2344,plain,
eq(apply(apply(apply(X1,apply(X2,g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))) = efalse,
inference(orient,[status(thm)],[t559]) ).
cnf(t2345,plain,
efalse = eq(apply(apply(X1,g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))),
inference(cp,[status(thm)],[t2344,t5]) ).
cnf(t2352,plain,
eq(apply(apply(X1,g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))) = efalse,
inference(orient,[status(thm)],[t2345]) ).
cnf(t2353,plain,
efalse = eq(apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),
inference(cp,[status(thm)],[t2352,t4]) ).
cnf(t0,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t6,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t0]) ).
cnf(t3510,plain,
efalse = etrue,
inference(step,[status(thm)],[t2353,t6]) ).
cnf(t2357,plain,
efalse = etrue,
inference(orient,[status(thm)],[t3510]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t2357]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL062-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 07:23:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 27.16/6.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.16/6.11 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------