%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL061-1 : 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 13.93s 2.26s
% Output : CNFRefutation 13.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 7 RR)
% Number of literals : 25 ( 24 equ; 3 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eg0,negated_conjecture,
apply(apply(apply(X,f(X)),g(X)),h(X)) != apply(f(X),apply(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(f(X1),apply(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(f(X1),apply(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(f(apply(apply(b,X1),X2)),apply(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(f(apply(apply(b,X1),X2)),apply(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(f(apply(apply(b,apply(t,X2)),X1)),apply(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(f(apply(apply(b,apply(t,X2)),X1)),apply(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(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),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)))))),
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(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),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)))))) = 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(f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),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)))))),
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(f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),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)))))) = efalse,
inference(orient,[status(thm)],[t533]) ).
cnf(t541,plain,
efalse = eq(apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),b))),apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),b))))),apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,X1)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),b)))))),
inference(cp,[status(thm)],[t540,t5]) ).
cnf(t548,plain,
eq(apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),b))),apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),b))))),apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,X1)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),b)))))) = efalse,
inference(orient,[status(thm)],[t541]) ).
cnf(t549,plain,
efalse = eq(apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))),apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))))),
inference(cp,[status(thm)],[t548,t4]) ).
cnf(t0,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t6,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t0]) ).
cnf(t832,plain,
efalse = etrue,
inference(step,[status(thm)],[t549,t6]) ).
cnf(t553,plain,
efalse = etrue,
inference(orient,[status(thm)],[t832]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t553]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL061-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.37 % Computer : n005.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Fri Sep 25 07:23:02 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 13.93/2.26 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.93/2.26 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------