%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL063-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:12:12 PM UTC 2026
% Result : Unsatisfiable 1.88s 1.89s
% Output : CNFRefutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% 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 : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_f_combinator,negated_conjecture,
apply(apply(apply(X1,f(X1)),g(X1)),h(X1)) != apply(apply(h(X1),g(X1)),f(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_f_combinator) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(t_definition,axiom,
apply(apply(t,X1),X2) = apply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_definition) ).
cnf(c_0_3,negated_conjecture,
apply(apply(apply(X1,f(X1)),g(X1)),h(X1)) != apply(apply(h(X1),g(X1)),f(X1)),
prove_f_combinator ).
cnf(c_0_4,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_5,negated_conjecture,
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(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,axiom,
apply(apply(t,X1),X2) = apply(X2,X1),
t_definition ).
cnf(c_0_7,negated_conjecture,
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(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,negated_conjecture,
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(spm,[status(thm)],[c_0_7,c_0_4]) ).
cnf(c_0_9,negated_conjecture,
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(spm,[status(thm)],[c_0_8,c_0_4]) ).
cnf(c_0_10,negated_conjecture,
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(spm,[status(thm)],[c_0_9,c_0_4]) ).
cnf(c_0_11,negated_conjecture,
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(spm,[status(thm)],[c_0_10,c_0_4]) ).
cnf(c_0_12,negated_conjecture,
apply(apply(X1,f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),X1))))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),X1)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),X1)))))) != apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),X1)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),X1))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),X1))))),
inference(spm,[status(thm)],[c_0_11,c_0_6]) ).
cnf(c_0_13,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_12,c_0_6]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL063-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.33 % Computer : n001.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Mon May 4 16:16:18 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.88/1.89 % Version : CSE_E---1.7
% 1.88/1.89 % Problem : theBenchmark.p
% 1.88/1.89 % SZS status Unsatisfiable for theBenchmark.p
% 1.88/1.89 % SZS output start CNFRefutation
% See solution above
% 1.88/1.89 % Total time : 1.371s
%------------------------------------------------------------------------------