%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL039-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.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 04:12:05 PM UTC 2026
% Result : Unsatisfiable 1.10s 1.61s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 5 RR)
% Number of literals : 12 ( 11 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_fixed_point,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(o_definition,axiom,
apply(apply(o,X1),X2) = apply(X2,apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',o_definition) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
cnf(m_definition,axiom,
apply(m,X1) = apply(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_definition) ).
cnf(c_0_4,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
prove_fixed_point ).
cnf(c_0_5,axiom,
apply(apply(o,X1),X2) = apply(X2,apply(X1,X2)),
o_definition ).
cnf(c_0_6,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_7,axiom,
apply(m,X1) = apply(X1,X1),
m_definition ).
cnf(c_0_8,negated_conjecture,
apply(apply(o,X1),f(X1)) != apply(X1,f(X1)),
inference(rw,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_9,plain,
apply(X1,apply(X2,apply(apply(b,X1),X2))) = apply(m,apply(apply(b,X1),X2)),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,negated_conjecture,
apply(apply(m,apply(apply(b,o),X1)),f(apply(X1,apply(apply(b,o),X1)))) != apply(apply(X1,apply(apply(b,o),X1)),f(apply(X1,apply(apply(b,o),X1)))),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : COL039-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 16:15:46 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.10/1.61 % Version : CSE_E---1.7
% 1.10/1.61 % Problem : theBenchmark.p
% 1.10/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 1.10/1.61 % SZS output start CNFRefutation
% See solution above
% 1.10/1.61 % Total time : 1.361s
%------------------------------------------------------------------------------