%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL032-1 : 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 : n008.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 1.17s 1.65s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 5 RR)
% Number of literals : 10 ( 9 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_fixed_point,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(q_definition,axiom,
apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',q_definition) ).
cnf(m_definition,axiom,
apply(m,X1) = apply(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_definition) ).
cnf(c_0_3,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
prove_fixed_point ).
cnf(c_0_4,axiom,
apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
q_definition ).
cnf(c_0_5,axiom,
apply(m,X1) = apply(X1,X1),
m_definition ).
cnf(c_0_6,negated_conjecture,
apply(f(apply(apply(q,X1),X2)),apply(X2,apply(X1,f(apply(apply(q,X1),X2))))) != apply(X2,apply(X1,f(apply(apply(q,X1),X2)))),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_7,plain,
apply(X1,apply(X2,apply(apply(q,X2),X1))) = apply(m,apply(apply(q,X2),X1)),
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_8,negated_conjecture,
apply(m,apply(apply(q,X1),f(apply(apply(q,apply(q,X1)),X1)))) != apply(X1,apply(apply(q,X1),f(apply(apply(q,apply(q,X1)),X1)))),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_8]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : COL032-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.08 % 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
% 0.09/0.27 % Computer : n008.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Mon May 4 16:14:13 EDT 2026
% 0.09/0.27 % CPUTime :
% 0.09/0.28 % start to proof: theBenchmark
% 1.17/1.65 % Version : CSE_E---1.7
% 1.17/1.65 % Problem : theBenchmark.p
% 1.17/1.65 % SZS status Unsatisfiable for theBenchmark.p
% 1.17/1.65 % SZS output start CNFRefutation
% See solution above
% 1.17/1.65 % Total time : 1.368s
%------------------------------------------------------------------------------