%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL044-1 : 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 04:12:07 PM UTC 2026
% Result : Unsatisfiable 1.31s 1.68s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% 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 : 8 ( 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 : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(n_definition,axiom,
apply(apply(apply(n,X1),X2),X3) = apply(apply(apply(X1,X3),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_definition) ).
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(c_0_3,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_4,axiom,
apply(apply(apply(n,X1),X2),X3) = apply(apply(apply(X1,X3),X2),X3),
n_definition ).
cnf(c_0_5,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
prove_fixed_point ).
cnf(c_0_6,plain,
apply(apply(apply(n,b),X1),X2) = apply(X2,apply(X1,X2)),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_7,plain,
apply(apply(apply(n,apply(b,X1)),X2),X3) = apply(apply(X1,apply(X3,X2)),X3),
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_8,negated_conjecture,
apply(apply(apply(n,b),X1),f(X1)) != apply(X1,f(X1)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,plain,
apply(apply(apply(n,apply(b,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X3,X2),X3)),
inference(spm,[status(thm)],[c_0_3,c_0_7]) ).
cnf(c_0_10,negated_conjecture,
apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1),X2),f(apply(apply(X2,X1),X2))) != apply(apply(apply(X2,X1),X2),f(apply(apply(X2,X1),X2))),
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 : COL044-1 : 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
% 0.07/0.24 % Computer : n012.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Mon May 4 16:15:16 EDT 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 1.31/1.68 % Version : CSE_E---1.7
% 1.31/1.68 % Problem : theBenchmark.p
% 1.31/1.68 % SZS status Unsatisfiable for theBenchmark.p
% 1.31/1.68 % SZS output start CNFRefutation
% See solution above
% 1.31/1.68 % Total time : 1.362s
%------------------------------------------------------------------------------