%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL037-1 : 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 : 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 1.70s 1.86s
% Output : CNFRefutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 5 RR)
% Number of literals : 15 ( 14 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 : 35 ( 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(s_definition,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
cnf(c_definition,axiom,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_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_4,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_5,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
s_definition ).
cnf(c_0_6,plain,
apply(apply(apply(apply(s,b),X1),X2),X3) = apply(X2,apply(apply(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,axiom,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
c_definition ).
cnf(c_0_8,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
prove_fixed_point ).
cnf(c_0_9,plain,
apply(apply(apply(apply(s,b),apply(c,X1)),X2),X3) = apply(X2,apply(apply(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
apply(apply(apply(s,apply(c,X1)),X2),X3) = apply(apply(X1,apply(X2,X3)),X3),
inference(spm,[status(thm)],[c_0_7,c_0_5]) ).
cnf(c_0_11,negated_conjecture,
apply(apply(apply(apply(s,b),apply(c,X1)),f(apply(X1,X2))),X2) != apply(apply(X1,X2),f(apply(X1,X2))),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
apply(apply(apply(apply(s,apply(c,c)),X1),X2),X3) = apply(apply(apply(X1,X2),X3),X2),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
apply(apply(apply(apply(s,apply(c,c)),apply(s,b)),apply(c,X1)),f(apply(X1,apply(c,X1)))) != apply(apply(X1,apply(c,X1)),f(apply(X1,apply(c,X1)))),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL037-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 16:15:58 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.70/1.86 % Version : CSE_E---1.7
% 1.70/1.86 % Problem : theBenchmark.p
% 1.70/1.86 % SZS status Unsatisfiable for theBenchmark.p
% 1.70/1.86 % SZS output start CNFRefutation
% See solution above
% 1.70/1.87 % Total time : 1.371s
%------------------------------------------------------------------------------