%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL046-1 : 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 : n031.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 04:12:08 PM UTC 2026
% Result : Unsatisfiable 20.57s 12.58s
% Output : CNFRefutation 20.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 6 RR)
% Number of literals : 21 ( 20 equ; 5 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(s_definition,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
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(m_definition,axiom,
apply(m,X1) = apply(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_definition) ).
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(c_0_4,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
s_definition ).
cnf(c_0_5,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_6,axiom,
apply(m,X1) = apply(X1,X1),
m_definition ).
cnf(c_0_7,plain,
apply(apply(apply(s,apply(apply(b,X1),X2)),X3),X4) = apply(apply(X1,apply(X2,X4)),apply(X3,X4)),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
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(s,X1),X1),X2) = apply(m,apply(X1,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_4]) ).
cnf(c_0_10,plain,
apply(apply(apply(s,X1),m),X2) = apply(apply(X1,X2),apply(X2,X2)),
inference(spm,[status(thm)],[c_0_4,c_0_6]) ).
cnf(c_0_11,plain,
apply(apply(apply(s,apply(apply(b,X1),X2)),X3),X2) = apply(apply(X1,apply(m,X2)),apply(X3,X2)),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_12,plain,
apply(apply(apply(apply(s,b),X1),X2),X3) = apply(X2,apply(apply(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_13,negated_conjecture,
apply(f(apply(apply(s,X1),X1)),apply(m,apply(X1,f(apply(apply(s,X1),X1))))) != apply(m,apply(X1,f(apply(apply(s,X1),X1)))),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,plain,
apply(apply(X1,apply(m,X2)),apply(m,X2)) = apply(apply(X1,apply(X2,X2)),apply(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_5]) ).
cnf(c_0_15,plain,
apply(apply(apply(s,apply(apply(s,b),X1)),X2),X3) = apply(X3,apply(apply(X1,X3),apply(X2,X3))),
inference(spm,[status(thm)],[c_0_4,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
apply(f(apply(apply(s,apply(X1,X1)),apply(X1,X1))),apply(m,apply(apply(m,X1),f(apply(apply(s,apply(X1,X1)),apply(X1,X1)))))) != apply(m,apply(apply(m,X1),f(apply(apply(s,apply(X1,X1)),apply(X1,X1))))),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
apply(apply(apply(s,apply(apply(s,b),X1)),X1),X2) = apply(X2,apply(m,apply(X1,X2))),
inference(spm,[status(thm)],[c_0_15,c_0_6]) ).
cnf(c_0_18,negated_conjecture,
apply(apply(apply(s,apply(apply(s,b),apply(m,X1))),apply(m,X1)),f(apply(apply(s,apply(X1,X1)),apply(X1,X1)))) != apply(m,apply(apply(m,X1),f(apply(apply(s,apply(X1,X1)),apply(X1,X1))))),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
apply(X1,apply(X2,apply(apply(b,X1),X2))) = apply(m,apply(apply(b,X1),X2)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_5]),c_0_19]),c_0_5]),c_0_19]),c_0_9]),c_0_5]),c_0_19]),c_0_5]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL046-1 : 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
% 0.14/0.33 % Computer : n031.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 16:17:23 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 20.57/12.58 % Version : CSE_E---1.7
% 20.57/12.58 % Problem : theBenchmark.p
% 20.57/12.58 % SZS status Unsatisfiable for theBenchmark.p
% 20.57/12.58 % SZS output start CNFRefutation
% See solution above
% 20.67/12.65 % Total time : 9.379s
%------------------------------------------------------------------------------