%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYO664-1 : TPTP v9.2.1. Released v7.3.0.
% 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 : n011.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 05:54:30 PM UTC 2026
% Result : Unsatisfiable 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 40 ( 7 unt; 20 nHn; 31 RR)
% Number of literals : 205 ( 0 equ; 146 neg)
% Maximal clause size : 14 ( 5 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 85 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_83,axiom,
( 'E'(s('0'),f(suc(X1)))
| 'LE'(f(X1),s('0'))
| ~ 'LE'(f(suc(X1)),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_83) ).
cnf(clause_58,axiom,
'LE'(f(X1),s(s('0'))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_58) ).
cnf(clause_20,axiom,
( 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0'))
| ~ 'LE'(f(X1),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_20) ).
cnf(clause_37,axiom,
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ iLEQ(suc(X4),suc(X3))
| ~ 'E'(s('0'),f(X3))
| ~ iLEQ(suc(X5),suc(X1))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X5))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X3),suc(X5))
| ~ 'E'(s('0'),f(suc(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_37) ).
cnf(clause_50,axiom,
( iLEQ(suc(X1),suc(X1))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_50) ).
cnf(clause_66,axiom,
( ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X3)))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X4))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X3))
| ~ iLEQ(suc(X4),suc(X1))
| ~ 'E'('0',f(X5))
| ~ iLEQ(suc(X1),suc(X5))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X5)))
| ~ 'E'('0',f(X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_66) ).
cnf(clause_6,axiom,
( iLEQ(suc(X1),suc(X1))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
cnf(clause_117,axiom,
( 'E'('0',f(suc(X1)))
| 'LE'(f(X1),'0')
| ~ 'LE'(f(suc(X1)),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_117) ).
cnf(clause_94,axiom,
( 'E'('0',f(X1))
| 'LE'(f(X1),'0')
| ~ 'LE'(f(X1),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_94) ).
cnf(clause_70,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_70) ).
cnf(c_0_10,axiom,
( 'E'(s('0'),f(suc(X1)))
| 'LE'(f(X1),s('0'))
| ~ 'LE'(f(suc(X1)),s(s('0'))) ),
clause_83 ).
cnf(c_0_11,axiom,
'LE'(f(X1),s(s('0'))),
clause_58 ).
cnf(c_0_12,axiom,
( 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0'))
| ~ 'LE'(f(X1),s(s('0'))) ),
clause_20 ).
cnf(c_0_13,axiom,
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ iLEQ(suc(X4),suc(X3))
| ~ 'E'(s('0'),f(X3))
| ~ iLEQ(suc(X5),suc(X1))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X5))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X3),suc(X5))
| ~ 'E'(s('0'),f(suc(X5))) ),
clause_37 ).
cnf(c_0_14,plain,
( 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]) ).
cnf(c_0_15,plain,
( 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_11])]) ).
cnf(c_0_16,plain,
( 'LE'(f(X1),s('0'))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X2),suc(X5))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X5))
| ~ 'E'(s('0'),f(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_17,plain,
( 'LE'(f(X1),s('0'))
| 'LE'(f(X2),s('0'))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X3),suc(X5))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X5))
| ~ 'E'(s('0'),f(X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
( 'LE'(f(X1),s('0'))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X3),s('0'))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X4),suc(X5))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(X5))
| ~ 'E'(s('0'),f(X4)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_15]) ).
cnf(c_0_19,plain,
( 'LE'(f(X1),s('0'))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X3),s('0'))
| 'LE'(f(X4),s('0'))
| ~ iLEQ(suc(X3),suc(X5))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X5),suc(X1))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(X5)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_14]),c_0_15]) ).
cnf(c_0_20,axiom,
( iLEQ(suc(X1),suc(X1))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1))) ),
clause_50 ).
cnf(c_0_21,plain,
( 'LE'(f(X1),s('0'))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X3),s('0'))
| 'LE'(f(X4),s('0'))
| 'LE'(f(X5),s('0'))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X5)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_14]),c_0_15]) ).
cnf(c_0_22,plain,
( 'LE'(f(X1),s('0'))
| iLEQ(suc(X1),suc(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_14]),c_0_15]) ).
cnf(c_0_23,axiom,
( ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X3)))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X4))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X3))
| ~ iLEQ(suc(X4),suc(X1))
| ~ 'E'('0',f(X5))
| ~ iLEQ(suc(X1),suc(X5))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X5)))
| ~ 'E'('0',f(X4)) ),
clause_66 ).
cnf(c_0_24,axiom,
( iLEQ(suc(X1),suc(X1))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1))) ),
clause_6 ).
cnf(c_0_25,plain,
( 'LE'(f(X1),s('0'))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X3),s('0'))
| 'LE'(f(X4),s('0'))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X4),suc(X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( 'LE'(f(X1),s('0'))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X3),s('0'))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X3)) ),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_28,plain,
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X1)) ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_29,plain,
( 'LE'(f(X1),s('0'))
| 'LE'(f(X2),s('0'))
| ~ iLEQ(suc(X2),suc(X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_30,plain,
( ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X1)) ),
inference(spm,[status(thm)],[c_0_28,c_0_24]) ).
cnf(c_0_31,axiom,
( 'E'('0',f(suc(X1)))
| 'LE'(f(X1),'0')
| ~ 'LE'(f(suc(X1)),s('0')) ),
clause_117 ).
cnf(c_0_32,plain,
'LE'(f(X1),s('0')),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_33,axiom,
( 'E'('0',f(X1))
| 'LE'(f(X1),'0')
| ~ 'LE'(f(X1),s('0')) ),
clause_94 ).
cnf(c_0_34,plain,
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1)) ),
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_35,plain,
( 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
cnf(c_0_36,plain,
( 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_32])]) ).
cnf(c_0_37,axiom,
~ 'LE'(f(z),'0'),
clause_70 ).
cnf(c_0_38,plain,
'LE'(f(X1),'0'),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_39,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO664-1 : TPTP v9.2.1. Released v7.3.0.
% 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
% 0.15/0.33 % Computer : n011.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 : Tue May 5 09:19:32 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------