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CSE_E---1.7.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SYO634-1 : TPTP v9.2.1. Released v7.1.0.
% 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 : n007.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 05:54:05 PM UTC 2026

% Result   : Unsatisfiable 1.26s 1.72s
% Output   : CNFRefutation 1.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   44 (  14 unt;   0 nHn;  19 RR)
%            Number of literals    :  192 (   0 equ; 158 neg)
%            Maximal clause size   :   11 (   4 avg)
%            Maximal term depth    :   14 (   4 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :  183 ( 175 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(clause_21_01,axiom,
    ( 'E'(f(X2),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0'))))))))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21_01) ).

cnf(clause_17_09,axiom,
    'E'(f(X1),s(s(s(s(s(s(s(s(s('0')))))))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17_09) ).

cnf(clause_11_03,axiom,
    'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0'))))))))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11_03) ).

cnf(clause_12_14,axiom,
    ( 'E'(f(X2),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X3),s(s(s(s(s(s(s(s('0'))))))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12_14) ).

cnf(clause_1_06,axiom,
    ( 'E'(f(X2),s(s(s(s(s(s('0')))))))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X3),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X4),s(s(s(s(s(s(s('0')))))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1_06) ).

cnf(clause_15_20,axiom,
    ( 'E'(f(X2),s(s(s(s(s('0'))))))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X3),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X5),s(s(s(s(s(s('0'))))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15_20) ).

cnf(clause_3_17,axiom,
    ( ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X2),s(s(s(s(s('0'))))))
    | ~ 'E'(f(X3),s('0'))
    | ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X5),s(s(s(s('0')))))
    | ~ 'E'(f(X6),s(s('0')))
    | ~ 'E'(f(X7),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X8),s(s(s('0'))))
    | ~ 'E'(f(X9),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X10),s(s(s(s(s(s('0')))))))
    | ~ 'E'(f(X11),'0') ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3_17) ).

cnf(clause_10_22,axiom,
    ( 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X11)),'0')
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X2),s(s(s(s(s('0'))))))
    | ~ 'E'(f(X3),s('0'))
    | ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X5),s(s(s(s('0')))))
    | ~ 'E'(f(X6),s(s('0')))
    | ~ 'E'(f(X7),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X8),s(s(s('0'))))
    | ~ 'E'(f(X9),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X10),s(s(s(s(s(s('0'))))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10_22) ).

cnf(clause_9_12,axiom,
    ( 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X7)),s(s(s(s('0')))))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X2),s(s(s(s(s('0'))))))
    | ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X4),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X5),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X6),s(s(s(s(s(s('0'))))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9_12) ).

cnf(clause_18_15,axiom,
    ( 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X8)),s(s(s('0'))))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X2),s(s(s(s(s('0'))))))
    | ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X4),s(s(s(s('0')))))
    | ~ 'E'(f(X5),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X6),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X7),s(s(s(s(s(s('0'))))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18_15) ).

cnf(clause_0_19,axiom,
    ( 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X9)),s(s('0')))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X2),s(s(s(s(s('0'))))))
    | ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X4),s(s(s(s('0')))))
    | ~ 'E'(f(X5),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X6),s(s(s('0'))))
    | ~ 'E'(f(X7),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X8),s(s(s(s(s(s('0'))))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_0_19) ).

cnf(clause_8_11,axiom,
    ( 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X10)),s('0'))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X2),s(s(s(s(s('0'))))))
    | ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X4),s(s(s(s('0')))))
    | ~ 'E'(f(X5),s(s('0')))
    | ~ 'E'(f(X6),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X7),s(s(s('0'))))
    | ~ 'E'(f(X8),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X9),s(s(s(s(s(s('0'))))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8_11) ).

cnf(c_0_12,axiom,
    ( 'E'(f(X2),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0'))))))))))) ),
    clause_21_01 ).

cnf(c_0_13,axiom,
    'E'(f(X1),s(s(s(s(s(s(s(s(s('0')))))))))),
    clause_17_09 ).

cnf(c_0_14,axiom,
    'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0'))))))))))),
    clause_11_03 ).

cnf(c_0_15,axiom,
    ( 'E'(f(X2),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X3),s(s(s(s(s(s(s(s('0'))))))))) ),
    clause_12_14 ).

cnf(c_0_16,plain,
    'E'(f(X1),s(s(s(s(s(s(s(s('0'))))))))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).

cnf(c_0_17,axiom,
    ( 'E'(f(X2),s(s(s(s(s(s('0')))))))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X3),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X4),s(s(s(s(s(s(s('0')))))))) ),
    clause_1_06 ).

cnf(c_0_18,plain,
    'E'(f(X1),s(s(s(s(s(s(s('0')))))))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_13]),c_0_14])]) ).

cnf(c_0_19,axiom,
    ( 'E'(f(X2),s(s(s(s(s('0'))))))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X3),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X5),s(s(s(s(s(s('0'))))))) ),
    clause_15_20 ).

cnf(c_0_20,plain,
    'E'(f(X1),s(s(s(s(s(s('0'))))))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_16]),c_0_13]),c_0_14])]) ).

cnf(c_0_21,axiom,
    ( ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X2),s(s(s(s(s('0'))))))
    | ~ 'E'(f(X3),s('0'))
    | ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X5),s(s(s(s('0')))))
    | ~ 'E'(f(X6),s(s('0')))
    | ~ 'E'(f(X7),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X8),s(s(s('0'))))
    | ~ 'E'(f(X9),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X10),s(s(s(s(s(s('0')))))))
    | ~ 'E'(f(X11),'0') ),
    clause_3_17 ).

cnf(c_0_22,plain,
    'E'(f(X1),s(s(s(s(s('0')))))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_18]),c_0_16]),c_0_13]),c_0_14])]) ).

cnf(c_0_23,axiom,
    ( 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X11)),'0')
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X2),s(s(s(s(s('0'))))))
    | ~ 'E'(f(X3),s('0'))
    | ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X5),s(s(s(s('0')))))
    | ~ 'E'(f(X6),s(s('0')))
    | ~ 'E'(f(X7),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X8),s(s(s('0'))))
    | ~ 'E'(f(X9),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X10),s(s(s(s(s(s('0'))))))) ),
    clause_10_22 ).

cnf(c_0_24,plain,
    ( ~ 'E'(f(X1),s(s(s(s('0')))))
    | ~ 'E'(f(X2),s(s(s('0'))))
    | ~ 'E'(f(X3),s(s('0')))
    | ~ 'E'(f(X4),s('0'))
    | ~ 'E'(f(X5),'0') ),
    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)],[c_0_21,c_0_22]),c_0_20]),c_0_18]),c_0_16]),c_0_13]),c_0_14])]) ).

cnf(c_0_25,axiom,
    ( 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X7)),s(s(s(s('0')))))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X2),s(s(s(s(s('0'))))))
    | ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X4),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X5),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X6),s(s(s(s(s(s('0'))))))) ),
    clause_9_12 ).

cnf(c_0_26,axiom,
    ( 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X8)),s(s(s('0'))))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X2),s(s(s(s(s('0'))))))
    | ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X4),s(s(s(s('0')))))
    | ~ 'E'(f(X5),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X6),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X7),s(s(s(s(s(s('0'))))))) ),
    clause_18_15 ).

cnf(c_0_27,axiom,
    ( 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X9)),s(s('0')))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X2),s(s(s(s(s('0'))))))
    | ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X4),s(s(s(s('0')))))
    | ~ 'E'(f(X5),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X6),s(s(s('0'))))
    | ~ 'E'(f(X7),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X8),s(s(s(s(s(s('0'))))))) ),
    clause_0_19 ).

cnf(c_0_28,plain,
    ( ~ 'E'(f(X1),s(s(s(s('0')))))
    | ~ 'E'(f(X2),s(s(s('0'))))
    | ~ 'E'(f(X3),s(s('0')))
    | ~ 'E'(f(X4),s('0')) ),
    inference(csr,[status(thm)],[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)],[c_0_23,c_0_22]),c_0_20]),c_0_18]),c_0_16]),c_0_13]),c_0_14])]),c_0_24]) ).

cnf(c_0_29,plain,
    'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s(s(s(s('0'))))),
    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)],[c_0_25,c_0_22]),c_0_20]),c_0_18]),c_0_16]),c_0_13]),c_0_14])]) ).

cnf(c_0_30,plain,
    ( 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s(s(s('0'))))
    | ~ 'E'(f(X2),s(s(s(s('0'))))) ),
    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)],[c_0_26,c_0_22]),c_0_20]),c_0_18]),c_0_16]),c_0_13]),c_0_14])]) ).

cnf(c_0_31,plain,
    ( 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s(s('0')))
    | ~ 'E'(f(X2),s(s(s(s('0')))))
    | ~ 'E'(f(X3),s(s(s('0')))) ),
    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)],[c_0_27,c_0_22]),c_0_20]),c_0_18]),c_0_16]),c_0_13]),c_0_14])]) ).

cnf(c_0_32,plain,
    ( ~ 'E'(f(X1),s(s(s('0'))))
    | ~ 'E'(f(X2),s(s('0')))
    | ~ 'E'(f(X3),s('0')) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,plain,
    'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s(s(s('0')))),
    inference(spm,[status(thm)],[c_0_30,c_0_29]) ).

cnf(c_0_34,plain,
    ( 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s(s('0')))
    | ~ 'E'(f(X2),s(s(s('0')))) ),
    inference(spm,[status(thm)],[c_0_31,c_0_29]) ).

cnf(c_0_35,axiom,
    ( 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X10)),s('0'))
    | ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
    | ~ 'E'(f(X2),s(s(s(s(s('0'))))))
    | ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
    | ~ 'E'(f(X4),s(s(s(s('0')))))
    | ~ 'E'(f(X5),s(s('0')))
    | ~ 'E'(f(X6),s(s(s(s(s(s(s('0'))))))))
    | ~ 'E'(f(X7),s(s(s('0'))))
    | ~ 'E'(f(X8),s(s(s(s(s(s(s(s(s('0'))))))))))
    | ~ 'E'(f(X9),s(s(s(s(s(s('0'))))))) ),
    clause_8_11 ).

cnf(c_0_36,plain,
    ( ~ 'E'(f(X1),s(s('0')))
    | ~ 'E'(f(X2),s('0')) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_37,plain,
    'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s(s('0'))),
    inference(spm,[status(thm)],[c_0_34,c_0_33]) ).

cnf(c_0_38,plain,
    ( 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s('0'))
    | ~ 'E'(f(X2),s(s(s(s('0')))))
    | ~ 'E'(f(X3),s(s(s('0'))))
    | ~ 'E'(f(X4),s(s('0'))) ),
    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)],[c_0_35,c_0_22]),c_0_20]),c_0_18]),c_0_16]),c_0_13]),c_0_14])]) ).

cnf(c_0_39,plain,
    ~ 'E'(f(X1),s('0')),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_40,plain,
    ( ~ 'E'(f(X1),s(s(s(s('0')))))
    | ~ 'E'(f(X2),s(s(s('0'))))
    | ~ 'E'(f(X3),s(s('0'))) ),
    inference(sr,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_41,plain,
    ( ~ 'E'(f(X1),s(s(s('0'))))
    | ~ 'E'(f(X2),s(s('0'))) ),
    inference(spm,[status(thm)],[c_0_40,c_0_29]) ).

cnf(c_0_42,plain,
    ~ 'E'(f(X1),s(s('0'))),
    inference(spm,[status(thm)],[c_0_41,c_0_33]) ).

cnf(c_0_43,plain,
    $false,
    inference(sr,[status(thm)],[c_0_37,c_0_42]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SYO634-1 : TPTP v9.2.1. Released v7.1.0.
% 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 : n007.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 09:17:39 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 1.26/1.72  % Version  : CSE_E---1.7
% 1.26/1.72  % Problem  : theBenchmark.p
% 1.26/1.72  % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.72  % SZS output start CNFRefutation
% See solution above
% 1.26/1.72  % Total time : 1.372s
%------------------------------------------------------------------------------