TSTP Solution File: SYO634-1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYO634-1 : TPTP v8.2.0. Released v7.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n029.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 21 08:49:06 EDT 2024

% Result   : Unsatisfiable 0.21s 0.50s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   49 (  13 unt;   0 nHn;  22 RR)
%            Number of literals    :  254 (   0 equ; 214 neg)
%            Maximal clause size   :   11 (   5 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   :  241 ( 229 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/sandbox/benchmark/theBenchmark.p',clause_21_01) ).

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/sandbox/benchmark/theBenchmark.p',clause_12_14) ).

cnf(clause_17_09,axiom,
    'E'(f(X1),s(s(s(s(s(s(s(s(s('0')))))))))),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_11_03) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_10_22) ).

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/sandbox/benchmark/theBenchmark.p',clause_8_11) ).

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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_0_19) ).

cnf(c_0_12,plain,
    ( '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'))))))))))) ),
    inference(fof_simplification,[status(thm)],[clause_21_01]) ).

cnf(c_0_13,plain,
    ( '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'))))))))) ),
    inference(fof_simplification,[status(thm)],[clause_12_14]) ).

cnf(c_0_14,plain,
    ( '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'))))))))))) ),
    c_0_12 ).

cnf(c_0_15,axiom,
    'E'(f(X1),s(s(s(s(s(s(s(s(s('0')))))))))),
    clause_17_09 ).

cnf(c_0_16,axiom,
    'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0'))))))))))),
    clause_11_03 ).

cnf(c_0_17,plain,
    ( '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')))))))) ),
    inference(fof_simplification,[status(thm)],[clause_1_06]) ).

cnf(c_0_18,plain,
    ( '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'))))))))) ),
    c_0_13 ).

cnf(c_0_19,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_14,c_0_15]),c_0_16])]) ).

cnf(c_0_20,plain,
    ( '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'))))))) ),
    inference(fof_simplification,[status(thm)],[clause_15_20]) ).

cnf(c_0_21,plain,
    ( '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')))))))) ),
    c_0_17 ).

cnf(c_0_22,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_18,c_0_19]),c_0_15]),c_0_16])]) ).

cnf(c_0_23,plain,
    ( ~ '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') ),
    inference(fof_simplification,[status(thm)],[clause_3_17]) ).

cnf(c_0_24,plain,
    ( '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'))))))) ),
    c_0_20 ).

cnf(c_0_25,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_21,c_0_22]),c_0_19]),c_0_15]),c_0_16])]) ).

cnf(c_0_26,plain,
    ( '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'))))))) ),
    inference(fof_simplification,[status(thm)],[clause_10_22]) ).

cnf(c_0_27,plain,
    ( ~ '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') ),
    c_0_23 ).

cnf(c_0_28,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_24,c_0_25]),c_0_22]),c_0_19]),c_0_15]),c_0_16])]) ).

cnf(c_0_29,plain,
    ( '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'))))))) ),
    inference(fof_simplification,[status(thm)],[clause_8_11]) ).

cnf(c_0_30,plain,
    ( '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'))))))) ),
    c_0_26 ).

cnf(c_0_31,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_27,c_0_28]),c_0_25]),c_0_22]),c_0_19]),c_0_15]),c_0_16])]) ).

cnf(c_0_32,plain,
    ( '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'))))))) ),
    inference(fof_simplification,[status(thm)],[clause_9_12]) ).

cnf(c_0_33,plain,
    ( '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'))))))) ),
    inference(fof_simplification,[status(thm)],[clause_18_15]) ).

cnf(c_0_34,plain,
    ( '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'))))))) ),
    c_0_29 ).

cnf(c_0_35,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_30,c_0_28]),c_0_25]),c_0_22]),c_0_19]),c_0_15]),c_0_16])]),c_0_31]) ).

cnf(c_0_36,plain,
    ( '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'))))))) ),
    c_0_32 ).

cnf(c_0_37,plain,
    ( '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'))))))) ),
    c_0_33 ).

cnf(c_0_38,plain,
    ( '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'))))))) ),
    inference(fof_simplification,[status(thm)],[clause_0_19]) ).

cnf(c_0_39,plain,
    ( ~ 'E'(f(X1),s(s(s(s('0')))))
    | ~ 'E'(f(X2),s(s(s('0'))))
    | ~ 'E'(f(X3),s(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_34,c_0_28]),c_0_25]),c_0_22]),c_0_19]),c_0_15]),c_0_16])]),c_0_35]) ).

cnf(c_0_40,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_36,c_0_28]),c_0_25]),c_0_22]),c_0_19]),c_0_15]),c_0_16])]) ).

cnf(c_0_41,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_37,c_0_28]),c_0_25]),c_0_22]),c_0_19]),c_0_15]),c_0_16])]) ).

cnf(c_0_42,plain,
    ( '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'))))))) ),
    c_0_38 ).

cnf(c_0_43,plain,
    ( ~ 'E'(f(X1),s(s(s('0'))))
    | ~ 'E'(f(X2),s(s('0'))) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_44,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_41,c_0_40]) ).

cnf(c_0_45,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_42,c_0_28]),c_0_25]),c_0_22]),c_0_19]),c_0_15]),c_0_16])]) ).

cnf(c_0_46,plain,
    ~ 'E'(f(X1),s(s('0'))),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_47,plain,
    ~ 'E'(f(X1),s(s(s('0')))),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_40]),c_0_46]) ).

cnf(c_0_48,plain,
    $false,
    inference(sr,[status(thm)],[c_0_44,c_0_47]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SYO634-1 : TPTP v8.2.0. Released v7.1.0.
% 0.03/0.14  % Command    : run_E %s %d THM
% 0.15/0.35  % Computer : n029.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon May 20 10:04:23 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.50  # Version: 3.1.0
% 0.21/0.50  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.50  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.50  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.50  # Starting sh5l with 300s (1) cores
% 0.21/0.50  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 14798 completed with status 0
% 0.21/0.50  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.21/0.50  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.50  # No SInE strategy applied
% 0.21/0.50  # Search class: FHHNM-FFLF21-DFFFFFNN
% 0.21/0.50  # partial match(2): FHUNM-FFSF21-DFFFFFNN
% 0.21/0.50  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.50  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 355s (1) cores
% 0.21/0.50  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.21/0.50  # Starting new_bool_3 with 296s (1) cores
% 0.21/0.50  # Starting new_bool_1 with 291s (1) cores
% 0.21/0.50  # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.21/0.50  # G-E--_302_C18_F1_URBAN_RG_S04BN with pid 14807 completed with status 0
% 0.21/0.50  # Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.21/0.50  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.50  # No SInE strategy applied
% 0.21/0.50  # Search class: FHHNM-FFLF21-DFFFFFNN
% 0.21/0.50  # partial match(2): FHUNM-FFSF21-DFFFFFNN
% 0.21/0.50  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.50  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 355s (1) cores
% 0.21/0.50  # Preprocessing time       : 0.002 s
% 0.21/0.50  
% 0.21/0.50  # Proof found!
% 0.21/0.50  # SZS status Unsatisfiable
% 0.21/0.50  # SZS output start CNFRefutation
% See solution above
% 0.21/0.50  # Parsed axioms                        : 23
% 0.21/0.50  # Removed by relevancy pruning/SinE    : 0
% 0.21/0.50  # Initial clauses                      : 23
% 0.21/0.50  # Removed in clause preprocessing      : 0
% 0.21/0.50  # Initial clauses in saturation        : 23
% 0.21/0.50  # Processed clauses                    : 28
% 0.21/0.50  # ...of these trivial                  : 0
% 0.21/0.50  # ...subsumed                          : 2
% 0.21/0.50  # ...remaining for further processing  : 26
% 0.21/0.50  # Other redundant clauses eliminated   : 0
% 0.21/0.50  # Clauses deleted for lack of memory   : 0
% 0.21/0.50  # Backward-subsumed                    : 8
% 0.21/0.50  # Backward-rewritten                   : 0
% 0.21/0.50  # Generated clauses                    : 9
% 0.21/0.50  # ...of the previous two non-redundant : 8
% 0.21/0.50  # ...aggressively subsumed             : 0
% 0.21/0.50  # Contextual simplify-reflections      : 2
% 0.21/0.50  # Paramodulations                      : 8
% 0.21/0.50  # Factorizations                       : 0
% 0.21/0.50  # NegExts                              : 0
% 0.21/0.50  # Equation resolutions                 : 0
% 0.21/0.50  # Disequality decompositions           : 0
% 0.21/0.50  # Total rewrite steps                  : 94
% 0.21/0.50  # ...of those cached                   : 68
% 0.21/0.50  # Propositional unsat checks           : 0
% 0.21/0.50  #    Propositional check models        : 0
% 0.21/0.50  #    Propositional check unsatisfiable : 0
% 0.21/0.50  #    Propositional clauses             : 0
% 0.21/0.50  #    Propositional clauses after purity: 0
% 0.21/0.50  #    Propositional unsat core size     : 0
% 0.21/0.50  #    Propositional preprocessing time  : 0.000
% 0.21/0.50  #    Propositional encoding time       : 0.000
% 0.21/0.50  #    Propositional solver time         : 0.000
% 0.21/0.50  #    Success case prop preproc time    : 0.000
% 0.21/0.50  #    Success case prop encoding time   : 0.000
% 0.21/0.50  #    Success case prop solver time     : 0.000
% 0.21/0.50  # Current number of processed clauses  : 17
% 0.21/0.50  #    Positive orientable unit clauses  : 15
% 0.21/0.50  #    Positive unorientable unit clauses: 0
% 0.21/0.50  #    Negative unit clauses             : 2
% 0.21/0.50  #    Non-unit-clauses                  : 0
% 0.21/0.50  # Current number of unprocessed clauses: 1
% 0.21/0.50  # ...number of literals in the above   : 2
% 0.21/0.50  # Current number of archived formulas  : 0
% 0.21/0.50  # Current number of archived clauses   : 9
% 0.21/0.50  # Clause-clause subsumption calls (NU) : 16
% 0.21/0.50  # Rec. Clause-clause subsumption calls : 16
% 0.21/0.50  # Non-unit clause-clause subsumptions  : 7
% 0.21/0.50  # Unit Clause-clause subsumption calls : 7
% 0.21/0.50  # Rewrite failures with RHS unbound    : 0
% 0.21/0.50  # BW rewrite match attempts            : 36
% 0.21/0.50  # BW rewrite match successes           : 2
% 0.21/0.50  # Condensation attempts                : 0
% 0.21/0.50  # Condensation successes               : 0
% 0.21/0.50  # Termbank termtop insertions          : 4755
% 0.21/0.50  # Search garbage collected termcells   : 182
% 0.21/0.50  
% 0.21/0.50  # -------------------------------------------------
% 0.21/0.50  # User time                : 0.006 s
% 0.21/0.50  # System time              : 0.004 s
% 0.21/0.50  # Total time               : 0.009 s
% 0.21/0.50  # Maximum resident set size: 1728 pages
% 0.21/0.50  
% 0.21/0.50  # -------------------------------------------------
% 0.21/0.50  # User time                : 0.028 s
% 0.21/0.50  # System time              : 0.011 s
% 0.21/0.50  # Total time               : 0.039 s
% 0.21/0.50  # Maximum resident set size: 1736 pages
% 0.21/0.50  % E---3.1 exiting
% 0.21/0.50  % E exiting
%------------------------------------------------------------------------------