TSTP Solution File: SYO666-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SYO666-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n027.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 : Fri Sep  1 04:12:51 EDT 2023

% Result   : Unsatisfiable 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   51 (   7 unt;   8 typ;   0 def)
%            Number of atoms       :  266 (   0 equ)
%            Maximal formula atoms :   17 (   6 avg)
%            Number of connectives :  419 ( 196   ~; 223   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   7 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   6   >;   3   *;   0   +;   0  <<)
%            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   :  110 (   4 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    suc: $i > $i ).

tff(decl_23,type,
    iLEQ: ( $i * $i ) > $o ).

tff(decl_24,type,
    '0': $i ).

tff(decl_25,type,
    f: $i > $i ).

tff(decl_26,type,
    'E': ( $i * $i ) > $o ).

tff(decl_27,type,
    z: $i ).

tff(decl_28,type,
    'LE': ( $i * $i ) > $o ).

tff(decl_29,type,
    s: $i > $i ).

cnf(clause_29,axiom,
    ( 'E'(s('0'),f(suc(X1)))
    | 'LE'(f(X1),s('0'))
    | ~ 'LE'(f(suc(X1)),s(s('0'))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_29) ).

cnf(clause_83,axiom,
    'LE'(f(X1),s(s('0'))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_83) ).

cnf(clause_185,axiom,
    ( 'E'(s('0'),f(X1))
    | 'LE'(f(X1),s('0'))
    | ~ 'LE'(f(X1),s(s('0'))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_185) ).

cnf(clause_179,axiom,
    ( ~ 'E'(s('0'),f(X1))
    | ~ iLEQ(suc(X2),suc(X3))
    | ~ 'E'(s('0'),f(X4))
    | ~ 'E'(s('0'),f(suc(X4)))
    | ~ iLEQ(suc(X5),suc(X2))
    | ~ 'E'(s('0'),f(X2))
    | ~ 'E'(s('0'),f(suc(X2)))
    | ~ iLEQ(suc(X1),suc(X5))
    | ~ 'E'(s('0'),f(suc(X1)))
    | ~ iLEQ(suc(X3),suc(X6))
    | ~ 'E'(s('0'),f(suc(X5)))
    | ~ 'E'(s('0'),f(X6))
    | ~ 'E'(s('0'),f(suc(X3)))
    | ~ iLEQ(suc(X4),suc(X1))
    | ~ 'E'(s('0'),f(X5))
    | ~ 'E'(s('0'),f(X3))
    | ~ 'E'(s('0'),f(suc(X6))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_179) ).

cnf(clause_70,axiom,
    ( iLEQ(suc(X1),suc(X1))
    | ~ 'E'(s('0'),f(X1))
    | ~ 'E'(s('0'),f(suc(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_70) ).

cnf(clause_102,axiom,
    ( ~ iLEQ(suc(X1),suc(X2))
    | ~ 'E'('0',f(suc(X3)))
    | ~ 'E'('0',f(suc(X1)))
    | ~ iLEQ(suc(X2),suc(X4))
    | ~ 'E'('0',f(suc(X2)))
    | ~ 'E'('0',f(X3))
    | ~ 'E'('0',f(suc(X5)))
    | ~ 'E'('0',f(X2))
    | ~ iLEQ(suc(X6),suc(X1))
    | ~ 'E'('0',f(X1))
    | ~ iLEQ(suc(X5),suc(X6))
    | ~ 'E'('0',f(suc(X4)))
    | ~ 'E'('0',f(X5))
    | ~ iLEQ(suc(X3),suc(X5))
    | ~ 'E'('0',f(suc(X6)))
    | ~ 'E'('0',f(X4))
    | ~ 'E'('0',f(X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_102) ).

cnf(clause_12,axiom,
    ( iLEQ(suc(X1),suc(X1))
    | ~ 'E'('0',f(X1))
    | ~ 'E'('0',f(suc(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12) ).

cnf(clause_123,axiom,
    ( 'E'('0',f(suc(X1)))
    | 'LE'(f(X1),'0')
    | ~ 'LE'(f(suc(X1)),s('0')) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_123) ).

cnf(clause_42,axiom,
    ( 'E'('0',f(X1))
    | 'LE'(f(X1),'0')
    | ~ 'LE'(f(X1),s('0')) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_42) ).

cnf(clause_98,axiom,
    ~ 'LE'(f(z),'0'),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_98) ).

cnf(c_0_10,axiom,
    ( 'E'(s('0'),f(suc(X1)))
    | 'LE'(f(X1),s('0'))
    | ~ 'LE'(f(suc(X1)),s(s('0'))) ),
    clause_29 ).

cnf(c_0_11,axiom,
    'LE'(f(X1),s(s('0'))),
    clause_83 ).

cnf(c_0_12,axiom,
    ( 'E'(s('0'),f(X1))
    | 'LE'(f(X1),s('0'))
    | ~ 'LE'(f(X1),s(s('0'))) ),
    clause_185 ).

cnf(c_0_13,axiom,
    ( ~ 'E'(s('0'),f(X1))
    | ~ iLEQ(suc(X2),suc(X3))
    | ~ 'E'(s('0'),f(X4))
    | ~ 'E'(s('0'),f(suc(X4)))
    | ~ iLEQ(suc(X5),suc(X2))
    | ~ 'E'(s('0'),f(X2))
    | ~ 'E'(s('0'),f(suc(X2)))
    | ~ iLEQ(suc(X1),suc(X5))
    | ~ 'E'(s('0'),f(suc(X1)))
    | ~ iLEQ(suc(X3),suc(X6))
    | ~ 'E'(s('0'),f(suc(X5)))
    | ~ 'E'(s('0'),f(X6))
    | ~ 'E'(s('0'),f(suc(X3)))
    | ~ iLEQ(suc(X4),suc(X1))
    | ~ 'E'(s('0'),f(X5))
    | ~ 'E'(s('0'),f(X3))
    | ~ 'E'(s('0'),f(suc(X6))) ),
    clause_179 ).

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'))
    | ~ 'E'(s('0'),f(suc(X2)))
    | ~ 'E'(s('0'),f(suc(X3)))
    | ~ 'E'(s('0'),f(suc(X4)))
    | ~ 'E'(s('0'),f(suc(X5)))
    | ~ 'E'(s('0'),f(suc(X6)))
    | ~ 'E'(s('0'),f(X2))
    | ~ 'E'(s('0'),f(X3))
    | ~ 'E'(s('0'),f(X4))
    | ~ 'E'(s('0'),f(X5))
    | ~ 'E'(s('0'),f(X6))
    | ~ iLEQ(suc(X2),suc(X5))
    | ~ iLEQ(suc(X3),suc(X6))
    | ~ iLEQ(suc(X4),suc(X1))
    | ~ iLEQ(suc(X5),suc(X4))
    | ~ iLEQ(suc(X6),suc(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'))
    | ~ 'E'(s('0'),f(suc(X3)))
    | ~ 'E'(s('0'),f(suc(X4)))
    | ~ 'E'(s('0'),f(suc(X5)))
    | ~ 'E'(s('0'),f(suc(X6)))
    | ~ 'E'(s('0'),f(X3))
    | ~ 'E'(s('0'),f(X4))
    | ~ 'E'(s('0'),f(X5))
    | ~ 'E'(s('0'),f(X6))
    | ~ iLEQ(suc(X1),suc(X5))
    | ~ iLEQ(suc(X3),suc(X6))
    | ~ iLEQ(suc(X4),suc(X2))
    | ~ iLEQ(suc(X5),suc(X4))
    | ~ iLEQ(suc(X6),suc(X1)) ),
    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'))
    | ~ 'E'(s('0'),f(suc(X4)))
    | ~ 'E'(s('0'),f(suc(X5)))
    | ~ 'E'(s('0'),f(suc(X6)))
    | ~ 'E'(s('0'),f(X4))
    | ~ 'E'(s('0'),f(X5))
    | ~ 'E'(s('0'),f(X6))
    | ~ iLEQ(suc(X3),suc(X5))
    | ~ iLEQ(suc(X1),suc(X6))
    | ~ iLEQ(suc(X4),suc(X2))
    | ~ iLEQ(suc(X5),suc(X4))
    | ~ iLEQ(suc(X6),suc(X3)) ),
    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'))
    | ~ 'E'(s('0'),f(suc(X5)))
    | ~ 'E'(s('0'),f(suc(X6)))
    | ~ 'E'(s('0'),f(X5))
    | ~ 'E'(s('0'),f(X6))
    | ~ iLEQ(suc(X2),suc(X5))
    | ~ iLEQ(suc(X4),suc(X6))
    | ~ iLEQ(suc(X1),suc(X3))
    | ~ iLEQ(suc(X5),suc(X1))
    | ~ iLEQ(suc(X6),suc(X2)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_14]),c_0_15]) ).

cnf(c_0_20,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'))
    | ~ 'E'(s('0'),f(suc(X6)))
    | ~ 'E'(s('0'),f(X6))
    | ~ iLEQ(suc(X4),suc(X1))
    | ~ iLEQ(suc(X2),suc(X6))
    | ~ iLEQ(suc(X5),suc(X3))
    | ~ iLEQ(suc(X1),suc(X5))
    | ~ iLEQ(suc(X6),suc(X4)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_14]),c_0_15]) ).

cnf(c_0_21,axiom,
    ( iLEQ(suc(X1),suc(X1))
    | ~ 'E'(s('0'),f(X1))
    | ~ 'E'(s('0'),f(suc(X1))) ),
    clause_70 ).

cnf(c_0_22,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'))
    | 'LE'(f(X6),s('0'))
    | ~ iLEQ(suc(X3),suc(X6))
    | ~ iLEQ(suc(X5),suc(X1))
    | ~ iLEQ(suc(X2),suc(X4))
    | ~ iLEQ(suc(X6),suc(X2))
    | ~ iLEQ(suc(X1),suc(X3)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_14]),c_0_15]) ).

cnf(c_0_23,plain,
    ( 'LE'(f(X1),s('0'))
    | iLEQ(suc(X1),suc(X1)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_14]),c_0_15]) ).

cnf(c_0_24,axiom,
    ( ~ iLEQ(suc(X1),suc(X2))
    | ~ 'E'('0',f(suc(X3)))
    | ~ 'E'('0',f(suc(X1)))
    | ~ iLEQ(suc(X2),suc(X4))
    | ~ 'E'('0',f(suc(X2)))
    | ~ 'E'('0',f(X3))
    | ~ 'E'('0',f(suc(X5)))
    | ~ 'E'('0',f(X2))
    | ~ iLEQ(suc(X6),suc(X1))
    | ~ 'E'('0',f(X1))
    | ~ iLEQ(suc(X5),suc(X6))
    | ~ 'E'('0',f(suc(X4)))
    | ~ 'E'('0',f(X5))
    | ~ iLEQ(suc(X3),suc(X5))
    | ~ 'E'('0',f(suc(X6)))
    | ~ 'E'('0',f(X4))
    | ~ 'E'('0',f(X6)) ),
    clause_102 ).

cnf(c_0_25,axiom,
    ( iLEQ(suc(X1),suc(X1))
    | ~ 'E'('0',f(X1))
    | ~ 'E'('0',f(suc(X1))) ),
    clause_12 ).

cnf(c_0_26,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(X1),suc(X5))
    | ~ iLEQ(suc(X4),suc(X2))
    | ~ iLEQ(suc(X3),suc(X4))
    | ~ iLEQ(suc(X5),suc(X3)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_27,plain,
    ( ~ 'E'('0',f(suc(X1)))
    | ~ 'E'('0',f(suc(X2)))
    | ~ 'E'('0',f(suc(X3)))
    | ~ 'E'('0',f(suc(X4)))
    | ~ 'E'('0',f(suc(X5)))
    | ~ 'E'('0',f(X1))
    | ~ 'E'('0',f(X2))
    | ~ 'E'('0',f(X3))
    | ~ 'E'('0',f(X4))
    | ~ 'E'('0',f(X5))
    | ~ iLEQ(suc(X2),suc(X1))
    | ~ iLEQ(suc(X4),suc(X2))
    | ~ iLEQ(suc(X5),suc(X3))
    | ~ iLEQ(suc(X1),suc(X5)) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,plain,
    ( 'LE'(f(X1),s('0'))
    | 'LE'(f(X2),s('0'))
    | 'LE'(f(X3),s('0'))
    | 'LE'(f(X4),s('0'))
    | ~ iLEQ(suc(X1),suc(X3))
    | ~ iLEQ(suc(X2),suc(X1))
    | ~ iLEQ(suc(X4),suc(X2)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_23]) ).

cnf(c_0_29,plain,
    ( ~ 'E'('0',f(suc(X1)))
    | ~ 'E'('0',f(suc(X2)))
    | ~ 'E'('0',f(suc(X3)))
    | ~ 'E'('0',f(suc(X4)))
    | ~ 'E'('0',f(X1))
    | ~ 'E'('0',f(X2))
    | ~ 'E'('0',f(X3))
    | ~ 'E'('0',f(X4))
    | ~ iLEQ(suc(X3),suc(X1))
    | ~ iLEQ(suc(X4),suc(X2))
    | ~ iLEQ(suc(X1),suc(X4)) ),
    inference(spm,[status(thm)],[c_0_27,c_0_25]) ).

cnf(c_0_30,plain,
    ( 'LE'(f(X1),s('0'))
    | 'LE'(f(X2),s('0'))
    | 'LE'(f(X3),s('0'))
    | ~ iLEQ(suc(X2),suc(X3))
    | ~ iLEQ(suc(X1),suc(X2)) ),
    inference(spm,[status(thm)],[c_0_28,c_0_23]) ).

cnf(c_0_31,plain,
    ( ~ 'E'('0',f(suc(X1)))
    | ~ 'E'('0',f(suc(X2)))
    | ~ 'E'('0',f(suc(X3)))
    | ~ 'E'('0',f(X1))
    | ~ 'E'('0',f(X2))
    | ~ 'E'('0',f(X3))
    | ~ iLEQ(suc(X3),suc(X2))
    | ~ iLEQ(suc(X1),suc(X3)) ),
    inference(spm,[status(thm)],[c_0_29,c_0_25]) ).

cnf(c_0_32,plain,
    ( 'LE'(f(X1),s('0'))
    | 'LE'(f(X2),s('0'))
    | ~ iLEQ(suc(X2),suc(X1)) ),
    inference(spm,[status(thm)],[c_0_30,c_0_23]) ).

cnf(c_0_33,plain,
    ( ~ 'E'('0',f(suc(X1)))
    | ~ 'E'('0',f(suc(X2)))
    | ~ 'E'('0',f(X1))
    | ~ 'E'('0',f(X2))
    | ~ iLEQ(suc(X1),suc(X2)) ),
    inference(spm,[status(thm)],[c_0_31,c_0_25]) ).

cnf(c_0_34,axiom,
    ( 'E'('0',f(suc(X1)))
    | 'LE'(f(X1),'0')
    | ~ 'LE'(f(suc(X1)),s('0')) ),
    clause_123 ).

cnf(c_0_35,plain,
    'LE'(f(X1),s('0')),
    inference(spm,[status(thm)],[c_0_32,c_0_23]) ).

cnf(c_0_36,axiom,
    ( 'E'('0',f(X1))
    | 'LE'(f(X1),'0')
    | ~ 'LE'(f(X1),s('0')) ),
    clause_42 ).

cnf(c_0_37,plain,
    ( ~ 'E'('0',f(suc(X1)))
    | ~ 'E'('0',f(X1)) ),
    inference(spm,[status(thm)],[c_0_33,c_0_25]) ).

cnf(c_0_38,plain,
    ( 'LE'(f(X1),'0')
    | 'E'('0',f(suc(X1))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).

cnf(c_0_39,plain,
    ( 'LE'(f(X1),'0')
    | 'E'('0',f(X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_35])]) ).

cnf(c_0_40,axiom,
    ~ 'LE'(f(z),'0'),
    clause_98 ).

cnf(c_0_41,plain,
    'LE'(f(X1),'0'),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).

cnf(c_0_42,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SYO666-1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sat Aug 26 07:50:04 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.58  % Version  : CSE_E---1.5
% 0.20/0.58  % Problem  : theBenchmark.p
% 0.20/0.58  % Proof found
% 0.20/0.58  % SZS status Theorem for theBenchmark.p
% 0.20/0.58  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.013000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.016000 s
%------------------------------------------------------------------------------