TSTP Solution File: LCL062-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LCL062-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n008.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 : Thu Aug 31 06:52:01 EDT 2023

% Result   : Unsatisfiable 4.36s 4.54s
% Output   : CNFRefutation 4.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   33
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   78 (  32 unt;   7 typ;   0 def)
%            Number of atoms       :  123 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  110 (  58   ~;  52   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  169 (  42 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    not: $i > $i ).

tff(decl_25,type,
    a: $i ).

tff(decl_26,type,
    b: $i ).

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

tff(decl_28,type,
    e: $i ).

cnf(condensed_detachment,axiom,
    ( is_a_theorem(X2)
    | ~ is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).

cnf(cn_1,axiom,
    is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).

cnf(cn_2,axiom,
    is_a_theorem(implies(implies(not(X1),X1),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_2) ).

cnf(cn_3,axiom,
    is_a_theorem(implies(X1,implies(not(X1),X2))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).

cnf(prove_cn_60,negated_conjecture,
    ~ is_a_theorem(implies(implies(a,implies(not(b),c)),implies(a,implies(implies(e,c),implies(implies(b,e),c))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_60) ).

cnf(c_0_5,axiom,
    ( is_a_theorem(X2)
    | ~ is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(X1) ),
    condensed_detachment ).

cnf(c_0_6,axiom,
    is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
    cn_1 ).

cnf(c_0_7,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
    | ~ is_a_theorem(implies(X3,X1)) ),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_8,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X3,X2))
    | ~ is_a_theorem(implies(X1,X3)) ),
    inference(spm,[status(thm)],[c_0_5,c_0_7]) ).

cnf(c_0_9,axiom,
    is_a_theorem(implies(implies(not(X1),X1),X1)),
    cn_2 ).

cnf(c_0_10,plain,
    ( is_a_theorem(implies(X1,implies(X2,X3)))
    | ~ is_a_theorem(implies(X1,implies(X4,X3)))
    | ~ is_a_theorem(implies(X2,X4)) ),
    inference(spm,[status(thm)],[c_0_8,c_0_7]) ).

cnf(c_0_11,axiom,
    is_a_theorem(implies(X1,implies(not(X1),X2))),
    cn_3 ).

cnf(c_0_12,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X1,implies(not(X2),X2))) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,plain,
    ( is_a_theorem(implies(X1,implies(X2,X3)))
    | ~ is_a_theorem(implies(X2,not(X1))) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(not(X2),not(X1))) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_15,plain,
    ( is_a_theorem(implies(not(X1),X2))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_5,c_0_11]) ).

cnf(c_0_16,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_17,plain,
    ( is_a_theorem(implies(X1,implies(X2,X3)))
    | ~ is_a_theorem(implies(X2,X4))
    | ~ is_a_theorem(implies(X4,X3)) ),
    inference(spm,[status(thm)],[c_0_10,c_0_16]) ).

cnf(c_0_18,plain,
    ( is_a_theorem(implies(implies(X1,X2),X2))
    | ~ is_a_theorem(implies(not(X2),X1)) ),
    inference(spm,[status(thm)],[c_0_12,c_0_7]) ).

cnf(c_0_19,plain,
    ( is_a_theorem(implies(X1,implies(X2,X3)))
    | ~ is_a_theorem(implies(X4,X3))
    | ~ is_a_theorem(X4) ),
    inference(spm,[status(thm)],[c_0_17,c_0_16]) ).

cnf(c_0_20,plain,
    is_a_theorem(implies(X1,X1)),
    inference(spm,[status(thm)],[c_0_12,c_0_11]) ).

cnf(c_0_21,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(not(X1),X2))
    | ~ is_a_theorem(implies(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_5,c_0_18]) ).

cnf(c_0_22,plain,
    ( is_a_theorem(implies(X1,implies(X2,X3)))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(implies(X2,X3),X1))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_24,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_6]) ).

cnf(c_0_25,plain,
    ( is_a_theorem(implies(implies(X1,X2),X2))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_24]) ).

cnf(c_0_26,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X1,implies(X3,X2)))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_8,c_0_25]) ).

cnf(c_0_27,plain,
    ( is_a_theorem(implies(X1,implies(not(X2),X3)))
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_8,c_0_11]) ).

cnf(c_0_28,plain,
    ( is_a_theorem(implies(implies(X1,X2),X2))
    | ~ is_a_theorem(implies(X3,X1))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_26,c_0_7]) ).

cnf(c_0_29,plain,
    ( is_a_theorem(implies(X1,implies(X2,X3)))
    | ~ is_a_theorem(implies(implies(not(X2),X4),X3)) ),
    inference(spm,[status(thm)],[c_0_17,c_0_11]) ).

cnf(c_0_30,plain,
    is_a_theorem(implies(implies(not(implies(not(X1),X1)),implies(not(X1),X1)),X1)),
    inference(spm,[status(thm)],[c_0_12,c_0_9]) ).

cnf(c_0_31,plain,
    ( is_a_theorem(implies(X1,implies(not(X2),X3)))
    | ~ is_a_theorem(implies(X1,X4))
    | ~ is_a_theorem(implies(X4,X2)) ),
    inference(spm,[status(thm)],[c_0_8,c_0_27]) ).

cnf(c_0_32,plain,
    ( is_a_theorem(implies(implies(X1,X2),X2))
    | ~ is_a_theorem(implies(not(X1),X1)) ),
    inference(spm,[status(thm)],[c_0_28,c_0_9]) ).

cnf(c_0_33,plain,
    is_a_theorem(implies(X1,implies(implies(not(X2),X2),X2))),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_34,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(not(X3),X4)))
    | ~ is_a_theorem(implies(implies(implies(X2,X5),implies(X1,X5)),X3)) ),
    inference(spm,[status(thm)],[c_0_31,c_0_6]) ).

cnf(c_0_35,plain,
    is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),X2)),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_36,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(not(X1),X1)) ),
    inference(spm,[status(thm)],[c_0_5,c_0_9]) ).

cnf(c_0_37,plain,
    ( is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,X3))))
    | ~ is_a_theorem(implies(X1,implies(X4,X2))) ),
    inference(spm,[status(thm)],[c_0_8,c_0_6]) ).

cnf(c_0_38,plain,
    is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(not(implies(X1,X2)),X3))),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_39,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
    | ~ is_a_theorem(implies(not(implies(implies(X1,X2),implies(X3,X2))),implies(X3,X1))) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_40,plain,
    is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))),
    inference(spm,[status(thm)],[c_0_29,c_0_20]) ).

cnf(c_0_41,plain,
    is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X1,X2))),
    inference(spm,[status(thm)],[c_0_12,c_0_38]) ).

cnf(c_0_42,plain,
    is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X1,X3))),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_43,plain,
    is_a_theorem(implies(implies(not(X1),X2),implies(not(implies(implies(X2,X1),X1)),X3))),
    inference(spm,[status(thm)],[c_0_34,c_0_41]) ).

cnf(c_0_44,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(implies(not(X1),X3),X2)) ),
    inference(spm,[status(thm)],[c_0_5,c_0_42]) ).

cnf(c_0_45,plain,
    is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X1),X1))),
    inference(spm,[status(thm)],[c_0_12,c_0_43]) ).

cnf(c_0_46,plain,
    is_a_theorem(implies(X1,implies(implies(X2,X1),X1))),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_47,plain,
    ( is_a_theorem(implies(X1,implies(X2,X1)))
    | ~ is_a_theorem(implies(X2,implies(X3,X1))) ),
    inference(spm,[status(thm)],[c_0_10,c_0_46]) ).

cnf(c_0_48,plain,
    is_a_theorem(implies(X1,implies(X2,X1))),
    inference(spm,[status(thm)],[c_0_47,c_0_11]) ).

cnf(c_0_49,plain,
    ( is_a_theorem(implies(X1,implies(X2,X3)))
    | ~ is_a_theorem(implies(implies(X4,X2),X3)) ),
    inference(spm,[status(thm)],[c_0_17,c_0_48]) ).

cnf(c_0_50,plain,
    is_a_theorem(implies(X1,implies(X2,implies(implies(X2,X3),X3)))),
    inference(spm,[status(thm)],[c_0_49,c_0_45]) ).

cnf(c_0_51,plain,
    is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))),
    inference(spm,[status(thm)],[c_0_49,c_0_20]) ).

cnf(c_0_52,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X1,implies(X3,X2)))
    | ~ is_a_theorem(implies(not(X2),X3)) ),
    inference(spm,[status(thm)],[c_0_8,c_0_18]) ).

cnf(c_0_53,plain,
    is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
    inference(spm,[status(thm)],[c_0_36,c_0_50]) ).

cnf(c_0_54,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(implies(X2,implies(not(X2),X3)),X1)) ),
    inference(spm,[status(thm)],[c_0_21,c_0_40]) ).

cnf(c_0_55,plain,
    is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))),
    inference(spm,[status(thm)],[c_0_39,c_0_51]) ).

cnf(c_0_56,negated_conjecture,
    ~ is_a_theorem(implies(implies(a,implies(not(b),c)),implies(a,implies(implies(e,c),implies(implies(b,e),c))))),
    prove_cn_60 ).

cnf(c_0_57,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(X1,X3)))
    | ~ is_a_theorem(implies(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_6]) ).

cnf(c_0_58,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(not(X2),implies(X1,X2))) ),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_59,plain,
    is_a_theorem(implies(X1,implies(not(implies(X2,X1)),X3))),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_60,negated_conjecture,
    ~ is_a_theorem(implies(implies(not(b),c),implies(implies(e,c),implies(implies(b,e),c)))),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_61,plain,
    ( is_a_theorem(implies(implies(X1,X2),X3))
    | ~ is_a_theorem(implies(not(X3),X1))
    | ~ is_a_theorem(implies(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_52,c_0_57]) ).

cnf(c_0_62,plain,
    is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X4,X2))))),
    inference(spm,[status(thm)],[c_0_49,c_0_48]) ).

cnf(c_0_63,plain,
    is_a_theorem(implies(not(implies(X1,not(X2))),X2)),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_64,negated_conjecture,
    ( ~ is_a_theorem(implies(not(implies(implies(e,c),implies(implies(b,e),c))),not(b)))
    | ~ is_a_theorem(implies(c,implies(implies(e,c),implies(implies(b,e),c)))) ),
    inference(spm,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_65,plain,
    is_a_theorem(implies(X1,implies(X2,implies(X3,X1)))),
    inference(spm,[status(thm)],[c_0_36,c_0_62]) ).

cnf(c_0_66,plain,
    ( is_a_theorem(implies(X1,not(X2)))
    | ~ is_a_theorem(implies(X2,implies(X1,not(X2)))) ),
    inference(spm,[status(thm)],[c_0_21,c_0_63]) ).

cnf(c_0_67,negated_conjecture,
    ~ is_a_theorem(implies(not(implies(implies(e,c),implies(implies(b,e),c))),not(b))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).

cnf(c_0_68,plain,
    ( is_a_theorem(implies(not(X1),not(X2)))
    | ~ is_a_theorem(implies(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_66,c_0_27]) ).

cnf(c_0_69,negated_conjecture,
    ~ is_a_theorem(implies(b,implies(implies(e,c),implies(implies(b,e),c)))),
    inference(spm,[status(thm)],[c_0_67,c_0_68]) ).

cnf(c_0_70,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_37]),c_0_53])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : LCL062-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36  % Computer : n008.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Thu Aug 24 18:41:47 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.22/0.58  start to proof: theBenchmark
% 4.36/4.54  % Version  : CSE_E---1.5
% 4.36/4.54  % Problem  : theBenchmark.p
% 4.36/4.54  % Proof found
% 4.36/4.54  % SZS status Theorem for theBenchmark.p
% 4.36/4.54  % SZS output start Proof
% See solution above
% 4.36/4.55  % Total time : 3.954000 s
% 4.36/4.55  % SZS output end Proof
% 4.36/4.55  % Total time : 3.957000 s
%------------------------------------------------------------------------------