TSTP Solution File: RNG039-2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG039-2 : 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 : n024.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 13:48:40 EDT 2023

% Result   : Unsatisfiable 0.19s 0.70s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   74 (  36 unt;  10 typ;   0 def)
%            Number of atoms       :  102 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   80 (  42   ~;  38   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   5   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   82 (  11 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    sum: ( $i * $i * $i ) > $o ).

tff(decl_25,type,
    multiply: ( $i * $i ) > $i ).

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

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

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

tff(decl_29,type,
    b: $i ).

tff(decl_30,type,
    c: $i ).

tff(decl_31,type,
    d: $i ).

cnf(multiplication_is_well_defined,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).

cnf(clause46,axiom,
    product(a,multiply(b,c),c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).

cnf(clause44,axiom,
    product(a,multiply(b,X1),multiply(X2,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).

cnf(transitivity,axiom,
    ( equalish(X1,X3)
    | ~ equalish(X1,X2)
    | ~ equalish(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).

cnf(closure_of_multiplication,axiom,
    product(X1,X2,multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).

cnf(product_substitution1,axiom,
    ( product(X2,X3,X4)
    | ~ equalish(X1,X2)
    | ~ product(X1,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution1) ).

cnf(multiplicative_identity1,axiom,
    product(additive_identity,X1,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).

cnf(product_substitution2,axiom,
    ( product(X3,X2,X4)
    | ~ equalish(X1,X2)
    | ~ product(X3,X1,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution2) ).

cnf(clause39,axiom,
    product(a,c,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).

cnf(clause60,axiom,
    product(c,a,multiply(a,d)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).

cnf(product_substitution3,axiom,
    ( product(X3,X4,X2)
    | ~ equalish(X1,X2)
    | ~ product(X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).

cnf(clause41,axiom,
    product(c,b,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).

cnf(clause43,axiom,
    product(X1,multiply(X1,X2),multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause43) ).

cnf(clause56,axiom,
    product(d,b,multiply(b,c)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).

cnf(clause42,axiom,
    product(d,a,d),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).

cnf(clause49,axiom,
    product(b,multiply(a,d),d),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).

cnf(clause50,axiom,
    product(b,c,multiply(d,b)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).

cnf(prove_c_equals_d,negated_conjecture,
    ~ equalish(c,d),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).

cnf(c_0_18,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    multiplication_is_well_defined ).

cnf(c_0_19,axiom,
    product(a,multiply(b,c),c),
    clause46 ).

cnf(c_0_20,plain,
    ( equalish(X1,c)
    | ~ product(a,multiply(b,c),X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_21,axiom,
    product(a,multiply(b,X1),multiply(X2,X1)),
    clause44 ).

cnf(c_0_22,axiom,
    ( equalish(X1,X3)
    | ~ equalish(X1,X2)
    | ~ equalish(X2,X3) ),
    transitivity ).

cnf(c_0_23,plain,
    equalish(multiply(X1,c),c),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_24,axiom,
    product(X1,X2,multiply(X1,X2)),
    closure_of_multiplication ).

cnf(c_0_25,plain,
    ( equalish(X1,c)
    | ~ equalish(X1,multiply(X2,c)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_26,plain,
    ( equalish(X1,multiply(X2,X3))
    | ~ product(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_24]) ).

cnf(c_0_27,axiom,
    ( product(X2,X3,X4)
    | ~ equalish(X1,X2)
    | ~ product(X1,X3,X4) ),
    product_substitution1 ).

cnf(c_0_28,axiom,
    product(additive_identity,X1,additive_identity),
    multiplicative_identity1 ).

cnf(c_0_29,plain,
    ( equalish(X1,c)
    | ~ product(X2,c,X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,plain,
    ( product(X1,X2,additive_identity)
    | ~ equalish(additive_identity,X1) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_31,plain,
    equalish(additive_identity,c),
    inference(spm,[status(thm)],[c_0_29,c_0_28]) ).

cnf(c_0_32,axiom,
    ( product(X3,X2,X4)
    | ~ equalish(X1,X2)
    | ~ product(X3,X1,X4) ),
    product_substitution2 ).

cnf(c_0_33,axiom,
    product(a,c,c),
    clause39 ).

cnf(c_0_34,axiom,
    product(c,a,multiply(a,d)),
    clause60 ).

cnf(c_0_35,axiom,
    ( product(X3,X4,X2)
    | ~ equalish(X1,X2)
    | ~ product(X3,X4,X1) ),
    product_substitution3 ).

cnf(c_0_36,plain,
    product(c,X1,additive_identity),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_37,axiom,
    product(c,b,c),
    clause41 ).

cnf(c_0_38,plain,
    ( product(a,X1,c)
    | ~ equalish(c,X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_39,plain,
    ( equalish(X1,multiply(a,d))
    | ~ product(c,a,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_34]) ).

cnf(c_0_40,plain,
    ( product(c,X1,X2)
    | ~ equalish(additive_identity,X2) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_41,plain,
    ( equalish(X1,c)
    | ~ product(c,b,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_37]) ).

cnf(c_0_42,axiom,
    product(X1,multiply(X1,X2),multiply(X1,X2)),
    clause43 ).

cnf(c_0_43,plain,
    ( product(a,multiply(a,d),c)
    | ~ product(c,a,c) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_44,plain,
    product(c,X1,c),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_36])]) ).

cnf(c_0_45,axiom,
    product(d,b,multiply(b,c)),
    clause56 ).

cnf(c_0_46,axiom,
    product(d,a,d),
    clause42 ).

cnf(c_0_47,axiom,
    product(b,multiply(a,d),d),
    clause49 ).

cnf(c_0_48,axiom,
    product(b,c,multiply(d,b)),
    clause50 ).

cnf(c_0_49,plain,
    ( equalish(X1,multiply(X2,X3))
    | ~ product(X2,multiply(X2,X3),X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_42]) ).

cnf(c_0_50,plain,
    product(a,multiply(a,d),c),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).

cnf(c_0_51,plain,
    ( equalish(X1,multiply(b,c))
    | ~ product(d,b,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_45]) ).

cnf(c_0_52,negated_conjecture,
    ~ equalish(c,d),
    prove_c_equals_d ).

cnf(c_0_53,plain,
    ( equalish(X1,d)
    | ~ product(d,a,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_46]) ).

cnf(c_0_54,plain,
    ( equalish(X1,d)
    | ~ product(b,multiply(a,d),X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_47]) ).

cnf(c_0_55,plain,
    ( product(b,X1,multiply(d,b))
    | ~ equalish(c,X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_48]) ).

cnf(c_0_56,plain,
    equalish(c,multiply(a,d)),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_57,plain,
    ( product(d,a,X1)
    | ~ equalish(d,X1) ),
    inference(spm,[status(thm)],[c_0_35,c_0_46]) ).

cnf(c_0_58,plain,
    ( equalish(X1,c)
    | ~ product(d,b,X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_51]) ).

cnf(c_0_59,negated_conjecture,
    ~ product(d,a,c),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_60,plain,
    ( product(X1,X2,X3)
    | ~ equalish(multiply(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_35,c_0_24]) ).

cnf(c_0_61,plain,
    equalish(multiply(d,b),d),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).

cnf(c_0_62,plain,
    ~ product(d,b,d),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).

cnf(c_0_63,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : RNG039-2 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun Aug 27 02:38:38 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.19/0.58  start to proof: theBenchmark
% 0.19/0.70  % Version  : CSE_E---1.5
% 0.19/0.70  % Problem  : theBenchmark.p
% 0.19/0.70  % Proof found
% 0.19/0.70  % SZS status Theorem for theBenchmark.p
% 0.19/0.70  % SZS output start Proof
% See solution above
% 0.19/0.71  % Total time : 0.119000 s
% 0.19/0.71  % SZS output end Proof
% 0.19/0.71  % Total time : 0.122000 s
%------------------------------------------------------------------------------