%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM851+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n002.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 10:41:02 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   28 (  11 unt;  17 typ;   0 def)
%            Number of atoms       :   11 (  10 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  12   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   5 con; 0-2 aty)
%            Number of variables   :   15 (   0 sgn;  10   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    vd471: $i ).

tff(decl_23,type,
    vd473: $i ).

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

tff(decl_25,type,
    vd469: $i ).

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

tff(decl_27,type,
    vd470: $i ).

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

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

tff(decl_30,type,
    v1: $i ).

tff(decl_31,type,
    less: ( $i * $i ) > $o ).

tff(decl_32,type,
    leq: ( $i * $i ) > $o ).

tff(decl_33,type,
    geq: ( $i * $i ) > $o ).

tff(decl_34,type,
    vskolem2: $i > $i ).

tff(decl_35,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk4_2: ( $i * $i ) > $i ).

fof('holds(conseq_conjunct2(conseq(302)), 475, 1)',conjecture,
    vmul(vplus(vd471,vd473),vd469) = vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct2(conseq(302)), 475, 1)') ).

fof('ass(cond(270, 0), 0)',axiom,
    ! [X7,X8] : vmul(X7,X8) = vmul(X8,X7),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).

fof('ass(cond(281, 0), 0)',axiom,
    ! [X4,X5,X6] : vmul(X4,vplus(X5,X6)) = vplus(vmul(X4,X5),vmul(X4,X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).

fof(c_0_3,negated_conjecture,
    vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq_conjunct2(conseq(302)), 475, 1)'])]) ).

fof(c_0_4,plain,
    ! [X100,X101] : vmul(X100,X101) = vmul(X101,X100),
    inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).

cnf(c_0_5,negated_conjecture,
    vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_6,plain,
    vmul(X1,X2) = vmul(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

fof(c_0_7,plain,
    ! [X97,X98,X99] : vmul(X97,vplus(X98,X99)) = vplus(vmul(X97,X98),vmul(X97,X99)),
    inference(variable_rename,[status(thm)],['ass(cond(281, 0), 0)']) ).

cnf(c_0_8,negated_conjecture,
    vmul(vd469,vplus(vd471,vd473)) != vplus(vmul(vd471,vd469),vmul(vd469,vd473)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5,c_0_6]),c_0_6]) ).

cnf(c_0_9,plain,
    vmul(X1,vplus(X2,X3)) = vplus(vmul(X1,X2),vmul(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_10,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_6])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM851+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.34  % Computer : n002.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit   : 300
% 0.16/0.35  % WCLimit    : 300
% 0.16/0.35  % DateTime   : Fri Aug 25 17:27:17 EDT 2023
% 0.16/0.35  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.007000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.011000 s
%------------------------------------------------------------------------------