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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : GRP775+1 : TPTP v9.2.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n023.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  5 04:27:15 PM UTC 2026

% Result   : Theorem 2.45s 2.03s
% Output   : CNFRefutation 2.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   83 (  26 unt;   0 def)
%            Number of atoms       :  185 (  95 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  187 (  85   ~;  84   |;  13   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :  146 (   0 sgn  27   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(sos01,axiom,
    ! [X1,X2,X3] : product(product(X3,X2),X1) = product(X3,product(X2,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).

fof(sos02,axiom,
    ! [X3] : product(X3,X3) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).

fof(sos04,axiom,
    ! [X6,X7] :
      ( r(X6,X7)
    <=> ( product(X6,X7) = X7
        & product(X7,X6) = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).

fof(sos05,axiom,
    ! [X8,X9] :
      ( d(X8,X9)
    <=> ? [X10] :
          ( r(X8,X10)
          & l(X10,X9) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).

fof(sos03,axiom,
    ! [X4,X5] :
      ( l(X4,X5)
    <=> ( product(X4,X5) = X4
        & product(X5,X4) = X5 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).

fof(goals,conjecture,
    ! [X11,X12] :
      ( d(X11,X12)
    <=> ( product(X11,product(X12,X11)) = X11
        & product(X12,product(X11,X12)) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(c_0_6,plain,
    ! [X26,X27,X28] : product(product(X28,X27),X26) = product(X28,product(X27,X26)),
    inference(variable_rename,[status(thm)],[sos01]) ).

fof(c_0_7,plain,
    ! [X29] : product(X29,X29) = X29,
    inference(variable_rename,[status(thm)],[sos02]) ).

cnf(c_0_8,plain,
    product(product(X1,X2),X3) = product(X1,product(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,plain,
    product(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_10,plain,
    ! [X32,X33] :
      ( ( product(X32,X33) = X33
        | ~ r(X32,X33) )
      & ( product(X33,X32) = X32
        | ~ r(X32,X33) )
      & ( product(X32,X33) != X33
        | product(X33,X32) != X32
        | r(X32,X33) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos04])])]) ).

fof(c_0_11,plain,
    ! [X34,X35,X37,X38,X39] :
      ( ( r(X34,esk1_2(X34,X35))
        | ~ d(X34,X35) )
      & ( l(esk1_2(X34,X35),X35)
        | ~ d(X34,X35) )
      & ( ~ r(X37,X39)
        | ~ l(X39,X38)
        | d(X37,X38) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[sos05])])])])])]) ).

cnf(c_0_12,plain,
    product(X1,product(X1,X2)) = product(X1,X2),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,plain,
    ( product(X1,X2) = X2
    | ~ r(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    ( r(X1,esk1_2(X1,X2))
    | ~ d(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_15,plain,
    ! [X30,X31] :
      ( ( product(X30,X31) = X30
        | ~ l(X30,X31) )
      & ( product(X31,X30) = X31
        | ~ l(X30,X31) )
      & ( product(X30,X31) != X30
        | product(X31,X30) != X31
        | l(X30,X31) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos03])])]) ).

cnf(c_0_16,plain,
    product(X1,product(X2,product(X1,product(X2,X3)))) = product(X1,product(X2,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_12]),c_0_8]),c_0_8]) ).

cnf(c_0_17,plain,
    ( product(X1,esk1_2(X1,X2)) = esk1_2(X1,X2)
    | ~ d(X1,X2) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,plain,
    ( product(X1,X2) = X1
    | ~ l(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,plain,
    ( l(esk1_2(X1,X2),X2)
    | ~ d(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_20,negated_conjecture,
    ~ ! [X11,X12] :
        ( d(X11,X12)
      <=> ( product(X11,product(X12,X11)) = X11
          & product(X12,product(X11,X12)) = X12 ) ),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_21,plain,
    ( product(X1,product(X2,product(X1,esk1_2(X2,X3)))) = product(X1,esk1_2(X2,X3))
    | ~ d(X2,X3) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_22,plain,
    ( product(X1,esk1_2(X2,X1)) = X1
    | ~ d(X2,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

fof(c_0_23,negated_conjecture,
    ( ( ~ d(esk2_0,esk3_0)
      | product(esk2_0,product(esk3_0,esk2_0)) != esk2_0
      | product(esk3_0,product(esk2_0,esk3_0)) != esk3_0 )
    & ( product(esk2_0,product(esk3_0,esk2_0)) = esk2_0
      | d(esk2_0,esk3_0) )
    & ( product(esk3_0,product(esk2_0,esk3_0)) = esk3_0
      | d(esk2_0,esk3_0) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).

cnf(c_0_24,plain,
    ( product(X1,product(X2,X1)) = X1
    | ~ d(X2,X1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_25,negated_conjecture,
    ( product(esk3_0,product(esk2_0,esk3_0)) = esk3_0
    | d(esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_26,plain,
    ( d(X1,X3)
    | ~ r(X1,X2)
    | ~ l(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_27,plain,
    ( r(X1,X2)
    | product(X1,X2) != X2
    | product(X2,X1) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_28,negated_conjecture,
    product(esk3_0,product(esk2_0,esk3_0)) = esk3_0,
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_29,plain,
    ( d(X1,X2)
    | product(X3,X1) != X1
    | product(X1,X3) != X3
    | ~ l(X3,X2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_30,negated_conjecture,
    product(esk3_0,product(esk2_0,product(esk3_0,X1))) = product(esk3_0,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_28]),c_0_8]) ).

cnf(c_0_31,plain,
    ( d(product(X1,X2),X3)
    | product(X1,product(X2,X1)) != X1
    | ~ l(X1,X3) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_12]),c_0_8]) ).

cnf(c_0_32,plain,
    product(X1,product(X2,product(X1,X2))) = product(X1,X2),
    inference(spm,[status(thm)],[c_0_9,c_0_8]) ).

cnf(c_0_33,negated_conjecture,
    ( product(esk3_0,product(esk2_0,esk1_2(esk3_0,X1))) = esk1_2(esk3_0,X1)
    | ~ d(esk3_0,X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_17]) ).

cnf(c_0_34,plain,
    ( d(product(X1,product(X2,X1)),X3)
    | ~ l(product(X1,X2),X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_12]),c_0_8]),c_0_8]),c_0_32])]) ).

cnf(c_0_35,plain,
    product(X1,product(X2,product(X3,product(X1,product(X2,X3))))) = product(X1,product(X2,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_32]),c_0_8]),c_0_8]) ).

cnf(c_0_36,plain,
    ( product(X1,product(esk1_2(X2,X1),X3)) = product(X1,X3)
    | ~ d(X2,X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_22]) ).

cnf(c_0_37,negated_conjecture,
    ( esk1_2(esk3_0,esk2_0) = product(esk3_0,esk2_0)
    | ~ d(esk3_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_33,c_0_22]) ).

cnf(c_0_38,plain,
    ( d(product(X1,product(X2,product(X3,product(X1,X2)))),X4)
    | ~ l(product(X1,product(X2,X3)),X4) ),
    inference(rw,[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_8]),c_0_8]),c_0_8]),c_0_8]),c_0_35]),c_0_8]),c_0_8]),c_0_8]),c_0_8]),c_0_35]) ).

cnf(c_0_39,negated_conjecture,
    ( product(esk2_0,product(esk3_0,product(esk2_0,X1))) = product(esk2_0,X1)
    | ~ d(esk3_0,esk2_0) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_8]) ).

cnf(c_0_40,plain,
    ( product(X1,X2) = X2
    | ~ r(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_41,negated_conjecture,
    ( d(esk2_0,X1)
    | ~ d(esk3_0,esk2_0)
    | ~ l(product(esk2_0,esk3_0),X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_9]),c_0_9]),c_0_12]) ).

cnf(c_0_42,plain,
    ( l(X1,X2)
    | product(X1,X2) != X1
    | product(X2,X1) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_43,negated_conjecture,
    ( d(esk3_0,X1)
    | ~ l(product(esk3_0,esk2_0),X1) ),
    inference(spm,[status(thm)],[c_0_34,c_0_28]) ).

cnf(c_0_44,plain,
    product(X1,product(X2,product(X3,product(X1,product(X2,product(X3,X4)))))) = product(X1,product(X2,product(X3,X4))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_16]),c_0_8]),c_0_8]) ).

cnf(c_0_45,plain,
    ( product(esk1_2(X1,X2),X1) = X1
    | ~ d(X1,X2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_14]) ).

cnf(c_0_46,negated_conjecture,
    ( ~ d(esk2_0,esk3_0)
    | product(esk2_0,product(esk3_0,esk2_0)) != esk2_0
    | product(esk3_0,product(esk2_0,esk3_0)) != esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_47,negated_conjecture,
    ( d(esk2_0,X1)
    | product(esk2_0,product(esk3_0,X1)) != product(esk2_0,esk3_0)
    | product(X1,product(esk2_0,esk3_0)) != X1
    | ~ d(esk3_0,esk2_0) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_8]) ).

cnf(c_0_48,negated_conjecture,
    ( d(esk3_0,X1)
    | product(esk3_0,product(esk2_0,X1)) != product(esk3_0,esk2_0)
    | product(X1,product(esk3_0,esk2_0)) != X1 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_42]),c_0_8]) ).

cnf(c_0_49,negated_conjecture,
    product(X1,product(esk3_0,product(esk2_0,product(X1,product(esk3_0,X2))))) = product(X1,product(esk3_0,X2)),
    inference(spm,[status(thm)],[c_0_44,c_0_30]) ).

cnf(c_0_50,plain,
    product(X1,product(X2,product(X3,product(X2,product(X1,product(X2,X3)))))) = product(X1,product(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_9]),c_0_8]) ).

cnf(c_0_51,negated_conjecture,
    product(X1,product(esk3_0,product(esk2_0,product(X1,esk3_0)))) = product(X1,esk3_0),
    inference(spm,[status(thm)],[c_0_44,c_0_28]) ).

cnf(c_0_52,plain,
    ( product(esk1_2(X1,X2),product(X1,X3)) = product(X1,X3)
    | ~ d(X1,X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_45]) ).

cnf(c_0_53,negated_conjecture,
    ( product(esk2_0,product(esk3_0,esk2_0)) != esk2_0
    | ~ d(esk2_0,esk3_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_28])]) ).

cnf(c_0_54,negated_conjecture,
    ( d(esk2_0,X1)
    | product(esk2_0,product(esk3_0,X1)) != product(esk2_0,esk3_0)
    | product(esk2_0,product(esk3_0,esk2_0)) != esk2_0
    | product(X1,product(esk2_0,esk3_0)) != X1 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_9])]) ).

cnf(c_0_55,negated_conjecture,
    product(X1,product(esk3_0,product(X1,product(esk2_0,product(X1,esk3_0))))) = product(X1,esk3_0),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).

cnf(c_0_56,plain,
    ( product(X1,X2) = X1
    | ~ l(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_57,plain,
    ( product(X1,product(esk1_2(X2,X3),product(X1,product(X2,X4)))) = product(X1,product(X2,X4))
    | ~ d(X2,X3) ),
    inference(spm,[status(thm)],[c_0_16,c_0_52]) ).

cnf(c_0_58,negated_conjecture,
    ( product(esk2_0,product(esk3_0,esk2_0)) = esk2_0
    | d(esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_59,negated_conjecture,
    product(esk2_0,product(esk3_0,esk2_0)) != esk2_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_9]),c_0_28])]) ).

cnf(c_0_60,negated_conjecture,
    product(esk3_0,product(X1,product(esk2_0,product(X1,esk3_0)))) = product(esk3_0,product(X1,esk3_0)),
    inference(spm,[status(thm)],[c_0_16,c_0_55]) ).

cnf(c_0_61,plain,
    ( product(esk1_2(X1,X2),X2) = esk1_2(X1,X2)
    | ~ d(X1,X2) ),
    inference(spm,[status(thm)],[c_0_56,c_0_19]) ).

cnf(c_0_62,negated_conjecture,
    ( product(esk3_0,product(esk1_2(esk2_0,X1),esk3_0)) = esk3_0
    | ~ d(esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_57,c_0_28]) ).

cnf(c_0_63,negated_conjecture,
    d(esk2_0,esk3_0),
    inference(sr,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_64,plain,
    ( product(X1,product(esk1_2(X1,X2),X3)) = product(esk1_2(X1,X2),X3)
    | ~ d(X1,X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_17]) ).

cnf(c_0_65,negated_conjecture,
    ( product(esk3_0,product(esk1_2(esk3_0,X1),product(esk2_0,esk3_0))) = esk3_0
    | ~ d(esk3_0,X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_45]),c_0_9]) ).

cnf(c_0_66,plain,
    ( product(esk1_2(X1,X2),product(X2,esk1_2(X1,X2))) = esk1_2(X1,X2)
    | ~ d(X1,X2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_61]) ).

cnf(c_0_67,negated_conjecture,
    product(esk3_0,esk1_2(esk2_0,esk3_0)) = esk3_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_61]),c_0_63])]) ).

cnf(c_0_68,negated_conjecture,
    ( product(esk1_2(esk3_0,X1),product(esk2_0,esk3_0)) = esk3_0
    | ~ d(esk3_0,X1) ),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_69,plain,
    ( d(X1,X2)
    | ~ l(X1,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_9]),c_0_9])]) ).

cnf(c_0_70,plain,
    ( d(X1,X2)
    | ~ d(X1,X3)
    | ~ l(esk1_2(X1,X3),X2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_14]) ).

cnf(c_0_71,negated_conjecture,
    product(esk1_2(esk2_0,esk3_0),esk3_0) = esk1_2(esk2_0,esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_63])]) ).

cnf(c_0_72,negated_conjecture,
    ( product(X1,product(esk2_0,esk3_0)) = product(X1,esk3_0)
    | ~ d(esk3_0,X1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_68]) ).

cnf(c_0_73,plain,
    ( d(X1,X2)
    | product(X2,X1) != X2
    | product(X1,X2) != X1 ),
    inference(spm,[status(thm)],[c_0_69,c_0_42]) ).

cnf(c_0_74,plain,
    ( d(X1,X2)
    | product(esk1_2(X1,X3),X2) != esk1_2(X1,X3)
    | product(X2,esk1_2(X1,X3)) != X2
    | ~ d(X1,X3) ),
    inference(spm,[status(thm)],[c_0_70,c_0_42]) ).

cnf(c_0_75,negated_conjecture,
    product(esk1_2(esk2_0,esk3_0),product(esk3_0,X1)) = product(esk1_2(esk2_0,esk3_0),X1),
    inference(spm,[status(thm)],[c_0_8,c_0_71]) ).

cnf(c_0_76,negated_conjecture,
    ( product(X1,product(esk2_0,esk3_0)) = product(X1,esk3_0)
    | product(esk3_0,X1) != esk3_0
    | product(X1,esk3_0) != X1 ),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

cnf(c_0_77,plain,
    ( esk1_2(X1,product(X1,X2)) = product(X1,X2)
    | ~ d(X1,product(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_61,c_0_52]) ).

cnf(c_0_78,plain,
    ( d(X1,product(X2,X3))
    | product(esk1_2(X1,X4),product(X2,X3)) != esk1_2(X1,X4)
    | product(X2,product(X3,esk1_2(X1,X4))) != product(X2,X3)
    | ~ d(X1,X4) ),
    inference(spm,[status(thm)],[c_0_74,c_0_8]) ).

cnf(c_0_79,negated_conjecture,
    product(esk1_2(esk2_0,esk3_0),product(esk2_0,esk3_0)) = esk1_2(esk2_0,esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_9]),c_0_71]),c_0_9])]) ).

cnf(c_0_80,plain,
    ( product(X1,product(X2,X1)) = X1
    | ~ d(X1,product(X1,X2)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_77]),c_0_8]) ).

cnf(c_0_81,negated_conjecture,
    d(esk2_0,product(esk2_0,esk3_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_67]),c_0_63])]) ).

cnf(c_0_82,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_59]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : GRP775+1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.10  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.31  % Computer : n023.cluster.edu
% 0.14/0.31  % Model    : x86_64 x86_64
% 0.14/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31  % Memory   : 8042.1875MB
% 0.14/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31  % CPULimit   : 300
% 0.14/0.31  % WCLimit    : 300
% 0.14/0.31  % DateTime   : Mon May  4 19:06:23 EDT 2026
% 0.14/0.31  % CPUTime    : 
% 0.14/0.32  % start to proof: theBenchmark
% 2.45/2.03  % Version  : CSE_E---1.7
% 2.45/2.03  % Problem  : theBenchmark.p
% 2.45/2.03  % SZS status Theorem for theBenchmark.p
% 2.45/2.03  % SZS output start CNFRefutation
% See solution above
% 2.45/2.04  % Total time : 1.372s
%------------------------------------------------------------------------------