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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : GEO298+1 : TPTP v9.2.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n004.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 04:20:17 PM UTC 2026

% Result   : Theorem 9.02s 6.69s
% Output   : CNFRefutation 9.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   63 (  36 unt;   0 def)
%            Number of atoms       :  289 ( 108 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives :  360 ( 134   ~; 133   |;  88   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   18 (  18 usr;  16 con; 0-3 aty)
%            Number of variables   :   94 (   0 sgn  40   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof('qu(cond(axiom(91), 0), imp(cond(axiom(91), 0)))',axiom,
    ! [X1,X2,X3,X4,X5] :
      ( ( X4 = X5
        & ron(X3,X4)
        & ron(X2,X4)
        & ron(X1,X4)
        & rline(X5)
        & X2 != X3
        & X1 != X3
        & X1 != X2
        & ? [X6] :
            ( X3 = X6
            & rpoint(X6) )
        & ? [X7] :
            ( X2 = X7
            & rpoint(X7) )
        & ? [X8] :
            ( X1 = X8
            & rpoint(X8) ) )
     => ( rR(X2,X1,X3)
        | rR(X1,X2,X3)
        | rR(X3,X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(91), 0), imp(cond(axiom(91), 0)))') ).

fof('and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))',axiom,
    ( ~ ? [X10] :
          ( ron(vd1187,X10)
          & ron(vd1186,X10)
          & ron(vd1185,X10)
          & rline(X10) )
    & vangle(vd1179,vd1178,vd1180) = vangle(vd1186,vd1185,vd1187)
    & vf(vd1178,vd1180) = vf(vd1185,vd1187)
    & vf(vd1178,vd1179) = vf(vd1185,vd1186)
    & ? [X11] :
        ( vd1187 = X11
        & rpoint(X11) )
    & ? [X12] :
        ( vd1186 = X12
        & rpoint(X12) )
    & ? [X13] :
        ( vd1185 = X13
        & rpoint(X13) )
    & vd1179 != vd1180
    & vd1178 != vd1180
    & vd1178 != vd1179
    & ? [X14] :
        ( vd1180 = X14
        & rpoint(X14) )
    & ? [X15] :
        ( vd1179 = X15
        & rpoint(X15) )
    & ? [X16] :
        ( vd1178 = X16
        & rpoint(X16) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))') ).

fof('qe(s3(plural(271)))',axiom,
    ? [X9] :
      ( vd1201 = X9
      & rpoint(X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qe(s3(plural(271)))') ).

fof('qu(cond(axiom(81), 0), imp(cond(axiom(81), 0)))',axiom,
    ! [X276,X277,X278] :
      ( ( rR(X277,X276,X278)
        & ? [X279] :
            ( X278 = X279
            & rpoint(X279) )
        & ? [X280] :
            ( X277 = X280
            & rpoint(X280) )
        & ? [X281] :
            ( X276 = X281
            & rpoint(X281) ) )
     => ( ~ rR(X276,X277,X278)
        & X276 != X278
        & X276 != X277
        & rR(X277,X278,X276) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(81), 0), imp(cond(axiom(81), 0)))') ).

fof('pred(s3(plural(315)), 0)',axiom,
    ron(vd1187,vd1232),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(s3(plural(315)), 0)') ).

fof('pred(293, 0)',axiom,
    rline(vd1232),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(293, 0)') ).

fof('pred(s2(plural(315)), 0)',axiom,
    ron(vd1201,vd1232),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(s2(plural(315)), 0)') ).

fof('holds(320, 1251, 0)',axiom,
    vd1201 != vd1187,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(320, 1251, 0)') ).

fof('dis(321)',conjecture,
    ( rR(vd1201,vd1185,vd1187)
    | rR(vd1187,vd1185,vd1201) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','dis(321)') ).

fof('pred(s1(plural(315)), 0)',axiom,
    ron(vd1185,vd1232),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(s1(plural(315)), 0)') ).

fof('qu(cond(axiom(99), 0), imp(cond(axiom(99), 0)))',axiom,
    ! [X74,X75,X76,X77] :
      ( ( rS(X74,X75,X76)
        & X76 = X77
        & rline(X77)
        & ? [X78] :
            ( X75 = X78
            & rpoint(X78) )
        & ? [X79] :
            ( X74 = X79
            & rpoint(X79) ) )
     => ~ ron(X74,X76) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(99), 0), imp(cond(axiom(99), 0)))') ).

fof('neg(neg(319))',axiom,
    ~ rR(vd1185,vd1201,vd1187),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','neg(neg(319))') ).

fof('neg(neg(270))',axiom,
    ~ ron(vd1187,vd1197),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','neg(neg(270))') ).

fof('holds(comma_conjunct2(comma_conjunct2(plural(271))), 1214, 0)',axiom,
    rS(vd1201,vd1187,vd1197),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(comma_conjunct2(comma_conjunct2(plural(271))), 1214, 0)') ).

fof('pred(269, 0)',axiom,
    rline(vd1197),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(269, 0)') ).

fof('pred(s3(plural(274)), 0)',axiom,
    ron(vd1185,vd1197),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(s3(plural(274)), 0)') ).

fof(c_0_16,plain,
    ! [X1539,X1540,X1541,X1542,X1543,X1544,X1545,X1546] :
      ( X1542 != X1543
      | ~ ron(X1541,X1542)
      | ~ ron(X1540,X1542)
      | ~ ron(X1539,X1542)
      | ~ rline(X1543)
      | X1540 = X1541
      | X1539 = X1541
      | X1539 = X1540
      | X1541 != X1544
      | ~ rpoint(X1544)
      | X1540 != X1545
      | ~ rpoint(X1545)
      | X1539 != X1546
      | ~ rpoint(X1546)
      | rR(X1540,X1539,X1541)
      | rR(X1539,X1540,X1541)
      | rR(X1541,X1539,X1540) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['qu(cond(axiom(91), 0), imp(cond(axiom(91), 0)))'])])]) ).

fof(c_0_17,plain,
    ! [X1548] :
      ( ( ~ ron(vd1187,X1548)
        | ~ ron(vd1186,X1548)
        | ~ ron(vd1185,X1548)
        | ~ rline(X1548) )
      & vangle(vd1179,vd1178,vd1180) = vangle(vd1186,vd1185,vd1187)
      & vf(vd1178,vd1180) = vf(vd1185,vd1187)
      & vf(vd1178,vd1179) = vf(vd1185,vd1186)
      & vd1187 = esk2_0
      & rpoint(esk2_0)
      & vd1186 = esk3_0
      & rpoint(esk3_0)
      & vd1185 = esk4_0
      & rpoint(esk4_0)
      & vd1179 != vd1180
      & vd1178 != vd1180
      & vd1178 != vd1179
      & vd1180 = esk5_0
      & rpoint(esk5_0)
      & vd1179 = esk6_0
      & rpoint(esk6_0)
      & vd1178 = esk7_0
      & rpoint(esk7_0) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))'])])])]) ).

cnf(c_0_18,plain,
    ( X4 = X3
    | X5 = X3
    | X5 = X4
    | rR(X4,X5,X3)
    | rR(X5,X4,X3)
    | rR(X3,X5,X4)
    | X1 != X2
    | ~ ron(X3,X1)
    | ~ ron(X4,X1)
    | ~ ron(X5,X1)
    | ~ rline(X2)
    | X3 != X6
    | ~ rpoint(X6)
    | X4 != X7
    | ~ rpoint(X7)
    | X5 != X8
    | ~ rpoint(X8) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_19,plain,
    rpoint(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_20,plain,
    vd1187 = esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_21,plain,
    ( vd1201 = esk1_0
    & rpoint(esk1_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],['qe(s3(plural(271)))'])]) ).

fof(c_0_22,plain,
    ! [X276,X277,X278] :
      ( ( rR(X277,X276,X278)
        & ? [X279] :
            ( X278 = X279
            & rpoint(X279) )
        & ? [X280] :
            ( X277 = X280
            & rpoint(X280) )
        & ? [X281] :
            ( X276 = X281
            & rpoint(X281) ) )
     => ( ~ rR(X276,X277,X278)
        & X276 != X278
        & X276 != X277
        & rR(X277,X278,X276) ) ),
    inference(fof_simplification,[status(thm)],['qu(cond(axiom(81), 0), imp(cond(axiom(81), 0)))']) ).

cnf(c_0_23,plain,
    ( X1 = X2
    | X3 = X2
    | X3 = X1
    | rR(X2,X1,X3)
    | rR(X1,X2,X3)
    | rR(X3,X2,X1)
    | ~ rpoint(X2)
    | ~ rpoint(X1)
    | ~ rpoint(X3)
    | ~ rline(X4)
    | ~ ron(X2,X4)
    | ~ ron(X1,X4)
    | ~ ron(X3,X4) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_18])])])]) ).

cnf(c_0_24,plain,
    ron(vd1187,vd1232),
    inference(split_conjunct,[status(thm)],['pred(s3(plural(315)), 0)']) ).

cnf(c_0_25,plain,
    rpoint(vd1187),
    inference(rw,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_26,plain,
    rline(vd1232),
    inference(split_conjunct,[status(thm)],['pred(293, 0)']) ).

cnf(c_0_27,plain,
    rpoint(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_28,plain,
    vd1201 = esk1_0,
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

fof(c_0_29,plain,
    ! [X1844,X1845,X1846,X1847,X1848,X1849] :
      ( ( ~ rR(X1844,X1845,X1846)
        | ~ rR(X1845,X1844,X1846)
        | X1846 != X1847
        | ~ rpoint(X1847)
        | X1845 != X1848
        | ~ rpoint(X1848)
        | X1844 != X1849
        | ~ rpoint(X1849) )
      & ( X1844 != X1846
        | ~ rR(X1845,X1844,X1846)
        | X1846 != X1847
        | ~ rpoint(X1847)
        | X1845 != X1848
        | ~ rpoint(X1848)
        | X1844 != X1849
        | ~ rpoint(X1849) )
      & ( X1844 != X1845
        | ~ rR(X1845,X1844,X1846)
        | X1846 != X1847
        | ~ rpoint(X1847)
        | X1845 != X1848
        | ~ rpoint(X1848)
        | X1844 != X1849
        | ~ rpoint(X1849) )
      & ( rR(X1845,X1846,X1844)
        | ~ rR(X1845,X1844,X1846)
        | X1846 != X1847
        | ~ rpoint(X1847)
        | X1845 != X1848
        | ~ rpoint(X1848)
        | X1844 != X1849
        | ~ rpoint(X1849) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).

cnf(c_0_30,plain,
    ( X1 = vd1187
    | X2 = vd1187
    | X2 = X1
    | rR(vd1187,X1,X2)
    | rR(X1,vd1187,X2)
    | rR(X2,vd1187,X1)
    | ~ rpoint(X1)
    | ~ rpoint(X2)
    | ~ ron(X1,vd1232)
    | ~ ron(X2,vd1232) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).

cnf(c_0_31,plain,
    ron(vd1201,vd1232),
    inference(split_conjunct,[status(thm)],['pred(s2(plural(315)), 0)']) ).

cnf(c_0_32,plain,
    rpoint(vd1201),
    inference(rw,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_33,plain,
    vd1201 != vd1187,
    inference(split_conjunct,[status(thm)],['holds(320, 1251, 0)']) ).

cnf(c_0_34,plain,
    rpoint(esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_35,plain,
    vd1185 = esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_36,negated_conjecture,
    ~ ( rR(vd1201,vd1185,vd1187)
      | rR(vd1187,vd1185,vd1201) ),
    inference(assume_negation,[status(cth)],['dis(321)']) ).

cnf(c_0_37,plain,
    ( rR(X1,X2,X3)
    | ~ rR(X1,X3,X2)
    | X2 != X4
    | ~ rpoint(X4)
    | X1 != X5
    | ~ rpoint(X5)
    | X3 != X6
    | ~ rpoint(X6) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_38,plain,
    ( X1 = vd1201
    | X1 = vd1187
    | rR(X1,vd1187,vd1201)
    | rR(vd1201,vd1187,X1)
    | rR(vd1187,vd1201,X1)
    | ~ rpoint(X1)
    | ~ ron(X1,vd1232) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),c_0_33]) ).

cnf(c_0_39,plain,
    ron(vd1185,vd1232),
    inference(split_conjunct,[status(thm)],['pred(s1(plural(315)), 0)']) ).

cnf(c_0_40,plain,
    rpoint(vd1185),
    inference(rw,[status(thm)],[c_0_34,c_0_35]) ).

fof(c_0_41,negated_conjecture,
    ( ~ rR(vd1201,vd1185,vd1187)
    & ~ rR(vd1187,vd1185,vd1201) ),
    inference(fof_nnf,[status(thm)],[c_0_36]) ).

fof(c_0_42,plain,
    ! [X74,X75,X76,X77] :
      ( ( rS(X74,X75,X76)
        & X76 = X77
        & rline(X77)
        & ? [X78] :
            ( X75 = X78
            & rpoint(X78) )
        & ? [X79] :
            ( X74 = X79
            & rpoint(X79) ) )
     => ~ ron(X74,X76) ),
    inference(fof_simplification,[status(thm)],['qu(cond(axiom(99), 0), imp(cond(axiom(99), 0)))']) ).

cnf(c_0_43,plain,
    ( rR(X1,X2,X3)
    | ~ rpoint(X3)
    | ~ rpoint(X1)
    | ~ rpoint(X2)
    | ~ rR(X1,X3,X2) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_37])])]) ).

cnf(c_0_44,plain,
    ( vd1187 = vd1185
    | vd1201 = vd1185
    | rR(vd1187,vd1201,vd1185)
    | rR(vd1201,vd1187,vd1185)
    | rR(vd1185,vd1187,vd1201) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).

cnf(c_0_45,negated_conjecture,
    ~ rR(vd1187,vd1185,vd1201),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

fof(c_0_46,plain,
    ! [X1628,X1629,X1630,X1631,X1632,X1633] :
      ( ~ rS(X1628,X1629,X1630)
      | X1630 != X1631
      | ~ rline(X1631)
      | X1629 != X1632
      | ~ rpoint(X1632)
      | X1628 != X1633
      | ~ rpoint(X1633)
      | ~ ron(X1628,X1630) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).

cnf(c_0_47,plain,
    ( vd1201 = vd1185
    | vd1187 = vd1185
    | rR(vd1185,vd1187,vd1201)
    | rR(vd1201,vd1187,vd1185) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_32]),c_0_25]),c_0_40])]),c_0_45]) ).

cnf(c_0_48,negated_conjecture,
    ~ rR(vd1201,vd1185,vd1187),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

fof(c_0_49,plain,
    ~ rR(vd1185,vd1201,vd1187),
    inference(fof_simplification,[status(thm)],['neg(neg(319))']) ).

cnf(c_0_50,plain,
    ( ~ rS(X1,X2,X3)
    | X3 != X4
    | ~ rline(X4)
    | X2 != X5
    | ~ rpoint(X5)
    | X1 != X6
    | ~ rpoint(X6)
    | ~ ron(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

fof(c_0_51,plain,
    ~ ron(vd1187,vd1197),
    inference(fof_simplification,[status(thm)],['neg(neg(270))']) ).

cnf(c_0_52,plain,
    ( vd1187 = vd1185
    | vd1201 = vd1185
    | rR(vd1185,vd1187,vd1201) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_47]),c_0_25]),c_0_32]),c_0_40])]),c_0_48]) ).

cnf(c_0_53,plain,
    ~ rR(vd1185,vd1201,vd1187),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_54,plain,
    ( ~ rS(X1,X2,X3)
    | ~ rpoint(X1)
    | ~ rpoint(X2)
    | ~ rline(X3)
    | ~ ron(X1,X3) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_50])])]) ).

cnf(c_0_55,plain,
    rS(vd1201,vd1187,vd1197),
    inference(split_conjunct,[status(thm)],['holds(comma_conjunct2(comma_conjunct2(plural(271))), 1214, 0)']) ).

cnf(c_0_56,plain,
    rline(vd1197),
    inference(split_conjunct,[status(thm)],['pred(269, 0)']) ).

cnf(c_0_57,plain,
    ~ ron(vd1187,vd1197),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_58,plain,
    ( vd1201 = vd1185
    | vd1187 = vd1185 ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_52]),c_0_25]),c_0_40]),c_0_32])]),c_0_53]) ).

cnf(c_0_59,plain,
    ron(vd1185,vd1197),
    inference(split_conjunct,[status(thm)],['pred(s3(plural(274)), 0)']) ).

cnf(c_0_60,plain,
    ~ ron(vd1201,vd1197),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_32]),c_0_25]),c_0_56])]) ).

cnf(c_0_61,plain,
    vd1201 = vd1185,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).

cnf(c_0_62,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61]),c_0_59])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : GEO298+1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32  % Computer : n004.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit   : 300
% 0.13/0.32  % WCLimit    : 300
% 0.13/0.32  % DateTime   : Mon May  4 17:52:47 EDT 2026
% 0.13/0.32  % CPUTime    : 
% 0.13/0.33  % start to proof: theBenchmark
% 9.02/6.69  % Version  : CSE_E---1.7
% 9.02/6.69  % Problem  : theBenchmark.p
% 9.02/6.69  % SZS status Theorem for theBenchmark.p
% 9.02/6.69  % SZS output start CNFRefutation
% See solution above
% 9.12/6.71  % Total time : 5.424s
%------------------------------------------------------------------------------