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ConnectPP---0.7.2.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : RNG065+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 08:55:03 AM UTC 2026

% Result   : Theorem 30.75s 41.04s
% Output   : Proof 30.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   11
% Syntax   : Number of formulae    :  110 (  69 unt;   0 def)
%            Number of atoms       :  222 (  12 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  201 (  89   ~;  85   |;  21   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;  10 con; 0-2 aty)
%            Number of variables   :   55 (   0 sgn  44   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mSumSc,axiom,
    ! [W0,W1] :
      ( ( aScalar0(W1)
        & aScalar0(W0) )
     => aScalar0(sdtpldt0(W0,W1)) ),
    file('theBenchmark.p',mSumSc) ).

fof(mMulSc,axiom,
    ! [W0,W1] :
      ( ( aScalar0(W1)
        & aScalar0(W0) )
     => aScalar0(sdtasdt0(W0,W1)) ),
    file('theBenchmark.p',mMulSc) ).

fof(mLETrn,axiom,
    ! [W0,W1,W2] :
      ( ( aScalar0(W2)
        & aScalar0(W1)
        & aScalar0(W0) )
     => ( ( sdtlseqdt0(W1,W2)
          & sdtlseqdt0(W0,W1) )
       => sdtlseqdt0(W0,W2) ) ),
    file('theBenchmark.p',mLETrn) ).

fof(mLEMon,axiom,
    ! [W0,W1,W2,W3] :
      ( ( aScalar0(W3)
        & aScalar0(W2)
        & aScalar0(W1)
        & aScalar0(W0) )
     => ( ( sdtlseqdt0(W2,W3)
          & sdtlseqdt0(W0,W1) )
       => sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) ),
    file('theBenchmark.p',mLEMon) ).

fof(m__1892,hypothesis,
    ( xR = sdtasdt0(xC,xG)
    & aScalar0(xR) ),
    file('theBenchmark.p',m__1892) ).

fof(m__1911,hypothesis,
    ( xP = sdtasdt0(xE,xH)
    & aScalar0(xP) ),
    file('theBenchmark.p',m__1911) ).

fof(m__1930,hypothesis,
    ( xS = sdtasdt0(xF,xD)
    & aScalar0(xS) ),
    file('theBenchmark.p',m__1930) ).

fof(m__1949,hypothesis,
    ( xN = sdtasdt0(xR,xS)
    & aScalar0(xN) ),
    file('theBenchmark.p',m__1949) ).

fof(m__2004,hypothesis,
    sdtlseqdt0(sdtasdt0(xP,xP),xN),
    file('theBenchmark.p',m__2004) ).

fof(m__2348,hypothesis,
    sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
    file('theBenchmark.p',m__2348) ).

fof(m__,conjecture,
    sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
    file('theBenchmark.p',m__) ).

fof(f_10_1,plain,
    ! [W0,W1] :
      ( aScalar0(sdtpldt0(W0,W1))
      | ~ aScalar0(W1)
      | ~ aScalar0(W0) ),
    inference(fof_nnf,[status(thm)],[mSumSc]) ).

fof(f_10_2,plain,
    ! [U_11,U_10] :
      ( aScalar0(sdtpldt0(U_11,U_10))
      | ~ aScalar0(U_10)
      | ~ aScalar0(U_11) ),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

fof(f_10_3,plain,
    ! [U_10,U_11] :
      ( aScalar0(sdtpldt0(U_11,U_10))
      | ~ aScalar0(U_10)
      | ~ aScalar0(U_11) ),
    inference(definitional_conversion,[status(esa)],[f_10_2]) ).

cnf(f_10_4,plain,
    ( aScalar0(sdtpldt0(U_11,U_10))
    | ~ aScalar0(U_10)
    | ~ aScalar0(U_11) ),
    inference(clausify,[status(thm)],[f_10_3]) ).

fof(f_11_1,plain,
    ! [W0,W1] :
      ( aScalar0(sdtasdt0(W0,W1))
      | ~ aScalar0(W1)
      | ~ aScalar0(W0) ),
    inference(fof_nnf,[status(thm)],[mMulSc]) ).

fof(f_11_2,plain,
    ! [U_13,U_12] :
      ( aScalar0(sdtasdt0(U_13,U_12))
      | ~ aScalar0(U_12)
      | ~ aScalar0(U_13) ),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

fof(f_11_3,plain,
    ! [U_13,U_12] :
      ( aScalar0(sdtasdt0(U_13,U_12))
      | ~ aScalar0(U_12)
      | ~ aScalar0(U_13) ),
    inference(definitional_conversion,[status(esa)],[f_11_2]) ).

cnf(f_11_4,plain,
    ( aScalar0(sdtasdt0(U_13,U_12))
    | ~ aScalar0(U_12)
    | ~ aScalar0(U_13) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

fof(f_22_1,plain,
    ! [W0,W1,W2] :
      ( sdtlseqdt0(W0,W2)
      | ~ sdtlseqdt0(W1,W2)
      | ~ sdtlseqdt0(W0,W1)
      | ~ aScalar0(W2)
      | ~ aScalar0(W1)
      | ~ aScalar0(W0) ),
    inference(fof_nnf,[status(thm)],[mLETrn]) ).

fof(f_22_2,plain,
    ! [U_37,U_36,U_35] :
      ( sdtlseqdt0(U_37,U_35)
      | ~ sdtlseqdt0(U_36,U_35)
      | ~ sdtlseqdt0(U_37,U_36)
      | ~ aScalar0(U_35)
      | ~ aScalar0(U_36)
      | ~ aScalar0(U_37) ),
    inference(variable_rename,[status(thm)],[f_22_1]) ).

fof(f_22_3,plain,
    ! [U_36,U_35,U_37] :
      ( sdtlseqdt0(U_37,U_35)
      | ~ sdtlseqdt0(U_36,U_35)
      | ~ sdtlseqdt0(U_37,U_36)
      | ~ aScalar0(U_35)
      | ~ aScalar0(U_36)
      | ~ aScalar0(U_37) ),
    inference(definitional_conversion,[status(esa)],[f_22_2]) ).

cnf(f_22_4,plain,
    ( sdtlseqdt0(U_37,U_35)
    | ~ sdtlseqdt0(U_36,U_35)
    | ~ sdtlseqdt0(U_37,U_36)
    | ~ aScalar0(U_35)
    | ~ aScalar0(U_36)
    | ~ aScalar0(U_37) ),
    inference(clausify,[status(thm)],[f_22_3]) ).

fof(f_23_1,plain,
    ! [W0,W1,W2,W3] :
      ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
      | ~ sdtlseqdt0(W2,W3)
      | ~ sdtlseqdt0(W0,W1)
      | ~ aScalar0(W3)
      | ~ aScalar0(W2)
      | ~ aScalar0(W1)
      | ~ aScalar0(W0) ),
    inference(fof_nnf,[status(thm)],[mLEMon]) ).

fof(f_23_2,plain,
    ! [U_41,U_40,U_39,U_38] :
      ( sdtlseqdt0(sdtpldt0(U_41,U_39),sdtpldt0(U_40,U_38))
      | ~ sdtlseqdt0(U_39,U_38)
      | ~ sdtlseqdt0(U_41,U_40)
      | ~ aScalar0(U_38)
      | ~ aScalar0(U_39)
      | ~ aScalar0(U_40)
      | ~ aScalar0(U_41) ),
    inference(variable_rename,[status(thm)],[f_23_1]) ).

fof(f_23_3,plain,
    ! [U_38,U_40,U_39,U_41] :
      ( sdtlseqdt0(sdtpldt0(U_41,U_39),sdtpldt0(U_40,U_38))
      | ~ sdtlseqdt0(U_39,U_38)
      | ~ sdtlseqdt0(U_41,U_40)
      | ~ aScalar0(U_38)
      | ~ aScalar0(U_39)
      | ~ aScalar0(U_40)
      | ~ aScalar0(U_41) ),
    inference(definitional_conversion,[status(esa)],[f_23_2]) ).

cnf(f_23_4,plain,
    ( sdtlseqdt0(sdtpldt0(U_41,U_39),sdtpldt0(U_40,U_38))
    | ~ sdtlseqdt0(U_39,U_38)
    | ~ sdtlseqdt0(U_41,U_40)
    | ~ aScalar0(U_38)
    | ~ aScalar0(U_39)
    | ~ aScalar0(U_40)
    | ~ aScalar0(U_41) ),
    inference(clausify,[status(thm)],[f_23_3]) ).

fof(f_52_1,plain,
    ( xR = sdtasdt0(xC,xG)
    & aScalar0(xR) ),
    inference(fof_nnf,[status(thm)],[m__1892]) ).

fof(f_52_2,plain,
    ( xR = sdtasdt0(xC,xG)
    & aScalar0(xR) ),
    inference(definitional_conversion,[status(esa)],[f_52_1]) ).

cnf(f_52_3,plain,
    aScalar0(xR),
    inference(clausify,[status(thm)],[f_52_2]) ).

fof(f_53_1,plain,
    ( xP = sdtasdt0(xE,xH)
    & aScalar0(xP) ),
    inference(fof_nnf,[status(thm)],[m__1911]) ).

fof(f_53_2,plain,
    ( xP = sdtasdt0(xE,xH)
    & aScalar0(xP) ),
    inference(definitional_conversion,[status(esa)],[f_53_1]) ).

cnf(f_53_3,plain,
    aScalar0(xP),
    inference(clausify,[status(thm)],[f_53_2]) ).

fof(f_54_1,plain,
    ( xS = sdtasdt0(xF,xD)
    & aScalar0(xS) ),
    inference(fof_nnf,[status(thm)],[m__1930]) ).

fof(f_54_2,plain,
    ( xS = sdtasdt0(xF,xD)
    & aScalar0(xS) ),
    inference(definitional_conversion,[status(esa)],[f_54_1]) ).

cnf(f_54_3,plain,
    aScalar0(xS),
    inference(clausify,[status(thm)],[f_54_2]) ).

fof(f_55_1,plain,
    ( xN = sdtasdt0(xR,xS)
    & aScalar0(xN) ),
    inference(fof_nnf,[status(thm)],[m__1949]) ).

fof(f_55_2,plain,
    ( xN = sdtasdt0(xR,xS)
    & aScalar0(xN) ),
    inference(definitional_conversion,[status(esa)],[f_55_1]) ).

cnf(f_55_3,plain,
    aScalar0(xN),
    inference(clausify,[status(thm)],[f_55_2]) ).

fof(f_57_1,plain,
    sdtlseqdt0(sdtasdt0(xP,xP),xN),
    inference(fof_nnf,[status(thm)],[m__2004]) ).

fof(f_57_2,plain,
    sdtlseqdt0(sdtasdt0(xP,xP),xN),
    inference(definitional_conversion,[status(esa)],[f_57_1]) ).

cnf(f_57_3,plain,
    sdtlseqdt0(sdtasdt0(xP,xP),xN),
    inference(clausify,[status(thm)],[f_57_2]) ).

fof(f_64_1,plain,
    sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
    inference(fof_nnf,[status(thm)],[m__2348]) ).

fof(f_64_2,plain,
    sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
    inference(definitional_conversion,[status(esa)],[f_64_1]) ).

cnf(f_64_3,plain,
    sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
    inference(clausify,[status(thm)],[f_64_2]) ).

fof(f_65_1,negated_conjecture,
    ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
    inference(negate,[status(cth)],[m__]) ).

fof(f_65_2,negated_conjecture,
    ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
    inference(definitional_conversion,[status(esa)],[f_65_1]) ).

cnf(f_65_3,negated_conjecture,
    ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
    inference(clausify,[status(thm)],[f_65_2]) ).

cnf(t1,plain,
    ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
    inference(start,[status(thm),parent(0:0)],[f_65_3]) ).

cnf(t2,plain,
    ( ~ aScalar0(sdtpldt0(xN,xN))
    | ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
    | ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN))
    | ~ sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
    | ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
    | sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
    inference(extension,[status(thm),parent(t1:1)],[f_22_4]) ).

cnf(t3,plain,
    $false,
    inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).

cnf(t4,plain,
    ( ~ aScalar0(sdtasdt0(xP,xP))
    | ~ aScalar0(sdtasdt0(xP,xP))
    | aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) ),
    inference(extension,[status(thm),parent(t2:2)],[f_10_4]) ).

cnf(t5,plain,
    $false,
    inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).

cnf(t6,plain,
    ( ~ aScalar0(xP)
    | ~ aScalar0(xP)
    | aScalar0(sdtasdt0(xP,xP)) ),
    inference(extension,[status(thm),parent(t4:2)],[f_11_4]) ).

cnf(t7,plain,
    $false,
    inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).

cnf(t8,plain,
    aScalar0(xP),
    inference(extension,[status(thm),parent(t6:2)],[f_53_3]) ).

cnf(t9,plain,
    $false,
    inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).

cnf(l4,lemma,
    aScalar0(xP),
    inference(lemma,[status(cth),parent(t6:2),below(t4:2)],[t6:2]) ).

cnf(t10,plain,
    aScalar0(xP),
    inference(lemma_extension,[status(thm),parent(t6:3)],[l4:1]) ).

cnf(t11,plain,
    $false,
    inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).

cnf(l3,lemma,
    aScalar0(sdtasdt0(xP,xP)),
    inference(lemma,[status(cth),parent(t4:2),below(t2:2)],[t4:2]) ).

cnf(t12,plain,
    aScalar0(sdtasdt0(xP,xP)),
    inference(lemma_extension,[status(thm),parent(t4:3)],[l3:1]) ).

cnf(t13,plain,
    $false,
    inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).

cnf(t14,plain,
    sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
    inference(extension,[status(thm),parent(t2:3)],[f_64_3]) ).

cnf(t15,plain,
    $false,
    inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:3]) ).

cnf(t16,plain,
    ( ~ aScalar0(xN)
    | ~ aScalar0(sdtasdt0(xP,xP))
    | ~ aScalar0(xN)
    | ~ sdtlseqdt0(sdtasdt0(xP,xP),xN)
    | ~ sdtlseqdt0(sdtasdt0(xP,xP),xN)
    | ~ aScalar0(sdtasdt0(xP,xP))
    | sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(xN,xN)) ),
    inference(extension,[status(thm),parent(t2:4)],[f_23_4]) ).

cnf(t17,plain,
    $false,
    inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:4]) ).

cnf(t18,plain,
    ( ~ aScalar0(xP)
    | ~ aScalar0(xP)
    | aScalar0(sdtasdt0(xP,xP)) ),
    inference(extension,[status(thm),parent(t16:2)],[f_11_4]) ).

cnf(t19,plain,
    $false,
    inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).

cnf(t20,plain,
    aScalar0(xP),
    inference(extension,[status(thm),parent(t18:2)],[f_53_3]) ).

cnf(t21,plain,
    $false,
    inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).

cnf(l8,lemma,
    aScalar0(xP),
    inference(lemma,[status(cth),parent(t18:2),below(t16:2)],[t18:2]) ).

cnf(t22,plain,
    aScalar0(xP),
    inference(lemma_extension,[status(thm),parent(t18:3)],[l8:1]) ).

cnf(t23,plain,
    $false,
    inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).

cnf(l7,lemma,
    aScalar0(sdtasdt0(xP,xP)),
    inference(lemma,[status(cth),parent(t16:2),below(t2:4)],[t16:2]) ).

cnf(t24,plain,
    sdtlseqdt0(sdtasdt0(xP,xP),xN),
    inference(extension,[status(thm),parent(t16:3)],[f_57_3]) ).

cnf(t25,plain,
    $false,
    inference(connection,[status(thm),parent(t24:1)],[t24:1,t16:3]) ).

cnf(l9,lemma,
    sdtlseqdt0(sdtasdt0(xP,xP),xN),
    inference(lemma,[status(cth),parent(t16:3),below(t2:4)],[t16:3]) ).

cnf(t26,plain,
    sdtlseqdt0(sdtasdt0(xP,xP),xN),
    inference(lemma_extension,[status(thm),parent(t16:4)],[l9:1]) ).

cnf(t27,plain,
    $false,
    inference(connection,[status(thm),parent(t26:1)],[t26:1,t16:4]) ).

cnf(t28,plain,
    aScalar0(xN),
    inference(extension,[status(thm),parent(t16:5)],[f_55_3]) ).

cnf(t29,plain,
    $false,
    inference(connection,[status(thm),parent(t28:1)],[t28:1,t16:5]) ).

cnf(l10,lemma,
    aScalar0(xN),
    inference(lemma,[status(cth),parent(t16:5),below(t2:4)],[t16:5]) ).

cnf(t30,plain,
    aScalar0(sdtasdt0(xP,xP)),
    inference(lemma_extension,[status(thm),parent(t16:6)],[l7:1]) ).

cnf(t31,plain,
    $false,
    inference(connection,[status(thm),parent(t30:1)],[t30:1,t16:6]) ).

cnf(t32,plain,
    aScalar0(xN),
    inference(lemma_extension,[status(thm),parent(t16:7)],[l10:1]) ).

cnf(t33,plain,
    $false,
    inference(connection,[status(thm),parent(t32:1)],[t32:1,t16:7]) ).

cnf(t34,plain,
    ( ~ aScalar0(sdtasdt0(xS,xS))
    | ~ aScalar0(sdtasdt0(xR,xR))
    | aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
    inference(extension,[status(thm),parent(t2:5)],[f_10_4]) ).

cnf(t35,plain,
    $false,
    inference(connection,[status(thm),parent(t34:1)],[t34:1,t2:5]) ).

cnf(t36,plain,
    ( ~ aScalar0(xR)
    | ~ aScalar0(xR)
    | aScalar0(sdtasdt0(xR,xR)) ),
    inference(extension,[status(thm),parent(t34:2)],[f_11_4]) ).

cnf(t37,plain,
    $false,
    inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).

cnf(t38,plain,
    aScalar0(xR),
    inference(extension,[status(thm),parent(t36:2)],[f_52_3]) ).

cnf(t39,plain,
    $false,
    inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).

cnf(l13,lemma,
    aScalar0(xR),
    inference(lemma,[status(cth),parent(t36:2),below(t34:2)],[t36:2]) ).

cnf(t40,plain,
    aScalar0(xR),
    inference(lemma_extension,[status(thm),parent(t36:3)],[l13:1]) ).

cnf(t41,plain,
    $false,
    inference(connection,[status(thm),parent(t40:1)],[t40:1,t36:3]) ).

cnf(t42,plain,
    ( ~ aScalar0(xS)
    | ~ aScalar0(xS)
    | aScalar0(sdtasdt0(xS,xS)) ),
    inference(extension,[status(thm),parent(t34:3)],[f_11_4]) ).

cnf(t43,plain,
    $false,
    inference(connection,[status(thm),parent(t42:1)],[t42:1,t34:3]) ).

cnf(t44,plain,
    aScalar0(xS),
    inference(extension,[status(thm),parent(t42:2)],[f_54_3]) ).

cnf(t45,plain,
    $false,
    inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).

cnf(l15,lemma,
    aScalar0(xS),
    inference(lemma,[status(cth),parent(t42:2),below(t34:3)],[t42:2]) ).

cnf(t46,plain,
    aScalar0(xS),
    inference(lemma_extension,[status(thm),parent(t42:3)],[l15:1]) ).

cnf(t47,plain,
    $false,
    inference(connection,[status(thm),parent(t46:1)],[t46:1,t42:3]) ).

cnf(t48,plain,
    ( ~ aScalar0(xN)
    | ~ aScalar0(xN)
    | aScalar0(sdtpldt0(xN,xN)) ),
    inference(extension,[status(thm),parent(t2:6)],[f_10_4]) ).

cnf(t49,plain,
    $false,
    inference(connection,[status(thm),parent(t48:1)],[t48:1,t2:6]) ).

cnf(t50,plain,
    aScalar0(xN),
    inference(extension,[status(thm),parent(t48:2)],[f_55_3]) ).

cnf(t51,plain,
    $false,
    inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).

cnf(l17,lemma,
    aScalar0(xN),
    inference(lemma,[status(cth),parent(t48:2),below(t2:6)],[t48:2]) ).

cnf(t52,plain,
    aScalar0(xN),
    inference(lemma_extension,[status(thm),parent(t48:3)],[l17:1]) ).

cnf(t53,plain,
    $false,
    inference(connection,[status(thm),parent(t52:1)],[t52:1,t48:3]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : RNG065+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03  This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04  % Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.38  % Computer : n007.cluster.edu
% 0.09/10.38  % Model    : x86_64 x86_64
% 0.09/10.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38  % Memory   : 8046.5625MB
% 0.09/10.38  % OS       : Linux 6.8.0-71-generic
% 0.09/10.38  % CPULimit : 300
% 0.09/10.38  % WCLimit  : 300
% 0.09/10.38  % DateTime : Sat Sep 19 20:45:45 UTC 2026
% 0.09/10.38  % CPUTime  : 
% 30.75/41.04  % SZS status Theorem for theBenchmark
% 30.75/41.04  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------