%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG067+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 08:55:04 AM UTC 2026
% Result : Theorem 30.42s 30.72s
% Output : Proof 30.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 143 ( 99 unt; 0 def)
% Number of atoms : 247 ( 12 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 190 ( 86 ~; 82 |; 18 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Maximal term depth : 5 ( 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 : 40 ( 0 sgn 32 !; 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(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__2104,hypothesis,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
file('theBenchmark.p',m__2104) ).
fof(m__,conjecture,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN),xN)),
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_12,U_13] :
( 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_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_40,U_38,U_41,U_39] :
( 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_58_1,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(fof_nnf,[status(thm)],[m__2104]) ).
fof(f_58_2,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(definitional_conversion,[status(esa)],[f_58_1]) ).
cnf(f_58_3,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN),xN)),
inference(negate,[status(cth)],[m__]) ).
fof(f_59_2,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN),xN)),
inference(definitional_conversion,[status(esa)],[f_59_1]) ).
cnf(f_59_3,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN),xN)),
inference(clausify,[status(thm)],[f_59_2]) ).
cnf(t1,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN),xN)),
inference(start,[status(thm),parent(0:0)],[f_59_3]) ).
cnf(t2,plain,
( ~ aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(xN)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),xN)
| ~ aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)))
| sdtlseqdt0(sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN),xN)) ),
inference(extension,[status(thm),parent(t1:1)],[f_23_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),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(sdtasdt0(xP,xP))
| ~ aScalar0(sdtasdt0(xP,xP))
| aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) ),
inference(extension,[status(thm),parent(t4:2)],[f_10_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ aScalar0(xP)
| ~ aScalar0(xP)
| aScalar0(sdtasdt0(xP,xP)) ),
inference(extension,[status(thm),parent(t6:2)],[f_11_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
aScalar0(xP),
inference(extension,[status(thm),parent(t8:2)],[f_53_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(l5,lemma,
aScalar0(xP),
inference(lemma,[status(cth),parent(t8:2),below(t6:2)],[t8:2]) ).
cnf(t12,plain,
aScalar0(xP),
inference(lemma_extension,[status(thm),parent(t8:3)],[l5:1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(l4,lemma,
aScalar0(sdtasdt0(xP,xP)),
inference(lemma,[status(cth),parent(t6:2),below(t4:2)],[t6:2]) ).
cnf(t14,plain,
aScalar0(sdtasdt0(xP,xP)),
inference(lemma_extension,[status(thm),parent(t6:3)],[l4:1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:3]) ).
cnf(t16,plain,
( ~ aScalar0(xP)
| ~ aScalar0(xP)
| aScalar0(sdtasdt0(xP,xP)) ),
inference(extension,[status(thm),parent(t4:3)],[f_11_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t4:3]) ).
cnf(t18,plain,
aScalar0(xP),
inference(extension,[status(thm),parent(t16:2)],[f_53_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(l7,lemma,
aScalar0(xP),
inference(lemma,[status(cth),parent(t16:2),below(t4:3)],[t16:2]) ).
cnf(t20,plain,
aScalar0(xP),
inference(lemma_extension,[status(thm),parent(t16:3)],[l7:1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(extension,[status(thm),parent(t2:3)],[f_57_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:3]) ).
cnf(l8,lemma,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(lemma,[status(cth),parent(t2:3),below(t1:1)],[t2:3]) ).
cnf(t24,plain,
( ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(xN)
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),xN)
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN)) ),
inference(extension,[status(thm),parent(t2:4)],[f_23_4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t2:4]) ).
cnf(t26,plain,
( ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(sdtasdt0(xP,xP))
| aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) ),
inference(extension,[status(thm),parent(t24:2)],[f_10_4]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( ~ aScalar0(xP)
| ~ aScalar0(xP)
| aScalar0(sdtasdt0(xP,xP)) ),
inference(extension,[status(thm),parent(t26:2)],[f_11_4]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
aScalar0(xP),
inference(extension,[status(thm),parent(t28:2)],[f_53_3]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(l12,lemma,
aScalar0(xP),
inference(lemma,[status(cth),parent(t28:2),below(t26:2)],[t28:2]) ).
cnf(t32,plain,
aScalar0(xP),
inference(lemma_extension,[status(thm),parent(t28:3)],[l12:1]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(l11,lemma,
aScalar0(sdtasdt0(xP,xP)),
inference(lemma,[status(cth),parent(t26:2),below(t24:2)],[t26:2]) ).
cnf(t34,plain,
aScalar0(sdtasdt0(xP,xP)),
inference(lemma_extension,[status(thm),parent(t26:3)],[l11:1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t26:3]) ).
cnf(t36,plain,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(lemma_extension,[status(thm),parent(t24:3)],[l8:1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t24:3]) ).
cnf(t38,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(extension,[status(thm),parent(t24:4)],[f_58_3]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t24:4]) ).
cnf(t40,plain,
aScalar0(xN),
inference(extension,[status(thm),parent(t24:5)],[f_55_3]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t24:5]) ).
cnf(t42,plain,
( ~ aScalar0(xP)
| ~ aScalar0(xP)
| aScalar0(sdtasdt0(xP,xP)) ),
inference(extension,[status(thm),parent(t24:6)],[f_11_4]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t24:6]) ).
cnf(t44,plain,
aScalar0(xP),
inference(extension,[status(thm),parent(t42:2)],[f_53_3]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(l16,lemma,
aScalar0(xP),
inference(lemma,[status(cth),parent(t42:2),below(t24:6)],[t42:2]) ).
cnf(t46,plain,
aScalar0(xP),
inference(lemma_extension,[status(thm),parent(t42:3)],[l16:1]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t42:3]) ).
cnf(t48,plain,
( ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
inference(extension,[status(thm),parent(t24:7)],[f_10_4]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t24:7]) ).
cnf(t50,plain,
( ~ aScalar0(xR)
| ~ aScalar0(xR)
| aScalar0(sdtasdt0(xR,xR)) ),
inference(extension,[status(thm),parent(t48:2)],[f_11_4]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
aScalar0(xR),
inference(extension,[status(thm),parent(t50:2)],[f_52_3]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(l19,lemma,
aScalar0(xR),
inference(lemma,[status(cth),parent(t50:2),below(t48:2)],[t50:2]) ).
cnf(t54,plain,
aScalar0(xR),
inference(lemma_extension,[status(thm),parent(t50:3)],[l19:1]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t50:3]) ).
cnf(t56,plain,
( ~ aScalar0(xS)
| ~ aScalar0(xS)
| aScalar0(sdtasdt0(xS,xS)) ),
inference(extension,[status(thm),parent(t48:3)],[f_11_4]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t48:3]) ).
cnf(t58,plain,
aScalar0(xS),
inference(extension,[status(thm),parent(t56:2)],[f_54_3]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t56:2]) ).
cnf(l21,lemma,
aScalar0(xS),
inference(lemma,[status(cth),parent(t56:2),below(t48:3)],[t56:2]) ).
cnf(t60,plain,
aScalar0(xS),
inference(lemma_extension,[status(thm),parent(t56:3)],[l21:1]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t56:3]) ).
cnf(t62,plain,
aScalar0(xN),
inference(extension,[status(thm),parent(t2:5)],[f_55_3]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t2:5]) ).
cnf(l22,lemma,
aScalar0(xN),
inference(lemma,[status(cth),parent(t2:5),below(t1:1)],[t2:5]) ).
cnf(t64,plain,
( ~ aScalar0(xP)
| ~ aScalar0(xP)
| aScalar0(sdtasdt0(xP,xP)) ),
inference(extension,[status(thm),parent(t2:6)],[f_11_4]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t2:6]) ).
cnf(t66,plain,
aScalar0(xP),
inference(extension,[status(thm),parent(t64:2)],[f_53_3]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(l24,lemma,
aScalar0(xP),
inference(lemma,[status(cth),parent(t64:2),below(t2:6)],[t64:2]) ).
cnf(t68,plain,
aScalar0(xP),
inference(lemma_extension,[status(thm),parent(t64:3)],[l24:1]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t64:3]) ).
cnf(t70,plain,
( ~ aScalar0(xN)
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN)) ),
inference(extension,[status(thm),parent(t2:7)],[f_10_4]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t2:7]) ).
cnf(t72,plain,
( ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
inference(extension,[status(thm),parent(t70:2)],[f_10_4]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t70:2]) ).
cnf(t74,plain,
( ~ aScalar0(xR)
| ~ aScalar0(xR)
| aScalar0(sdtasdt0(xR,xR)) ),
inference(extension,[status(thm),parent(t72:2)],[f_11_4]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t72:2]) ).
cnf(t76,plain,
aScalar0(xR),
inference(extension,[status(thm),parent(t74:2)],[f_52_3]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t74:2]) ).
cnf(l28,lemma,
aScalar0(xR),
inference(lemma,[status(cth),parent(t74:2),below(t72:2)],[t74:2]) ).
cnf(t78,plain,
aScalar0(xR),
inference(lemma_extension,[status(thm),parent(t74:3)],[l28:1]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t74:3]) ).
cnf(t80,plain,
( ~ aScalar0(xS)
| ~ aScalar0(xS)
| aScalar0(sdtasdt0(xS,xS)) ),
inference(extension,[status(thm),parent(t72:3)],[f_11_4]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t72:3]) ).
cnf(t82,plain,
aScalar0(xS),
inference(extension,[status(thm),parent(t80:2)],[f_54_3]) ).
cnf(t83,plain,
$false,
inference(connection,[status(thm),parent(t82:1)],[t82:1,t80:2]) ).
cnf(l30,lemma,
aScalar0(xS),
inference(lemma,[status(cth),parent(t80:2),below(t72:3)],[t80:2]) ).
cnf(t84,plain,
aScalar0(xS),
inference(lemma_extension,[status(thm),parent(t80:3)],[l30:1]) ).
cnf(t85,plain,
$false,
inference(connection,[status(thm),parent(t84:1)],[t84:1,t80:3]) ).
cnf(t86,plain,
aScalar0(xN),
inference(lemma_extension,[status(thm),parent(t70:3)],[l22:1]) ).
cnf(t87,plain,
$false,
inference(connection,[status(thm),parent(t86:1)],[t86:1,t70:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG067+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n005.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 19 20:47:49 UTC 2026
% 0.09/0.38 % CPUTime :
% 30.42/30.72 % SZS status Theorem for theBenchmark
% 30.42/30.72 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------