%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM436+1 : 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 : n026.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 08:52:14 AM UTC 2026
% Result : Theorem 31.65s 32.03s
% Output : Proof 31.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 128 ( 68 unt; 2 def)
% Number of atoms : 320 ( 64 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 330 ( 138 ~; 128 |; 57 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 103 ( 8 sgn 74 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mIntNeg,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('theBenchmark.p',mIntNeg) ).
fof(mIntPlus,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mIntPlus) ).
fof(mIntMult,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mIntMult) ).
fof(mDivisor,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) ) ),
file('theBenchmark.p',mDivisor) ).
fof(mEquMod,definition,
! [W0,W1,W2] :
( ( W2 != sz00
& aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
file('theBenchmark.p',mEquMod) ).
fof(m__979,hypothesis,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
file('theBenchmark.p',m__979) ).
fof(m__1032,hypothesis,
( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xm) ),
file('theBenchmark.p',m__1032) ).
fof(m__1071,hypothesis,
( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm))
& sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)) ),
file('theBenchmark.p',m__1071) ).
fof(m__,conjecture,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
& sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
file('theBenchmark.p',m__) ).
fof(f_4_1,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mIntNeg]) ).
fof(f_4_2,plain,
! [U_1] :
( aInteger0(smndt0(U_1))
| ~ aInteger0(U_1) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_1] :
( aInteger0(smndt0(U_1))
| ~ aInteger0(U_1) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( aInteger0(smndt0(U_1))
| ~ aInteger0(U_1) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [W0,W1] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mIntPlus]) ).
fof(f_5_2,plain,
! [U_3,U_2] :
( aInteger0(sdtpldt0(U_3,U_2))
| ~ aInteger0(U_2)
| ~ aInteger0(U_3) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_2,U_3] :
( aInteger0(sdtpldt0(U_3,U_2))
| ~ aInteger0(U_2)
| ~ aInteger0(U_3) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( aInteger0(sdtpldt0(U_3,U_2))
| ~ aInteger0(U_2)
| ~ aInteger0(U_3) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [W0,W1] :
( aInteger0(sdtasdt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mIntMult]) ).
fof(f_6_2,plain,
! [U_5,U_4] :
( aInteger0(sdtasdt0(U_5,U_4))
| ~ aInteger0(U_4)
| ~ aInteger0(U_5) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_5,U_4] :
( aInteger0(sdtasdt0(U_5,U_4))
| ~ aInteger0(U_4)
| ~ aInteger0(U_5) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( aInteger0(sdtasdt0(U_5,U_4))
| ~ aInteger0(U_4)
| ~ aInteger0(U_5) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_18_1,plain,
! [W0] :
( ! [W1] :
( ( aDivisorOf0(W1,W0)
| ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1) )
& ( ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mDivisor]) ).
fof(f_18_2,plain,
! [U_29] :
( ! [U_28] :
( ( aDivisorOf0(U_28,U_29)
| ! [U_27] :
( sdtasdt0(U_28,U_27) != U_29
| ~ aInteger0(U_27) )
| U_28 = sz00
| ~ aInteger0(U_28) )
& ( ( ? [U_26] :
( sdtasdt0(U_28,U_26) = U_29
& aInteger0(U_26) )
& U_28 != sz00
& aInteger0(U_28) )
| ~ aDivisorOf0(U_28,U_29) ) )
| ~ aInteger0(U_29) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_29] :
( ( ! [U_31] :
( aDivisorOf0(U_31,U_29)
| ! [U_27] :
( sdtasdt0(U_31,U_27) != U_29
| ~ aInteger0(U_27) )
| U_31 = sz00
| ~ aInteger0(U_31) )
& ! [U_30] :
( ( ? [U_26] :
( sdtasdt0(U_30,U_26) = U_29
& aInteger0(U_26) )
& U_30 != sz00
& aInteger0(U_30) )
| ~ aDivisorOf0(U_30,U_29) ) )
| ~ aInteger0(U_29) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
! [U_29] :
( ( ! [U_31] :
( aDivisorOf0(U_31,U_29)
| ! [U_27] :
( sdtasdt0(U_31,U_27) != U_29
| ~ aInteger0(U_27) )
| U_31 = sz00
| ~ aInteger0(U_31) )
& ! [U_30] :
( ( sdtasdt0(U_30,sK1(U_29,U_30)) = U_29
& aInteger0(sK1(U_29,U_30))
& U_30 != sz00
& aInteger0(U_30) )
| ~ aDivisorOf0(U_30,U_29) ) )
| ~ aInteger0(U_29) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_26,sK1(U_29,U_30))],[f_18_3]) ).
fof(f_18_5,plain,
( ! [U_29,U_30] :
( sdtasdt0(U_30,sK1(U_29,U_30)) = U_29
| ~ sP6(U_29,U_30) )
& ! [U_29,U_30] :
( aInteger0(sK1(U_29,U_30))
| ~ sP6(U_29,U_30) )
& ! [U_29,U_30] :
( U_30 != sz00
| ~ sP6(U_29,U_30) )
& ! [U_29,U_30] :
( aInteger0(U_30)
| ~ sP6(U_29,U_30) )
& ! [U_27,U_29,U_30,U_31] :
( aDivisorOf0(U_31,U_29)
| sdtasdt0(U_31,U_27) != U_29
| ~ aInteger0(U_27)
| U_31 = sz00
| ~ aInteger0(U_31)
| ~ sP7(U_27,U_29,U_30,U_31) )
& ! [U_27,U_29,U_30,U_31] :
( sP6(U_29,U_30)
| ~ aDivisorOf0(U_30,U_29)
| ~ sP7(U_27,U_29,U_30,U_31) )
& ! [U_27,U_29,U_30,U_31] :
( sP7(U_27,U_29,U_30,U_31)
| ~ aInteger0(U_29) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6,sP7])],[f_18_4]) ).
cnf(f_18_6,plain,
( sP7(U_27,U_29,U_30,U_31)
| ~ aInteger0(U_29) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_8,plain,
( aDivisorOf0(U_31,U_29)
| sdtasdt0(U_31,U_27) != U_29
| ~ aInteger0(U_27)
| U_31 = sz00
| ~ aInteger0(U_31)
| ~ sP7(U_27,U_29,U_30,U_31) ),
inference(clausify,[status(thm)],[f_18_5]) ).
fof(f_19_1,plain,
! [W0,W1,W2] :
( ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
& ( aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1)))
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ) )
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mEquMod]) ).
fof(f_19_2,plain,
! [U_34,U_33,U_32] :
( ( ( sdteqdtlpzmzozddtrp0(U_34,U_33,U_32)
| ~ aDivisorOf0(U_32,sdtpldt0(U_34,smndt0(U_33))) )
& ( aDivisorOf0(U_32,sdtpldt0(U_34,smndt0(U_33)))
| ~ sdteqdtlpzmzozddtrp0(U_34,U_33,U_32) ) )
| U_32 = sz00
| ~ aInteger0(U_32)
| ~ aInteger0(U_33)
| ~ aInteger0(U_34) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_33,U_32,U_34] :
( sdteqdtlpzmzozddtrp0(U_34,U_33,U_32)
| ~ aDivisorOf0(U_32,sdtpldt0(U_34,smndt0(U_33)))
| ~ sP8(U_33,U_32,U_34) )
& ! [U_33,U_32,U_34] :
( aDivisorOf0(U_32,sdtpldt0(U_34,smndt0(U_33)))
| ~ sdteqdtlpzmzozddtrp0(U_34,U_33,U_32)
| ~ sP8(U_33,U_32,U_34) )
& ! [U_33,U_32,U_34] :
( sP8(U_33,U_32,U_34)
| U_32 = sz00
| ~ aInteger0(U_32)
| ~ aInteger0(U_33)
| ~ aInteger0(U_34) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_19_2]) ).
cnf(f_19_4,plain,
( sP8(U_33,U_32,U_34)
| U_32 = sz00
| ~ aInteger0(U_32)
| ~ aInteger0(U_33)
| ~ aInteger0(U_34) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_6,plain,
( sdteqdtlpzmzozddtrp0(U_34,U_33,U_32)
| ~ aDivisorOf0(U_32,sdtpldt0(U_34,smndt0(U_33)))
| ~ sP8(U_33,U_32,U_34) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_23_1,plain,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
inference(fof_nnf,[status(thm)],[m__979]) ).
fof(f_23_2,plain,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
inference(definitional_conversion,[status(esa)],[f_23_1]) ).
cnf(f_23_3,plain,
aInteger0(xa),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
aInteger0(xb),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_5,plain,
aInteger0(xp),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_6,plain,
xp != sz00,
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_7,plain,
aInteger0(xq),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_8,plain,
xq != sz00,
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_25_1,plain,
( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xm) ),
inference(fof_nnf,[status(thm)],[m__1032]) ).
fof(f_25_2,plain,
( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xm) ),
inference(definitional_conversion,[status(esa)],[f_25_1]) ).
cnf(f_25_3,plain,
aInteger0(xm),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm))
& sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)) ),
inference(fof_nnf,[status(thm)],[m__1071]) ).
fof(f_26_2,plain,
( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm))
& sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)) ),
inference(definitional_conversion,[status(esa)],[f_26_1]) ).
cnf(f_26_3,plain,
sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,negated_conjecture,
~ ( sdteqdtlpzmzozddtrp0(xa,xb,xq)
& sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_27_2,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
inference(fof_nnf,[status(thm)],[f_27_1]) ).
fof(f_27_3,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
inference(definitional_conversion,[status(esa)],[f_27_2]) ).
cnf(f_27_4,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(t1,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
inference(start,[status(thm),parent(0:0)],[f_27_4]) ).
cnf(t2,plain,
( ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ~ sP8(xb,xp,xa)
| sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
inference(extension,[status(thm),parent(t1:1)],[f_19_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ aInteger0(xb)
| ~ aInteger0(xp)
| xp = sz00
| ~ aInteger0(xa)
| sP8(xb,xp,xa) ),
inference(extension,[status(thm),parent(t2:2)],[f_19_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
aInteger0(xa),
inference(extension,[status(thm),parent(t4:2)],[f_23_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
xp != sz00,
inference(extension,[status(thm),parent(t4:3)],[f_23_6]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
aInteger0(xp),
inference(extension,[status(thm),parent(t4:4)],[f_23_5]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:4]) ).
cnf(t12,plain,
aInteger0(xb),
inference(extension,[status(thm),parent(t4:5)],[f_23_4]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:5]) ).
cnf(t14,plain,
( ~ aInteger0(xp)
| xp = sz00
| ~ aInteger0(sdtasdt0(xq,xm))
| sdtasdt0(xp,sdtasdt0(xq,xm)) != sdtpldt0(xa,smndt0(xb))
| ~ sP7(sdtasdt0(xq,xm),sdtpldt0(xa,smndt0(xb)),U_792,xp)
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))) ),
inference(extension,[status(thm),parent(t2:3)],[f_18_8]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:3]) ).
cnf(t16,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| sP7(sdtasdt0(xq,xm),sdtpldt0(xa,smndt0(xb)),U_792,xp) ),
inference(extension,[status(thm),parent(t14:2)],[f_18_6]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa)
| aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(extension,[status(thm),parent(t16:2)],[f_5_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
aInteger0(xa),
inference(extension,[status(thm),parent(t18:2)],[f_23_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ aInteger0(xb)
| aInteger0(smndt0(xb)) ),
inference(extension,[status(thm),parent(t18:3)],[f_4_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
aInteger0(xb),
inference(extension,[status(thm),parent(t22:2)],[f_23_4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(extension,[status(thm),parent(t14:3)],[f_26_3]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t14:3]) ).
cnf(t28,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xq)
| aInteger0(sdtasdt0(xq,xm)) ),
inference(extension,[status(thm),parent(t14:4)],[f_6_4]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t14:4]) ).
cnf(t30,plain,
aInteger0(xq),
inference(extension,[status(thm),parent(t28:2)],[f_23_7]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
aInteger0(xm),
inference(extension,[status(thm),parent(t28:3)],[f_25_3]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
xp != sz00,
inference(extension,[status(thm),parent(t14:5)],[f_23_6]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t14:5]) ).
cnf(t36,plain,
aInteger0(xp),
inference(extension,[status(thm),parent(t14:6)],[f_23_5]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t14:6]) ).
cnf(t38,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ sP8(xb,xq,xa)
| sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
inference(extension,[status(thm),parent(t1:2)],[f_19_6]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t1:2]) ).
cnf(t40,plain,
( ~ aInteger0(xb)
| ~ aInteger0(xq)
| xq = sz00
| ~ aInteger0(xa)
| sP8(xb,xq,xa) ),
inference(extension,[status(thm),parent(t38:2)],[f_19_4]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
aInteger0(xa),
inference(extension,[status(thm),parent(t40:2)],[f_23_3]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
xq != sz00,
inference(extension,[status(thm),parent(t40:3)],[f_23_8]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t40:3]) ).
cnf(t46,plain,
aInteger0(xq),
inference(extension,[status(thm),parent(t40:4)],[f_23_7]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t40:4]) ).
cnf(t48,plain,
aInteger0(xb),
inference(extension,[status(thm),parent(t40:5)],[f_23_4]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t40:5]) ).
cnf(t50,plain,
( ~ aInteger0(xq)
| xq = sz00
| ~ aInteger0(sdtasdt0(xp,xm))
| sdtasdt0(xq,sdtasdt0(xp,xm)) != sdtpldt0(xa,smndt0(xb))
| ~ sP7(sdtasdt0(xp,xm),sdtpldt0(xa,smndt0(xb)),U_811,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) ),
inference(extension,[status(thm),parent(t38:3)],[f_18_8]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t38:3]) ).
cnf(t52,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| sP7(sdtasdt0(xp,xm),sdtpldt0(xa,smndt0(xb)),U_811,xq) ),
inference(extension,[status(thm),parent(t50:2)],[f_18_6]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
( ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa)
| aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(extension,[status(thm),parent(t52:2)],[f_5_4]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
aInteger0(xa),
inference(extension,[status(thm),parent(t54:2)],[f_23_3]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
( ~ aInteger0(xb)
| aInteger0(smndt0(xb)) ),
inference(extension,[status(thm),parent(t54:3)],[f_4_4]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t54:3]) ).
cnf(t60,plain,
aInteger0(xb),
inference(extension,[status(thm),parent(t58:2)],[f_23_4]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t58:2]) ).
cnf(t62,plain,
( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm))
| sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtpldt0(xa,smndt0(xb)) ),
inference(extension,[status(thm),parent(t50:3)],[equality_2]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t50:3]) ).
cnf(t64,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(extension,[status(thm),parent(t62:2)],[f_26_4]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t62:2]) ).
cnf(t66,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xp)
| aInteger0(sdtasdt0(xp,xm)) ),
inference(extension,[status(thm),parent(t50:4)],[f_6_4]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t50:4]) ).
cnf(t68,plain,
aInteger0(xp),
inference(extension,[status(thm),parent(t66:2)],[f_23_5]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t66:2]) ).
cnf(t70,plain,
aInteger0(xm),
inference(extension,[status(thm),parent(t66:3)],[f_25_3]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t66:3]) ).
cnf(t72,plain,
xq != sz00,
inference(extension,[status(thm),parent(t50:5)],[f_23_8]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t50:5]) ).
cnf(t74,plain,
aInteger0(xq),
inference(extension,[status(thm),parent(t50:6)],[f_23_7]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t50:6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM436+1 : 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
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 19 18:28:06 UTC 2026
% 0.10/0.38 % CPUTime :
% 31.65/32.03 % SZS status Theorem for theBenchmark
% 31.65/32.03 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------