%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM434+1 : 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 : n019.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 223.40s 223.78s
% Output : Proof 223.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 179 ( 107 unt; 2 def)
% Number of atoms : 413 ( 110 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 414 ( 180 ~; 173 |; 52 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 136 ( 13 sgn 85 !; 6 ?)
% 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(mZeroDiv,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W1 = sz00
| W0 = sz00 ) ) ),
file('theBenchmark.p',mZeroDiv) ).
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__1003,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
file('theBenchmark.p',m__1003) ).
fof(m__,conjecture,
? [W0] :
( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ),
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_17_1,plain,
! [W0,W1] :
( W1 = sz00
| W0 = sz00
| sdtasdt0(W0,W1) != sz00
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[mZeroDiv]) ).
fof(f_17_2,plain,
! [U_25,U_24] :
( U_24 = sz00
| U_25 = sz00
| sdtasdt0(U_25,U_24) != sz00
| ~ aInteger0(U_24)
| ~ aInteger0(U_25) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_24,U_25] :
( U_24 = sz00
| U_25 = sz00
| sdtasdt0(U_25,U_24) != sz00
| ~ aInteger0(U_24)
| ~ aInteger0(U_25) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
( U_24 = sz00
| U_25 = sz00
| sdtasdt0(U_25,U_24) != sz00
| ~ aInteger0(U_24)
| ~ aInteger0(U_25) ),
inference(clausify,[status(thm)],[f_17_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_29,U_27,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_29,U_27,U_30,U_31) )
& ! [U_29,U_27,U_30,U_31] :
( sP6(U_29,U_30)
| ~ aDivisorOf0(U_30,U_29)
| ~ sP7(U_29,U_27,U_30,U_31) )
& ! [U_29,U_27,U_30,U_31] :
( sP7(U_29,U_27,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_29,U_27,U_30,U_31)
| ~ aInteger0(U_29) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_7,plain,
( sP6(U_29,U_30)
| ~ aDivisorOf0(U_30,U_29)
| ~ sP7(U_29,U_27,U_30,U_31) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_11,plain,
( aInteger0(sK1(U_29,U_30))
| ~ sP6(U_29,U_30) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_12,plain,
( sdtasdt0(U_30,sK1(U_29,U_30)) = U_29
| ~ sP6(U_29,U_30) ),
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_34,U_32,U_33] :
( sdteqdtlpzmzozddtrp0(U_34,U_33,U_32)
| ~ aDivisorOf0(U_32,sdtpldt0(U_34,smndt0(U_33)))
| ~ sP8(U_34,U_32,U_33) )
& ! [U_34,U_32,U_33] :
( aDivisorOf0(U_32,sdtpldt0(U_34,smndt0(U_33)))
| ~ sdteqdtlpzmzozddtrp0(U_34,U_33,U_32)
| ~ sP8(U_34,U_32,U_33) )
& ! [U_34,U_32,U_33] :
( sP8(U_34,U_32,U_33)
| 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_34,U_32,U_33)
| U_32 = sz00
| ~ aInteger0(U_32)
| ~ aInteger0(U_33)
| ~ aInteger0(U_34) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
( aDivisorOf0(U_32,sdtpldt0(U_34,smndt0(U_33)))
| ~ sdteqdtlpzmzozddtrp0(U_34,U_33,U_32)
| ~ sP8(U_34,U_32,U_33) ),
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_24_1,plain,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
inference(fof_nnf,[status(thm)],[m__1003]) ).
fof(f_24_2,plain,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
inference(definitional_conversion,[status(esa)],[f_24_1]) ).
cnf(f_24_3,plain,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,negated_conjecture,
~ ? [W0] :
( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_25_2,negated_conjecture,
! [W0] :
( sdtasdt0(sdtasdt0(xp,xq),W0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(W0) ),
inference(fof_nnf,[status(thm)],[f_25_1]) ).
fof(f_25_3,negated_conjecture,
! [U_44] :
( sdtasdt0(sdtasdt0(xp,xq),U_44) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(U_44) ),
inference(variable_rename,[status(thm)],[f_25_2]) ).
fof(f_25_4,negated_conjecture,
! [U_44] :
( sdtasdt0(sdtasdt0(xp,xq),U_44) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(U_44) ),
inference(definitional_conversion,[status(esa)],[f_25_3]) ).
cnf(f_25_5,negated_conjecture,
( sdtasdt0(sdtasdt0(xp,xq),U_44) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(U_44) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_6,axiom,
( sdtasdt0(Eq_x_0,Eq_x_1) = sdtasdt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sdteqdtlpzmzozddtrp0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sdteqdtlpzmzozddtrp0(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
( ~ aInteger0(sK1(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq)))
| sdtasdt0(sdtasdt0(xp,xq),sK1(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) != sdtpldt0(xa,smndt0(xb)) ),
inference(start,[status(thm),parent(0:0)],[f_25_5]) ).
cnf(t2,plain,
( ~ sP6(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))
| sdtasdt0(sdtasdt0(xp,xq),sK1(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) = sdtpldt0(xa,smndt0(xb)) ),
inference(extension,[status(thm),parent(t1:1)],[f_18_12]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
| ~ sP7(sdtpldt0(xa,smndt0(xb)),U_5350,sdtasdt0(xp,xq),U_5352)
| sP6(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq)) ),
inference(extension,[status(thm),parent(t2:2)],[f_18_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| sP7(sdtpldt0(xa,smndt0(xb)),U_5350,sdtasdt0(xp,xq),U_5352) ),
inference(extension,[status(thm),parent(t4:2)],[f_18_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(extension,[status(thm),parent(t6:2)],[f_5_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ aInteger0(xb)
| aInteger0(smndt0(xb)) ),
inference(extension,[status(thm),parent(t8:2)],[f_4_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
aInteger0(xb),
inference(extension,[status(thm),parent(t10:2)],[f_23_4]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
aInteger0(xa),
inference(extension,[status(thm),parent(t8:3)],[f_23_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:3]) ).
cnf(t16,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
| ~ sP8(xa,sdtasdt0(xp,xq),xb)
| aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) ),
inference(extension,[status(thm),parent(t4:3)],[f_19_5]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t4:3]) ).
cnf(t18,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xb)
| ~ aInteger0(sdtasdt0(xp,xq))
| sdtasdt0(xp,xq) = sz00
| sP8(xa,sdtasdt0(xp,xq),xb) ),
inference(extension,[status(thm),parent(t16:2)],[f_19_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xp)
| xp = sz00
| xq = sz00
| sdtasdt0(xp,xq) != sz00 ),
inference(extension,[status(thm),parent(t18:2)],[f_17_4]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
xq != sz00,
inference(extension,[status(thm),parent(t20:2)],[f_23_8]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
xp != sz00,
inference(extension,[status(thm),parent(t20:3)],[f_23_6]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
aInteger0(xp),
inference(extension,[status(thm),parent(t20:4)],[f_23_5]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t20:4]) ).
cnf(t28,plain,
aInteger0(xq),
inference(extension,[status(thm),parent(t20:5)],[f_23_7]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t20:5]) ).
cnf(t30,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xq)
| aInteger0(sdtasdt0(xp,xq)) ),
inference(extension,[status(thm),parent(t18:3)],[f_6_4]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t18:3]) ).
cnf(t32,plain,
aInteger0(xq),
inference(extension,[status(thm),parent(t30:2)],[f_23_7]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
aInteger0(xp),
inference(extension,[status(thm),parent(t30:3)],[f_23_5]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t30:3]) ).
cnf(t36,plain,
aInteger0(xb),
inference(extension,[status(thm),parent(t18:4)],[f_23_4]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t18:4]) ).
cnf(t38,plain,
aInteger0(xa),
inference(extension,[status(thm),parent(t18:5)],[f_23_3]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t18:5]) ).
cnf(t40,plain,
( xa != xa
| sdtasdt0(xp,xq) != sdtasdt0(xp,xq)
| xb != xb
| ~ sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
| sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)) ),
inference(extension,[status(thm),parent(t16:3)],[equality_10]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t16:3]) ).
cnf(t42,plain,
( xa != xa
| sdtasdt0(xp,xq) != sdtasdt0(xp,xq)
| xb != xb
| ~ sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
| sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)) ),
inference(extension,[status(thm),parent(t40:2)],[equality_10]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
inference(extension,[status(thm),parent(t42:2)],[f_24_3]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
xb = xb,
inference(extension,[status(thm),parent(t42:3)],[equality_1]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t42:3]) ).
cnf(t48,plain,
sdtasdt0(xp,xq) = sdtasdt0(xp,xq),
inference(extension,[status(thm),parent(t42:4)],[equality_1]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t42:4]) ).
cnf(t50,plain,
xa = xa,
inference(extension,[status(thm),parent(t42:5)],[equality_1]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t42:5]) ).
cnf(t52,plain,
xb = xb,
inference(extension,[status(thm),parent(t40:3)],[equality_1]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t40:3]) ).
cnf(t54,plain,
( xq != xq
| xp != xp
| sdtasdt0(xp,xq) = sdtasdt0(xp,xq) ),
inference(extension,[status(thm),parent(t40:4)],[equality_6]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t40:4]) ).
cnf(t56,plain,
xp = xp,
inference(extension,[status(thm),parent(t54:2)],[equality_1]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
xq = xq,
inference(extension,[status(thm),parent(t54:3)],[equality_1]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t54:3]) ).
cnf(t60,plain,
xa = xa,
inference(extension,[status(thm),parent(t40:5)],[equality_1]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t40:5]) ).
cnf(t62,plain,
( ~ sP6(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))
| aInteger0(sK1(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) ),
inference(extension,[status(thm),parent(t1:2)],[f_18_11]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t1:2]) ).
cnf(t64,plain,
( ~ aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
| ~ sP7(sdtpldt0(xa,smndt0(xb)),U_5396,sdtasdt0(xp,xq),U_5398)
| sP6(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq)) ),
inference(extension,[status(thm),parent(t62:2)],[f_18_7]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t62:2]) ).
cnf(t66,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| sP7(sdtpldt0(xa,smndt0(xb)),U_5396,sdtasdt0(xp,xq),U_5398) ),
inference(extension,[status(thm),parent(t64:2)],[f_18_6]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(t68,plain,
( ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(extension,[status(thm),parent(t66:2)],[f_5_4]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t66:2]) ).
cnf(t70,plain,
( ~ aInteger0(xb)
| aInteger0(smndt0(xb)) ),
inference(extension,[status(thm),parent(t68:2)],[f_4_4]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t68:2]) ).
cnf(t72,plain,
aInteger0(xb),
inference(extension,[status(thm),parent(t70:2)],[f_23_4]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t70:2]) ).
cnf(t74,plain,
aInteger0(xa),
inference(extension,[status(thm),parent(t68:3)],[f_23_3]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t68:3]) ).
cnf(t76,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
| ~ sP8(xa,sdtasdt0(xp,xq),xb)
| aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) ),
inference(extension,[status(thm),parent(t64:3)],[f_19_5]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t64:3]) ).
cnf(t78,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xb)
| ~ aInteger0(sdtasdt0(xp,xq))
| sdtasdt0(xp,xq) = sz00
| sP8(xa,sdtasdt0(xp,xq),xb) ),
inference(extension,[status(thm),parent(t76:2)],[f_19_4]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t76:2]) ).
cnf(t80,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xp)
| xp = sz00
| xq = sz00
| sdtasdt0(xp,xq) != sz00 ),
inference(extension,[status(thm),parent(t78:2)],[f_17_4]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t78:2]) ).
cnf(t82,plain,
xq != sz00,
inference(extension,[status(thm),parent(t80:2)],[f_23_8]) ).
cnf(t83,plain,
$false,
inference(connection,[status(thm),parent(t82:1)],[t82:1,t80:2]) ).
cnf(t84,plain,
xp != sz00,
inference(extension,[status(thm),parent(t80:3)],[f_23_6]) ).
cnf(t85,plain,
$false,
inference(connection,[status(thm),parent(t84:1)],[t84:1,t80:3]) ).
cnf(t86,plain,
aInteger0(xp),
inference(extension,[status(thm),parent(t80:4)],[f_23_5]) ).
cnf(t87,plain,
$false,
inference(connection,[status(thm),parent(t86:1)],[t86:1,t80:4]) ).
cnf(t88,plain,
aInteger0(xq),
inference(extension,[status(thm),parent(t80:5)],[f_23_7]) ).
cnf(t89,plain,
$false,
inference(connection,[status(thm),parent(t88:1)],[t88:1,t80:5]) ).
cnf(t90,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xq)
| aInteger0(sdtasdt0(xp,xq)) ),
inference(extension,[status(thm),parent(t78:3)],[f_6_4]) ).
cnf(t91,plain,
$false,
inference(connection,[status(thm),parent(t90:1)],[t90:1,t78:3]) ).
cnf(t92,plain,
aInteger0(xq),
inference(extension,[status(thm),parent(t90:2)],[f_23_7]) ).
cnf(t93,plain,
$false,
inference(connection,[status(thm),parent(t92:1)],[t92:1,t90:2]) ).
cnf(t94,plain,
aInteger0(xp),
inference(extension,[status(thm),parent(t90:3)],[f_23_5]) ).
cnf(t95,plain,
$false,
inference(connection,[status(thm),parent(t94:1)],[t94:1,t90:3]) ).
cnf(t96,plain,
aInteger0(xb),
inference(extension,[status(thm),parent(t78:4)],[f_23_4]) ).
cnf(t97,plain,
$false,
inference(connection,[status(thm),parent(t96:1)],[t96:1,t78:4]) ).
cnf(t98,plain,
aInteger0(xa),
inference(extension,[status(thm),parent(t78:5)],[f_23_3]) ).
cnf(t99,plain,
$false,
inference(connection,[status(thm),parent(t98:1)],[t98:1,t78:5]) ).
cnf(t100,plain,
( xa != xa
| sdtasdt0(xp,xq) != sdtasdt0(xp,xq)
| xb != xb
| ~ sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
| sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)) ),
inference(extension,[status(thm),parent(t76:3)],[equality_10]) ).
cnf(t101,plain,
$false,
inference(connection,[status(thm),parent(t100:1)],[t100:1,t76:3]) ).
cnf(t102,plain,
( xa != xa
| sdtasdt0(xp,xq) != sdtasdt0(xp,xq)
| xb != xb
| ~ sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
| sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)) ),
inference(extension,[status(thm),parent(t100:2)],[equality_10]) ).
cnf(t103,plain,
$false,
inference(connection,[status(thm),parent(t102:1)],[t102:1,t100:2]) ).
cnf(t104,plain,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
inference(extension,[status(thm),parent(t102:2)],[f_24_3]) ).
cnf(t105,plain,
$false,
inference(connection,[status(thm),parent(t104:1)],[t104:1,t102:2]) ).
cnf(t106,plain,
xb = xb,
inference(extension,[status(thm),parent(t102:3)],[equality_1]) ).
cnf(t107,plain,
$false,
inference(connection,[status(thm),parent(t106:1)],[t106:1,t102:3]) ).
cnf(t108,plain,
sdtasdt0(xp,xq) = sdtasdt0(xp,xq),
inference(extension,[status(thm),parent(t102:4)],[equality_1]) ).
cnf(t109,plain,
$false,
inference(connection,[status(thm),parent(t108:1)],[t108:1,t102:4]) ).
cnf(t110,plain,
xa = xa,
inference(extension,[status(thm),parent(t102:5)],[equality_1]) ).
cnf(t111,plain,
$false,
inference(connection,[status(thm),parent(t110:1)],[t110:1,t102:5]) ).
cnf(t112,plain,
xb = xb,
inference(extension,[status(thm),parent(t100:3)],[equality_1]) ).
cnf(t113,plain,
$false,
inference(connection,[status(thm),parent(t112:1)],[t112:1,t100:3]) ).
cnf(t114,plain,
( xq != xq
| xp != xp
| sdtasdt0(xp,xq) = sdtasdt0(xp,xq) ),
inference(extension,[status(thm),parent(t100:4)],[equality_6]) ).
cnf(t115,plain,
$false,
inference(connection,[status(thm),parent(t114:1)],[t114:1,t100:4]) ).
cnf(t116,plain,
xp = xp,
inference(extension,[status(thm),parent(t114:2)],[equality_1]) ).
cnf(t117,plain,
$false,
inference(connection,[status(thm),parent(t116:1)],[t116:1,t114:2]) ).
cnf(t118,plain,
xq = xq,
inference(extension,[status(thm),parent(t114:3)],[equality_1]) ).
cnf(t119,plain,
$false,
inference(connection,[status(thm),parent(t118:1)],[t118:1,t114:3]) ).
cnf(t120,plain,
xa = xa,
inference(extension,[status(thm),parent(t100:5)],[equality_1]) ).
cnf(t121,plain,
$false,
inference(connection,[status(thm),parent(t120:1)],[t120:1,t100:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM434+1 : 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
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 18:25:36 UTC 2026
% 0.08/0.37 % CPUTime :
% 223.40/223.78 % SZS status Theorem for theBenchmark
% 223.40/223.78 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------