TSTP Solution File: NUM426+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM426+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 : Fri May 19 11:40:32 EDT 2023
% Result : Theorem 61.95s 15.39s
% Output : Refutation 61.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 36
% Syntax : Number of formulae : 123 ( 36 unt; 12 typ; 0 def)
% Number of atoms : 308 ( 112 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 794 ( 87 ~; 49 |; 70 &; 542 @)
% ( 2 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 103 ( 0 ^; 98 !; 5 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(aInteger0_type,type,
aInteger0: $i > $o ).
thf(aDivisorOf0_type,type,
aDivisorOf0: $i > $i > $o ).
thf(sz00_type,type,
sz00: $i ).
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(sdteqdtlpzmzozddtrp0_type,type,
sdteqdtlpzmzozddtrp0: $i > $i > $i > $o ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(smndt0_type,type,
smndt0: $i > $i ).
thf(xq_type,type,
xq: $i ).
thf(xn_type,type,
xn: $i ).
thf(xb_type,type,
xb: $i ).
thf(xa_type,type,
xa: $i ).
thf(sz10_type,type,
sz10: $i ).
thf(23,axiom,
( ( aInteger0 @ xa )
& ( aInteger0 @ xb )
& ( aInteger0 @ xq )
& ( xq != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__704) ).
thf(101,plain,
( ( aInteger0 @ xa )
& ( aInteger0 @ xb )
& ( aInteger0 @ xq )
& ( xq != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(104,plain,
aInteger0 @ xb,
inference(cnf,[status(esa)],[101]) ).
thf(9,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( aInteger0 @ ( smndt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
thf(41,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( aInteger0 @ ( smndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(42,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( aInteger0 @ ( smndt0 @ A ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(201,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ xb )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[104,42]) ).
thf(202,plain,
aInteger0 @ ( smndt0 @ xb ),
inference(pattern_uni,[status(thm)],[201:[bind(A,$thf( xb ))]]) ).
thf(3,axiom,
aInteger0 @ sz10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
thf(28,plain,
aInteger0 @ sz10,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ! [B: $i] :
( ( aDivisorOf0 @ B @ A )
<=> ( ( aInteger0 @ B )
& ( B != sz00 )
& ? [C: $i] :
( ( aInteger0 @ C )
& ( ( sdtasdt0 @ B @ C )
= A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
thf(72,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ! [B: $i] :
( ( ( aDivisorOf0 @ B @ A )
=> ( ( aInteger0 @ B )
& ( B != sz00 )
& ? [C: $i] :
( ( aInteger0 @ C )
& ( ( sdtasdt0 @ B @ C )
= A ) ) ) )
& ( ( ( aInteger0 @ B )
& ( B != sz00 )
& ? [C: $i] :
( ( aInteger0 @ C )
& ( ( sdtasdt0 @ B @ C )
= A ) ) )
=> ( aDivisorOf0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(73,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ! [B: $i] :
( ( aDivisorOf0 @ B @ A )
=> ( ( aInteger0 @ B )
& ( B != sz00 )
& ? [C: $i] :
( ( aInteger0 @ C )
& ( ( sdtasdt0 @ B @ C )
= A ) ) ) )
& ! [B: $i] :
( ( ( aInteger0 @ B )
& ( B != sz00 )
& ? [C: $i] :
( ( aInteger0 @ C )
& ( ( sdtasdt0 @ B @ C )
= A ) ) )
=> ( aDivisorOf0 @ B @ A ) ) ) ),
inference(miniscope,[status(thm)],[72]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aDivisorOf0 @ B @ A )
| ( B != sz00 ) ),
inference(cnf,[status(esa)],[73]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( B != sz00 )
| ~ ( aInteger0 @ A )
| ~ ( aDivisorOf0 @ B @ A ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(80,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aDivisorOf0 @ sz00 @ A ) ),
inference(simp,[status(thm)],[79]) ).
thf(383,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ sz10 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28,80]) ).
thf(384,plain,
~ ( aDivisorOf0 @ sz00 @ sz10 ),
inference(pattern_uni,[status(thm)],[383:[bind(A,$thf( sz10 ))]]) ).
thf(103,plain,
aInteger0 @ xq,
inference(cnf,[status(esa)],[101]) ).
thf(371,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ xq )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,80]) ).
thf(372,plain,
~ ( aDivisorOf0 @ sz00 @ xq ),
inference(pattern_uni,[status(thm)],[371:[bind(A,$thf( xq ))]]) ).
thf(4,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntegers) ).
thf(29,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,axiom,
( ( aInteger0 @ xn )
& ( ( sdtasdt0 @ xq @ xn )
= ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__747) ).
thf(87,plain,
( ( aInteger0 @ xn )
& ( ( sdtasdt0 @ xq @ xn )
= ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(89,plain,
aInteger0 @ xn,
inference(cnf,[status(esa)],[87]) ).
thf(379,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ xn )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[89,80]) ).
thf(380,plain,
~ ( aDivisorOf0 @ sz00 @ xn ),
inference(pattern_uni,[status(thm)],[379:[bind(A,$thf( xn ))]]) ).
thf(199,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ xq )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,42]) ).
thf(200,plain,
aInteger0 @ ( smndt0 @ xq ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( xq ))]]) ).
thf(251,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ xq ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[200,42]) ).
thf(252,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ xq ) ),
inference(pattern_uni,[status(thm)],[251:[bind(A,$thf( smndt0 @ xq ))]]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
thf(39,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C )
& ( C != sz00 ) )
=> ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
<=> ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).
thf(48,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C )
& ( C != sz00 ) )
=> ( ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
=> ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) ) )
& ( ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) )
=> ( sdteqdtlpzmzozddtrp0 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(24,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulOne) ).
thf(107,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
| ( B = sz00 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
| ( B = sz00 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
& ( ( smndt0 @ A )
= ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMinOne) ).
thf(34,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
& ( ( smndt0 @ A )
= ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(35,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(37,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ~ ( aInteger0 @ A ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(102,plain,
xq != sz00,
inference(cnf,[status(esa)],[101]) ).
thf(106,plain,
xq != sz00,
inference(lifteq,[status(thm)],[102]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) )
= ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
thf(84,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) )
= ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(15,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
thf(61,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
aInteger0 @ sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
thf(33,plain,
aInteger0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(205,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ sz00 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33,42]) ).
thf(206,plain,
aInteger0 @ ( smndt0 @ sz00 ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( sz00 ))]]) ).
thf(105,plain,
aInteger0 @ xa,
inference(cnf,[status(esa)],[101]) ).
thf(191,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ xa )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,42]) ).
thf(192,plain,
aInteger0 @ ( smndt0 @ xa ),
inference(pattern_uni,[status(thm)],[191:[bind(A,$thf( xa ))]]) ).
thf(36,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( ( smndt0 @ A )
= ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(38,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) )
= ( smndt0 @ A ) )
| ~ ( aInteger0 @ A ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(387,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ sz00 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33,80]) ).
thf(388,plain,
~ ( aDivisorOf0 @ sz00 @ sz00 ),
inference(pattern_uni,[status(thm)],[387:[bind(A,$thf( sz00 ))]]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(189,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ xn )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[89,42]) ).
thf(190,plain,
aInteger0 @ ( smndt0 @ xn ),
inference(pattern_uni,[status(thm)],[189:[bind(A,$thf( xn ))]]) ).
thf(211,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ xn ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[190,42]) ).
thf(212,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ xn ) ),
inference(pattern_uni,[status(thm)],[211:[bind(A,$thf( smndt0 @ xn ))]]) ).
thf(22,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
thf(96,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(88,plain,
( ( sdtasdt0 @ xq @ xn )
= ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(90,plain,
( ( sdtpldt0 @ xa @ ( smndt0 @ xb ) )
= ( sdtasdt0 @ xq @ xn ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(1,conjecture,
( ( sdtasdt0 @ xq @ ( smndt0 @ xn ) )
= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
( ( sdtasdt0 @ xq @ ( smndt0 @ xn ) )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(26,plain,
( ( sdtasdt0 @ xq @ ( smndt0 @ xn ) )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(27,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ ( smndt0 @ xn ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(181,plain,
( ( ( sdtasdt0 @ xq @ ( smndt0 @ xn ) )
!= ( sdtasdt0 @ xq @ xn ) )
| ( ( sdtpldt0 @ xa @ ( smndt0 @ xb ) )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ) ),
inference(paramod_ordered,[status(thm)],[90,27]) ).
thf(184,plain,
( ( xq != xq )
| ( ( smndt0 @ xn )
!= xn )
| ( xa != xb )
| ( ( smndt0 @ xa )
!= ( smndt0 @ xb ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(186,plain,
( ( ( smndt0 @ xn )
!= xn )
| ( xa != xb )
| ( ( smndt0 @ xa )
!= ( smndt0 @ xb ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(233,plain,
( ( ( smndt0 @ xn )
!= xn )
| ( xa != xb )
| ( xa != xb ) ),
inference(simp,[status(thm)],[186]) ).
thf(244,plain,
( ( ( smndt0 @ xn )
!= xn )
| ( xa != xb ) ),
inference(simp,[status(thm)],[233]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( B != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0 @ A @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModRef) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( B != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0 @ A @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ( B = sz00 )
| ( sdteqdtlpzmzozddtrp0 @ A @ A @ B ) ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B = sz00 )
| ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ( sdteqdtlpzmzozddtrp0 @ A @ A @ B ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(203,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ sz10 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28,42]) ).
thf(204,plain,
aInteger0 @ ( smndt0 @ sz10 ),
inference(pattern_uni,[status(thm)],[203:[bind(A,$thf( sz10 ))]]) ).
thf(21,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
thf(91,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(222,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ xa ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[192,42]) ).
thf(223,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ xa ) ),
inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( smndt0 @ xa ))]]) ).
thf(373,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ xb )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[104,80]) ).
thf(374,plain,
~ ( aDivisorOf0 @ sz00 @ xb ),
inference(pattern_uni,[status(thm)],[373:[bind(A,$thf( xb ))]]) ).
thf(25,axiom,
sdteqdtlpzmzozddtrp0 @ xa @ xb @ xq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__724) ).
thf(112,plain,
sdteqdtlpzmzozddtrp0 @ xa @ xb @ xq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistrib) ).
thf(43,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(389,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ xa )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,80]) ).
thf(390,plain,
~ ( aDivisorOf0 @ sz00 @ xa ),
inference(pattern_uni,[status(thm)],[389:[bind(A,$thf( xa ))]]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
thf(55,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(182,plain,
( ( xq != xq )
| ( ( smndt0 @ xn )
!= xn )
| ( ( sdtpldt0 @ xa @ ( smndt0 @ xb ) )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(185,plain,
( ( ( smndt0 @ xn )
!= xn )
| ( ( sdtpldt0 @ xa @ ( smndt0 @ xb ) )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(262,plain,
( ( ( smndt0 @ xn )
!= xn )
| ( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ xn ) ) ),
inference(rewrite,[status(thm)],[185,90]) ).
thf(183,plain,
( ( ( sdtasdt0 @ xq @ ( smndt0 @ xn ) )
!= ( sdtasdt0 @ xq @ xn ) )
| ( xa != xb )
| ( ( smndt0 @ xa )
!= ( smndt0 @ xb ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(363,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ xb ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[202,80]) ).
thf(364,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ xb ) ),
inference(pattern_uni,[status(thm)],[363:[bind(A,$thf( smndt0 @ xb ))]]) ).
thf(57503,plain,
$false,
inference(cvc4,[status(thm)],[202,384,372,29,380,252,41,39,48,58,107,200,69,101,42,37,106,84,61,89,206,192,33,28,38,388,53,212,96,105,244,32,34,204,27,103,91,66,223,80,374,112,72,43,87,104,26,390,55,262,30,190,183,90,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM426+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n001.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Thu May 18 17:16:51 EDT 2023
% 0.17/0.37 % CPUTime :
% 0.99/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.07 % [INFO] Parsing done (154ms).
% 1.45/1.08 % [INFO] Running in sequential loop mode.
% 1.73/1.29 % [INFO] eprover registered as external prover.
% 1.73/1.30 % [INFO] cvc4 registered as external prover.
% 1.73/1.30 % [INFO] Scanning for conjecture ...
% 1.97/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.08/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.08/1.41 % [INFO] Found a conjecture and 23 axioms. Running axiom selection ...
% 2.08/1.45 % [INFO] Axiom selection finished. Selected 23 axioms (removed 0 axioms).
% 2.31/1.47 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.48 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.49 % [INFO] Problem is first-order (TPTP FOF).
% 2.31/1.49 % [INFO] Type checking passed.
% 2.31/1.49 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 61.95/15.38 % External prover 'cvc4' found a proof!
% 61.95/15.39 % [INFO] Killing All external provers ...
% 61.95/15.39 % Time passed: 14859ms (effective reasoning time: 14304ms)
% 61.95/15.39 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 61.95/15.39 % Axioms used in derivation (23): mAddComm, m__724, mAddNeg, mMulOne, mAddZero, mAddAsso, mIntMult, mDivisor, mIntNeg, mMulMinOne, m__747, mMulComm, mMulZero, mEquMod, mZeroDiv, mDistrib, mMulAsso, mIntPlus, mEquModRef, mIntegers, m__704, mIntOne, mIntZero
% 61.95/15.39 % No. of inferences in proof: 111
% 61.95/15.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14859 ms resp. 14304 ms w/o parsing
% 61.95/15.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 61.95/15.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------