TSTP Solution File: NUM423+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM423+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 11:40:31 EDT 2023
% Result : Theorem 3.64s 1.84s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 31
% Syntax : Number of formulae : 54 ( 6 unt; 10 typ; 0 def)
% Number of atoms : 151 ( 51 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 427 ( 9 ~; 8 |; 58 &; 311 @)
% ( 2 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 67 ( 0 ^; 61 !; 6 ?; 67 :)
% 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(xa_type,type,
xa: $i ).
thf(sz10_type,type,
sz10: $i ).
thf(19,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
thf(88,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(20,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
thf(93,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
thf(74,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,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(77,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)],[16]) ).
thf(14,axiom,
aInteger0 @ sz10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
thf(73,plain,
aInteger0 @ sz10,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(21,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulOne) ).
thf(98,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(22,axiom,
aInteger0 @ sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
thf(103,plain,
aInteger0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(7,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( aInteger0 @ ( smndt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
thf(48,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( aInteger0 @ ( smndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,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(50,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)],[8]) ).
thf(6,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(36,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)],[6]) ).
thf(18,axiom,
( ( aInteger0 @ xa )
& ( aInteger0 @ xq )
& ( xq != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__671) ).
thf(83,plain,
( ( aInteger0 @ xa )
& ( aInteger0 @ xq )
& ( xq != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,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(28,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)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,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(80,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)],[17]) ).
thf(5,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntegers) ).
thf(35,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,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(55,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)],[9]) ).
thf(1,conjecture,
( ? [A: $i] :
( ( aInteger0 @ A )
& ( ( sdtasdt0 @ xq @ A )
= ( sdtpldt0 @ xa @ ( smndt0 @ xa ) ) ) )
| ( aDivisorOf0 @ xq @ ( sdtpldt0 @ xa @ ( smndt0 @ xa ) ) )
| ( sdteqdtlpzmzozddtrp0 @ xa @ xa @ xq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ? [A: $i] :
( ( aInteger0 @ A )
& ( ( sdtasdt0 @ xq @ A )
= ( sdtpldt0 @ xa @ ( smndt0 @ xa ) ) ) )
| ( aDivisorOf0 @ xq @ ( sdtpldt0 @ xa @ ( smndt0 @ xa ) ) )
| ( sdteqdtlpzmzozddtrp0 @ xa @ xa @ xq ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(23,plain,
~ ( ? [A: $i] :
( ( aInteger0 @ A )
& ( ( sdtasdt0 @ xq @ A )
= ( sdtpldt0 @ xa @ ( smndt0 @ xa ) ) ) )
| ( aDivisorOf0 @ xq @ ( sdtpldt0 @ xa @ ( smndt0 @ xa ) ) )
| ( sdteqdtlpzmzozddtrp0 @ xa @ xa @ xq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
thf(68,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,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(62,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)],[11]) ).
thf(104,plain,
$false,
inference(cvc4,[status(thm)],[88,93,74,60,65,77,73,98,103,48,50,36,83,28,33,80,35,55,23,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM423+3 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 16:50:43 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.93/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/0.98 % [INFO] Parsing done (120ms).
% 1.29/0.99 % [INFO] Running in sequential loop mode.
% 1.64/1.18 % [INFO] eprover registered as external prover.
% 1.74/1.19 % [INFO] cvc4 registered as external prover.
% 1.74/1.19 % [INFO] Scanning for conjecture ...
% 1.88/1.24 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.88/1.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.26 % [INFO] Found a conjecture and 20 axioms. Running axiom selection ...
% 1.92/1.30 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 1.92/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.12/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.12/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 2.12/1.33 % [INFO] Type checking passed.
% 2.12/1.34 % [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 ...
% 3.64/1.84 % External prover 'cvc4' found a proof!
% 3.64/1.84 % [INFO] Killing All external provers ...
% 3.64/1.84 % Time passed: 1305ms (effective reasoning time: 847ms)
% 3.64/1.84 % 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)>
% 3.64/1.84 % Axioms used in derivation (20): mAddComm, mAddNeg, mMulOne, mAddZero, mAddAsso, mIntMult, mDivisor, mMulMinOne, mMulComm, mMulZero, mEquMod, mZeroDiv, mDistrib, mMulAsso, mIntPlus, m__671, mIntNeg, mIntegers, mIntOne, mIntZero
% 3.64/1.84 % No. of inferences in proof: 44
% 3.64/1.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1305 ms resp. 847 ms w/o parsing
% 3.64/1.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.64/1.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------