TSTP Solution File: RNG093+2 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : RNG093+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 11:49:22 EDT 2023
% Result : Theorem 4.50s 2.13s
% Output : Refutation 4.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 40
% Syntax : Number of formulae : 69 ( 9 unt; 13 typ; 0 def)
% Number of atoms : 270 ( 53 equ; 0 cnn)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 786 ( 4 ~; 5 |; 103 &; 568 @)
% ( 7 <=>; 99 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 131 ( 0 ^; 121 !; 10 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
thf(aSet0_type,type,
aSet0: $i > $o ).
thf(sdtpldt1_type,type,
sdtpldt1: $i > $i > $i ).
thf(aElementOf0_type,type,
aElementOf0: $i > $i > $o ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(sdtasasdt0_type,type,
sdtasasdt0: $i > $i > $i ).
thf(aIdeal0_type,type,
aIdeal0: $i > $o ).
thf(aElement0_type,type,
aElement0: $i > $o ).
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(xI_type,type,
xI: $i ).
thf(xJ_type,type,
xJ: $i ).
thf(sz10_type,type,
sz10: $i ).
thf(sz00_type,type,
sz00: $i ).
thf(smndt0_type,type,
smndt0: $i > $i ).
thf(10,axiom,
aElement0 @ sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
thf(88,plain,
aElement0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
thf(142,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(3,axiom,
sz10 != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).
thf(42,plain,
sz10 != sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
( ( ( aSet0 @ ( sdtasasdt0 @ xI @ xJ ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtasasdt0 @ xI @ xJ ) )
<=> ( ( aElementOf0 @ A @ xI )
& ( aElementOf0 @ A @ xJ ) ) ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtasasdt0 @ xI @ xJ ) )
=> ( ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtasasdt0 @ xI @ xJ ) )
=> ( aElementOf0 @ ( sdtpldt0 @ A @ B ) @ ( sdtasasdt0 @ xI @ xJ ) ) )
& ! [B: $i] :
( ( aElement0 @ B )
=> ( aElementOf0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasasdt0 @ xI @ xJ ) ) ) ) )
| ( aIdeal0 @ ( sdtasasdt0 @ xI @ xJ ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( aSet0 @ ( sdtasasdt0 @ xI @ xJ ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtasasdt0 @ xI @ xJ ) )
<=> ( ( aElementOf0 @ A @ xI )
& ( aElementOf0 @ A @ xJ ) ) ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtasasdt0 @ xI @ xJ ) )
=> ( ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtasasdt0 @ xI @ xJ ) )
=> ( aElementOf0 @ ( sdtpldt0 @ A @ B ) @ ( sdtasasdt0 @ xI @ xJ ) ) )
& ! [B: $i] :
( ( aElement0 @ B )
=> ( aElementOf0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasasdt0 @ xI @ xJ ) ) ) ) )
| ( aIdeal0 @ ( sdtasasdt0 @ xI @ xJ ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ ( ( ( aSet0 @ ( sdtasasdt0 @ xI @ xJ ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtasasdt0 @ xI @ xJ ) )
=> ( ( aElementOf0 @ A @ xI )
& ( aElementOf0 @ A @ xJ ) ) )
& ( ( ( aElementOf0 @ A @ xI )
& ( aElementOf0 @ A @ xJ ) )
=> ( aElementOf0 @ A @ ( sdtasasdt0 @ xI @ xJ ) ) ) ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtasasdt0 @ xI @ xJ ) )
=> ( ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtasasdt0 @ xI @ xJ ) )
=> ( aElementOf0 @ ( sdtpldt0 @ A @ B ) @ ( sdtasasdt0 @ xI @ xJ ) ) )
& ! [B: $i] :
( ( aElement0 @ B )
=> ( aElementOf0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasasdt0 @ xI @ xJ ) ) ) ) )
| ( aIdeal0 @ ( sdtasasdt0 @ xI @ xJ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtpldt1 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ? [E: $i,F: $i] :
( ( aElementOf0 @ E @ A )
& ( aElementOf0 @ F @ B )
& ( ( sdtpldt0 @ E @ F )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtpldt1 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ? [E: $i,F: $i] :
( ( aElementOf0 @ E @ A )
& ( aElementOf0 @ F @ B )
& ( ( sdtpldt0 @ E @ F )
= D ) ) )
& ( ? [E: $i,F: $i] :
( ( aElementOf0 @ E @ A )
& ( aElementOf0 @ F @ B )
& ( ( sdtpldt0 @ E @ F )
= D ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ? [E: $i,F: $i] :
( ( aElementOf0 @ E @ A )
& ( aElementOf0 @ F @ B )
& ( ( sdtpldt0 @ E @ F )
= D ) ) )
& ( ? [E: $i,F: $i] :
( ( aElementOf0 @ E @ A )
& ( aElementOf0 @ F @ B )
& ( ( sdtpldt0 @ E @ F )
= D ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtpldt1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
thf(169,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
thf(130,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(23,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
& ( ( smndt0 @ A )
= ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).
thf(150,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
& ( ( smndt0 @ A )
= ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtasasdt0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aElementOf0 @ D @ A )
& ( aElementOf0 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSInt) ).
thf(171,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtasasdt0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElementOf0 @ D @ A )
& ( aElementOf0 @ D @ B ) ) )
& ( ( ( aElementOf0 @ D @ A )
& ( aElementOf0 @ D @ B ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElementOf0 @ D @ A )
& ( aElementOf0 @ D @ B ) ) )
& ( ( ( aElementOf0 @ D @ A )
& ( aElementOf0 @ D @ B ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtasasdt0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(17,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(136,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
thf(83,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(21,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).
thf(147,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
| ( B = sz00 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCancel) ).
thf(133,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
| ( B = sz00 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ( ( ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( aElementOf0 @ C @ B ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetEq) ).
thf(160,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ( ( ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( aElementOf0 @ C @ B ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
thf(137,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(22,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(148,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
thf(45,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( aIdeal0 @ A )
& ( aIdeal0 @ B ) )
=> ( aIdeal0 @ ( sdtpldt1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIdeSum) ).
thf(140,plain,
! [A: $i,B: $i] :
( ( ( aIdeal0 @ A )
& ( aIdeal0 @ B ) )
=> ( aIdeal0 @ ( sdtpldt1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
aElement0 @ sz10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
thf(91,plain,
aElement0 @ sz10,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ B @ C ) @ A )
= ( sdtpldt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
thf(155,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ B @ C ) @ A )
= ( sdtpldt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(5,axiom,
( ( aSet0 @ xI )
& ! [A: $i] :
( ( aElementOf0 @ A @ xI )
=> ( ! [B: $i] :
( ( aElementOf0 @ B @ xI )
=> ( aElementOf0 @ ( sdtpldt0 @ A @ B ) @ xI ) )
& ! [B: $i] :
( ( aElement0 @ B )
=> ( aElementOf0 @ ( sdtasdt0 @ B @ A ) @ xI ) ) ) )
& ( aIdeal0 @ xI )
& ( aSet0 @ xJ )
& ! [A: $i] :
( ( aElementOf0 @ A @ xJ )
=> ( ! [B: $i] :
( ( aElementOf0 @ B @ xJ )
=> ( aElementOf0 @ ( sdtpldt0 @ A @ B ) @ xJ ) )
& ! [B: $i] :
( ( aElement0 @ B )
=> ( aElementOf0 @ ( sdtasdt0 @ B @ A ) @ xJ ) ) ) )
& ( aIdeal0 @ xJ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1150) ).
thf(50,plain,
( ( aSet0 @ xI )
& ! [A: $i] :
( ( aElementOf0 @ A @ xI )
=> ( ! [B: $i] :
( ( aElementOf0 @ B @ xI )
=> ( aElementOf0 @ ( sdtpldt0 @ A @ B ) @ xI ) )
& ! [B: $i] :
( ( aElement0 @ B )
=> ( aElementOf0 @ ( sdtasdt0 @ B @ A ) @ xI ) ) ) )
& ( aIdeal0 @ xI )
& ( aSet0 @ xJ )
& ! [A: $i] :
( ( aElementOf0 @ A @ xJ )
=> ( ! [B: $i] :
( ( aElementOf0 @ B @ xJ )
=> ( aElementOf0 @ ( sdtpldt0 @ A @ B ) @ xJ ) )
& ! [B: $i] :
( ( aElement0 @ B )
=> ( aElementOf0 @ ( sdtasdt0 @ B @ A ) @ xJ ) ) ) )
& ( aIdeal0 @ xJ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i] :
( ( aIdeal0 @ A )
<=> ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( aElementOf0 @ ( sdtpldt0 @ B @ C ) @ A ) )
& ! [C: $i] :
( ( aElement0 @ C )
=> ( aElementOf0 @ ( sdtasdt0 @ C @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
thf(67,plain,
! [A: $i] :
( ( ( aIdeal0 @ A )
=> ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( aElementOf0 @ ( sdtpldt0 @ B @ C ) @ A ) )
& ! [C: $i] :
( ( aElement0 @ C )
=> ( aElementOf0 @ ( sdtasdt0 @ C @ B ) @ A ) ) ) ) ) )
& ( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( aElementOf0 @ ( sdtpldt0 @ B @ C ) @ A ) )
& ! [C: $i] :
( ( aElement0 @ C )
=> ( aElementOf0 @ ( sdtasdt0 @ C @ B ) @ A ) ) ) ) )
=> ( aIdeal0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
thf(127,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(28,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).
thf(200,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(6,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( aElement0 @ ( smndt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
thf(62,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( aElement0 @ ( smndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(209,plain,
$false,
inference(cvc4,[status(thm)],[88,142,42,29,92,169,130,150,171,136,83,147,89,133,160,137,148,45,64,140,91,155,50,67,127,200,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG093+2 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n029.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 20:34:59 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.96/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.01 % [INFO] Parsing done (147ms).
% 1.45/1.02 % [INFO] Running in sequential loop mode.
% 1.80/1.23 % [INFO] eprover registered as external prover.
% 1.80/1.23 % [INFO] cvc4 registered as external prover.
% 1.80/1.23 % [INFO] Scanning for conjecture ...
% 1.93/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.93/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.93/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.93/1.32 % [INFO] Found a conjecture and 26 axioms. Running axiom selection ...
% 2.20/1.37 % [INFO] Axiom selection finished. Selected 26 axioms (removed 0 axioms).
% 2.20/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.20/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.40/1.41 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.40/1.41 % [INFO] Problem is first-order (TPTP FOF).
% 2.40/1.42 % [INFO] Type checking passed.
% 2.40/1.42 % [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 ...
% 4.50/2.13 % External prover 'cvc4' found a proof!
% 4.50/2.13 % [INFO] Killing All external provers ...
% 4.50/2.13 % Time passed: 1608ms (effective reasoning time: 1110ms)
% 4.50/2.13 % 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)>
% 4.50/2.13 % Axioms used in derivation (26): mAddComm, mMulZero, mSetSort, m__1150, mMulAsso, mMulMnOne, mDefSSum, mMulUnit, mCancel, mAddInvr, mMulComm, mSortsC, mDefIdeal, mSortsC_01, mEOfElem, mAddZero, mIdeSum, mDefSInt, mAddAsso, mSortsB_02, mSortsU, mSetEq, mAMDistr, mElmSort, mUnNeZr, mSortsB
% 4.50/2.13 % No. of inferences in proof: 56
% 4.50/2.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1608 ms resp. 1110 ms w/o parsing
% 4.87/2.18 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.87/2.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------