TSTP Solution File: RNG088+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : RNG088+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 11:49:21 EDT 2023
% Result : Theorem 4.24s 2.03s
% Output : Refutation 4.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 49
% Syntax : Number of formulae : 80 ( 9 unt; 20 typ; 0 def)
% Number of atoms : 267 ( 61 equ; 0 cnn)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 746 ( 4 ~; 2 |; 117 &; 535 @)
% ( 5 <=>; 83 =>; 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 : 23 ( 20 usr; 13 con; 0-2 aty)
% Number of variables : 123 ( 0 ^; 105 !; 18 ?; 123 :)
% 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(xk_type,type,
xk: $i ).
thf(xm_type,type,
xm: $i ).
thf(xI_type,type,
xI: $i ).
thf(xl_type,type,
xl: $i ).
thf(xn_type,type,
xn: $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(xx_type,type,
xx: $i ).
thf(xy_type,type,
xy: $i ).
thf(xz_type,type,
xz: $i ).
thf(23,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(138,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
thf(120,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(52,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,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(46,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)],[7]) ).
thf(28,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(164,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)],[28]) ).
thf(13,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
thf(61,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
sz10 != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).
thf(33,plain,
sz10 != sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).
thf(53,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,axiom,
( ? [A: $i,B: $i] :
( ( aElementOf0 @ A @ xI )
& ( aElementOf0 @ B @ xJ )
& ( ( sdtpldt0 @ A @ B )
= xx ) )
& ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) )
& ? [A: $i,B: $i] :
( ( aElementOf0 @ A @ xI )
& ( aElementOf0 @ B @ xJ )
& ( ( sdtpldt0 @ A @ B )
= xy ) )
& ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElement0 @ xz ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
thf(73,plain,
( ? [A: $i,B: $i] :
( ( aElementOf0 @ A @ xI )
& ( aElementOf0 @ B @ xJ )
& ( ( sdtpldt0 @ A @ B )
= xx ) )
& ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) )
& ? [A: $i,B: $i] :
( ( aElementOf0 @ A @ xI )
& ( aElementOf0 @ B @ xJ )
& ( ( sdtpldt0 @ A @ B )
= xy ) )
& ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElement0 @ xz ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
thf(180,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(5,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
thf(39,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,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(135,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)],[22]) ).
thf(26,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(150,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)],[26]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
thf(36,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
thf(68,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( aElement0 @ ( smndt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
thf(44,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( aElement0 @ ( smndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(11,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(54,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)],[11]) ).
thf(8,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(49,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)],[8]) ).
thf(18,axiom,
( ( aElementOf0 @ xk @ xI )
& ( aElementOf0 @ xl @ xJ )
& ( xx
= ( sdtpldt0 @ xk @ xl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).
thf(86,plain,
( ( aElementOf0 @ xk @ xI )
& ( aElementOf0 @ xl @ xJ )
& ( xx
= ( sdtpldt0 @ xk @ xl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(27,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).
thf(159,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(24,axiom,
( ( aElementOf0 @ xm @ xI )
& ( aElementOf0 @ xn @ xJ )
& ( xy
= ( sdtpldt0 @ xm @ xn ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__967) ).
thf(140,plain,
( ( aElementOf0 @ xm @ xI )
& ( aElementOf0 @ xn @ xJ )
& ( xy
= ( sdtpldt0 @ xm @ xn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(19,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(91,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)],[19]) ).
thf(14,axiom,
aElement0 @ sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
thf(66,plain,
aElement0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(21,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__870) ).
thf(123,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)],[21]) ).
thf(25,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(145,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)],[25]) ).
thf(15,axiom,
aElement0 @ sz10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
thf(67,plain,
aElement0 @ sz10,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(30,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(182,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)],[30]) ).
thf(1,conjecture,
( ( aElementOf0 @ ( sdtpldt0 @ xk @ xm ) @ xI )
& ( aElementOf0 @ ( sdtpldt0 @ xl @ xn ) @ xJ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( aElementOf0 @ ( sdtpldt0 @ xk @ xm ) @ xI )
& ( aElementOf0 @ ( sdtpldt0 @ xl @ xn ) @ xJ ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(31,plain,
~ ( ( aElementOf0 @ ( sdtpldt0 @ xk @ xm ) @ xI )
& ( aElementOf0 @ ( sdtpldt0 @ xl @ xn ) @ xJ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(220,plain,
$false,
inference(cvc4,[status(thm)],[138,120,52,46,164,61,33,53,73,180,39,135,150,36,68,44,59,54,49,86,159,140,91,66,123,145,67,182,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : RNG088+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 20:32:34 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.83/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.97 % [INFO] Parsing done (128ms).
% 1.20/0.98 % [INFO] Running in sequential loop mode.
% 1.56/1.17 % [INFO] eprover registered as external prover.
% 1.56/1.17 % [INFO] cvc4 registered as external prover.
% 1.56/1.18 % [INFO] Scanning for conjecture ...
% 1.89/1.23 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.89/1.23 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.89/1.24 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.00/1.25 % [INFO] Found a conjecture and 28 axioms. Running axiom selection ...
% 2.00/1.30 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 2.00/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.30/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.30/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.30/1.34 % [INFO] Problem is first-order (TPTP FOF).
% 2.30/1.35 % [INFO] Type checking passed.
% 2.30/1.35 % [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 ...
% 4.24/2.02 % External prover 'cvc4' found a proof!
% 4.24/2.02 % [INFO] Killing All external provers ...
% 4.24/2.02 % Time passed: 1505ms (effective reasoning time: 1046ms)
% 4.24/2.03 % 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)>
% 4.24/2.03 % Axioms used in derivation (28): mAddComm, mMulZero, m__870, m__901, mSetSort, mAddZero, mMulAsso, mMulMnOne, m__934, mDefSSum, mMulUnit, mCancel, mAddInvr, mMulComm, m__967, mSortsC, mDefIdeal, mSortsC_01, mEOfElem, mDefSInt, mAddAsso, mSortsB_02, mSortsU, mSetEq, mAMDistr, mElmSort, mUnNeZr, mSortsB
% 4.24/2.03 % No. of inferences in proof: 60
% 4.24/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1505 ms resp. 1046 ms w/o parsing
% 4.51/2.07 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.51/2.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------