TSTP Solution File: RNG091+1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : RNG091+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 : Tue May 21 02:37:47 EDT 2024
% Result : Theorem 5.11s 2.57s
% Output : Refutation 5.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 53
% Syntax : Number of formulae : 88 ( 13 unt; 20 typ; 0 def)
% Number of atoms : 243 ( 61 equ; 0 cnn)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 710 ( 4 ~; 2 |; 97 &; 531 @)
% ( 5 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 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 : 103 ( 0 ^ 93 !; 10 ?; 103 :)
% 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(xx_type,type,
xx: $i ).
thf(xy_type,type,
xy: $i ).
thf(xI_type,type,
xI: $i ).
thf(xJ_type,type,
xJ: $i ).
thf(xz_type,type,
xz: $i ).
thf(smndt0_type,type,
smndt0: $i > $i ).
thf(sz10_type,type,
sz10: $i ).
thf(sz00_type,type,
sz00: $i ).
thf(xk_type,type,
xk: $i ).
thf(xl_type,type,
xl: $i ).
thf(xm_type,type,
xm: $i ).
thf(xn_type,type,
xn: $i ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
| ( B = sz00 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCancel) ).
thf(138,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)],[23]) ).
thf(28,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
& ( ( smndt0 @ A )
= ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMnOne) ).
thf(153,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)],[28]) ).
thf(3,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( aElement0 @ ( smndt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsU) ).
thf(37,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( aElement0 @ ( smndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
thf(125,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)],[19]) ).
thf(17,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
thf(117,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(24,axiom,
( ( sdtpldt0 @ xx @ xy )
= ( sdtpldt0 @ ( sdtpldt0 @ xk @ xm ) @ ( sdtpldt0 @ xl @ xn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1061) ).
thf(141,plain,
( ( sdtpldt0 @ xx @ xy )
= ( sdtpldt0 @ ( sdtpldt0 @ xk @ xm ) @ ( sdtpldt0 @ xl @ xn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
thf(96,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)],[15]) ).
thf(20,axiom,
( ( aElementOf0 @ ( sdtpldt0 @ xk @ xm ) @ xI )
& ( aElementOf0 @ ( sdtpldt0 @ xl @ xn ) @ xJ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__994) ).
thf(128,plain,
( ( aElementOf0 @ ( sdtpldt0 @ xk @ xm ) @ xI )
& ( aElementOf0 @ ( sdtpldt0 @ xl @ xn ) @ xJ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,axiom,
aElement0 @ sz10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
thf(45,plain,
aElement0 @ sz10,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSort) ).
thf(39,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).
thf(112,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',mSetEq) ).
thf(48,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)],[10]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',mDefSInt) ).
thf(67,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)],[14]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
thf(122,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(9,axiom,
( ( sdtasdt0 @ xz @ xx )
= ( sdtpldt0 @ ( sdtasdt0 @ xz @ xk ) @ ( sdtasdt0 @ xz @ xl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1098) ).
thf(46,plain,
( ( sdtasdt0 @ xz @ xx )
= ( sdtpldt0 @ ( sdtasdt0 @ xz @ xk ) @ ( sdtasdt0 @ xz @ xl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
thf(176,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(7,axiom,
aElement0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
thf(44,plain,
aElement0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
( ( aIdeal0 @ xI )
& ( aIdeal0 @ xJ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
thf(59,plain,
( ( aIdeal0 @ xI )
& ( aIdeal0 @ xJ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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/sandbox/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(1,conjecture,
( ( aElementOf0 @ ( sdtpldt0 @ xx @ xy ) @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElementOf0 @ ( sdtasdt0 @ xz @ xx ) @ ( sdtpldt1 @ xI @ xJ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( aElementOf0 @ ( sdtpldt0 @ xx @ xy ) @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElementOf0 @ ( sdtasdt0 @ xz @ xx ) @ ( sdtpldt1 @ xI @ xJ ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ( ( aElementOf0 @ ( sdtpldt0 @ xx @ xy ) @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElementOf0 @ ( sdtasdt0 @ xz @ xx ) @ ( sdtpldt1 @ xI @ xJ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
thf(143,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(6,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSetSort) ).
thf(43,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
sz10 != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnNeZr) ).
thf(40,plain,
sz10 != sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,axiom,
( ( aElementOf0 @ xm @ xI )
& ( aElementOf0 @ xn @ xJ )
& ( xy
= ( sdtpldt0 @ xm @ xn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__967) ).
thf(158,plain,
( ( aElementOf0 @ xm @ xI )
& ( aElementOf0 @ xn @ xJ )
& ( xy
= ( sdtpldt0 @ xm @ xn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(32,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddInvr) ).
thf(171,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(27,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
thf(151,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(31,axiom,
( ( aElementOf0 @ ( sdtasdt0 @ xz @ xk ) @ xI )
& ( aElementOf0 @ ( sdtasdt0 @ xz @ xl ) @ xJ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1021) ).
thf(168,plain,
( ( aElementOf0 @ ( sdtasdt0 @ xz @ xk ) @ xI )
& ( aElementOf0 @ ( sdtasdt0 @ xz @ xl ) @ xJ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(26,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
thf(146,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(21,axiom,
( ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElement0 @ xz ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__901) ).
thf(131,plain,
( ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) )
& ( aElement0 @ xz ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
thf(163,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)],[30]) ).
thf(13,axiom,
( ( aElementOf0 @ xk @ xI )
& ( aElementOf0 @ xl @ xJ )
& ( xx
= ( sdtpldt0 @ xk @ xl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__934) ).
thf(62,plain,
( ( aElementOf0 @ xk @ xI )
& ( aElementOf0 @ xl @ xJ )
& ( xx
= ( sdtpldt0 @ xk @ xl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',mDefSSum) ).
thf(178,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)],[34]) ).
thf(217,plain,
$false,
inference(cvc4,[status(thm)],[138,153,37,125,117,141,96,128,45,39,112,48,67,122,46,57,176,44,59,135,35,143,43,40,158,171,151,168,146,131,163,62,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : RNG091+1 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.18 % Command : run_Leo-III %s %d
% 0.18/0.40 % Computer : n018.cluster.edu
% 0.18/0.40 % Model : x86_64 x86_64
% 0.18/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40 % Memory : 8042.1875MB
% 0.18/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40 % CPULimit : 300
% 0.18/0.40 % WCLimit : 300
% 0.18/0.40 % DateTime : Sat May 18 12:26:09 EDT 2024
% 0.18/0.41 % CPUTime :
% 1.04/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.11 % [INFO] Parsing done (128ms).
% 1.25/1.12 % [INFO] Running in sequential loop mode.
% 1.84/1.38 % [INFO] eprover registered as external prover.
% 1.84/1.38 % [INFO] cvc4 registered as external prover.
% 1.84/1.39 % [INFO] Scanning for conjecture ...
% 2.04/1.45 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.45 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 32 axioms. Running axiom selection ...
% 2.04/1.53 % [INFO] Axiom selection finished. Selected 32 axioms (removed 0 axioms).
% 2.04/1.54 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.39/1.54 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.39/1.57 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.39/1.57 % [INFO] Problem is first-order (TPTP FOF).
% 2.39/1.57 % [INFO] Type checking passed.
% 2.39/1.58 % [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 ...
% 5.11/2.56 % External prover 'cvc4' found a proof!
% 5.11/2.56 % [INFO] Killing All external provers ...
% 5.11/2.56 % Time passed: 2005ms (effective reasoning time: 1436ms)
% 5.11/2.56 % 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)>
% 5.11/2.56 % Axioms used in derivation (32): mAddComm, mMulZero, m__870, m__901, m__994, mSetSort, mAddZero, mMulAsso, mMulMnOne, m__934, mDefSSum, mCancel, mAddInvr, m__1098, mMulComm, m__1021, m__967, mSortsC, mDefIdeal, mSortsC_01, mEOfElem, mDefSInt, mAddAsso, mMulUnit, m__1061, mSortsB_02, mSortsU, mSetEq, mAMDistr, mElmSort, mUnNeZr, mSortsB
% 5.11/2.56 % No. of inferences in proof: 68
% 5.11/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2005 ms resp. 1436 ms w/o parsing
% 5.20/2.62 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.20/2.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------