TSTP Solution File: COM018+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM018+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 10:13:54 EDT 2023
% Result : Theorem 7.15s 2.58s
% Output : Refutation 7.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 43
% Syntax : Number of formulae : 117 ( 32 unt; 20 typ; 0 def)
% Number of atoms : 372 ( 15 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 985 ( 64 ~; 52 |; 128 &; 670 @)
% ( 6 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 9 con; 0-3 aty)
% Number of variables : 155 ( 0 ^; 134 !; 21 ?; 155 :)
% Comments :
%------------------------------------------------------------------------------
thf(aElement0_type,type,
aElement0: $i > $o ).
thf(aRewritingSystem0_type,type,
aRewritingSystem0: $i > $o ).
thf(sdtmndtplgtdt0_type,type,
sdtmndtplgtdt0: $i > $i > $i > $o ).
thf(aReductOfIn0_type,type,
aReductOfIn0: $i > $i > $i > $o ).
thf(sdtmndtasgtdt0_type,type,
sdtmndtasgtdt0: $i > $i > $i > $o ).
thf(isConfluent0_type,type,
isConfluent0: $i > $o ).
thf(isLocallyConfluent0_type,type,
isLocallyConfluent0: $i > $o ).
thf(isTerminating0_type,type,
isTerminating0: $i > $o ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(aNormalFormOfIn0_type,type,
aNormalFormOfIn0: $i > $i > $i > $o ).
thf(xw_type,type,
xw: $i ).
thf(xR_type,type,
xR: $i ).
thf(xa_type,type,
xa: $i ).
thf(xb_type,type,
xb: $i ).
thf(xc_type,type,
xc: $i ).
thf(xv_type,type,
xv: $i ).
thf(xu_type,type,
xu: $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(sk3_type,type,
sk3: $i > $i ).
thf(sk4_type,type,
sk4: $i > $i ).
thf(18,axiom,
( ( aElement0 @ xv )
& ( aReductOfIn0 @ xv @ xa @ xR )
& ( sdtmndtasgtdt0 @ xv @ xR @ xc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__779) ).
thf(88,plain,
( ( aElement0 @ xv )
& ( aReductOfIn0 @ xv @ xa @ xR )
& ( sdtmndtasgtdt0 @ xv @ xR @ xc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,axiom,
( ( aElement0 @ xu )
& ( aReductOfIn0 @ xu @ xa @ xR )
& ( sdtmndtasgtdt0 @ xu @ xR @ xb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__755) ).
thf(110,plain,
( ( aElement0 @ xu )
& ( aReductOfIn0 @ xu @ xa @ xR )
& ( sdtmndtasgtdt0 @ xu @ xR @ xb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(16,axiom,
( ( isLocallyConfluent0 @ xR )
& ( isTerminating0 @ xR ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656_01) ).
thf(82,plain,
( ( isLocallyConfluent0 @ xR )
& ( isTerminating0 @ xR ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(84,plain,
isLocallyConfluent0 @ xR,
inference(cnf,[status(esa)],[82]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C )
& ( aElement0 @ D ) )
=> ( ( ( sdtmndtasgtdt0 @ A @ B @ C )
& ( sdtmndtasgtdt0 @ C @ B @ D ) )
=> ( sdtmndtasgtdt0 @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCRTrans) ).
thf(28,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C )
& ( aElement0 @ D ) )
=> ( ( ( sdtmndtasgtdt0 @ A @ B @ C )
& ( sdtmndtasgtdt0 @ C @ B @ D ) )
=> ( sdtmndtasgtdt0 @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,axiom,
( ( aElement0 @ xw )
& ( sdtmndtasgtdt0 @ xu @ xR @ xw )
& ( sdtmndtasgtdt0 @ xv @ xR @ xw ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__799) ).
thf(92,plain,
( ( aElement0 @ xw )
& ( sdtmndtasgtdt0 @ xu @ xR @ xw )
& ( sdtmndtasgtdt0 @ xv @ xR @ xw ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C )
& ( sdtmndtasgtdt0 @ A @ xR @ B )
& ( sdtmndtasgtdt0 @ A @ xR @ C ) )
=> ( ( iLess0 @ A @ xa )
=> ? [D: $i] :
( ( aElement0 @ D )
& ( sdtmndtasgtdt0 @ B @ xR @ D )
& ( sdtmndtasgtdt0 @ C @ xR @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__715) ).
thf(96,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C )
& ( sdtmndtasgtdt0 @ A @ xR @ B )
& ( sdtmndtasgtdt0 @ A @ xR @ C ) )
=> ( ( iLess0 @ A @ xa )
=> ? [D: $i] :
( ( aElement0 @ D )
& ( sdtmndtasgtdt0 @ B @ xR @ D )
& ( sdtmndtasgtdt0 @ C @ xR @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B ) )
=> ! [C: $i] :
( ( aReductOfIn0 @ C @ A @ B )
=> ( aElement0 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mReduct) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B ) )
=> ! [C: $i] :
( ( aReductOfIn0 @ C @ A @ B )
=> ( aElement0 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(90,plain,
aReductOfIn0 @ xv @ xa @ xR,
inference(cnf,[status(esa)],[88]) ).
thf(7,axiom,
( ( aElement0 @ xa )
& ( aElement0 @ xb )
& ( aElement0 @ xc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731) ).
thf(43,plain,
( ( aElement0 @ xa )
& ( aElement0 @ xb )
& ( aElement0 @ xc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(45,plain,
aElement0 @ xb,
inference(cnf,[status(esa)],[43]) ).
thf(22,axiom,
aRewritingSystem0 @ xR,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
thf(102,plain,
aRewritingSystem0 @ xR,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B ) )
=> ! [C: $i] :
( ( aNormalFormOfIn0 @ C @ A @ B )
<=> ( ( aElement0 @ C )
& ( sdtmndtasgtdt0 @ A @ B @ C )
& ~ ? [D: $i] : ( aReductOfIn0 @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNFRDef) ).
thf(103,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B ) )
=> ! [C: $i] :
( ( ( aNormalFormOfIn0 @ C @ A @ B )
=> ( ( aElement0 @ C )
& ( sdtmndtasgtdt0 @ A @ B @ C )
& ~ ? [D: $i] : ( aReductOfIn0 @ D @ C @ B ) ) )
& ( ( ( aElement0 @ C )
& ( sdtmndtasgtdt0 @ A @ B @ C )
& ~ ? [D: $i] : ( aReductOfIn0 @ D @ C @ B ) )
=> ( aNormalFormOfIn0 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(104,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B ) )
=> ( ! [C: $i] :
( ( aNormalFormOfIn0 @ C @ A @ B )
=> ( ( aElement0 @ C )
& ( sdtmndtasgtdt0 @ A @ B @ C )
& ~ ? [D: $i] : ( aReductOfIn0 @ D @ C @ B ) ) )
& ! [C: $i] :
( ( ( aElement0 @ C )
& ( sdtmndtasgtdt0 @ A @ B @ C )
& ~ ? [D: $i] : ( aReductOfIn0 @ D @ C @ B ) )
=> ( aNormalFormOfIn0 @ C @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[103]) ).
thf(105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aRewritingSystem0 @ B )
| ~ ( aNormalFormOfIn0 @ C @ A @ B )
| ~ ( aReductOfIn0 @ D @ C @ B ) ),
inference(cnf,[status(esa)],[104]) ).
thf(178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aNormalFormOfIn0 @ C @ A @ B )
| ~ ( aReductOfIn0 @ D @ C @ B )
| ( ( aRewritingSystem0 @ xR )
!= ( aRewritingSystem0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[102,105]) ).
thf(179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aNormalFormOfIn0 @ B @ A @ xR )
| ~ ( aReductOfIn0 @ C @ B @ xR ) ),
inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( A )),bind(B,$thf( xR ))]]) ).
thf(182,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aNormalFormOfIn0 @ B @ A @ xR )
| ~ ( aReductOfIn0 @ C @ B @ xR ) ),
inference(simp,[status(thm)],[179]) ).
thf(195,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNormalFormOfIn0 @ B @ A @ xR )
| ~ ( aReductOfIn0 @ C @ B @ xR )
| ( ( aElement0 @ xb )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,182]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ~ ( aNormalFormOfIn0 @ A @ xb @ xR )
| ~ ( aReductOfIn0 @ B @ A @ xR ) ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( xb ))]]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ~ ( aNormalFormOfIn0 @ A @ xb @ xR )
| ~ ( aReductOfIn0 @ B @ A @ xR ) ),
inference(simp,[status(thm)],[196]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ~ ( aNormalFormOfIn0 @ A @ xb @ xR )
| ( ( aReductOfIn0 @ xv @ xa @ xR )
!= ( aReductOfIn0 @ B @ A @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[90,207]) ).
thf(223,plain,
~ ( aNormalFormOfIn0 @ xa @ xb @ xR ),
inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( xa )),bind(B,$thf( xv ))]]) ).
thf(112,plain,
aReductOfIn0 @ xu @ xa @ xR,
inference(cnf,[status(esa)],[110]) ).
thf(17,axiom,
( ( sdtmndtplgtdt0 @ xa @ xR @ xb )
& ( sdtmndtplgtdt0 @ xa @ xR @ xc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731_02) ).
thf(85,plain,
( ( sdtmndtplgtdt0 @ xa @ xR @ xb )
& ( sdtmndtplgtdt0 @ xa @ xR @ xc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(87,plain,
sdtmndtplgtdt0 @ xa @ xR @ xb,
inference(cnf,[status(esa)],[85]) ).
thf(1,conjecture,
? [A: $i] : ( aNormalFormOfIn0 @ A @ xw @ xR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] : ( aNormalFormOfIn0 @ A @ xw @ xR ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(25,plain,
~ ? [A: $i] : ( aNormalFormOfIn0 @ A @ xw @ xR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,plain,
! [A: $i] :
~ ( aNormalFormOfIn0 @ A @ xw @ xR ),
inference(cnf,[status(esa)],[25]) ).
thf(5,axiom,
! [A: $i] :
( ( aRewritingSystem0 @ A )
=> ( ( isConfluent0 @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( aElement0 @ B )
& ( aElement0 @ C )
& ( aElement0 @ D )
& ( sdtmndtasgtdt0 @ B @ A @ C )
& ( sdtmndtasgtdt0 @ B @ A @ D ) )
=> ? [E: $i] :
( ( aElement0 @ E )
& ( sdtmndtasgtdt0 @ C @ A @ E )
& ( sdtmndtasgtdt0 @ D @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCRDef) ).
thf(30,plain,
! [A: $i] :
( ( aRewritingSystem0 @ A )
=> ( ( ( isConfluent0 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( aElement0 @ B )
& ( aElement0 @ C )
& ( aElement0 @ D )
& ( sdtmndtasgtdt0 @ B @ A @ C )
& ( sdtmndtasgtdt0 @ B @ A @ D ) )
=> ? [E: $i] :
( ( aElement0 @ E )
& ( sdtmndtasgtdt0 @ C @ A @ E )
& ( sdtmndtasgtdt0 @ D @ A @ E ) ) ) )
& ( ! [B: $i,C: $i,D: $i] :
( ( ( aElement0 @ B )
& ( aElement0 @ C )
& ( aElement0 @ D )
& ( sdtmndtasgtdt0 @ B @ A @ C )
& ( sdtmndtasgtdt0 @ B @ A @ D ) )
=> ? [E: $i] :
( ( aElement0 @ E )
& ( sdtmndtasgtdt0 @ C @ A @ E )
& ( sdtmndtasgtdt0 @ D @ A @ E ) ) )
=> ( isConfluent0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(94,plain,
sdtmndtasgtdt0 @ xu @ xR @ xw,
inference(cnf,[status(esa)],[92]) ).
thf(8,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(47,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(32,plain,
! [A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ( aElement0 @ ( sk4 @ A ) )
| ( isConfluent0 @ A ) ),
inference(cnf,[status(esa)],[30]) ).
thf(271,plain,
! [A: $i] :
( ( aElement0 @ ( sk4 @ A ) )
| ( isConfluent0 @ A )
| ( ( aRewritingSystem0 @ xR )
!= ( aRewritingSystem0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,32]) ).
thf(272,plain,
( ( aElement0 @ ( sk4 @ xR ) )
| ( isConfluent0 @ xR ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( xR ))]]) ).
thf(220,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aNormalFormOfIn0 @ B @ A @ xR )
| ( ( aReductOfIn0 @ xv @ xa @ xR )
!= ( aReductOfIn0 @ C @ B @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[90,182]) ).
thf(221,plain,
! [A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aNormalFormOfIn0 @ xa @ A @ xR ) ),
inference(pattern_uni,[status(thm)],[220:[bind(A,$thf( A )),bind(B,$thf( xa )),bind(C,$thf( xv ))]]) ).
thf(300,plain,
! [A: $i] :
( ( isConfluent0 @ xR )
| ~ ( aNormalFormOfIn0 @ xa @ A @ xR )
| ( ( aElement0 @ ( sk4 @ xR ) )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[272,221]) ).
thf(301,plain,
( ( isConfluent0 @ xR )
| ~ ( aNormalFormOfIn0 @ xa @ ( sk4 @ xR ) @ xR ) ),
inference(pattern_uni,[status(thm)],[300:[bind(A,$thf( sk4 @ xR ))]]) ).
thf(37,plain,
! [A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ( aElement0 @ ( sk3 @ A ) )
| ( isConfluent0 @ A ) ),
inference(cnf,[status(esa)],[30]) ).
thf(44,plain,
aElement0 @ xc,
inference(cnf,[status(esa)],[43]) ).
thf(256,plain,
! [A: $i] :
( ~ ( aNormalFormOfIn0 @ xa @ A @ xR )
| ( ( aElement0 @ xc )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44,221]) ).
thf(257,plain,
~ ( aNormalFormOfIn0 @ xa @ xc @ xR ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( xc ))]]) ).
thf(46,plain,
aElement0 @ xa,
inference(cnf,[status(esa)],[43]) ).
thf(93,plain,
sdtmndtasgtdt0 @ xv @ xR @ xw,
inference(cnf,[status(esa)],[92]) ).
thf(91,plain,
aElement0 @ xv,
inference(cnf,[status(esa)],[88]) ).
thf(260,plain,
! [A: $i] :
( ~ ( aNormalFormOfIn0 @ xa @ A @ xR )
| ( ( aElement0 @ xv )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[91,221]) ).
thf(261,plain,
~ ( aNormalFormOfIn0 @ xa @ xv @ xR ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( xv ))]]) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aRewritingSystem0 @ B )
| ~ ( aElement0 @ C )
| ~ ( aElement0 @ D )
| ~ ( sdtmndtasgtdt0 @ A @ B @ C )
| ~ ( sdtmndtasgtdt0 @ C @ B @ D )
| ( sdtmndtasgtdt0 @ A @ B @ D ) ),
inference(cnf,[status(esa)],[28]) ).
thf(89,plain,
sdtmndtasgtdt0 @ xv @ xR @ xc,
inference(cnf,[status(esa)],[88]) ).
thf(264,plain,
! [A: $i] :
( ~ ( aNormalFormOfIn0 @ xa @ A @ xR )
| ( ( aElement0 @ xa )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[46,221]) ).
thf(265,plain,
~ ( aNormalFormOfIn0 @ xa @ xa @ xR ),
inference(pattern_uni,[status(thm)],[264:[bind(A,$thf( xa ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( aRewritingSystem0 @ A )
=> ( ( isTerminating0 @ A )
<=> ! [B: $i,C: $i] :
( ( ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtmndtplgtdt0 @ B @ A @ C )
=> ( iLess0 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTermin) ).
thf(60,plain,
! [A: $i] :
( ( aRewritingSystem0 @ A )
=> ( ( ( isTerminating0 @ A )
=> ! [B: $i,C: $i] :
( ( ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtmndtplgtdt0 @ B @ A @ C )
=> ( iLess0 @ C @ B ) ) ) )
& ( ! [B: $i,C: $i] :
( ( ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtmndtplgtdt0 @ B @ A @ C )
=> ( iLess0 @ C @ B ) ) )
=> ( isTerminating0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C )
& ( aElement0 @ D ) )
=> ( ( ( sdtmndtplgtdt0 @ A @ B @ C )
& ( sdtmndtplgtdt0 @ C @ B @ D ) )
=> ( sdtmndtplgtdt0 @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCTrans) ).
thf(73,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C )
& ( aElement0 @ D ) )
=> ( ( ( sdtmndtplgtdt0 @ A @ B @ C )
& ( sdtmndtplgtdt0 @ C @ B @ D ) )
=> ( sdtmndtplgtdt0 @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(310,plain,
! [A: $i] :
( ( aElement0 @ ( sk3 @ A ) )
| ( isConfluent0 @ A )
| ( ( aRewritingSystem0 @ xR )
!= ( aRewritingSystem0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,37]) ).
thf(311,plain,
( ( aElement0 @ ( sk3 @ xR ) )
| ( isConfluent0 @ xR ) ),
inference(pattern_uni,[status(thm)],[310:[bind(A,$thf( xR ))]]) ).
thf(113,plain,
aElement0 @ xu,
inference(cnf,[status(esa)],[110]) ).
thf(258,plain,
! [A: $i] :
( ~ ( aNormalFormOfIn0 @ xa @ A @ xR )
| ( ( aElement0 @ xu )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[113,221]) ).
thf(259,plain,
~ ( aNormalFormOfIn0 @ xa @ xu @ xR ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( xu ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( aRewritingSystem0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mRelSort) ).
thf(27,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i] :
( ( aRewritingSystem0 @ A )
=> ( ( isLocallyConfluent0 @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( aElement0 @ B )
& ( aElement0 @ C )
& ( aElement0 @ D )
& ( aReductOfIn0 @ C @ B @ A )
& ( aReductOfIn0 @ D @ B @ A ) )
=> ? [E: $i] :
( ( aElement0 @ E )
& ( sdtmndtasgtdt0 @ C @ A @ E )
& ( sdtmndtasgtdt0 @ D @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mWCRDef) ).
thf(49,plain,
! [A: $i] :
( ( aRewritingSystem0 @ A )
=> ( ( ( isLocallyConfluent0 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( aElement0 @ B )
& ( aElement0 @ C )
& ( aElement0 @ D )
& ( aReductOfIn0 @ C @ B @ A )
& ( aReductOfIn0 @ D @ B @ A ) )
=> ? [E: $i] :
( ( aElement0 @ E )
& ( sdtmndtasgtdt0 @ C @ A @ E )
& ( sdtmndtasgtdt0 @ D @ A @ E ) ) ) )
& ( ! [B: $i,C: $i,D: $i] :
( ( ( aElement0 @ B )
& ( aElement0 @ C )
& ( aElement0 @ D )
& ( aReductOfIn0 @ C @ B @ A )
& ( aReductOfIn0 @ D @ B @ A ) )
=> ? [E: $i] :
( ( aElement0 @ E )
& ( sdtmndtasgtdt0 @ C @ A @ E )
& ( sdtmndtasgtdt0 @ D @ A @ E ) ) )
=> ( isLocallyConfluent0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(86,plain,
sdtmndtplgtdt0 @ xa @ xR @ xc,
inference(cnf,[status(esa)],[85]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mWFOrd) ).
thf(81,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(31,plain,
! [A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ( sdtmndtasgtdt0 @ ( sk2 @ A ) @ A @ ( sk4 @ A ) )
| ( isConfluent0 @ A ) ),
inference(cnf,[status(esa)],[30]) ).
thf(229,plain,
! [A: $i] :
( ( sdtmndtasgtdt0 @ ( sk2 @ A ) @ A @ ( sk4 @ A ) )
| ( isConfluent0 @ A )
| ( ( aRewritingSystem0 @ xR )
!= ( aRewritingSystem0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,31]) ).
thf(230,plain,
( ( sdtmndtasgtdt0 @ ( sk2 @ xR ) @ xR @ ( sk4 @ xR ) )
| ( isConfluent0 @ xR ) ),
inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( xR ))]]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtmndtasgtdt0 @ A @ B @ C )
<=> ( ( A = C )
| ( sdtmndtplgtdt0 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCRDef) ).
thf(66,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C ) )
=> ( ( ( sdtmndtasgtdt0 @ A @ B @ C )
=> ( ( A = C )
| ( sdtmndtplgtdt0 @ A @ B @ C ) ) )
& ( ( ( A = C )
| ( sdtmndtplgtdt0 @ A @ B @ C ) )
=> ( sdtmndtasgtdt0 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtmndtplgtdt0 @ A @ B @ C )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCbr) ).
thf(48,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(95,plain,
aElement0 @ xw,
inference(cnf,[status(esa)],[92]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtmndtplgtdt0 @ A @ B @ C )
<=> ( ( aReductOfIn0 @ C @ A @ B )
| ? [D: $i] :
( ( aElement0 @ D )
& ( aReductOfIn0 @ D @ A @ B )
& ( sdtmndtplgtdt0 @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCDef) ).
thf(75,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C ) )
=> ( ( ( sdtmndtplgtdt0 @ A @ B @ C )
=> ( ( aReductOfIn0 @ C @ A @ B )
| ? [D: $i] :
( ( aElement0 @ D )
& ( aReductOfIn0 @ D @ A @ B )
& ( sdtmndtplgtdt0 @ D @ B @ C ) ) ) )
& ( ( ( aReductOfIn0 @ C @ A @ B )
| ? [D: $i] :
( ( aElement0 @ D )
& ( aReductOfIn0 @ D @ A @ B )
& ( sdtmndtplgtdt0 @ D @ B @ C ) ) )
=> ( sdtmndtplgtdt0 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(83,plain,
isTerminating0 @ xR,
inference(cnf,[status(esa)],[82]) ).
thf(21,axiom,
! [A: $i] :
( ( ( aRewritingSystem0 @ A )
& ( isTerminating0 @ A ) )
=> ! [B: $i] :
( ( aElement0 @ B )
=> ? [C: $i] : ( aNormalFormOfIn0 @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTermNF) ).
thf(100,plain,
! [A: $i] :
( ( ( aRewritingSystem0 @ A )
& ( isTerminating0 @ A ) )
=> ! [B: $i] :
( ( aElement0 @ B )
=> ? [C: $i] : ( aNormalFormOfIn0 @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(111,plain,
sdtmndtasgtdt0 @ xu @ xR @ xb,
inference(cnf,[status(esa)],[110]) ).
thf(496,plain,
$false,
inference(cvc4,[status(thm)],[88,110,84,28,92,96,41,223,112,43,87,26,30,94,47,301,37,25,257,46,93,261,29,221,89,265,60,85,102,73,105,311,32,45,44,259,27,49,86,113,81,230,103,91,66,48,95,182,31,75,207,272,82,83,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : COM018+1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n003.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Fri May 19 03:21:01 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.13/1.00 % [INFO] Parsing done (131ms).
% 1.13/1.01 % [INFO] Running in sequential loop mode.
% 1.81/1.21 % [INFO] eprover registered as external prover.
% 1.81/1.22 % [INFO] cvc4 registered as external prover.
% 1.81/1.22 % [INFO] Scanning for conjecture ...
% 1.90/1.26 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.90/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.90/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.90/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.90/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.90/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.90/1.31 % [INFO] Found a conjecture and 22 axioms. Running axiom selection ...
% 2.19/1.35 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.19/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.19/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.19/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.19/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.19/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.19/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.19/1.38 % [INFO] Problem is first-order (TPTP FOF).
% 2.19/1.38 % [INFO] Type checking passed.
% 2.38/1.38 % [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 ...
% 7.15/2.58 % External prover 'cvc4' found a proof!
% 7.15/2.58 % [INFO] Killing All external provers ...
% 7.15/2.58 % Time passed: 2045ms (effective reasoning time: 1569ms)
% 7.15/2.58 % 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)>
% 7.15/2.58 % Axioms used in derivation (22): mTermNF, m__779, mTermin, m__656_01, mTCTrans, mNFRDef, mReduct, m__715, mTCDef, mRelSort, mTCRDef, mWFOrd, m__656, m__755, m__731_02, m__731, m__799, mWCRDef, mTCRTrans, mTCbr, mElmSort, mCRDef
% 7.15/2.58 % No. of inferences in proof: 97
% 7.15/2.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2045 ms resp. 1569 ms w/o parsing
% 7.15/2.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.15/2.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------