TSTP Solution File: COM020+4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM020+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 10:13:55 EDT 2023
% Result : Theorem 100.48s 25.50s
% Output : Refutation 100.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 45
% Syntax : Number of formulae : 187 ( 35 unt; 21 typ; 0 def)
% Number of atoms : 771 ( 112 equ; 0 cnn)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 2060 ( 187 ~; 217 |; 260 &;1322 @)
% ( 6 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 12 con; 0-3 aty)
% Number of variables : 182 ( 0 ^; 125 !; 57 ?; 182 :)
% 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(xb_type,type,
xb: $i ).
thf(xR_type,type,
xR: $i ).
thf(xd_type,type,
xd: $i ).
thf(xa_type,type,
xa: $i ).
thf(xc_type,type,
xc: $i ).
thf(xu_type,type,
xu: $i ).
thf(xv_type,type,
xv: $i ).
thf(xw_type,type,
xw: $i ).
thf(sk1_type,type,
sk1: $i > $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(13,axiom,
( ( aElement0 @ xv )
& ( aReductOfIn0 @ xv @ xa @ xR )
& ( ( xv = xc )
| ( ( ( aReductOfIn0 @ xc @ xv @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xv @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xc ) ) )
& ( sdtmndtplgtdt0 @ xv @ xR @ xc ) ) )
& ( sdtmndtasgtdt0 @ xv @ xR @ xc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__779) ).
thf(132,plain,
( ( aElement0 @ xv )
& ( aReductOfIn0 @ xv @ xa @ xR )
& ( ( xv = xc )
| ( ( ( aReductOfIn0 @ xc @ xv @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xv @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xc ) ) )
& ( sdtmndtplgtdt0 @ xv @ xR @ xc ) ) )
& ( sdtmndtasgtdt0 @ xv @ xR @ xc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(134,plain,
aReductOfIn0 @ xv @ xa @ xR,
inference(cnf,[status(esa)],[132]) ).
thf(135,plain,
aElement0 @ xv,
inference(cnf,[status(esa)],[132]) ).
thf(1,conjecture,
? [A: $i] :
( ( aElement0 @ A )
& ( ( xb = A )
| ( aReductOfIn0 @ A @ xb @ xR )
| ? [B: $i] :
( ( aElement0 @ B )
& ( aReductOfIn0 @ B @ xb @ xR )
& ( sdtmndtplgtdt0 @ B @ xR @ A ) )
| ( sdtmndtplgtdt0 @ xb @ xR @ A )
| ( sdtmndtasgtdt0 @ xb @ xR @ A ) )
& ( ( xd = A )
| ( aReductOfIn0 @ A @ xd @ xR )
| ? [B: $i] :
( ( aElement0 @ B )
& ( aReductOfIn0 @ B @ xd @ xR )
& ( sdtmndtplgtdt0 @ B @ xR @ A ) )
| ( sdtmndtplgtdt0 @ xd @ xR @ A )
| ( sdtmndtasgtdt0 @ xd @ xR @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( aElement0 @ A )
& ( ( xb = A )
| ( aReductOfIn0 @ A @ xb @ xR )
| ? [B: $i] :
( ( aElement0 @ B )
& ( aReductOfIn0 @ B @ xb @ xR )
& ( sdtmndtplgtdt0 @ B @ xR @ A ) )
| ( sdtmndtplgtdt0 @ xb @ xR @ A )
| ( sdtmndtasgtdt0 @ xb @ xR @ A ) )
& ( ( xd = A )
| ( aReductOfIn0 @ A @ xd @ xR )
| ? [B: $i] :
( ( aElement0 @ B )
& ( aReductOfIn0 @ B @ xd @ xR )
& ( sdtmndtplgtdt0 @ B @ xR @ A ) )
| ( sdtmndtplgtdt0 @ xd @ xR @ A )
| ( sdtmndtasgtdt0 @ xd @ xR @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(26,plain,
~ ? [A: $i] :
( ( aElement0 @ A )
& ( ( xb = A )
| ( aReductOfIn0 @ A @ xb @ xR )
| ? [B: $i] :
( ( aElement0 @ B )
& ( aReductOfIn0 @ B @ xb @ xR )
& ( sdtmndtplgtdt0 @ B @ xR @ A ) )
| ( sdtmndtplgtdt0 @ xb @ xR @ A )
| ( sdtmndtasgtdt0 @ xb @ xR @ A ) )
& ( ( xd = A )
| ( aReductOfIn0 @ A @ xd @ xR )
| ? [B: $i] :
( ( aElement0 @ B )
& ( aReductOfIn0 @ B @ xd @ xR )
& ( sdtmndtplgtdt0 @ B @ xR @ A ) )
| ( sdtmndtplgtdt0 @ xd @ xR @ A )
| ( sdtmndtasgtdt0 @ xd @ xR @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,plain,
! [A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aReductOfIn0 @ A @ xb @ xR )
| ~ ( sk1 @ A ) ),
inference(cnf,[status(esa)],[26]) ).
thf(285,plain,
! [A: $i] :
( ~ ( aReductOfIn0 @ A @ xb @ xR )
| ~ ( sk1 @ A )
| ( ( aElement0 @ xv )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[135,28]) ).
thf(286,plain,
( ~ ( aReductOfIn0 @ xv @ xb @ xR )
| ~ ( sk1 @ xv ) ),
inference(pattern_uni,[status(thm)],[285:[bind(A,$thf( xv ))]]) ).
thf(818,plain,
( ~ ( sk1 @ xv )
| ( ( aReductOfIn0 @ xv @ xa @ xR )
!= ( aReductOfIn0 @ xv @ xb @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[134,286]) ).
thf(826,plain,
( ~ ( sk1 @ xv )
| ( xv != xv )
| ( xa != xb )
| ( xR != xR ) ),
inference(simp,[status(thm)],[818]) ).
thf(830,plain,
( ~ ( sk1 @ xv )
| ( xa != xb ) ),
inference(simp,[status(thm)],[826]) ).
thf(21,axiom,
( ( aElement0 @ xd )
& ( ( xw = xd )
| ( ( ( aReductOfIn0 @ xd @ xw @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xw @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xd ) ) )
& ( sdtmndtplgtdt0 @ xw @ xR @ xd ) ) )
& ( sdtmndtasgtdt0 @ xw @ xR @ xd )
& ~ ? [A: $i] : ( aReductOfIn0 @ A @ xd @ xR )
& ( aNormalFormOfIn0 @ xd @ xw @ xR ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__818) ).
thf(186,plain,
( ( aElement0 @ xd )
& ( ( xw = xd )
| ( ( ( aReductOfIn0 @ xd @ xw @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xw @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xd ) ) )
& ( sdtmndtplgtdt0 @ xw @ xR @ xd ) ) )
& ( sdtmndtasgtdt0 @ xw @ xR @ xd )
& ~ ? [A: $i] : ( aReductOfIn0 @ A @ xd @ xR )
& ( aNormalFormOfIn0 @ xd @ xw @ xR ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(188,plain,
! [A: $i] :
~ ( aReductOfIn0 @ A @ xd @ xR ),
inference(cnf,[status(esa)],[186]) ).
thf(19,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(173,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)],[19]) ).
thf(193,plain,
aElement0 @ xd,
inference(cnf,[status(esa)],[186]) ).
thf(295,plain,
! [A: $i] :
( ~ ( aReductOfIn0 @ A @ xb @ xR )
| ~ ( sk1 @ A )
| ( ( aElement0 @ xd )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[193,28]) ).
thf(296,plain,
( ~ ( aReductOfIn0 @ xd @ xb @ xR )
| ~ ( sk1 @ xd ) ),
inference(pattern_uni,[status(thm)],[295:[bind(A,$thf( xd ))]]) ).
thf(32,plain,
! [A: $i] :
( ~ ( aElement0 @ A )
| ( sk1 @ A )
| ( xd != A ) ),
inference(cnf,[status(esa)],[26]) ).
thf(38,plain,
! [A: $i] :
( ( xd != A )
| ~ ( aElement0 @ A )
| ( sk1 @ A ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(39,plain,
( ~ ( aElement0 @ xd )
| ( sk1 @ xd ) ),
inference(simp,[status(thm)],[38]) ).
thf(273,plain,
( ~ $true
| ( sk1 @ xd ) ),
inference(rewrite,[status(thm)],[39,193]) ).
thf(274,plain,
sk1 @ xd,
inference(simp,[status(thm)],[273]) ).
thf(894,plain,
( ~ ( aReductOfIn0 @ xd @ xb @ xR )
| ~ $true ),
inference(rewrite,[status(thm)],[296,274]) ).
thf(895,plain,
~ ( aReductOfIn0 @ xd @ xb @ xR ),
inference(simp,[status(thm)],[894]) ).
thf(4,axiom,
( ( ( aReductOfIn0 @ xb @ xa @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xa @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xb ) ) )
& ( sdtmndtplgtdt0 @ xa @ xR @ xb )
& ( ( aReductOfIn0 @ xc @ xa @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xa @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xc ) ) )
& ( sdtmndtplgtdt0 @ xa @ xR @ xc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731_02) ).
thf(43,plain,
( ( ( aReductOfIn0 @ xb @ xa @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xa @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xb ) ) )
& ( sdtmndtplgtdt0 @ xa @ xR @ xb )
& ( ( aReductOfIn0 @ xc @ xa @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xa @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xc ) ) )
& ( sdtmndtplgtdt0 @ xa @ xR @ xc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(47,plain,
( ( aReductOfIn0 @ xb @ xa @ xR )
| ( aReductOfIn0 @ sk2 @ xa @ xR ) ),
inference(cnf,[status(esa)],[43]) ).
thf(191,plain,
( ( xw = xd )
| ( sdtmndtplgtdt0 @ xw @ xR @ xd ) ),
inference(cnf,[status(esa)],[186]) ).
thf(196,plain,
( ( xw = xd )
| ( sdtmndtplgtdt0 @ xw @ xR @ xd ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(27,plain,
! [A: $i] :
( ~ ( aElement0 @ A )
| ~ ( sdtmndtplgtdt0 @ xb @ xR @ A )
| ~ ( sk1 @ A ) ),
inference(cnf,[status(esa)],[26]) ).
thf(256,plain,
! [A: $i] :
( ~ ( aElement0 @ xd )
| ~ ( aElement0 @ A )
| ~ ( sdtmndtplgtdt0 @ xb @ xR @ A )
| ( ( sk1 @ xd )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[39,27]) ).
thf(257,plain,
( ~ ( aElement0 @ xd )
| ~ ( aElement0 @ xd )
| ~ ( sdtmndtplgtdt0 @ xb @ xR @ xd ) ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( xd ))]]) ).
thf(264,plain,
( ~ ( aElement0 @ xd )
| ~ ( sdtmndtplgtdt0 @ xb @ xR @ xd ) ),
inference(simp,[status(thm)],[257]) ).
thf(462,plain,
( ~ $true
| ~ ( sdtmndtplgtdt0 @ xb @ xR @ xd ) ),
inference(rewrite,[status(thm)],[264,193]) ).
thf(463,plain,
~ ( sdtmndtplgtdt0 @ xb @ xR @ xd ),
inference(simp,[status(thm)],[462]) ).
thf(634,plain,
( ( xw = xd )
| ( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
!= ( sdtmndtplgtdt0 @ xb @ xR @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[196,463]) ).
thf(669,plain,
( ( xw = xd )
| ( xw != xb )
| ( xR != xR )
| ( xd != xd ) ),
inference(simp,[status(thm)],[634]) ).
thf(676,plain,
( ( xw = xd )
| ( xw != xb ) ),
inference(simp,[status(thm)],[669]) ).
thf(30,plain,
! [A: $i] :
( ~ ( aElement0 @ A )
| ( sk1 @ A )
| ~ ( sdtmndtasgtdt0 @ xd @ xR @ A ) ),
inference(cnf,[status(esa)],[26]) ).
thf(364,plain,
! [A: $i] :
( ( sk1 @ A )
| ~ ( sdtmndtasgtdt0 @ xd @ xR @ A )
| ( ( aElement0 @ xv )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[135,30]) ).
thf(365,plain,
( ( sk1 @ xv )
| ~ ( sdtmndtasgtdt0 @ xd @ xR @ xv ) ),
inference(pattern_uni,[status(thm)],[364:[bind(A,$thf( xv ))]]) ).
thf(258,plain,
! [A: $i] :
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ A )
| ~ ( sk1 @ A )
| ( ( aElement0 @ xv )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[135,27]) ).
thf(259,plain,
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ xv )
| ~ ( sk1 @ xv ) ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( xv ))]]) ).
thf(344,plain,
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ xv )
| ( ( sk1 @ xv )
!= ( sk1 @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[274,259]) ).
thf(347,plain,
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ xv )
| ( xv != xd ) ),
inference(simp,[status(thm)],[344]) ).
thf(5,axiom,
( ( aElement0 @ xu )
& ( aReductOfIn0 @ xu @ xa @ xR )
& ( ( xu = xb )
| ( ( ( aReductOfIn0 @ xb @ xu @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xu @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xb ) ) )
& ( sdtmndtplgtdt0 @ xu @ xR @ xb ) ) )
& ( sdtmndtasgtdt0 @ xu @ xR @ xb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__755) ).
thf(52,plain,
( ( aElement0 @ xu )
& ( aReductOfIn0 @ xu @ xa @ xR )
& ( ( xu = xb )
| ( ( ( aReductOfIn0 @ xb @ xu @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xu @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xb ) ) )
& ( sdtmndtplgtdt0 @ xu @ xR @ xb ) ) )
& ( sdtmndtasgtdt0 @ xu @ xR @ xb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(56,plain,
aElement0 @ xu,
inference(cnf,[status(esa)],[52]) ).
thf(137,plain,
( ( xv = xc )
| ( sdtmndtplgtdt0 @ xv @ xR @ xc ) ),
inference(cnf,[status(esa)],[132]) ).
thf(142,plain,
( ( xv = xc )
| ( sdtmndtplgtdt0 @ xv @ xR @ xc ) ),
inference(lifteq,[status(thm)],[137]) ).
thf(3,axiom,
! [A: $i] :
( ( aRewritingSystem0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mRelSort) ).
thf(42,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
( ( aElement0 @ xa )
& ( aElement0 @ xb )
& ( aElement0 @ xc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731) ).
thf(144,plain,
( ( aElement0 @ xa )
& ( aElement0 @ xb )
& ( aElement0 @ xc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(145,plain,
aElement0 @ xc,
inference(cnf,[status(esa)],[144]) ).
thf(287,plain,
! [A: $i] :
( ~ ( aReductOfIn0 @ A @ xb @ xR )
| ~ ( sk1 @ A )
| ( ( aElement0 @ xc )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[145,28]) ).
thf(288,plain,
( ~ ( aReductOfIn0 @ xc @ xb @ xR )
| ~ ( sk1 @ xc ) ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( xc ))]]) ).
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(125,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(46,plain,
( ( aReductOfIn0 @ xc @ xa @ xR )
| ( aReductOfIn0 @ sk3 @ xa @ xR ) ),
inference(cnf,[status(esa)],[43]) ).
thf(283,plain,
! [A: $i] :
( ~ ( aReductOfIn0 @ A @ xb @ xR )
| ~ ( sk1 @ A )
| ( ( aElement0 @ xu )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[56,28]) ).
thf(284,plain,
( ~ ( aReductOfIn0 @ xu @ xb @ xR )
| ~ ( sk1 @ xu ) ),
inference(pattern_uni,[status(thm)],[283:[bind(A,$thf( xu ))]]) ).
thf(17,axiom,
( ( aElement0 @ xw )
& ( ( xu = xw )
| ( ( ( aReductOfIn0 @ xw @ xu @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xu @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xw ) ) )
& ( sdtmndtplgtdt0 @ xu @ xR @ xw ) ) )
& ( sdtmndtasgtdt0 @ xu @ xR @ xw )
& ( ( xv = xw )
| ( ( ( aReductOfIn0 @ xw @ xv @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xv @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xw ) ) )
& ( sdtmndtplgtdt0 @ xv @ xR @ xw ) ) )
& ( sdtmndtasgtdt0 @ xv @ xR @ xw ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__799) ).
thf(152,plain,
( ( aElement0 @ xw )
& ( ( xu = xw )
| ( ( ( aReductOfIn0 @ xw @ xu @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xu @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xw ) ) )
& ( sdtmndtplgtdt0 @ xu @ xR @ xw ) ) )
& ( sdtmndtasgtdt0 @ xu @ xR @ xw )
& ( ( xv = xw )
| ( ( ( aReductOfIn0 @ xw @ xv @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xv @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xw ) ) )
& ( sdtmndtplgtdt0 @ xv @ xR @ xw ) ) )
& ( sdtmndtasgtdt0 @ xv @ xR @ xw ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(57,plain,
aReductOfIn0 @ xu @ xa @ xR,
inference(cnf,[status(esa)],[52]) ).
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(78,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(260,plain,
! [A: $i] :
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ A )
| ~ ( sk1 @ A )
| ( ( aElement0 @ xc )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[145,27]) ).
thf(261,plain,
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ xc )
| ~ ( sk1 @ xc ) ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( xc ))]]) ).
thf(20,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(179,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)],[20]) ).
thf(833,plain,
( ( xa != xb )
| ( ( sk1 @ xv )
!= ( sk1 @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[274,830]) ).
thf(834,plain,
( ( xa != xb )
| ( xv != xd ) ),
inference(simp,[status(thm)],[833]) ).
thf(147,plain,
aElement0 @ xa,
inference(cnf,[status(esa)],[144]) ).
thf(34,plain,
! [A: $i] :
( ~ ( aElement0 @ A )
| ( xb != A )
| ~ ( sk1 @ A ) ),
inference(cnf,[status(esa)],[26]) ).
thf(40,plain,
! [A: $i] :
( ( xb != A )
| ~ ( aElement0 @ A )
| ~ ( sk1 @ A ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(41,plain,
( ~ ( aElement0 @ xb )
| ~ ( sk1 @ xb ) ),
inference(simp,[status(thm)],[40]) ).
thf(146,plain,
aElement0 @ xb,
inference(cnf,[status(esa)],[144]) ).
thf(242,plain,
( ~ $true
| ~ ( sk1 @ xb ) ),
inference(rewrite,[status(thm)],[41,146]) ).
thf(243,plain,
~ ( sk1 @ xb ),
inference(simp,[status(thm)],[242]) ).
thf(158,plain,
aElement0 @ xw,
inference(cnf,[status(esa)],[152]) ).
thf(269,plain,
! [A: $i] :
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ A )
| ~ ( sk1 @ A )
| ( ( aElement0 @ xw )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[158,27]) ).
thf(270,plain,
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ xw )
| ~ ( sk1 @ xw ) ),
inference(pattern_uni,[status(thm)],[269:[bind(A,$thf( xw ))]]) ).
thf(23,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(201,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)],[23]) ).
thf(790,plain,
( ~ ( sk1 @ xu )
| ( ( aReductOfIn0 @ xu @ xa @ xR )
!= ( aReductOfIn0 @ xu @ xb @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[57,284]) ).
thf(802,plain,
( ~ ( sk1 @ xu )
| ( xu != xu )
| ( xa != xb )
| ( xR != xR ) ),
inference(simp,[status(thm)],[790]) ).
thf(804,plain,
( ~ ( sk1 @ xu )
| ( xa != xb ) ),
inference(simp,[status(thm)],[802]) ).
thf(807,plain,
( ( xa != xb )
| ( ( sk1 @ xu )
!= ( sk1 @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[274,804]) ).
thf(810,plain,
( ( xa != xb )
| ( xu != xd ) ),
inference(simp,[status(thm)],[807]) ).
thf(192,plain,
sdtmndtasgtdt0 @ xw @ xR @ xd,
inference(cnf,[status(esa)],[186]) ).
thf(157,plain,
( ( xu = xw )
| ( sdtmndtplgtdt0 @ xu @ xR @ xw ) ),
inference(cnf,[status(esa)],[152]) ).
thf(165,plain,
( ( xw = xu )
| ( sdtmndtplgtdt0 @ xu @ xR @ xw ) ),
inference(lifteq,[status(thm)],[157]) ).
thf(33,plain,
! [A: $i] :
( ~ ( aElement0 @ A )
| ( sk1 @ A )
| ~ ( sdtmndtplgtdt0 @ xd @ xR @ A ) ),
inference(cnf,[status(esa)],[26]) ).
thf(8,axiom,
aRewritingSystem0 @ xR,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
thf(77,plain,
aRewritingSystem0 @ xR,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(24,axiom,
( ! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C )
& ( aReductOfIn0 @ B @ A @ xR )
& ( aReductOfIn0 @ C @ A @ xR ) )
=> ? [D: $i] :
( ( aElement0 @ D )
& ( ( B = D )
| ( ( ( aReductOfIn0 @ D @ B @ xR )
| ? [E: $i] :
( ( aElement0 @ E )
& ( aReductOfIn0 @ E @ B @ xR )
& ( sdtmndtplgtdt0 @ E @ xR @ D ) ) )
& ( sdtmndtplgtdt0 @ B @ xR @ D ) ) )
& ( sdtmndtasgtdt0 @ B @ xR @ D )
& ( ( C = D )
| ( ( ( aReductOfIn0 @ D @ C @ xR )
| ? [E: $i] :
( ( aElement0 @ E )
& ( aReductOfIn0 @ E @ C @ xR )
& ( sdtmndtplgtdt0 @ E @ xR @ D ) ) )
& ( sdtmndtplgtdt0 @ C @ xR @ D ) ) )
& ( sdtmndtasgtdt0 @ C @ xR @ D ) ) )
& ( isLocallyConfluent0 @ xR )
& ! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( ( aReductOfIn0 @ B @ A @ xR )
| ? [C: $i] :
( ( aElement0 @ C )
& ( aReductOfIn0 @ C @ A @ xR )
& ( sdtmndtplgtdt0 @ C @ xR @ B ) )
| ( sdtmndtplgtdt0 @ A @ xR @ B ) )
=> ( iLess0 @ B @ A ) ) )
& ( isTerminating0 @ xR ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656_01) ).
thf(207,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C )
& ( aReductOfIn0 @ B @ A @ xR )
& ( aReductOfIn0 @ C @ A @ xR ) )
=> ? [D: $i] :
( ( aElement0 @ D )
& ( ( B = D )
| ( ( ( aReductOfIn0 @ D @ B @ xR )
| ? [E: $i] :
( ( aElement0 @ E )
& ( aReductOfIn0 @ E @ B @ xR )
& ( sdtmndtplgtdt0 @ E @ xR @ D ) ) )
& ( sdtmndtplgtdt0 @ B @ xR @ D ) ) )
& ( sdtmndtasgtdt0 @ B @ xR @ D )
& ( ( C = D )
| ( ( ( aReductOfIn0 @ D @ C @ xR )
| ? [E: $i] :
( ( aElement0 @ E )
& ( aReductOfIn0 @ E @ C @ xR )
& ( sdtmndtplgtdt0 @ E @ xR @ D ) ) )
& ( sdtmndtplgtdt0 @ C @ xR @ D ) ) )
& ( sdtmndtasgtdt0 @ C @ xR @ D ) ) )
& ( isLocallyConfluent0 @ xR )
& ! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( ( aReductOfIn0 @ B @ A @ xR )
| ? [C: $i] :
( ( aElement0 @ C )
& ( aReductOfIn0 @ C @ A @ xR )
& ( sdtmndtplgtdt0 @ C @ xR @ B ) )
| ( sdtmndtplgtdt0 @ A @ xR @ B ) )
=> ( iLess0 @ B @ A ) ) )
& ( isTerminating0 @ xR ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(212,plain,
isLocallyConfluent0 @ xR,
inference(cnf,[status(esa)],[207]) ).
thf(265,plain,
! [A: $i] :
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ A )
| ~ ( sk1 @ A )
| ( ( aElement0 @ xa )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,27]) ).
thf(266,plain,
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ xa )
| ~ ( sk1 @ xa ) ),
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( xa ))]]) ).
thf(51,plain,
sdtmndtplgtdt0 @ xa @ xR @ xc,
inference(cnf,[status(esa)],[43]) ).
thf(353,plain,
( ~ ( sk1 @ xc )
| ( ( sdtmndtplgtdt0 @ xa @ xR @ xc )
!= ( sdtmndtplgtdt0 @ xb @ xR @ xc ) ) ),
inference(paramod_ordered,[status(thm)],[51,261]) ).
thf(356,plain,
( ~ ( sk1 @ xc )
| ( xa != xb )
| ( xR != xR )
| ( xc != xc ) ),
inference(simp,[status(thm)],[353]) ).
thf(358,plain,
( ~ ( sk1 @ xc )
| ( xa != xb ) ),
inference(simp,[status(thm)],[356]) ).
thf(397,plain,
( ( xa != xb )
| ( ( sk1 @ xc )
!= ( sk1 @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[274,358]) ).
thf(398,plain,
( ( xa != xb )
| ( xc != xd ) ),
inference(simp,[status(thm)],[397]) ).
thf(15,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(148,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)],[15]) ).
thf(45,plain,
( ( aReductOfIn0 @ xc @ xa @ xR )
| ( sdtmndtplgtdt0 @ sk3 @ xR @ xc ) ),
inference(cnf,[status(esa)],[43]) ).
thf(161,plain,
sdtmndtasgtdt0 @ xu @ xR @ xw,
inference(cnf,[status(esa)],[152]) ).
thf(6,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(64,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)],[6]) ).
thf(44,plain,
sdtmndtplgtdt0 @ xa @ xR @ xb,
inference(cnf,[status(esa)],[43]) ).
thf(59,plain,
sdtmndtasgtdt0 @ xu @ xR @ xb,
inference(cnf,[status(esa)],[52]) ).
thf(49,plain,
( ( aReductOfIn0 @ xc @ xa @ xR )
| ( aElement0 @ sk3 ) ),
inference(cnf,[status(esa)],[43]) ).
thf(18,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(172,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(361,plain,
! [A: $i] :
( ( sk1 @ A )
| ~ ( sdtmndtasgtdt0 @ xd @ xR @ A )
| ( ( aElement0 @ xu )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[56,30]) ).
thf(362,plain,
( ( sk1 @ xu )
| ~ ( sdtmndtasgtdt0 @ xd @ xR @ xu ) ),
inference(pattern_uni,[status(thm)],[361:[bind(A,$thf( xu ))]]) ).
thf(208,plain,
isTerminating0 @ xR,
inference(cnf,[status(esa)],[207]) ).
thf(390,plain,
! [A: $i] :
( ( aReductOfIn0 @ xv @ xa @ xR )
!= ( aReductOfIn0 @ A @ xd @ xR ) ),
inference(paramod_ordered,[status(thm)],[134,188]) ).
thf(392,plain,
! [A: $i] :
( ( xv != A )
| ( xa != xd )
| ( xR != xR ) ),
inference(simp,[status(thm)],[390]) ).
thf(394,plain,
xa != xd,
inference(simp,[status(thm)],[392]) ).
thf(156,plain,
( ( xv = xw )
| ( sdtmndtplgtdt0 @ xv @ xR @ xw ) ),
inference(cnf,[status(esa)],[152]) ).
thf(167,plain,
( ( xw = xv )
| ( sdtmndtplgtdt0 @ xv @ xR @ xw ) ),
inference(lifteq,[status(thm)],[156]) ).
thf(35,plain,
! [A: $i] :
( ~ ( aElement0 @ A )
| ~ ( sdtmndtasgtdt0 @ xb @ xR @ A )
| ~ ( sk1 @ A ) ),
inference(cnf,[status(esa)],[26]) ).
thf(162,plain,
sdtmndtasgtdt0 @ xv @ xR @ xw,
inference(cnf,[status(esa)],[152]) ).
thf(254,plain,
! [A: $i] :
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ A )
| ~ ( sk1 @ A )
| ( ( aElement0 @ xu )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[56,27]) ).
thf(255,plain,
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ xu )
| ~ ( sk1 @ xu ) ),
inference(pattern_uni,[status(thm)],[254:[bind(A,$thf( xu ))]]) ).
thf(352,plain,
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ xc )
| ( ( sk1 @ xc )
!= ( sk1 @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[274,261]) ).
thf(355,plain,
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ xc )
| ( xc != xd ) ),
inference(simp,[status(thm)],[352]) ).
thf(194,plain,
aNormalFormOfIn0 @ xd @ xw @ xR,
inference(cnf,[status(esa)],[186]) ).
thf(48,plain,
( ( aReductOfIn0 @ xb @ xa @ xR )
| ( aElement0 @ sk2 ) ),
inference(cnf,[status(esa)],[43]) ).
thf(58,plain,
( ( xu = xb )
| ( sdtmndtplgtdt0 @ xu @ xR @ xb ) ),
inference(cnf,[status(esa)],[52]) ).
thf(63,plain,
( ( xu = xb )
| ( sdtmndtplgtdt0 @ xu @ xR @ xb ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(281,plain,
( ( sk1 @ xd )
!= ( sk1 @ xb ) ),
inference(paramod_ordered,[status(thm)],[274,243]) ).
thf(282,plain,
xd != xb,
inference(simp,[status(thm)],[281]) ).
thf(16,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(150,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)],[16]) ).
thf(22,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(199,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)],[22]) ).
thf(311,plain,
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ xu )
| ( ( sk1 @ xu )
!= ( sk1 @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[274,255]) ).
thf(314,plain,
( ~ ( sdtmndtplgtdt0 @ xb @ xR @ xu )
| ( xu != xd ) ),
inference(simp,[status(thm)],[311]) ).
thf(506,plain,
( ~ ( sk1 @ xa )
| ( ( sdtmndtplgtdt0 @ xa @ xR @ xb )
!= ( sdtmndtplgtdt0 @ xb @ xR @ xa ) ) ),
inference(paramod_ordered,[status(thm)],[44,266]) ).
thf(514,plain,
( ~ ( sk1 @ xa )
| ( xa != xb )
| ( xR != xR )
| ( xa != xb ) ),
inference(simp,[status(thm)],[506]) ).
thf(517,plain,
( ~ ( sk1 @ xa )
| ( xa != xb ) ),
inference(simp,[status(thm)],[514]) ).
thf(11,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(114,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)],[11]) ).
thf(139,plain,
sdtmndtasgtdt0 @ xv @ xR @ xc,
inference(cnf,[status(esa)],[132]) ).
thf(7,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(75,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)],[7]) ).
thf(289,plain,
! [A: $i] :
( ~ ( aReductOfIn0 @ A @ xb @ xR )
| ~ ( sk1 @ A )
| ( ( aElement0 @ xw )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[158,28]) ).
thf(290,plain,
( ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ~ ( sk1 @ xw ) ),
inference(pattern_uni,[status(thm)],[289:[bind(A,$thf( xw ))]]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mWFOrd) ).
thf(235,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aReductOfIn0 @ B @ xb @ xR )
| ~ ( sdtmndtplgtdt0 @ B @ xR @ A )
| ~ ( sk1 @ A ) ),
inference(cnf,[status(esa)],[26]) ).
thf(293,plain,
! [A: $i] :
( ~ ( aReductOfIn0 @ A @ xb @ xR )
| ~ ( sk1 @ A )
| ( ( aElement0 @ xa )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,28]) ).
thf(294,plain,
( ~ ( aReductOfIn0 @ xa @ xb @ xR )
| ~ ( sk1 @ xa ) ),
inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( xa ))]]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C )
& ( ( A = B )
| ( aReductOfIn0 @ B @ A @ xR )
| ? [D: $i] :
( ( aElement0 @ D )
& ( aReductOfIn0 @ D @ A @ xR )
& ( sdtmndtplgtdt0 @ D @ xR @ B ) )
| ( sdtmndtplgtdt0 @ A @ xR @ B )
| ( sdtmndtasgtdt0 @ A @ xR @ B ) )
& ( ( A = C )
| ( aReductOfIn0 @ C @ A @ xR )
| ? [D: $i] :
( ( aElement0 @ D )
& ( aReductOfIn0 @ D @ A @ xR )
& ( sdtmndtplgtdt0 @ D @ xR @ C ) )
| ( sdtmndtplgtdt0 @ A @ xR @ C )
| ( sdtmndtasgtdt0 @ A @ xR @ C ) ) )
=> ( ( iLess0 @ A @ xa )
=> ? [D: $i] :
( ( aElement0 @ D )
& ( ( B = D )
| ( ( ( aReductOfIn0 @ D @ B @ xR )
| ? [E: $i] :
( ( aElement0 @ E )
& ( aReductOfIn0 @ E @ B @ xR )
& ( sdtmndtplgtdt0 @ E @ xR @ D ) ) )
& ( sdtmndtplgtdt0 @ B @ xR @ D ) ) )
& ( sdtmndtasgtdt0 @ B @ xR @ D )
& ( ( C = D )
| ( ( ( aReductOfIn0 @ D @ C @ xR )
| ? [E: $i] :
( ( aElement0 @ E )
& ( aReductOfIn0 @ E @ C @ xR )
& ( sdtmndtplgtdt0 @ E @ xR @ D ) ) )
& ( sdtmndtplgtdt0 @ C @ xR @ D ) ) )
& ( sdtmndtasgtdt0 @ C @ xR @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__715) ).
thf(79,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C )
& ( ( A = B )
| ( aReductOfIn0 @ B @ A @ xR )
| ? [D: $i] :
( ( aElement0 @ D )
& ( aReductOfIn0 @ D @ A @ xR )
& ( sdtmndtplgtdt0 @ D @ xR @ B ) )
| ( sdtmndtplgtdt0 @ A @ xR @ B )
| ( sdtmndtasgtdt0 @ A @ xR @ B ) )
& ( ( A = C )
| ( aReductOfIn0 @ C @ A @ xR )
| ? [D: $i] :
( ( aElement0 @ D )
& ( aReductOfIn0 @ D @ A @ xR )
& ( sdtmndtplgtdt0 @ D @ xR @ C ) )
| ( sdtmndtplgtdt0 @ A @ xR @ C )
| ( sdtmndtasgtdt0 @ A @ xR @ C ) ) )
=> ( ( iLess0 @ A @ xa )
=> ? [D: $i] :
( ( aElement0 @ D )
& ( ( B = D )
| ( ( ( aReductOfIn0 @ D @ B @ xR )
| ? [E: $i] :
( ( aElement0 @ E )
& ( aReductOfIn0 @ E @ B @ xR )
& ( sdtmndtplgtdt0 @ E @ xR @ D ) ) )
& ( sdtmndtplgtdt0 @ B @ xR @ D ) ) )
& ( sdtmndtasgtdt0 @ B @ xR @ D )
& ( ( C = D )
| ( ( ( aReductOfIn0 @ D @ C @ xR )
| ? [E: $i] :
( ( aElement0 @ E )
& ( aReductOfIn0 @ E @ C @ xR )
& ( sdtmndtplgtdt0 @ E @ xR @ D ) ) )
& ( sdtmndtplgtdt0 @ C @ xR @ D ) ) )
& ( sdtmndtasgtdt0 @ C @ xR @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(96349,plain,
$false,
inference(cvc4,[status(thm)],[830,188,173,895,47,676,365,347,56,142,42,288,52,125,196,46,284,152,57,78,261,179,834,147,132,243,270,201,810,28,192,165,33,77,193,212,134,266,398,148,45,161,64,44,286,59,259,27,144,49,804,172,274,362,208,394,135,167,35,162,255,355,194,145,48,63,282,150,199,463,314,43,517,26,158,186,114,139,75,290,235,207,36,146,30,51,294,358,79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM020+4 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 19 03:19:40 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.01 % [INFO] Parsing done (153ms).
% 1.23/1.02 % [INFO] Running in sequential loop mode.
% 1.82/1.23 % [INFO] eprover registered as external prover.
% 1.93/1.23 % [INFO] cvc4 registered as external prover.
% 1.93/1.23 % [INFO] Scanning for conjecture ...
% 1.95/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.95/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.95/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.95/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.95/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.95/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.17/1.33 % [INFO] Found a conjecture and 23 axioms. Running axiom selection ...
% 2.32/1.39 % [INFO] Axiom selection finished. Selected 23 axioms (removed 0 axioms).
% 2.32/1.40 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.32/1.41 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.32/1.41 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.32/1.42 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.32/1.42 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.32/1.43 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.32/1.43 % [INFO] Problem is first-order (TPTP FOF).
% 2.32/1.44 % [INFO] Type checking passed.
% 2.32/1.44 % [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 ...
% 100.48/25.50 % External prover 'cvc4' found a proof!
% 100.48/25.50 % [INFO] Killing All external provers ...
% 100.48/25.50 % Time passed: 24977ms (effective reasoning time: 24481ms)
% 100.48/25.50 % 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)>
% 100.48/25.50 % Axioms used in derivation (23): 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, m__818, mTCbr, mElmSort, mCRDef
% 100.48/25.50 % No. of inferences in proof: 166
% 100.48/25.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 24977 ms resp. 24481 ms w/o parsing
% 100.48/25.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 100.48/25.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------