TSTP Solution File: COM021+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM021+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 58.06s 12.95s
% Output : Refutation 58.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 46
% Syntax : Number of formulae : 124 ( 40 unt; 21 typ; 0 def)
% Number of atoms : 372 ( 39 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 963 ( 77 ~; 50 |; 132 &; 633 @)
% ( 6 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 11 con; 0-3 aty)
% Number of variables : 141 ( 0 ^; 123 !; 18 ?; 141 :)
% 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(xv_type,type,
xv: $i ).
thf(xa_type,type,
xa: $i ).
thf(xc_type,type,
xc: $i ).
thf(xw_type,type,
xw: $i ).
thf(xu_type,type,
xu: $i ).
thf(xx_type,type,
xx: $i ).
thf(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(12,axiom,
( ( aElement0 @ xv )
& ( aReductOfIn0 @ xv @ xa @ xR )
& ( sdtmndtasgtdt0 @ xv @ xR @ xc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__779) ).
thf(50,plain,
( ( aElement0 @ xv )
& ( aReductOfIn0 @ xv @ xa @ xR )
& ( sdtmndtasgtdt0 @ xv @ xR @ xc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(51,plain,
sdtmndtasgtdt0 @ xv @ xR @ xc,
inference(cnf,[status(esa)],[50]) ).
thf(1,conjecture,
sdtmndtasgtdt0 @ xb @ xR @ xd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( sdtmndtasgtdt0 @ xb @ xR @ xd ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(27,plain,
~ ( sdtmndtasgtdt0 @ xb @ xR @ xd ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(168,plain,
( ( sdtmndtasgtdt0 @ xv @ xR @ xc )
!= ( sdtmndtasgtdt0 @ xb @ xR @ xd ) ),
inference(paramod_ordered,[status(thm)],[51,27]) ).
thf(169,plain,
( ( xv != xb )
| ( xR != xR )
| ( xc != xd ) ),
inference(simp,[status(thm)],[168]) ).
thf(170,plain,
( ( xv != xb )
| ( xc != xd ) ),
inference(simp,[status(thm)],[169]) ).
thf(14,axiom,
( ( aElement0 @ xa )
& ( aElement0 @ xb )
& ( aElement0 @ xc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731) ).
thf(55,plain,
( ( aElement0 @ xa )
& ( aElement0 @ xb )
& ( aElement0 @ xc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(56,plain,
aElement0 @ xc,
inference(cnf,[status(esa)],[55]) ).
thf(52,plain,
aReductOfIn0 @ xv @ xa @ xR,
inference(cnf,[status(esa)],[50]) ).
thf(17,axiom,
( ( isLocallyConfluent0 @ xR )
& ( isTerminating0 @ xR ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656_01) ).
thf(65,plain,
( ( isLocallyConfluent0 @ xR )
& ( isTerminating0 @ xR ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(53,plain,
aElement0 @ xv,
inference(cnf,[status(esa)],[50]) ).
thf(25,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(109,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)],[25]) ).
thf(9,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(41,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)],[9]) ).
thf(23,axiom,
( ( aElement0 @ xx )
& ( sdtmndtasgtdt0 @ xb @ xR @ xx )
& ( sdtmndtasgtdt0 @ xd @ xR @ xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__850) ).
thf(98,plain,
( ( aElement0 @ xx )
& ( sdtmndtasgtdt0 @ xb @ xR @ xx )
& ( sdtmndtasgtdt0 @ xd @ xR @ xx ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(16,axiom,
( ( aElement0 @ xw )
& ( sdtmndtasgtdt0 @ xu @ xR @ xw )
& ( sdtmndtasgtdt0 @ xv @ xR @ xw ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__799) ).
thf(61,plain,
( ( aElement0 @ xw )
& ( sdtmndtasgtdt0 @ xu @ xR @ xw )
& ( sdtmndtasgtdt0 @ xv @ xR @ xw ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(63,plain,
sdtmndtasgtdt0 @ xu @ xR @ xw,
inference(cnf,[status(esa)],[61]) ).
thf(10,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(43,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)],[10]) ).
thf(18,axiom,
( ( sdtmndtplgtdt0 @ xa @ xR @ xb )
& ( sdtmndtplgtdt0 @ xa @ xR @ xc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731_02) ).
thf(68,plain,
( ( sdtmndtplgtdt0 @ xa @ xR @ xb )
& ( sdtmndtplgtdt0 @ xa @ xR @ xc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(69,plain,
sdtmndtplgtdt0 @ xa @ xR @ xc,
inference(cnf,[status(esa)],[68]) ).
thf(101,plain,
aElement0 @ xx,
inference(cnf,[status(esa)],[98]) ).
thf(26,axiom,
( ( aElement0 @ xu )
& ( aReductOfIn0 @ xu @ xa @ xR )
& ( sdtmndtasgtdt0 @ xu @ xR @ xb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__755) ).
thf(116,plain,
( ( aElement0 @ xu )
& ( aReductOfIn0 @ xu @ xa @ xR )
& ( sdtmndtasgtdt0 @ xu @ xR @ xb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(117,plain,
sdtmndtasgtdt0 @ xu @ xR @ xb,
inference(cnf,[status(esa)],[116]) ).
thf(287,plain,
( ( sdtmndtasgtdt0 @ xu @ xR @ xb )
!= ( sdtmndtasgtdt0 @ xb @ xR @ xd ) ),
inference(paramod_ordered,[status(thm)],[117,27]) ).
thf(288,plain,
( ( xu != xb )
| ( xR != xR )
| ( xd != xb ) ),
inference(simp,[status(thm)],[287]) ).
thf(289,plain,
( ( xu != xb )
| ( xd != xb ) ),
inference(simp,[status(thm)],[288]) ).
thf(57,plain,
aElement0 @ xb,
inference(cnf,[status(esa)],[55]) ).
thf(4,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(29,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)],[4]) ).
thf(62,plain,
sdtmndtasgtdt0 @ xv @ xR @ xw,
inference(cnf,[status(esa)],[61]) ).
thf(204,plain,
( ( sdtmndtasgtdt0 @ xv @ xR @ xw )
!= ( sdtmndtasgtdt0 @ xb @ xR @ xd ) ),
inference(paramod_ordered,[status(thm)],[62,27]) ).
thf(205,plain,
( ( xv != xb )
| ( xR != xR )
| ( xw != xd ) ),
inference(simp,[status(thm)],[204]) ).
thf(206,plain,
( ( xv != xb )
| ( xw != xd ) ),
inference(simp,[status(thm)],[205]) ).
thf(24,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(102,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)],[24]) ).
thf(13,axiom,
aNormalFormOfIn0 @ xd @ xw @ xR,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__818) ).
thf(54,plain,
aNormalFormOfIn0 @ xd @ xw @ xR,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
aRewritingSystem0 @ xR,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
thf(86,plain,
aRewritingSystem0 @ xR,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(110,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)],[109]) ).
thf(111,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)],[110]) ).
thf(152,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)],[86,111]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aNormalFormOfIn0 @ B @ A @ xR )
| ~ ( aReductOfIn0 @ C @ B @ xR ) ),
inference(pattern_uni,[status(thm)],[152:[bind(A,$thf( A )),bind(B,$thf( xR ))]]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aNormalFormOfIn0 @ B @ A @ xR )
| ~ ( aReductOfIn0 @ C @ B @ xR ) ),
inference(simp,[status(thm)],[153]) ).
thf(200,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aReductOfIn0 @ C @ B @ xR )
| ( ( aNormalFormOfIn0 @ xd @ xw @ xR )
!= ( aNormalFormOfIn0 @ B @ A @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[54,155]) ).
thf(201,plain,
! [A: $i] :
( ~ ( aElement0 @ xw )
| ~ ( aReductOfIn0 @ A @ xd @ xR ) ),
inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( xw )),bind(B,$thf( xd ))]]) ).
thf(203,plain,
! [A: $i] :
( ~ ( aElement0 @ xw )
| ~ ( aReductOfIn0 @ A @ xd @ xR ) ),
inference(simp,[status(thm)],[201]) ).
thf(64,plain,
aElement0 @ xw,
inference(cnf,[status(esa)],[61]) ).
thf(296,plain,
! [A: $i] :
( ~ $true
| ~ ( aReductOfIn0 @ A @ xd @ xR ) ),
inference(rewrite,[status(thm)],[203,64]) ).
thf(297,plain,
! [A: $i] :
~ ( aReductOfIn0 @ A @ xd @ xR ),
inference(simp,[status(thm)],[296]) ).
thf(298,plain,
! [A: $i] :
( ( aReductOfIn0 @ xv @ xa @ xR )
!= ( aReductOfIn0 @ A @ xd @ xR ) ),
inference(paramod_ordered,[status(thm)],[52,297]) ).
thf(300,plain,
! [A: $i] :
( ( xv != A )
| ( xa != xd )
| ( xR != xR ) ),
inference(simp,[status(thm)],[298]) ).
thf(302,plain,
xa != xd,
inference(simp,[status(thm)],[300]) ).
thf(6,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(33,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: $i] :
( ( aRewritingSystem0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mRelSort) ).
thf(28,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,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(35,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)],[8]) ).
thf(38,plain,
! [A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ( aElement0 @ ( sk2 @ A ) )
| ( isTerminating0 @ A ) ),
inference(cnf,[status(esa)],[35]) ).
thf(70,plain,
sdtmndtplgtdt0 @ xa @ xR @ xb,
inference(cnf,[status(esa)],[68]) ).
thf(5,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(31,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)],[5]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ~ ( isTerminating0 @ A )
| ~ ( aElement0 @ B )
| ( aNormalFormOfIn0 @ ( sk1 @ B @ A ) @ B @ A ) ),
inference(cnf,[status(esa)],[31]) ).
thf(7,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(34,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
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(59,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(118,plain,
aReductOfIn0 @ xu @ xa @ xR,
inference(cnf,[status(esa)],[116]) ).
thf(19,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(71,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)],[19]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mWFOrd) ).
thf(49,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(66,plain,
isTerminating0 @ xR,
inference(cnf,[status(esa)],[65]) ).
thf(100,plain,
sdtmndtasgtdt0 @ xb @ xR @ xx,
inference(cnf,[status(esa)],[98]) ).
thf(239,plain,
( ( sdtmndtasgtdt0 @ xb @ xR @ xx )
!= ( sdtmndtasgtdt0 @ xb @ xR @ xd ) ),
inference(paramod_ordered,[status(thm)],[100,27]) ).
thf(240,plain,
( ( xb != xb )
| ( xR != xR )
| ( xx != xd ) ),
inference(simp,[status(thm)],[239]) ).
thf(241,plain,
xx != xd,
inference(simp,[status(thm)],[240]) ).
thf(67,plain,
isLocallyConfluent0 @ xR,
inference(cnf,[status(esa)],[65]) ).
thf(99,plain,
sdtmndtasgtdt0 @ xd @ xR @ xx,
inference(cnf,[status(esa)],[98]) ).
thf(22,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(87,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)],[22]) ).
thf(20,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(75,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)],[20]) ).
thf(233,plain,
( ( sdtmndtasgtdt0 @ xu @ xR @ xw )
!= ( sdtmndtasgtdt0 @ xb @ xR @ xd ) ),
inference(paramod_ordered,[status(thm)],[63,27]) ).
thf(234,plain,
( ( xu != xb )
| ( xR != xR )
| ( xw != xd ) ),
inference(simp,[status(thm)],[233]) ).
thf(235,plain,
( ( xu != xb )
| ( xw != xd ) ),
inference(simp,[status(thm)],[234]) ).
thf(119,plain,
aElement0 @ xu,
inference(cnf,[status(esa)],[116]) ).
thf(58,plain,
aElement0 @ xa,
inference(cnf,[status(esa)],[55]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ~ ( isTerminating0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aElement0 @ C )
| ~ ( sdtmndtplgtdt0 @ B @ A @ C )
| ( iLess0 @ C @ B ) ),
inference(cnf,[status(esa)],[35]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aRewritingSystem0 @ B )
| ~ ( aReductOfIn0 @ C @ A @ B )
| ( aElement0 @ C ) ),
inference(cnf,[status(esa)],[29]) ).
thf(39450,plain,
$false,
inference(cvc4,[status(thm)],[170,56,52,65,53,109,41,98,63,43,55,69,101,289,57,29,61,116,206,117,102,302,33,28,38,297,70,64,32,34,27,59,118,71,54,49,86,66,155,241,35,50,67,31,99,87,75,235,119,58,36,30,51,68,62,111,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : COM021+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n024.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 19 03:19:37 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.86/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.99 % [INFO] Parsing done (139ms).
% 1.18/1.00 % [INFO] Running in sequential loop mode.
% 1.74/1.20 % [INFO] eprover registered as external prover.
% 1.74/1.20 % [INFO] cvc4 registered as external prover.
% 1.80/1.21 % [INFO] Scanning for conjecture ...
% 1.90/1.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.90/1.26 % [INFO] Definitions in FOF are currently treated as axioms.
% 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.
% 1.90/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.90/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.90/1.29 % [INFO] Found a conjecture and 24 axioms. Running axiom selection ...
% 2.19/1.34 % [INFO] Axiom selection finished. Selected 24 axioms (removed 0 axioms).
% 2.19/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.19/1.35 % [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.
% 2.19/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.19/1.36 % [INFO] Problem is first-order (TPTP FOF).
% 2.19/1.37 % [INFO] Type checking passed.
% 2.19/1.37 % [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 ...
% 58.06/12.95 % External prover 'cvc4' found a proof!
% 58.06/12.95 % [INFO] Killing All external provers ...
% 58.06/12.95 % Time passed: 12421ms (effective reasoning time: 11949ms)
% 58.06/12.95 % 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)>
% 58.06/12.95 % Axioms used in derivation (24): 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, m__850, mWCRDef, mTCRTrans, m__818, mTCbr, mElmSort, mCRDef
% 58.06/12.95 % No. of inferences in proof: 103
% 58.06/12.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12421 ms resp. 11949 ms w/o parsing
% 58.06/12.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 58.06/12.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------