TSTP Solution File: COM018+4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM018+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 44.74s 9.79s
% Output : Refutation 44.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 40
% Syntax : Number of formulae : 65 ( 7 unt; 17 typ; 0 def)
% Number of atoms : 439 ( 26 equ; 0 cnn)
% Maximal formula atoms : 33 ( 9 avg)
% Number of connectives : 1259 ( 8 ~; 77 |; 240 &; 860 @)
% ( 6 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 9 con; 0-3 aty)
% Number of variables : 150 ( 0 ^; 97 !; 53 ?; 150 :)
% 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(xb_type,type,
xb: $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(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(142,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(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(46,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(24,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mWFOrd) ).
thf(216,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(23,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(188,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)],[23]) ).
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(173,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(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(73,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(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(108,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(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(167,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(22,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(182,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)],[22]) ).
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(72,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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(126,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(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(69,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(14,axiom,
( ( aElement0 @ xa )
& ( aElement0 @ xb )
& ( aElement0 @ xc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731) ).
thf(138,plain,
( ( aElement0 @ xa )
& ( aElement0 @ xb )
& ( aElement0 @ xc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
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(37,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(1,conjecture,
? [A: $i] :
( ( ( aElement0 @ A )
& ( ( xw = A )
| ( aReductOfIn0 @ A @ xw @ xR )
| ? [B: $i] :
( ( aElement0 @ B )
& ( aReductOfIn0 @ B @ xw @ xR )
& ( sdtmndtplgtdt0 @ B @ xR @ A ) )
| ( sdtmndtplgtdt0 @ xw @ xR @ A )
| ( sdtmndtasgtdt0 @ xw @ xR @ A ) )
& ~ ? [B: $i] : ( aReductOfIn0 @ B @ A @ xR ) )
| ( aNormalFormOfIn0 @ A @ xw @ xR ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( ( aElement0 @ A )
& ( ( xw = A )
| ( aReductOfIn0 @ A @ xw @ xR )
| ? [B: $i] :
( ( aElement0 @ B )
& ( aReductOfIn0 @ B @ xw @ xR )
& ( sdtmndtplgtdt0 @ B @ xR @ A ) )
| ( sdtmndtplgtdt0 @ xw @ xR @ A )
| ( sdtmndtasgtdt0 @ xw @ xR @ A ) )
& ~ ? [B: $i] : ( aReductOfIn0 @ B @ A @ xR ) )
| ( aNormalFormOfIn0 @ A @ xw @ xR ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(25,plain,
~ ? [A: $i] :
( ( ( aElement0 @ A )
& ( ( xw = A )
| ( aReductOfIn0 @ A @ xw @ xR )
| ? [B: $i] :
( ( aElement0 @ B )
& ( aReductOfIn0 @ B @ xw @ xR )
& ( sdtmndtplgtdt0 @ B @ xR @ A ) )
| ( sdtmndtplgtdt0 @ xw @ xR @ A )
| ( sdtmndtasgtdt0 @ xw @ xR @ A ) )
& ~ ? [B: $i] : ( aReductOfIn0 @ B @ A @ xR ) )
| ( aNormalFormOfIn0 @ A @ xw @ xR ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(166,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(21,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(180,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)],[21]) ).
thf(8,axiom,
aRewritingSystem0 @ xR,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
thf(71,plain,
aRewritingSystem0 @ xR,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
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(144,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(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(119,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(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(58,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(3,axiom,
! [A: $i] :
( ( aRewritingSystem0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mRelSort) ).
thf(36,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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(146,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(26877,plain,
$false,
inference(cvc4,[status(thm)],[142,46,216,188,173,73,108,167,182,72,126,69,138,37,25,166,180,71,144,119,58,36,146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COM018+4 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 03:45:43 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.98/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.37/1.03 % [INFO] Parsing done (156ms).
% 1.37/1.04 % [INFO] Running in sequential loop mode.
% 1.85/1.24 % [INFO] eprover registered as external prover.
% 1.85/1.24 % [INFO] cvc4 registered as external prover.
% 1.85/1.25 % [INFO] Scanning for conjecture ...
% 1.85/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.85/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.85/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.85/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.85/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.85/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.15/1.34 % [INFO] Found a conjecture and 22 axioms. Running axiom selection ...
% 2.15/1.39 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.38/1.40 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.41 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.41 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.42 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.42 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.42 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.43 % [INFO] Problem is first-order (TPTP FOF).
% 2.38/1.44 % [INFO] Type checking passed.
% 2.38/1.44 % [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 ...
% 44.74/9.79 % External prover 'cvc4' found a proof!
% 44.74/9.79 % [INFO] Killing All external provers ...
% 44.74/9.79 % Time passed: 9277ms (effective reasoning time: 8748ms)
% 44.74/9.79 % 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)>
% 44.74/9.79 % 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
% 44.74/9.79 % No. of inferences in proof: 48
% 44.74/9.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9277 ms resp. 8748 ms w/o parsing
% 44.74/9.83 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 44.74/9.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------