TSTP Solution File: COM019+4 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM019+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 221.21s 63.52s
% Output : Refutation 221.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 56
% Syntax : Number of formulae : 345 ( 42 unt; 32 typ; 0 def)
% Number of atoms : 1247 ( 348 equ; 0 cnn)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 3348 ( 416 ~; 514 |; 248 &;2096 @)
% ( 6 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 17 con; 0-4 aty)
% Number of variables : 199 ( 0 ^; 148 !; 51 ?; 199 :)
% 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(xd_type,type,
xd: $i ).
thf(xR_type,type,
xR: $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 ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i > $i > $i > $i > $i ).
thf(sk5_type,type,
sk5: $i > $i ).
thf(sk6_type,type,
sk6: $i > $i ).
thf(sk7_type,type,
sk7: $i > $i ).
thf(sk8_type,type,
sk8: $i > $i > $i > $o ).
thf(sk9_type,type,
sk9: $i > $i > $o ).
thf(sk10_type,type,
sk10: $i > $i > $i > $i ).
thf(sk17_type,type,
sk17: $i ).
thf(sk19_type,type,
sk19: $i ).
thf(sk20_type,type,
sk20: $i ).
thf(sk24_type,type,
sk24: $i ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtmndtplgtdt0 @ A @ B @ C )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCbr) ).
thf(69,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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/sandbox/benchmark/theBenchmark.p',m__731_02) ).
thf(34,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(36,plain,
sdtmndtplgtdt0 @ xa @ xR @ xc,
inference(cnf,[status(esa)],[34]) ).
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/sandbox/benchmark/theBenchmark.p',m__755) ).
thf(43,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(44,plain,
aElement0 @ xu,
inference(cnf,[status(esa)],[43]) ).
thf(1,conjecture,
( ( xb = xd )
| ( aReductOfIn0 @ xd @ xb @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xb @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xd ) )
| ( sdtmndtplgtdt0 @ xb @ xR @ xd )
| ( sdtmndtasgtdt0 @ xb @ xR @ xd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xb = xd )
| ( aReductOfIn0 @ xd @ xb @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xb @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xd ) )
| ( sdtmndtplgtdt0 @ xb @ xR @ xd )
| ( sdtmndtasgtdt0 @ xb @ xR @ xd ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(26,plain,
~ ( ( xb = xd )
| ( aReductOfIn0 @ xd @ xb @ xR )
| ? [A: $i] :
( ( aElement0 @ A )
& ( aReductOfIn0 @ A @ xb @ xR )
& ( sdtmndtplgtdt0 @ A @ xR @ xd ) )
| ( sdtmndtplgtdt0 @ xb @ xR @ xd )
| ( sdtmndtasgtdt0 @ xb @ xR @ xd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(30,plain,
! [A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aReductOfIn0 @ A @ xb @ xR )
| ~ ( sdtmndtplgtdt0 @ A @ xR @ xd ) ),
inference(cnf,[status(esa)],[26]) ).
thf(231,plain,
! [A: $i] :
( ~ ( aReductOfIn0 @ A @ xb @ xR )
| ~ ( sdtmndtplgtdt0 @ A @ xR @ xd )
| ( ( aElement0 @ xu )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44,30]) ).
thf(232,plain,
( ~ ( aReductOfIn0 @ xu @ xb @ xR )
| ~ ( sdtmndtplgtdt0 @ xu @ xR @ xd ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( xu ))]]) ).
thf(599,plain,
( ~ ( aReductOfIn0 @ xu @ xb @ xR )
| ( ( sdtmndtplgtdt0 @ xu @ xR @ xd )
!= ( sdtmndtplgtdt0 @ xa @ xR @ xc ) ) ),
inference(paramod_ordered,[status(thm)],[36,232]) ).
thf(618,plain,
( ~ ( aReductOfIn0 @ xu @ xb @ xR )
| ( xu != xa )
| ( xR != xR )
| ( xc != xd ) ),
inference(simp,[status(thm)],[599]) ).
thf(629,plain,
( ~ ( aReductOfIn0 @ xu @ xb @ xR )
| ( xu != xa )
| ( xc != xd ) ),
inference(simp,[status(thm)],[618]) ).
thf(14,axiom,
( ( aElement0 @ xa )
& ( aElement0 @ xb )
& ( aElement0 @ xc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).
thf(135,plain,
( ( aElement0 @ xa )
& ( aElement0 @ xb )
& ( aElement0 @ xc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(138,plain,
aElement0 @ xa,
inference(cnf,[status(esa)],[135]) ).
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/sandbox/benchmark/theBenchmark.p',m__818) ).
thf(177,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(185,plain,
( ( xw = xd )
| ( sdtmndtplgtdt0 @ xw @ xR @ xd ) ),
inference(cnf,[status(esa)],[177]) ).
thf(186,plain,
( ( xw = xd )
| ( sdtmndtplgtdt0 @ xw @ xR @ xd ) ),
inference(lifteq,[status(thm)],[185]) ).
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/sandbox/benchmark/theBenchmark.p',m__799) ).
thf(143,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(146,plain,
sdtmndtasgtdt0 @ xu @ xR @ xw,
inference(cnf,[status(esa)],[143]) ).
thf(29,plain,
~ ( sdtmndtasgtdt0 @ xb @ xR @ xd ),
inference(cnf,[status(esa)],[26]) ).
thf(319,plain,
( ( sdtmndtasgtdt0 @ xu @ xR @ xw )
!= ( sdtmndtasgtdt0 @ xb @ xR @ xd ) ),
inference(paramod_ordered,[status(thm)],[146,29]) ).
thf(320,plain,
( ( xu != xb )
| ( xR != xR )
| ( xw != xd ) ),
inference(simp,[status(thm)],[319]) ).
thf(321,plain,
( ( xu != xb )
| ( xw != xd ) ),
inference(simp,[status(thm)],[320]) ).
thf(550,plain,
( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
| ( xu != xb )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[186,321]) ).
thf(551,plain,
( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
| ( xu != xb ) ),
inference(pattern_uni,[status(thm)],[550:[]]) ).
thf(49,plain,
aReductOfIn0 @ xu @ xa @ xR,
inference(cnf,[status(esa)],[43]) ).
thf(593,plain,
( ~ ( sdtmndtplgtdt0 @ xu @ xR @ xd )
| ( ( aReductOfIn0 @ xu @ xa @ xR )
!= ( aReductOfIn0 @ xu @ xb @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[49,232]) ).
thf(609,plain,
( ~ ( sdtmndtplgtdt0 @ xu @ xR @ xd )
| ( xu != xu )
| ( xa != xb )
| ( xR != xR ) ),
inference(simp,[status(thm)],[593]) ).
thf(620,plain,
( ~ ( sdtmndtplgtdt0 @ xu @ xR @ xd )
| ( xa != xb ) ),
inference(simp,[status(thm)],[609]) ).
thf(927,plain,
( ( xu != xb )
| ( xa != xb )
| ( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
!= ( sdtmndtplgtdt0 @ xu @ xR @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[551,620]) ).
thf(935,plain,
( ( xu != xb )
| ( xa != xb )
| ( xw != xu )
| ( xR != xR )
| ( xd != xd ) ),
inference(simp,[status(thm)],[927]) ).
thf(941,plain,
( ( xu != xb )
| ( xa != xb )
| ( xw != xu ) ),
inference(simp,[status(thm)],[935]) ).
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/sandbox/benchmark/theBenchmark.p',mNFRDef) ).
thf(170,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(147,plain,
aElement0 @ xw,
inference(cnf,[status(esa)],[143]) ).
thf(243,plain,
! [A: $i] :
( ~ ( aReductOfIn0 @ A @ xb @ xR )
| ~ ( sdtmndtplgtdt0 @ A @ xR @ xd )
| ( ( aElement0 @ xw )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,30]) ).
thf(244,plain,
( ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ~ ( sdtmndtplgtdt0 @ xw @ xR @ xd ) ),
inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( xw ))]]) ).
thf(1405,plain,
( ( xu != xb )
| ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
!= ( sdtmndtplgtdt0 @ xw @ xR @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[551,244]) ).
thf(1406,plain,
( ( xu != xb )
| ~ ( aReductOfIn0 @ xw @ xb @ xR ) ),
inference(pattern_uni,[status(thm)],[1405:[]]) ).
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/sandbox/benchmark/theBenchmark.p',m__779) ).
thf(123,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(127,plain,
( ( xv = xc )
| ( sdtmndtplgtdt0 @ xv @ xR @ xc ) ),
inference(cnf,[status(esa)],[123]) ).
thf(133,plain,
( ( xv = xc )
| ( sdtmndtplgtdt0 @ xv @ xR @ xc ) ),
inference(lifteq,[status(thm)],[127]) ).
thf(130,plain,
aReductOfIn0 @ xv @ xa @ xR,
inference(cnf,[status(esa)],[123]) ).
thf(448,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xc )
| ( aReductOfIn0 @ xc @ xa @ xR )
| ( xv != xv ) ),
inference(paramod_ordered,[status(thm)],[133,130]) ).
thf(449,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xc )
| ( aReductOfIn0 @ xc @ xa @ xR ) ),
inference(pattern_uni,[status(thm)],[448:[]]) ).
thf(152,plain,
( ( xu = xw )
| ( sdtmndtplgtdt0 @ xu @ xR @ xw ) ),
inference(cnf,[status(esa)],[143]) ).
thf(156,plain,
( ( xw = xu )
| ( sdtmndtplgtdt0 @ xu @ xR @ xw ) ),
inference(lifteq,[status(thm)],[152]) ).
thf(178,plain,
sdtmndtasgtdt0 @ xw @ xR @ xd,
inference(cnf,[status(esa)],[177]) ).
thf(322,plain,
( ( sdtmndtasgtdt0 @ xw @ xR @ xd )
!= ( sdtmndtasgtdt0 @ xb @ xR @ xd ) ),
inference(paramod_ordered,[status(thm)],[178,29]) ).
thf(323,plain,
( ( xw != xb )
| ( xR != xR )
| ( xd != xd ) ),
inference(simp,[status(thm)],[322]) ).
thf(324,plain,
xw != xb,
inference(simp,[status(thm)],[323]) ).
thf(471,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xw )
| ( xu != xb )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[156,324]) ).
thf(472,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xw )
| ( xu != xb ) ),
inference(pattern_uni,[status(thm)],[471:[]]) ).
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/sandbox/benchmark/theBenchmark.p',mCRDef) ).
thf(55,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(56,plain,
! [A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ( sdtmndtasgtdt0 @ ( sk5 @ A ) @ A @ ( sk7 @ A ) )
| ( isConfluent0 @ A ) ),
inference(cnf,[status(esa)],[55]) ).
thf(1426,plain,
( ( xw = xd )
| ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
!= ( sdtmndtplgtdt0 @ xw @ xR @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[186,244]) ).
thf(1427,plain,
( ( xw = xd )
| ~ ( aReductOfIn0 @ xw @ xb @ xR ) ),
inference(pattern_uni,[status(thm)],[1426:[]]) ).
thf(144,plain,
sdtmndtasgtdt0 @ xv @ xR @ xw,
inference(cnf,[status(esa)],[143]) ).
thf(1654,plain,
( ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ( sdtmndtasgtdt0 @ xv @ xR @ xd )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[1427,144]) ).
thf(1655,plain,
( ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ( sdtmndtasgtdt0 @ xv @ xR @ xd ) ),
inference(pattern_uni,[status(thm)],[1654:[]]) ).
thf(42,plain,
( ( aReductOfIn0 @ xb @ xa @ xR )
| ( aElement0 @ sk1 ) ),
inference(cnf,[status(esa)],[34]) ).
thf(184,plain,
aNormalFormOfIn0 @ xd @ xw @ xR,
inference(cnf,[status(esa)],[177]) ).
thf(1612,plain,
( ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ( aNormalFormOfIn0 @ xd @ xd @ xR )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[1427,184]) ).
thf(1613,plain,
( ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ( aNormalFormOfIn0 @ xd @ xd @ xR ) ),
inference(pattern_uni,[status(thm)],[1612:[]]) ).
thf(1649,plain,
( ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ~ ( sdtmndtplgtdt0 @ xd @ xR @ xd )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[1427,244]) ).
thf(1650,plain,
( ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ~ ( sdtmndtplgtdt0 @ xd @ xR @ xd ) ),
inference(pattern_uni,[status(thm)],[1649:[]]) ).
thf(37,plain,
( ( aReductOfIn0 @ xb @ xa @ xR )
| ( sdtmndtplgtdt0 @ sk1 @ xR @ xb ) ),
inference(cnf,[status(esa)],[34]) ).
thf(316,plain,
( ( sdtmndtasgtdt0 @ xv @ xR @ xw )
!= ( sdtmndtasgtdt0 @ xb @ xR @ xd ) ),
inference(paramod_ordered,[status(thm)],[144,29]) ).
thf(317,plain,
( ( xv != xb )
| ( xR != xR )
| ( xw != xd ) ),
inference(simp,[status(thm)],[316]) ).
thf(318,plain,
( ( xv != xb )
| ( xw != xd ) ),
inference(simp,[status(thm)],[317]) ).
thf(569,plain,
( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
| ( xv != xb )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[186,318]) ).
thf(570,plain,
( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
| ( xv != xb ) ),
inference(pattern_uni,[status(thm)],[569:[]]) ).
thf(45,plain,
( ( xu = xb )
| ( aReductOfIn0 @ xb @ xu @ xR )
| ( sdtmndtplgtdt0 @ sk3 @ xR @ xb ) ),
inference(cnf,[status(esa)],[43]) ).
thf(52,plain,
( ( xu = xb )
| ( aReductOfIn0 @ xb @ xu @ xR )
| ( sdtmndtplgtdt0 @ sk3 @ xR @ xb ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(705,plain,
( ( xw = xd )
| ( xa != xb )
| ( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
!= ( sdtmndtplgtdt0 @ xu @ xR @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[186,620]) ).
thf(716,plain,
( ( xw = xd )
| ( xa != xb )
| ( xw != xu )
| ( xR != xR )
| ( xd != xd ) ),
inference(simp,[status(thm)],[705]) ).
thf(724,plain,
( ( xw = xd )
| ( xa != xb )
| ( xw != xu ) ),
inference(simp,[status(thm)],[716]) ).
thf(128,plain,
aElement0 @ xv,
inference(cnf,[status(esa)],[123]) ).
thf(227,plain,
! [A: $i] :
( ~ ( aReductOfIn0 @ A @ xb @ xR )
| ~ ( sdtmndtplgtdt0 @ A @ xR @ xd )
| ( ( aElement0 @ xv )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[128,30]) ).
thf(228,plain,
( ~ ( aReductOfIn0 @ xv @ xb @ xR )
| ~ ( sdtmndtplgtdt0 @ xv @ xR @ xd ) ),
inference(pattern_uni,[status(thm)],[227:[bind(A,$thf( xv ))]]) ).
thf(57,plain,
! [A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ( aElement0 @ ( sk7 @ A ) )
| ( isConfluent0 @ A ) ),
inference(cnf,[status(esa)],[55]) ).
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/sandbox/benchmark/theBenchmark.p',m__715) ).
thf(70,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(78,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( sk8 @ A @ B @ C )
| ~ ( iLess0 @ A @ xa )
| ( aElement0 @ ( sk10 @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(136,plain,
aElement0 @ xc,
inference(cnf,[status(esa)],[135]) ).
thf(229,plain,
! [A: $i] :
( ~ ( aReductOfIn0 @ A @ xb @ xR )
| ~ ( sdtmndtplgtdt0 @ A @ xR @ xd )
| ( ( aElement0 @ xc )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[136,30]) ).
thf(230,plain,
( ~ ( aReductOfIn0 @ xc @ xb @ xR )
| ~ ( sdtmndtplgtdt0 @ xc @ xR @ xd ) ),
inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( xc ))]]) ).
thf(253,plain,
( ~ ( aReductOfIn0 @ xc @ xb @ xR )
| ( ( sdtmndtplgtdt0 @ xc @ xR @ xd )
!= ( sdtmndtplgtdt0 @ xa @ xR @ xc ) ) ),
inference(paramod_ordered,[status(thm)],[36,230]) ).
thf(257,plain,
( ~ ( aReductOfIn0 @ xc @ xb @ xR )
| ( xc != xa )
| ( xR != xR )
| ( xc != xd ) ),
inference(simp,[status(thm)],[253]) ).
thf(261,plain,
( ~ ( aReductOfIn0 @ xc @ xb @ xR )
| ( xc != xa )
| ( xc != xd ) ),
inference(simp,[status(thm)],[257]) ).
thf(474,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xw )
| ( sdtmndtasgtdt0 @ xv @ xR @ xu )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[156,144]) ).
thf(475,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xw )
| ( sdtmndtasgtdt0 @ xv @ xR @ xu ) ),
inference(pattern_uni,[status(thm)],[474:[]]) ).
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/sandbox/benchmark/theBenchmark.p',mTermin) ).
thf(164,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(179,plain,
aElement0 @ xd,
inference(cnf,[status(esa)],[177]) ).
thf(573,plain,
( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
| ( sdtmndtasgtdt0 @ xu @ xR @ xd )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[186,146]) ).
thf(574,plain,
( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
| ( sdtmndtasgtdt0 @ xu @ xR @ xd ) ),
inference(pattern_uni,[status(thm)],[573:[]]) ).
thf(479,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xw )
| ( sdtmndtasgtdt0 @ xu @ xR @ xu )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[156,146]) ).
thf(480,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xw )
| ( sdtmndtasgtdt0 @ xu @ xR @ xu ) ),
inference(pattern_uni,[status(thm)],[479:[]]) ).
thf(1681,plain,
( ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ( sdtmndtasgtdt0 @ xd @ xR @ xd )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[1427,178]) ).
thf(1682,plain,
( ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ( sdtmndtasgtdt0 @ xd @ xR @ xd ) ),
inference(pattern_uni,[status(thm)],[1681:[]]) ).
thf(484,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xw )
| ( sdtmndtasgtdt0 @ xu @ xR @ xd )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[156,178]) ).
thf(485,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xw )
| ( sdtmndtasgtdt0 @ xu @ xR @ xd ) ),
inference(pattern_uni,[status(thm)],[484:[]]) ).
thf(61,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ~ ( isConfluent0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aElement0 @ C )
| ~ ( aElement0 @ D )
| ~ ( sdtmndtasgtdt0 @ B @ A @ C )
| ~ ( sdtmndtasgtdt0 @ B @ A @ D )
| ( sdtmndtasgtdt0 @ C @ A @ ( sk4 @ D @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(129,plain,
( ( xv = xc )
| ( aReductOfIn0 @ xc @ xv @ xR )
| ( aElement0 @ sk17 ) ),
inference(cnf,[status(esa)],[123]) ).
thf(132,plain,
( ( xv = xc )
| ( aReductOfIn0 @ xc @ xv @ xR )
| ( aElement0 @ sk17 ) ),
inference(lifteq,[status(thm)],[129]) ).
thf(1393,plain,
( ( xv != xb )
| ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
!= ( sdtmndtplgtdt0 @ xw @ xR @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[570,244]) ).
thf(1394,plain,
( ( xv != xb )
| ~ ( aReductOfIn0 @ xw @ xb @ xR ) ),
inference(pattern_uni,[status(thm)],[1393:[]]) ).
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/sandbox/benchmark/theBenchmark.p',mTCRDef) ).
thf(116,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(302,plain,
( ~ ( sdtmndtplgtdt0 @ xv @ xR @ xd )
| ( ( aReductOfIn0 @ xv @ xa @ xR )
!= ( aReductOfIn0 @ xv @ xb @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[130,228]) ).
thf(307,plain,
( ~ ( sdtmndtplgtdt0 @ xv @ xR @ xd )
| ( xv != xv )
| ( xa != xb )
| ( xR != xR ) ),
inference(simp,[status(thm)],[302]) ).
thf(312,plain,
( ~ ( sdtmndtplgtdt0 @ xv @ xR @ xd )
| ( xa != xb ) ),
inference(simp,[status(thm)],[307]) ).
thf(74,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aElement0 @ C )
| ~ ( aElement0 @ D )
| ~ ( aReductOfIn0 @ D @ A @ xR )
| ~ ( sdtmndtplgtdt0 @ D @ xR @ B )
| ~ ( sk9 @ A @ C )
| ( sk8 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[70]) ).
thf(60,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ~ ( isConfluent0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aElement0 @ C )
| ~ ( aElement0 @ D )
| ~ ( sdtmndtasgtdt0 @ B @ A @ C )
| ~ ( sdtmndtasgtdt0 @ B @ A @ D )
| ( sdtmndtasgtdt0 @ D @ A @ ( sk4 @ D @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(41,plain,
( ( aReductOfIn0 @ xb @ xa @ xR )
| ( aReductOfIn0 @ sk1 @ xa @ xR ) ),
inference(cnf,[status(esa)],[34]) ).
thf(666,plain,
( ( aReductOfIn0 @ xb @ xa @ xR )
| ( ( aReductOfIn0 @ sk1 @ xa @ xR )
!= ( aReductOfIn0 @ xb @ xa @ xR ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[41]) ).
thf(668,plain,
( ( aReductOfIn0 @ xb @ xa @ xR )
| ( sk1 != xb )
| ( xa != xa )
| ( xR != xR ) ),
inference(simp,[status(thm)],[666]) ).
thf(678,plain,
( ( aReductOfIn0 @ xb @ xa @ xR )
| ( sk1 != xb ) ),
inference(simp,[status(thm)],[668]) ).
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/sandbox/benchmark/theBenchmark.p',m__656_01) ).
thf(198,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(201,plain,
isTerminating0 @ xR,
inference(cnf,[status(esa)],[198]) ).
thf(46,plain,
( ( xu = xb )
| ( sdtmndtplgtdt0 @ xu @ xR @ xb ) ),
inference(cnf,[status(esa)],[43]) ).
thf(51,plain,
( ( xu = xb )
| ( sdtmndtplgtdt0 @ xu @ xR @ xb ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(797,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( sdtmndtplgtdt0 @ xu @ xR @ xw )
| ( xu != xu ) ),
inference(paramod_ordered,[status(thm)],[51,472]) ).
thf(798,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( sdtmndtplgtdt0 @ xu @ xR @ xw ) ),
inference(pattern_uni,[status(thm)],[797:[]]) ).
thf(38,plain,
( ( aReductOfIn0 @ xc @ xa @ xR )
| ( aReductOfIn0 @ sk2 @ xa @ xR ) ),
inference(cnf,[status(esa)],[34]) ).
thf(330,plain,
( ( aReductOfIn0 @ xc @ xa @ xR )
| ( ( aReductOfIn0 @ sk2 @ xa @ xR )
!= ( aReductOfIn0 @ xc @ xa @ xR ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[38]) ).
thf(334,plain,
( ( aReductOfIn0 @ xc @ xa @ xR )
| ( ( aReductOfIn0 @ sk2 @ xa @ xR )
!= ( aReductOfIn0 @ xc @ xa @ xR ) ) ),
inference(simp,[status(thm)],[330]) ).
thf(148,plain,
( ( xv = xw )
| ( sdtmndtplgtdt0 @ xv @ xR @ xw ) ),
inference(cnf,[status(esa)],[143]) ).
thf(160,plain,
( ( xw = xv )
| ( sdtmndtplgtdt0 @ xv @ xR @ xw ) ),
inference(lifteq,[status(thm)],[148]) ).
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/sandbox/benchmark/theBenchmark.p',mTCDef) ).
thf(192,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(137,plain,
aElement0 @ xb,
inference(cnf,[status(esa)],[135]) ).
thf(3,axiom,
! [A: $i] :
( ( aRewritingSystem0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mRelSort) ).
thf(33,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,plain,
~ ( aReductOfIn0 @ xd @ xb @ xR ),
inference(cnf,[status(esa)],[26]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ~ ( aElement0 @ B )
| ~ ( sdtmndtasgtdt0 @ ( sk6 @ A ) @ A @ B )
| ~ ( sdtmndtasgtdt0 @ ( sk7 @ A ) @ A @ B )
| ( isConfluent0 @ A ) ),
inference(cnf,[status(esa)],[55]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ~ ( aElement0 @ B )
| ~ ( sdtmndtasgtdt0 @ ( sk6 @ A ) @ A @ B )
| ~ ( sdtmndtasgtdt0 @ ( sk7 @ A ) @ A @ B )
| ( isConfluent0 @ A ) ),
inference(simp,[status(thm)],[58]) ).
thf(124,plain,
sdtmndtasgtdt0 @ xv @ xR @ xc,
inference(cnf,[status(esa)],[123]) ).
thf(283,plain,
( ( sdtmndtasgtdt0 @ xv @ xR @ xc )
!= ( sdtmndtasgtdt0 @ xb @ xR @ xd ) ),
inference(paramod_ordered,[status(thm)],[124,29]) ).
thf(284,plain,
( ( xv != xb )
| ( xR != xR )
| ( xc != xd ) ),
inference(simp,[status(thm)],[283]) ).
thf(285,plain,
( ( xv != xb )
| ( xc != xd ) ),
inference(simp,[status(thm)],[284]) ).
thf(577,plain,
( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
| ( sdtmndtasgtdt0 @ xd @ xR @ xd )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[186,178]) ).
thf(578,plain,
( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
| ( sdtmndtasgtdt0 @ xd @ xR @ xd ) ),
inference(pattern_uni,[status(thm)],[577:[]]) ).
thf(50,plain,
( ( xu = xb )
| ( aReductOfIn0 @ xb @ xu @ xR )
| ( aReductOfIn0 @ sk3 @ xu @ xR ) ),
inference(cnf,[status(esa)],[43]) ).
thf(53,plain,
( ( xu = xb )
| ( aReductOfIn0 @ xb @ xu @ xR )
| ( aReductOfIn0 @ sk3 @ xu @ xR ) ),
inference(lifteq,[status(thm)],[50]) ).
thf(16,axiom,
! [A: $i] :
( ( ( aRewritingSystem0 @ A )
& ( isTerminating0 @ A ) )
=> ! [B: $i] :
( ( aElement0 @ B )
=> ? [C: $i] : ( aNormalFormOfIn0 @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermNF) ).
thf(141,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(326,plain,
( ( aReductOfIn0 @ xc @ xa @ xR )
| ( ( aReductOfIn0 @ sk2 @ xa @ xR )
!= ( aReductOfIn0 @ xd @ xb @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[38,28]) ).
thf(337,plain,
( ( aReductOfIn0 @ xc @ xa @ xR )
| ( sk2 != xd )
| ( xa != xb )
| ( xR != xR ) ),
inference(simp,[status(thm)],[326]) ).
thf(339,plain,
( ( aReductOfIn0 @ xc @ xa @ xR )
| ( sk2 != xd )
| ( xa != xb ) ),
inference(simp,[status(thm)],[337]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aElement0 @ C )
| ( sk9 @ A @ C )
| ~ ( sdtmndtplgtdt0 @ A @ xR @ C )
| ( sk8 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[70]) ).
thf(48,plain,
sdtmndtasgtdt0 @ xu @ xR @ xb,
inference(cnf,[status(esa)],[43]) ).
thf(392,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( sdtmndtasgtdt0 @ xb @ xR @ xb )
| ( xu != xu ) ),
inference(paramod_ordered,[status(thm)],[51,48]) ).
thf(393,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( sdtmndtasgtdt0 @ xb @ xR @ xb ) ),
inference(pattern_uni,[status(thm)],[392:[]]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aElement0 @ C )
| ~ ( sdtmndtplgtdt0 @ A @ xR @ B )
| ~ ( sk9 @ A @ C )
| ( sk8 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[70]) ).
thf(301,plain,
( ~ ( sdtmndtplgtdt0 @ xc @ xR @ xd )
| ( ( aReductOfIn0 @ xv @ xa @ xR )
!= ( aReductOfIn0 @ xc @ xb @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[130,230]) ).
thf(306,plain,
( ~ ( sdtmndtplgtdt0 @ xc @ xR @ xd )
| ( xv != xc )
| ( xa != xb )
| ( xR != xR ) ),
inference(simp,[status(thm)],[301]) ).
thf(311,plain,
( ~ ( sdtmndtplgtdt0 @ xc @ xR @ xd )
| ( xv != xc )
| ( xa != xb ) ),
inference(simp,[status(thm)],[306]) ).
thf(335,plain,
( ( aReductOfIn0 @ xc @ xa @ xR )
| ( sk2 != xc )
| ( xa != xa )
| ( xR != xR ) ),
inference(simp,[status(thm)],[330]) ).
thf(343,plain,
( ( aReductOfIn0 @ xc @ xa @ xR )
| ( sk2 != xc ) ),
inference(simp,[status(thm)],[335]) ).
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/sandbox/benchmark/theBenchmark.p',mWCRDef) ).
thf(105,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(424,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xc )
| ( sdtmndtasgtdt0 @ xc @ xR @ xc )
| ( xv != xv ) ),
inference(paramod_ordered,[status(thm)],[133,124]) ).
thf(425,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xc )
| ( sdtmndtasgtdt0 @ xc @ xR @ xc ) ),
inference(pattern_uni,[status(thm)],[424:[]]) ).
thf(443,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xc )
| ( sdtmndtasgtdt0 @ xc @ xR @ xw )
| ( xv != xv ) ),
inference(paramod_ordered,[status(thm)],[133,144]) ).
thf(444,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xc )
| ( sdtmndtasgtdt0 @ xc @ xR @ xw ) ),
inference(pattern_uni,[status(thm)],[443:[]]) ).
thf(31,plain,
xb != xd,
inference(cnf,[status(esa)],[26]) ).
thf(32,plain,
xd != xb,
inference(lifteq,[status(thm)],[31]) ).
thf(270,plain,
( ( aReductOfIn0 @ xu @ xa @ xR )
!= ( aReductOfIn0 @ xd @ xb @ xR ) ),
inference(paramod_ordered,[status(thm)],[49,28]) ).
thf(274,plain,
( ( xu != xd )
| ( xa != xb )
| ( xR != xR ) ),
inference(simp,[status(thm)],[270]) ).
thf(279,plain,
( ( xu != xd )
| ( xa != xb ) ),
inference(simp,[status(thm)],[274]) ).
thf(64,plain,
! [A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ( aElement0 @ ( sk5 @ A ) )
| ( isConfluent0 @ A ) ),
inference(cnf,[status(esa)],[55]) ).
thf(554,plain,
( ( xw = xd )
| ( xa != xb )
| ( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
!= ( sdtmndtplgtdt0 @ xv @ xR @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[186,312]) ).
thf(580,plain,
( ( xw = xd )
| ( xa != xb )
| ( xw != xv )
| ( xR != xR )
| ( xd != xd ) ),
inference(simp,[status(thm)],[554]) ).
thf(584,plain,
( ( xw = xd )
| ( xa != xb )
| ( xw != xv ) ),
inference(simp,[status(thm)],[580]) ).
thf(381,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( xw != xd )
| ( xu != xu ) ),
inference(paramod_ordered,[status(thm)],[51,321]) ).
thf(382,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( xw != xd ) ),
inference(pattern_uni,[status(thm)],[381:[]]) ).
thf(643,plain,
( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
| ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[186,382]) ).
thf(644,plain,
( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
| ( sdtmndtplgtdt0 @ xu @ xR @ xb ) ),
inference(pattern_uni,[status(thm)],[643:[]]) ).
thf(3751,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
!= ( sdtmndtplgtdt0 @ xu @ xR @ xb ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[644]) ).
thf(3758,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
!= ( sdtmndtplgtdt0 @ xu @ xR @ xb ) ) ),
inference(simp,[status(thm)],[3751]) ).
thf(59,plain,
! [A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ( sdtmndtasgtdt0 @ ( sk5 @ A ) @ A @ ( sk6 @ A ) )
| ( isConfluent0 @ A ) ),
inference(cnf,[status(esa)],[55]) ).
thf(183,plain,
! [A: $i] :
~ ( aReductOfIn0 @ A @ xd @ xR ),
inference(cnf,[status(esa)],[177]) ).
thf(272,plain,
! [A: $i] :
( ( aReductOfIn0 @ xu @ xa @ xR )
!= ( aReductOfIn0 @ A @ xd @ xR ) ),
inference(paramod_ordered,[status(thm)],[49,183]) ).
thf(276,plain,
! [A: $i] :
( ( xu != A )
| ( xa != xd )
| ( xR != xR ) ),
inference(simp,[status(thm)],[272]) ).
thf(281,plain,
xa != xd,
inference(simp,[status(thm)],[276]) ).
thf(27,plain,
~ ( sdtmndtplgtdt0 @ xb @ xR @ xd ),
inference(cnf,[status(esa)],[26]) ).
thf(8,axiom,
aRewritingSystem0 @ xR,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
thf(68,plain,
aRewritingSystem0 @ xR,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1138,plain,
! [A: $i] :
( ( aElement0 @ ( sk7 @ A ) )
| ( isConfluent0 @ A )
| ( ( aRewritingSystem0 @ xR )
!= ( aRewritingSystem0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[68,57]) ).
thf(1139,plain,
( ( aElement0 @ ( sk7 @ xR ) )
| ( isConfluent0 @ xR ) ),
inference(pattern_uni,[status(thm)],[1138:[bind(A,$thf( xR ))]]) ).
thf(303,plain,
( ( aReductOfIn0 @ xv @ xa @ xR )
!= ( aReductOfIn0 @ xd @ xb @ xR ) ),
inference(paramod_ordered,[status(thm)],[130,28]) ).
thf(308,plain,
( ( xv != xd )
| ( xa != xb )
| ( xR != xR ) ),
inference(simp,[status(thm)],[303]) ).
thf(313,plain,
( ( xv != xd )
| ( xa != xb ) ),
inference(simp,[status(thm)],[308]) ).
thf(539,plain,
( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
| ( aNormalFormOfIn0 @ xd @ xd @ xR )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[186,184]) ).
thf(540,plain,
( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
| ( aNormalFormOfIn0 @ xd @ xd @ xR ) ),
inference(pattern_uni,[status(thm)],[539:[]]) ).
thf(47,plain,
( ( xu = xb )
| ( aReductOfIn0 @ xb @ xu @ xR )
| ( aElement0 @ sk3 ) ),
inference(cnf,[status(esa)],[43]) ).
thf(54,plain,
( ( xu = xb )
| ( aReductOfIn0 @ xb @ xu @ xR )
| ( aElement0 @ sk3 ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(180,plain,
( ( xw = xd )
| ( aReductOfIn0 @ xd @ xw @ xR )
| ( aElement0 @ sk24 ) ),
inference(cnf,[status(esa)],[177]) ).
thf(187,plain,
( ( xw = xd )
| ( aReductOfIn0 @ xd @ xw @ xR )
| ( aElement0 @ sk24 ) ),
inference(lifteq,[status(thm)],[180]) ).
thf(566,plain,
( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
| ( sdtmndtasgtdt0 @ xv @ xR @ xd )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[186,144]) ).
thf(567,plain,
( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
| ( sdtmndtasgtdt0 @ xv @ xR @ xd ) ),
inference(pattern_uni,[status(thm)],[566:[]]) ).
thf(39,plain,
( ( aReductOfIn0 @ xc @ xa @ xR )
| ( aElement0 @ sk2 ) ),
inference(cnf,[status(esa)],[34]) ).
thf(150,plain,
( ( xu = xw )
| ( aReductOfIn0 @ xw @ xu @ xR )
| ( aElement0 @ sk19 ) ),
inference(cnf,[status(esa)],[143]) ).
thf(158,plain,
( ( xw = xu )
| ( aReductOfIn0 @ xw @ xu @ xR )
| ( aElement0 @ sk19 ) ),
inference(lifteq,[status(thm)],[150]) ).
thf(1747,plain,
( ( xw = xu )
| ( aElement0 @ sk19 )
| ( xu != xb )
| ( ( aReductOfIn0 @ xw @ xu @ xR )
!= ( aReductOfIn0 @ xw @ xb @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[158,1406]) ).
thf(1863,plain,
( ( xw = xu )
| ( aElement0 @ sk19 )
| ( xu != xb )
| ( xw != xw )
| ( xu != xb )
| ( xR != xR ) ),
inference(simp,[status(thm)],[1747]) ).
thf(1875,plain,
( ( xw = xu )
| ( aElement0 @ sk19 )
| ( xu != xb ) ),
inference(simp,[status(thm)],[1863]) ).
thf(2895,plain,
( ( aElement0 @ sk19 )
| ( xu != xb )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[1875,324]) ).
thf(2896,plain,
( ( aElement0 @ sk19 )
| ( xu != xb ) ),
inference(pattern_uni,[status(thm)],[2895:[]]) ).
thf(153,plain,
( ( xv = xw )
| ( aReductOfIn0 @ xw @ xv @ xR )
| ( aElement0 @ sk20 ) ),
inference(cnf,[status(esa)],[143]) ).
thf(155,plain,
( ( xw = xv )
| ( aReductOfIn0 @ xw @ xv @ xR )
| ( aElement0 @ sk20 ) ),
inference(lifteq,[status(thm)],[153]) ).
thf(1481,plain,
( ( xw = xv )
| ( aElement0 @ sk20 )
| ( xv != xb )
| ( ( aReductOfIn0 @ xw @ xv @ xR )
!= ( aReductOfIn0 @ xw @ xb @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[155,1394]) ).
thf(1515,plain,
( ( xw = xv )
| ( aElement0 @ sk20 )
| ( xv != xb )
| ( xw != xw )
| ( xv != xb )
| ( xR != xR ) ),
inference(simp,[status(thm)],[1481]) ).
thf(1530,plain,
( ( xw = xv )
| ( aElement0 @ sk20 )
| ( xv != xb ) ),
inference(simp,[status(thm)],[1515]) ).
thf(2460,plain,
( ( aElement0 @ sk20 )
| ( xv != xb )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[1530,324]) ).
thf(2461,plain,
( ( aElement0 @ sk20 )
| ( xv != xb ) ),
inference(pattern_uni,[status(thm)],[2460:[]]) ).
thf(461,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xw )
| ( aNormalFormOfIn0 @ xd @ xu @ xR )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[156,184]) ).
thf(462,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xw )
| ( aNormalFormOfIn0 @ xd @ xu @ xR ) ),
inference(pattern_uni,[status(thm)],[461:[]]) ).
thf(519,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xw )
| ( sdtmndtasgtdt0 @ xv @ xR @ xv )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[160,144]) ).
thf(520,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xw )
| ( sdtmndtasgtdt0 @ xv @ xR @ xv ) ),
inference(pattern_uni,[status(thm)],[519:[]]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aRewritingSystem0 @ B ) )
=> ! [C: $i] :
( ( aReductOfIn0 @ C @ A @ B )
=> ( aElement0 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mReduct) ).
thf(66,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(1380,plain,
! [A: $i] :
( ( sdtmndtasgtdt0 @ ( sk5 @ A ) @ A @ ( sk6 @ A ) )
| ( isConfluent0 @ A )
| ( ( aRewritingSystem0 @ xR )
!= ( aRewritingSystem0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[68,59]) ).
thf(1381,plain,
( ( sdtmndtasgtdt0 @ ( sk5 @ xR ) @ xR @ ( sk6 @ xR ) )
| ( isConfluent0 @ xR ) ),
inference(pattern_uni,[status(thm)],[1380:[bind(A,$thf( xR ))]]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mWFOrd) ).
thf(226,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(35,plain,
sdtmndtplgtdt0 @ xa @ xR @ xb,
inference(cnf,[status(esa)],[34]) ).
thf(241,plain,
! [A: $i] :
( ~ ( aReductOfIn0 @ A @ xb @ xR )
| ~ ( sdtmndtplgtdt0 @ A @ xR @ xd )
| ( ( aElement0 @ xa )
!= ( aElement0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[138,30]) ).
thf(242,plain,
( ~ ( aReductOfIn0 @ xa @ xb @ xR )
| ~ ( sdtmndtplgtdt0 @ xa @ xR @ xd ) ),
inference(pattern_uni,[status(thm)],[241:[bind(A,$thf( xa ))]]) ).
thf(1167,plain,
( ~ ( aReductOfIn0 @ xa @ xb @ xR )
| ( ( sdtmndtplgtdt0 @ xa @ xR @ xc )
!= ( sdtmndtplgtdt0 @ xa @ xR @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[36,242]) ).
thf(1177,plain,
( ~ ( aReductOfIn0 @ xa @ xb @ xR )
| ( xa != xa )
| ( xR != xR )
| ( xc != xd ) ),
inference(simp,[status(thm)],[1167]) ).
thf(1203,plain,
( ~ ( aReductOfIn0 @ xa @ xb @ xR )
| ( xc != xd ) ),
inference(simp,[status(thm)],[1177]) ).
thf(916,plain,
( ( xu != xb )
| ( xa != xb )
| ( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
!= ( sdtmndtplgtdt0 @ xv @ xR @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[551,312]) ).
thf(933,plain,
( ( xu != xb )
| ( xa != xb )
| ( xw != xv )
| ( xR != xR )
| ( xd != xd ) ),
inference(simp,[status(thm)],[916]) ).
thf(939,plain,
( ( xu != xb )
| ( xa != xb )
| ( xw != xv ) ),
inference(simp,[status(thm)],[933]) ).
thf(346,plain,
( ( aElement0 @ sk2 )
| ~ ( sdtmndtplgtdt0 @ xc @ xR @ xd )
| ( ( aReductOfIn0 @ xc @ xa @ xR )
!= ( aReductOfIn0 @ xc @ xb @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[39,230]) ).
thf(353,plain,
( ( aElement0 @ sk2 )
| ~ ( sdtmndtplgtdt0 @ xc @ xR @ xd )
| ( xc != xc )
| ( xa != xb )
| ( xR != xR ) ),
inference(simp,[status(thm)],[346]) ).
thf(355,plain,
( ( aElement0 @ sk2 )
| ~ ( sdtmndtplgtdt0 @ xc @ xR @ xd )
| ( xa != xb ) ),
inference(simp,[status(thm)],[353]) ).
thf(63,plain,
! [A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ( aElement0 @ ( sk6 @ A ) )
| ( isConfluent0 @ A ) ),
inference(cnf,[status(esa)],[55]) ).
thf(268,plain,
( ~ ( sdtmndtplgtdt0 @ xc @ xR @ xd )
| ( ( aReductOfIn0 @ xu @ xa @ xR )
!= ( aReductOfIn0 @ xc @ xb @ xR ) ) ),
inference(paramod_ordered,[status(thm)],[49,230]) ).
thf(277,plain,
( ~ ( sdtmndtplgtdt0 @ xc @ xR @ xd )
| ( xu != xc )
| ( xa != xb )
| ( xR != xR ) ),
inference(simp,[status(thm)],[268]) ).
thf(282,plain,
( ~ ( sdtmndtplgtdt0 @ xc @ xR @ xd )
| ( xu != xc )
| ( xa != xb ) ),
inference(simp,[status(thm)],[277]) ).
thf(957,plain,
( ( xv != xb )
| ( xa != xb )
| ( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
!= ( sdtmndtplgtdt0 @ xu @ xR @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[570,620]) ).
thf(965,plain,
( ( xv != xb )
| ( xa != xb )
| ( xw != xu )
| ( xR != xR )
| ( xd != xd ) ),
inference(simp,[status(thm)],[957]) ).
thf(971,plain,
( ( xv != xb )
| ( xa != xb )
| ( xw != xu ) ),
inference(simp,[status(thm)],[965]) ).
thf(255,plain,
( ( sdtmndtplgtdt0 @ xa @ xR @ xc )
!= ( sdtmndtplgtdt0 @ xb @ xR @ xd ) ),
inference(paramod_ordered,[status(thm)],[36,27]) ).
thf(259,plain,
( ( xa != xb )
| ( xR != xR )
| ( xc != xd ) ),
inference(simp,[status(thm)],[255]) ).
thf(263,plain,
( ( xa != xb )
| ( xc != xd ) ),
inference(simp,[status(thm)],[259]) ).
thf(524,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xw )
| ( sdtmndtasgtdt0 @ xu @ xR @ xv )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[160,146]) ).
thf(525,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xw )
| ( sdtmndtasgtdt0 @ xu @ xR @ xv ) ),
inference(pattern_uni,[status(thm)],[524:[]]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aRewritingSystem0 @ B )
| ~ ( aReductOfIn0 @ C @ A @ B )
| ( aElement0 @ C ) ),
inference(cnf,[status(esa)],[66]) ).
thf(1051,plain,
! [A: $i] :
( ( sdtmndtasgtdt0 @ ( sk5 @ A ) @ A @ ( sk7 @ A ) )
| ( isConfluent0 @ A )
| ( ( aRewritingSystem0 @ xR )
!= ( aRewritingSystem0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[68,56]) ).
thf(1052,plain,
( ( sdtmndtasgtdt0 @ ( sk5 @ xR ) @ xR @ ( sk7 @ xR ) )
| ( isConfluent0 @ xR ) ),
inference(pattern_uni,[status(thm)],[1051:[bind(A,$thf( xR ))]]) ).
thf(496,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xw )
| ( aNormalFormOfIn0 @ xd @ xv @ xR )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[160,184]) ).
thf(497,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xw )
| ( aNormalFormOfIn0 @ xd @ xv @ xR ) ),
inference(pattern_uni,[status(thm)],[496:[]]) ).
thf(516,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xw )
| ( xv != xb )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[160,324]) ).
thf(517,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xw )
| ( xv != xb ) ),
inference(pattern_uni,[status(thm)],[516:[]]) ).
thf(40,plain,
( ( aReductOfIn0 @ xc @ xa @ xR )
| ( sdtmndtplgtdt0 @ sk2 @ xR @ xc ) ),
inference(cnf,[status(esa)],[34]) ).
thf(389,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( aReductOfIn0 @ xb @ xa @ xR )
| ( xu != xu ) ),
inference(paramod_ordered,[status(thm)],[51,49]) ).
thf(390,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( aReductOfIn0 @ xb @ xa @ xR ) ),
inference(pattern_uni,[status(thm)],[389:[]]) ).
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/sandbox/benchmark/theBenchmark.p',mTCRTrans) ).
thf(139,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(667,plain,
( ( aReductOfIn0 @ xb @ xa @ xR )
| ( ( aReductOfIn0 @ sk1 @ xa @ xR )
!= ( aReductOfIn0 @ xb @ xa @ xR ) ) ),
inference(simp,[status(thm)],[666]) ).
thf(3889,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( ( sdtmndtplgtdt0 @ xu @ xR @ xw )
!= ( sdtmndtplgtdt0 @ xu @ xR @ xb ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[798]) ).
thf(3896,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( ( sdtmndtplgtdt0 @ xu @ xR @ xw )
!= ( sdtmndtplgtdt0 @ xu @ xR @ xb ) ) ),
inference(simp,[status(thm)],[3889]) ).
thf(513,plain,
( ( xw = xv )
| ( xa != xb )
| ( ( sdtmndtplgtdt0 @ xv @ xR @ xw )
!= ( sdtmndtplgtdt0 @ xv @ xR @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[160,312]) ).
thf(531,plain,
( ( xw = xv )
| ( xa != xb )
| ( xv != xv )
| ( xR != xR )
| ( xw != xd ) ),
inference(simp,[status(thm)],[513]) ).
thf(536,plain,
( ( xw = xv )
| ( xa != xb )
| ( xw != xd ) ),
inference(simp,[status(thm)],[531]) ).
thf(1677,plain,
( ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ( sdtmndtasgtdt0 @ xu @ xR @ xd )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[1427,146]) ).
thf(1678,plain,
( ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ( sdtmndtasgtdt0 @ xu @ xR @ xd ) ),
inference(pattern_uni,[status(thm)],[1677:[]]) ).
thf(254,plain,
( ~ ( aReductOfIn0 @ xv @ xb @ xR )
| ( ( sdtmndtplgtdt0 @ xv @ xR @ xd )
!= ( sdtmndtplgtdt0 @ xa @ xR @ xc ) ) ),
inference(paramod_ordered,[status(thm)],[36,228]) ).
thf(258,plain,
( ~ ( aReductOfIn0 @ xv @ xb @ xR )
| ( xv != xa )
| ( xR != xR )
| ( xc != xd ) ),
inference(simp,[status(thm)],[254]) ).
thf(262,plain,
( ~ ( aReductOfIn0 @ xv @ xb @ xR )
| ( xv != xa )
| ( xc != xd ) ),
inference(simp,[status(thm)],[258]) ).
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/sandbox/benchmark/theBenchmark.p',mTCTrans) ).
thf(190,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(948,plain,
( ( xv != xb )
| ( xa != xb )
| ( ( sdtmndtplgtdt0 @ xw @ xR @ xd )
!= ( sdtmndtplgtdt0 @ xv @ xR @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[570,312]) ).
thf(961,plain,
( ( xv != xb )
| ( xa != xb )
| ( xw != xv )
| ( xR != xR )
| ( xd != xd ) ),
inference(simp,[status(thm)],[948]) ).
thf(967,plain,
( ( xv != xb )
| ( xa != xb )
| ( xw != xv ) ),
inference(simp,[status(thm)],[961]) ).
thf(210,plain,
isLocallyConfluent0 @ xR,
inference(cnf,[status(esa)],[198]) ).
thf(3029,plain,
! [A: $i] :
( ( aElement0 @ ( sk6 @ A ) )
| ( isConfluent0 @ A )
| ( ( aRewritingSystem0 @ xR )
!= ( aRewritingSystem0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[68,63]) ).
thf(3030,plain,
( ( aElement0 @ ( sk6 @ xR ) )
| ( isConfluent0 @ xR ) ),
inference(pattern_uni,[status(thm)],[3029:[bind(A,$thf( xR ))]]) ).
thf(394,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( sdtmndtasgtdt0 @ xb @ xR @ xw )
| ( xu != xu ) ),
inference(paramod_ordered,[status(thm)],[51,146]) ).
thf(395,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( sdtmndtasgtdt0 @ xb @ xR @ xw ) ),
inference(pattern_uni,[status(thm)],[394:[]]) ).
thf(527,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xw )
| ( sdtmndtasgtdt0 @ xv @ xR @ xd )
| ( xw != xw ) ),
inference(paramod_ordered,[status(thm)],[160,178]) ).
thf(528,plain,
( ( sdtmndtplgtdt0 @ xv @ xR @ xw )
| ( sdtmndtasgtdt0 @ xv @ xR @ xd ) ),
inference(pattern_uni,[status(thm)],[527:[]]) ).
thf(700,plain,
( ( xw = xu )
| ( xa != xb )
| ( ( sdtmndtplgtdt0 @ xu @ xR @ xw )
!= ( sdtmndtplgtdt0 @ xu @ xR @ xd ) ) ),
inference(paramod_ordered,[status(thm)],[156,620]) ).
thf(715,plain,
( ( xw = xu )
| ( xa != xb )
| ( xu != xu )
| ( xR != xR )
| ( xw != xd ) ),
inference(simp,[status(thm)],[700]) ).
thf(723,plain,
( ( xw = xu )
| ( xa != xb )
| ( xw != xd ) ),
inference(simp,[status(thm)],[715]) ).
thf(3885,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( sdtmndtplgtdt0 @ xb @ xR @ xw )
| ( xu != xu ) ),
inference(paramod_ordered,[status(thm)],[51,798]) ).
thf(3886,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( sdtmndtplgtdt0 @ xb @ xR @ xw ) ),
inference(pattern_uni,[status(thm)],[3885:[]]) ).
thf(18,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSort) ).
thf(163,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(62,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aRewritingSystem0 @ A )
| ~ ( isConfluent0 @ A )
| ~ ( aElement0 @ B )
| ~ ( aElement0 @ C )
| ~ ( aElement0 @ D )
| ~ ( sdtmndtasgtdt0 @ B @ A @ C )
| ~ ( sdtmndtasgtdt0 @ B @ A @ D )
| ( aElement0 @ ( sk4 @ D @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(3211,plain,
! [A: $i] :
( ( aElement0 @ ( sk5 @ A ) )
| ( isConfluent0 @ A )
| ( ( aRewritingSystem0 @ xR )
!= ( aRewritingSystem0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[68,64]) ).
thf(3212,plain,
( ( aElement0 @ ( sk5 @ xR ) )
| ( isConfluent0 @ xR ) ),
inference(pattern_uni,[status(thm)],[3211:[bind(A,$thf( xR ))]]) ).
thf(2997,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( aElement0 @ sk19 )
| ( xu != xu ) ),
inference(paramod_ordered,[status(thm)],[51,2896]) ).
thf(2998,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ( aElement0 @ sk19 ) ),
inference(pattern_uni,[status(thm)],[2997:[]]) ).
thf(1564,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ~ ( aReductOfIn0 @ xw @ xb @ xR )
| ( xu != xu ) ),
inference(paramod_ordered,[status(thm)],[51,1406]) ).
thf(1565,plain,
( ( sdtmndtplgtdt0 @ xu @ xR @ xb )
| ~ ( aReductOfIn0 @ xw @ xb @ xR ) ),
inference(pattern_uni,[status(thm)],[1564:[]]) ).
thf(274181,plain,
$false,
inference(cvc4,[status(thm)],[69,629,138,941,170,1406,449,472,56,1655,42,1613,1650,37,570,184,52,724,228,57,78,261,29,475,164,179,321,574,480,1682,485,147,61,132,1394,133,116,312,74,60,678,201,798,334,160,70,192,137,33,28,38,65,551,324,285,578,156,53,141,124,339,77,393,41,73,311,128,343,105,244,425,444,32,34,279,64,584,44,3758,59,281,27,1139,313,144,49,540,382,54,187,230,567,318,39,2896,155,2461,462,520,66,198,1381,130,135,226,35,1203,939,123,355,63,282,971,263,48,525,67,177,1052,1427,143,497,43,517,40,26,158,390,186,55,139,667,3896,536,620,1678,262,146,30,51,190,183,36,967,210,242,136,3030,395,528,644,723,3886,163,68,62,178,3212,232,2998,1565]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : COM019+4 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n023.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 03:36:14 EDT 2023
% 0.15/0.36 % CPUTime :
% 1.00/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.42/1.01 % [INFO] Parsing done (145ms).
% 1.42/1.01 % [INFO] Running in sequential loop mode.
% 1.84/1.23 % [INFO] eprover registered as external prover.
% 1.91/1.23 % [INFO] cvc4 registered as external prover.
% 1.91/1.24 % [INFO] Scanning for conjecture ...
% 1.91/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.19/1.34 % [INFO] Found a conjecture and 23 axioms. Running axiom selection ...
% 2.38/1.39 % [INFO] Axiom selection finished. Selected 23 axioms (removed 0 axioms).
% 2.38/1.40 % [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] Definitions in FOF are currently treated as axioms.
% 2.38/1.43 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.43 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.44 % [INFO] Problem is first-order (TPTP FOF).
% 2.38/1.45 % [INFO] Type checking passed.
% 2.38/1.45 % [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 ...
% 221.21/63.52 % External prover 'cvc4' found a proof!
% 221.21/63.52 % [INFO] Killing All external provers ...
% 221.21/63.52 % Time passed: 62984ms (effective reasoning time: 62500ms)
% 221.21/63.52 % 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)>
% 221.21/63.52 % 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
% 221.21/63.52 % No. of inferences in proof: 313
% 221.21/63.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 62984 ms resp. 62500 ms w/o parsing
% 221.65/63.62 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 221.65/63.63 % [INFO] Killing All external provers ...
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