TSTP Solution File: ANA092^1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : ANA092^1 : TPTP v8.2.0. Released v7.0.0.
% 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 : Mon May 20 18:39:44 EDT 2024
% Result : Theorem 135.32s 22.40s
% Output : Refutation 135.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 15
% Syntax : Number of formulae : 87 ( 5 unt; 12 typ; 0 def)
% Number of atoms : 385 ( 33 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 808 ( 82 ~; 100 |; 9 &; 592 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 105 ( 0 ^ 98 !; 5 ?; 105 :)
% ( 2 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/realax/real\'_type',type,
'\'type/realax/real\'': $tType ).
thf('\'const/sets/inf\'_type',type,
'\'const/sets/inf\'': ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).
thf('\'const/sets/IN\'_type',type,
'\'const/sets/IN\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('\'const/sets/EMPTY\'_type',type,
'\'const/sets/EMPTY\'':
!>[TA: $tType] : ( TA > $o ) ).
thf('\'const/realax/real_le\'_type',type,
'\'const/realax/real_le\'': '\'type/realax/real\'' > '\'type/realax/real\'' > $o ).
thf(sk1_type,type,
sk1: '\'type/realax/real\'' ).
thf(sk2_type,type,
sk2: '\'type/realax/real\'' > $o ).
thf(sk3_type,type,
sk3: '\'type/realax/real\'' ).
thf(sk4_type,type,
sk4: ( '\'type/realax/real\'' > $o ) > $o ).
thf(sk5_type,type,
sk5: '\'type/realax/real\'' > ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).
thf(sk6_type,type,
sk6: '\'type/realax/real\'' > ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).
thf(sk8_type,type,
sk8: '\'type/realax/real\'' ).
thf(1,conjecture,
! [TA: $tType,A: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o,C: TA] :
( ( ( B
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
& ? [D: '\'type/realax/real\''] :
! [E: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ E @ B )
=> ( '\'const/realax/real_le\'' @ D @ E ) ) )
=> ( ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ B ) )
= ( ! [D: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ D @ B )
=> ( '\'const/realax/real_le\'' @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_LE_INF_EQ_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o,C: TA] :
( ( ( B
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
& ? [D: '\'type/realax/real\''] :
! [E: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ E @ B )
=> ( '\'const/realax/real_le\'' @ D @ E ) ) )
=> ( ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ B ) )
= ( ! [D: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ D @ B )
=> ( '\'const/realax/real_le\'' @ A @ D ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o] :
( ( ( B
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
& ? [C: '\'type/realax/real\''] :
! [D: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ D @ B )
=> ( '\'const/realax/real_le\'' @ C @ D ) ) )
=> ( ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ B ) )
= ( ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ B )
=> ( '\'const/realax/real_le\'' @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
!= ( ! [A: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
=> ( '\'const/realax/real_le\'' @ sk1 @ A ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(9,plain,
( ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
!= ( ! [A: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
=> ( '\'const/realax/real_le\'' @ sk1 @ A ) ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(28,plain,
( ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
| ! [A: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
=> ( '\'const/realax/real_le\'' @ sk1 @ A ) ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(31,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
| ( '\'const/realax/real_le\'' @ sk1 @ A )
| ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(4,axiom,
! [A: '\'type/realax/real\'' > $o] :
( ( ( A
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
& ? [B: '\'type/realax/real\''] :
! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_le\'' @ B @ C ) ) )
=> ( ! [B: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
=> ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) )
& ! [B: '\'type/realax/real\''] :
( ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_le\'' @ B @ C ) )
=> ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_') ).
thf(13,plain,
! [A: '\'type/realax/real\'' > $o] :
( ( ( A
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
& ? [B: '\'type/realax/real\''] :
! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_le\'' @ B @ C ) ) )
=> ( ! [B: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
=> ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) )
& ! [B: '\'type/realax/real\''] :
( ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_le\'' @ B @ C ) )
=> ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ B @ A ) @ A )
| ( sk4 @ A ) ),
inference(cnf,[status(esa)],[13]) ).
thf(22,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ B @ A ) @ A )
| ( sk4 @ A ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(8,plain,
( sk2
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ),
inference(cnf,[status(esa)],[5]) ).
thf(10,plain,
( sk2
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(141,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ B @ A ) @ A )
| ( sk4 @ A )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[22,10]) ).
thf(142,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ A @ sk2 ) @ sk2 )
| ( sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[141:[bind(A,$thf( sk2 )),bind(B,$thf( B ))]]) ).
thf(164,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ A @ sk2 ) @ sk2 )
| ( sk4 @ sk2 ) ),
inference(simp,[status(thm)],[142]) ).
thf(7,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
| ( '\'const/realax/real_le\'' @ sk3 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(183,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( sk4 @ sk2 )
| ( '\'const/realax/real_le\'' @ sk3 @ B )
| ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ A @ sk2 ) @ sk2 )
!= ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[164,7]) ).
thf(184,plain,
! [A: '\'type/realax/real\''] :
( ( sk4 @ sk2 )
| ( '\'const/realax/real_le\'' @ sk3 @ ( sk5 @ A @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( C )),bind(B,$thf( sk5 @ C @ sk2 ))]]) ).
thf(194,plain,
! [A: '\'type/realax/real\''] :
( ( sk4 @ sk2 )
| ( '\'const/realax/real_le\'' @ sk3 @ ( sk5 @ A @ sk2 ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(17,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ~ ( '\'const/realax/real_le\'' @ B @ ( sk5 @ B @ A ) )
| ( sk4 @ A ) ),
inference(cnf,[status(esa)],[13]) ).
thf(20,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ~ ( '\'const/realax/real_le\'' @ B @ ( sk5 @ B @ A ) )
| ( sk4 @ A ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(573,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o,A: '\'type/realax/real\''] :
( ( sk4 @ sk2 )
| ( B
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ( sk4 @ B )
| ( ( '\'const/realax/real_le\'' @ sk3 @ ( sk5 @ A @ sk2 ) )
!= ( '\'const/realax/real_le\'' @ C @ ( sk5 @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[194,20]) ).
thf(574,plain,
( ( sk4 @ sk2 )
| ( sk2
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ( sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[573:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(624,plain,
( ( sk4 @ sk2 )
| ( sk2
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) ),
inference(simp,[status(thm)],[574]) ).
thf(625,plain,
sk4 @ sk2,
inference(simplifyReflect,[status(thm)],[624,10]) ).
thf(15,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk4 @ A )
| ~ ( '\'const/realax/real_le\'' @ B @ ( sk6 @ B @ A ) )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(23,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk4 @ A )
| ~ ( '\'const/realax/real_le\'' @ B @ ( sk6 @ B @ A ) )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(1373,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( '\'const/realax/real_le\'' @ B @ ( sk6 @ B @ A ) )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) )
| ( ( sk4 @ sk2 )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[625,23]) ).
thf(1374,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/realax/real_le\'' @ A @ ( sk6 @ A @ sk2 ) )
| ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1373:[bind(A,$thf( sk2 )),bind(B,$thf( B ))]]) ).
thf(1411,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/realax/real_le\'' @ A @ ( sk6 @ A @ sk2 ) )
| ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(simp,[status(thm)],[1374]) ).
thf(53407,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
| ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ sk2 ) )
| ( ( '\'const/realax/real_le\'' @ sk1 @ A )
!= ( '\'const/realax/real_le\'' @ B @ ( sk6 @ B @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,1411]) ).
thf(53408,plain,
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
| ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
| ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[53407:[bind(A,$thf( sk6 @ sk1 @ sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(53529,plain,
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
| ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(simp,[status(thm)],[53408]) ).
thf(18,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk4 @ A )
| ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
| ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) ),
inference(cnf,[status(esa)],[13]) ).
thf(21,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk4 @ A )
| ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
| ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) ),
inference(simp,[status(thm)],[18]) ).
thf(890,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
| ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B )
| ( ( sk4 @ sk2 )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[625,21]) ).
thf(891,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
| ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ sk2 ) @ A ) ),
inference(pattern_uni,[status(thm)],[890:[bind(A,$thf( sk2 )),bind(B,$thf( B ))]]) ).
thf(958,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
| ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ sk2 ) @ A ) ),
inference(simp,[status(thm)],[891]) ).
thf(3,axiom,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\'',C: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_le\'' @ A @ B )
& ( '\'const/realax/real_le\'' @ B @ C ) )
=> ( '\'const/realax/real_le\'' @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_') ).
thf(11,plain,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\'',C: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_le\'' @ A @ B )
& ( '\'const/realax/real_le\'' @ B @ C ) )
=> ( '\'const/realax/real_le\'' @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ~ ( '\'const/realax/real_le\'' @ A @ B )
| ~ ( '\'const/realax/real_le\'' @ B @ C )
| ( '\'const/realax/real_le\'' @ A @ C ) ),
inference(cnf,[status(esa)],[11]) ).
thf(27,plain,
( ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
| ~ ! [A: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
=> ( '\'const/realax/real_le\'' @ sk1 @ A ) ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(29,plain,
( ~ ( '\'const/realax/real_le\'' @ sk1 @ sk8 )
| ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(58,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ~ ( '\'const/realax/real_le\'' @ A @ B )
| ~ ( '\'const/realax/real_le\'' @ B @ C )
| ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
| ( ( '\'const/realax/real_le\'' @ A @ C )
!= ( '\'const/realax/real_le\'' @ sk1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[12,29]) ).
thf(59,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/realax/real_le\'' @ sk1 @ A )
| ~ ( '\'const/realax/real_le\'' @ A @ sk8 )
| ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk8 ))]]) ).
thf(81,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/realax/real_le\'' @ sk1 @ A )
| ~ ( '\'const/realax/real_le\'' @ A @ sk8 )
| ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(5433,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
| ~ ( '\'const/realax/real_le\'' @ sk1 @ B )
| ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
| ( ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ sk2 ) @ A )
!= ( '\'const/realax/real_le\'' @ B @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[958,81]) ).
thf(5434,plain,
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
| ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
| ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[5433:[bind(A,$thf( sk8 )),bind(B,$thf( '\'const/sets/inf\'' @ sk2 ))]]) ).
thf(5617,plain,
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
| ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(simp,[status(thm)],[5434]) ).
thf(14,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk4 @ A )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ B @ A ) @ A )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(19,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk4 @ A )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ B @ A ) @ A )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(30,plain,
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
| ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(255,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk4 @ A )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ B @ A ) @ A )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
| ( ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) )
!= ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,30]) ).
thf(256,plain,
( ~ ( sk4 @ sk2 )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[255:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(626,plain,
( ~ $true
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 ) ),
inference(rewrite,[status(thm)],[256,625]) ).
thf(627,plain,
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 ) ),
inference(simp,[status(thm)],[626]) ).
thf(1985,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
| ( '\'const/realax/real_le\'' @ sk1 @ A )
| ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
| ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
!= ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[627,31]) ).
thf(1986,plain,
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
| ( '\'const/realax/real_le\'' @ sk1 @ ( sk6 @ sk1 @ sk2 ) )
| ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1985:[bind(A,$thf( sk6 @ sk1 @ sk2 ))]]) ).
thf(53423,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
| ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
| ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk2 ) )
| ( ( '\'const/realax/real_le\'' @ sk1 @ ( sk6 @ sk1 @ sk2 ) )
!= ( '\'const/realax/real_le\'' @ A @ ( sk6 @ A @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1986,1411]) ).
thf(53424,plain,
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
| ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
| ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[53423:[bind(A,$thf( sk1 ))]]) ).
thf(53531,plain,
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
| ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(simp,[status(thm)],[53424]) ).
thf(53780,plain,
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
| ( ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
!= ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[53531,30]) ).
thf(53781,plain,
'\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2,
inference(pattern_uni,[status(thm)],[53780:[]]) ).
thf(54095,plain,
( ~ $true
| ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(rewrite,[status(thm)],[5617,53781]) ).
thf(54096,plain,
~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ),
inference(simp,[status(thm)],[54095]) ).
thf(634,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ B @ A ) @ A )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) )
| ( ( sk4 @ sk2 )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[625,19]) ).
thf(635,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ A @ sk2 ) @ sk2 )
| ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[634:[bind(A,$thf( sk2 )),bind(B,$thf( B ))]]) ).
thf(638,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ A @ sk2 ) @ sk2 )
| ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
inference(simp,[status(thm)],[635]) ).
thf(5639,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ A @ sk2 ) @ sk2 )
| ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
| ( ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk2 ) )
!= ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[638,5617]) ).
thf(5640,plain,
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
| ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5639:[bind(A,$thf( sk1 ))]]) ).
thf(54093,plain,
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
| ~ $true ),
inference(rewrite,[status(thm)],[5640,53781]) ).
thf(54094,plain,
'\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2,
inference(simp,[status(thm)],[54093]) ).
thf(60307,plain,
( ~ $true
| $false ),
inference(rewrite,[status(thm)],[53529,54096,54094]) ).
thf(60308,plain,
$false,
inference(simp,[status(thm)],[60307]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09 % Problem : ANA092^1 : TPTP v8.2.0. Released v7.0.0.
% 0.03/0.11 % Command : run_Leo-III %s %d
% 0.10/0.31 % Computer : n016.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon May 20 07:58:24 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.94/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/1.09 % [INFO] Parsing done (172ms).
% 1.31/1.10 % [INFO] Running in sequential loop mode.
% 1.74/1.45 % [INFO] nitpick registered as external prover.
% 1.74/1.45 % [INFO] Scanning for conjecture ...
% 2.02/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.02/1.59 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.02/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.02/1.61 % [INFO] Type checking passed.
% 2.02/1.61 % [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 ...
% 135.32/22.39 % [INFO] Killing All external provers ...
% 135.32/22.40 % Time passed: 21933ms (effective reasoning time: 21286ms)
% 135.32/22.40 % 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)>
% 135.32/22.40 % Axioms used in derivation (2): thm/sets/INF_, thm/realax/REAL_LE_TRANS_
% 135.32/22.40 % No. of inferences in proof: 75
% 135.32/22.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21933 ms resp. 21286 ms w/o parsing
% 135.32/22.46 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 135.32/22.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------