TSTP Solution File: SEV493^1 by Leo-III-SAT---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SEV493^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n029.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 Jun 24 16:00:23 EDT 2024
% Result : Theorem 178.22s 29.85s
% Output : Refutation 178.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 4
% Syntax : Number of formulae : 82 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 427 ( 63 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 806 ( 94 ~; 96 |; 18 &; 578 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 93 ( 0 ^ 89 !; 4 ?; 93 :)
% 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/FINITE\'_type',type,
'\'const/sets/FINITE\'':
!>[TA: $tType] : ( ( 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\'' > $o ).
thf(sk2_type,type,
sk2: '\'type/realax/real\'' ).
thf(sk3_type,type,
sk3: ( '\'type/realax/real\'' > $o ) > $o ).
thf(sk4_type,type,
sk4: '\'type/realax/real\'' > ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).
thf(sk5_type,type,
sk5: '\'type/realax/real\'' > ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).
thf(sk6_type,type,
sk6: ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).
thf(6,axiom,
! [A: '\'type/realax/real\'' > $o] :
( ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
& ( A
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) )
=> ? [B: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
& ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_le\'' @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_FINITE_LEMMA_') ).
thf(29,plain,
! [A: '\'type/realax/real\'' > $o] :
( ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
& ( A
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) )
=> ? [B: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
& ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_le\'' @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(31,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
| ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
| ( '\'const/realax/real_le\'' @ ( sk6 @ A ) @ B ) ),
inference(cnf,[status(esa)],[29]) ).
thf(33,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ~ ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
| ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
| ( '\'const/realax/real_le\'' @ ( sk6 @ A ) @ B ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(1,conjecture,
! [A: '\'type/realax/real\'' > $o] :
( ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
& ( A
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) )
=> ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( '\'const/sets/inf\'' @ A ) @ A )
& ! [B: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
=> ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_FINITE_') ).
thf(2,negated_conjecture,
~ ! [A: '\'type/realax/real\'' > $o] :
( ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
& ( A
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) )
=> ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( '\'const/sets/inf\'' @ A ) @ A )
& ! [B: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
=> ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: '\'type/realax/real\'' > $o] :
( ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
& ( A
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) )
=> ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( '\'const/sets/inf\'' @ A ) @ A )
& ! [B: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
=> ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
( sk1
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ),
inference(cnf,[status(esa)],[7]) ).
thf(12,plain,
( sk1
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(2141,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
| ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
| ( '\'const/realax/real_le\'' @ ( sk6 @ A ) @ B )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33,12]) ).
thf(2142,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ sk1 )
| ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk1 )
| ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ A ) ),
inference(pattern_uni,[status(thm)],[2141:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(2341,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ sk1 )
| ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk1 )
| ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ A ) ),
inference(simp,[status(thm)],[2142]) ).
thf(11,plain,
'\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ sk1,
inference(cnf,[status(esa)],[7]) ).
thf(39272,plain,
! [A: '\'type/realax/real\''] :
( ~ $true
| ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk1 )
| ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ A ) ),
inference(rewrite,[status(thm)],[2341,11]) ).
thf(39273,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk1 )
| ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ A ) ),
inference(simp,[status(thm)],[39272]) ).
thf(30,plain,
! [A: '\'type/realax/real\'' > $o] :
( ~ ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
| ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ A ) @ A ) ),
inference(cnf,[status(esa)],[29]) ).
thf(32,plain,
! [A: '\'type/realax/real\'' > $o] :
( ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ~ ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(1455,plain,
! [A: '\'type/realax/real\'' > $o] :
( ~ ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ A ) @ A )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[32,12]) ).
thf(1456,plain,
( ~ ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ sk1 )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1455:[bind(A,$thf( sk1 ))]]) ).
thf(1607,plain,
( ~ $true
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[1456,11]) ).
thf(1608,plain,
'\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 ) @ sk1,
inference(simp,[status(thm)],[1607]) ).
thf(9,plain,
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( '\'const/sets/inf\'' @ sk1 ) @ sk1 )
| ~ ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ sk1 ) @ sk2 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(1615,plain,
( ~ ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ sk1 ) @ sk2 )
| ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 ) @ sk1 )
!= ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( '\'const/sets/inf\'' @ sk1 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1608,9]) ).
thf(1652,plain,
( ~ ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ sk1 ) @ sk2 )
| ( ( sk6 @ sk1 )
!= ( '\'const/sets/inf\'' @ sk1 ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[1615]) ).
thf(1672,plain,
( ~ ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ sk1 ) @ sk2 )
| ( ( sk6 @ sk1 )
!= ( '\'const/sets/inf\'' @ sk1 ) ) ),
inference(simp,[status(thm)],[1652]) ).
thf(39369,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk1 )
| ( ( sk6 @ sk1 )
!= ( '\'const/sets/inf\'' @ sk1 ) )
| ( ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ A )
!= ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[39273,1672]) ).
thf(39581,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk1 )
| ( ( sk6 @ sk1 )
!= ( '\'const/sets/inf\'' @ sk1 ) )
| ( ( sk6 @ sk1 )
!= ( '\'const/sets/inf\'' @ sk1 ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[39369]) ).
thf(39655,plain,
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk2 @ sk1 )
| ( ( sk6 @ sk1 )
!= ( '\'const/sets/inf\'' @ sk1 ) ) ),
inference(simp,[status(thm)],[39581]) ).
thf(3,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/sandbox2/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)],[3]) ).
thf(17,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ B @ A ) @ A )
| ( sk3 @ 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/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ B @ A ) @ A )
| ( sk3 @ A ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(208,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ B @ A ) @ A )
| ( sk3 @ A )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[20,12]) ).
thf(209,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ A @ sk1 ) @ sk1 )
| ( sk3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(258,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ A @ sk1 ) @ sk1 )
| ( sk3 @ sk1 ) ),
inference(simp,[status(thm)],[209]) ).
thf(18,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ~ ( '\'const/realax/real_le\'' @ B @ ( sk4 @ B @ A ) )
| ( sk3 @ A ) ),
inference(cnf,[status(esa)],[13]) ).
thf(21,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ~ ( '\'const/realax/real_le\'' @ B @ ( sk4 @ B @ A ) )
| ( sk3 @ A ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(335,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( '\'const/realax/real_le\'' @ B @ ( sk4 @ B @ A ) )
| ( sk3 @ A )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[21,12]) ).
thf(336,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/realax/real_le\'' @ A @ ( sk4 @ A @ sk1 ) )
| ( sk3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[335:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(383,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/realax/real_le\'' @ A @ ( sk4 @ A @ sk1 ) )
| ( sk3 @ sk1 ) ),
inference(simp,[status(thm)],[336]) ).
thf(39482,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk1 )
| ( sk3 @ sk1 )
| ( ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ A )
!= ( '\'const/realax/real_le\'' @ B @ ( sk4 @ B @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[39273,383]) ).
thf(39483,plain,
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 )
| ( sk3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[39482:[bind(A,$thf( sk4 @ ( sk6 @ sk1 ) @ sk1 )),bind(B,$thf( sk6 @ sk1 ))]]) ).
thf(39974,plain,
! [A: '\'type/realax/real\''] :
( ( sk3 @ sk1 )
| ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ A @ sk1 ) @ sk1 )
!= ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[258,39483]) ).
thf(39975,plain,
sk3 @ sk1,
inference(pattern_uni,[status(thm)],[39974:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(15,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk3 @ A )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ B @ A ) @ 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] :
( ~ ( sk3 @ A )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ B @ A ) @ A )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(40112,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ B @ A ) @ A )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) )
| ( ( sk3 @ sk1 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[39975,23]) ).
thf(40113,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ A @ sk1 ) @ sk1 )
| ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[40112:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(40124,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ A @ sk1 ) @ sk1 )
| ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk1 ) ) ),
inference(simp,[status(thm)],[40113]) ).
thf(50373,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk1 ) )
| ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ B )
| ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ A @ sk1 ) @ sk1 )
!= ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[40124,39273]) ).
thf(50374,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk1 ) )
| ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ ( sk5 @ A @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[50373:[bind(A,$thf( C )),bind(B,$thf( sk5 @ C @ sk1 ))]]) ).
thf(50705,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk1 ) )
| ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ ( sk5 @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[50374]) ).
thf(16,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk3 @ A )
| ~ ( '\'const/realax/real_le\'' @ B @ ( sk5 @ B @ A ) )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(22,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk3 @ A )
| ~ ( '\'const/realax/real_le\'' @ B @ ( sk5 @ B @ A ) )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(79318,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o,A: '\'type/realax/real\''] :
( ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk1 ) )
| ~ ( sk3 @ B )
| ( '\'const/realax/real_le\'' @ C @ ( '\'const/sets/inf\'' @ B ) )
| ( ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ ( sk5 @ A @ sk1 ) )
!= ( '\'const/realax/real_le\'' @ C @ ( sk5 @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[50705,22]) ).
thf(79319,plain,
( ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ ( '\'const/sets/inf\'' @ sk1 ) )
| ~ ( sk3 @ sk1 )
| ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ ( '\'const/sets/inf\'' @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[79318:[bind(A,$thf( sk6 @ sk1 )),bind(B,$thf( sk1 )),bind(C,$thf( sk6 @ sk1 ))]]) ).
thf(79816,plain,
( ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ ( '\'const/sets/inf\'' @ sk1 ) )
| ~ ( sk3 @ sk1 ) ),
inference(simp,[status(thm)],[79319]) ).
thf(14,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk3 @ A )
| ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
| ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) ),
inference(cnf,[status(esa)],[13]) ).
thf(19,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk3 @ A )
| ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
| ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) ),
inference(simp,[status(thm)],[14]) ).
thf(1640,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk3 @ A )
| ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B )
| ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 ) @ sk1 )
!= ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1608,19]) ).
thf(1641,plain,
( ~ ( sk3 @ sk1 )
| ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[1640:[bind(A,$thf( sk1 )),bind(B,$thf( sk6 @ sk1 ))]]) ).
thf(5,axiom,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_le\'' @ A @ B )
& ( '\'const/realax/real_le\'' @ B @ A ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_ANTISYM_') ).
thf(26,plain,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_le\'' @ A @ B )
& ( '\'const/realax/real_le\'' @ B @ A ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_le\'' @ A @ B )
& ( '\'const/realax/real_le\'' @ B @ A ) )
= ( A = B ) ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_le\'' @ A @ B )
& ( '\'const/realax/real_le\'' @ B @ A ) )
= ( A = B ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(1711,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ~ ( sk3 @ sk1 )
| ( ( '\'const/realax/real_le\'' @ B @ A )
= ( A = B ) )
| ( ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ sk1 ) @ ( sk6 @ sk1 ) )
!= ( '\'const/realax/real_le\'' @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1641,28]) ).
thf(1712,plain,
( ~ ( sk3 @ sk1 )
| ( ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ ( '\'const/sets/inf\'' @ sk1 ) )
= ( ( '\'const/sets/inf\'' @ sk1 )
= ( sk6 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[1711:[bind(A,$thf( '\'const/sets/inf\'' @ sk1 )),bind(B,$thf( sk6 @ sk1 ))]]) ).
thf(40058,plain,
( ~ $true
| ( ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ ( '\'const/sets/inf\'' @ sk1 ) )
= ( ( '\'const/sets/inf\'' @ sk1 )
= ( sk6 @ sk1 ) ) ) ),
inference(rewrite,[status(thm)],[1712,39975]) ).
thf(40059,plain,
( ( '\'const/realax/real_le\'' @ ( sk6 @ sk1 ) @ ( '\'const/sets/inf\'' @ sk1 ) )
= ( ( '\'const/sets/inf\'' @ sk1 )
= ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[40058]) ).
thf(79826,plain,
( ( ( '\'const/sets/inf\'' @ sk1 )
= ( sk6 @ sk1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[79816,39975,40059]) ).
thf(79827,plain,
( ( '\'const/sets/inf\'' @ sk1 )
= ( sk6 @ sk1 ) ),
inference(simp,[status(thm)],[79826]) ).
thf(79828,plain,
( ( sk6 @ sk1 )
= ( '\'const/sets/inf\'' @ sk1 ) ),
inference(lifteq,[status(thm)],[79827]) ).
thf(79901,plain,
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk2 @ sk1 )
| ( ( '\'const/sets/inf\'' @ sk1 )
!= ( '\'const/sets/inf\'' @ sk1 ) ) ),
inference(rewrite,[status(thm)],[39655,79828]) ).
thf(79902,plain,
~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk2 @ sk1 ),
inference(simp,[status(thm)],[79901]) ).
thf(8,plain,
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( '\'const/sets/inf\'' @ sk1 ) @ sk1 )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk2 @ sk1 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(1636,plain,
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk2 @ sk1 )
| ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 ) @ sk1 )
!= ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( '\'const/sets/inf\'' @ sk1 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1608,8]) ).
thf(1644,plain,
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk2 @ sk1 )
| ( ( sk6 @ sk1 )
!= ( '\'const/sets/inf\'' @ sk1 ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[1636]) ).
thf(1664,plain,
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk2 @ sk1 )
| ( ( sk6 @ sk1 )
!= ( '\'const/sets/inf\'' @ sk1 ) ) ),
inference(simp,[status(thm)],[1644]) ).
thf(79850,plain,
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk2 @ sk1 )
| ( ( '\'const/sets/inf\'' @ sk1 )
!= ( '\'const/sets/inf\'' @ sk1 ) ) ),
inference(rewrite,[status(thm)],[1664,79828]) ).
thf(79851,plain,
'\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk2 @ sk1,
inference(simp,[status(thm)],[79850]) ).
thf(80216,plain,
~ $true,
inference(rewrite,[status(thm)],[79902,79851]) ).
thf(80217,plain,
$false,
inference(simp,[status(thm)],[80216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEV493^1 : TPTP v8.2.0. Released v7.0.0.
% 0.08/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 21 19:16:10 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.94/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.02 % [INFO] Parsing done (132ms).
% 1.23/1.03 % [INFO] Running in sequential loop mode.
% 1.91/1.34 % [INFO] nitpick registered as external prover.
% 1.91/1.34 % [INFO] Scanning for conjecture ...
% 2.12/1.43 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.12/1.46 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.20/1.47 % [INFO] Problem is higher-order (TPTP THF).
% 2.20/1.48 % [INFO] Type checking passed.
% 2.20/1.48 % [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 ...
% 178.22/29.84 % [INFO] Killing All external provers ...
% 178.22/29.84 % Time passed: 29300ms (effective reasoning time: 28799ms)
% 178.22/29.84 % 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)>
% 178.22/29.84 % Axioms used in derivation (3): thm/sets/INF_FINITE_LEMMA_, thm/sets/INF_, thm/realax/REAL_LE_ANTISYM_
% 178.22/29.84 % No. of inferences in proof: 82
% 178.22/29.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 29300 ms resp. 28799 ms w/o parsing
% 178.22/29.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 178.22/29.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------