TSTP Solution File: SEV261^5 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEV261^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 : Tue May 21 04:10:15 EDT 2024
% Result : Theorem 67.47s 11.16s
% Output : Refutation 67.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 17
% Syntax : Number of formulae : 134 ( 9 unt; 16 typ; 0 def)
% Number of atoms : 638 ( 152 equ; 0 cnn)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 584 ( 151 ~; 235 |; 42 &; 141 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 215 ( 135 ^ 67 !; 13 ?; 215 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_type,type,
sk1: $o ).
thf(sk2_type,type,
sk2: a > $o ).
thf(sk3_type,type,
sk3: $o ).
thf(sk4_type,type,
sk4: a > $o ).
thf(sk5_type,type,
sk5: $o ).
thf(sk6_type,type,
sk6: ( a > $o ) > $o ).
thf(sk7_type,type,
sk7: a > $o ).
thf(sk8_type,type,
sk8: a > $o ).
thf(sk9_type,type,
sk9: a > $o ).
thf(sk10_type,type,
sk10: a > $o ).
thf(sk17_type,type,
sk17: a ).
thf(sk20_type,type,
sk20: a ).
thf(sk21_type,type,
sk21: a > $o ).
thf(sk23_type,type,
sk23: a ).
thf(sk43_type,type,
sk43: a ).
thf(1,conjecture,
( ! [A: a > $o] :
( ( A
= ( ^ [B: a] : $false ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : ~ $false ) ) ) )
& ! [A: a > $o] :
( ( A
= ( ^ [B: a] : ~ $false ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : ~ $false ) ) ) )
& ! [A: ( a > $o ) > $o,B: a > $o] :
( ( ! [C: a > $o] :
( ( A @ C )
=> ( ( C
= ( ^ [D: a] : $false ) )
| ( C
= ( ^ [D: a] : ~ $false ) ) ) )
& ( B
= ( ^ [C: a] :
? [D: a > $o] :
( ( A @ D )
& ( D @ C ) ) ) ) )
=> ( ( B
= ( ^ [C: a] : $false ) )
| ( B
= ( ^ [C: a] : ~ $false ) ) ) )
& ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ( ( A
= ( ^ [D: a] : $false ) )
| ( A
= ( ^ [D: a] : ~ $false ) ) )
& ( ( B
= ( ^ [D: a] : $false ) )
| ( B
= ( ^ [D: a] : ~ $false ) ) )
& ( C
= ( ^ [D: a] :
( ( A @ D )
& ( B @ D ) ) ) ) )
=> ( ( C
= ( ^ [D: a] : $false ) )
| ( C
= ( ^ [D: a] : ~ $false ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cINDISCRETE_TOPOLOGY_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: a > $o] :
( ( A
= ( ^ [B: a] : $false ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : ~ $false ) ) ) )
& ! [A: a > $o] :
( ( A
= ( ^ [B: a] : ~ $false ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : ~ $false ) ) ) )
& ! [A: ( a > $o ) > $o,B: a > $o] :
( ( ! [C: a > $o] :
( ( A @ C )
=> ( ( C
= ( ^ [D: a] : $false ) )
| ( C
= ( ^ [D: a] : ~ $false ) ) ) )
& ( B
= ( ^ [C: a] :
? [D: a > $o] :
( ( A @ D )
& ( D @ C ) ) ) ) )
=> ( ( B
= ( ^ [C: a] : $false ) )
| ( B
= ( ^ [C: a] : ~ $false ) ) ) )
& ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ( ( A
= ( ^ [D: a] : $false ) )
| ( A
= ( ^ [D: a] : ~ $false ) ) )
& ( ( B
= ( ^ [D: a] : $false ) )
| ( B
= ( ^ [D: a] : ~ $false ) ) )
& ( C
= ( ^ [D: a] :
( ( A @ D )
& ( B @ D ) ) ) ) )
=> ( ( C
= ( ^ [D: a] : $false ) )
| ( C
= ( ^ [D: a] : ~ $false ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: a > $o] :
( ( A
= ( ^ [B: a] : $false ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) ) ) )
& ! [A: a > $o] :
( ( A
= ( ^ [B: a] : $true ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) ) ) )
& ! [A: ( a > $o ) > $o,B: a > $o] :
( ( ! [C: a > $o] :
( ( A @ C )
=> ( ( C
= ( ^ [D: a] : $false ) )
| ( C
= ( ^ [D: a] : $true ) ) ) )
& ( B
= ( ^ [C: a] :
? [D: a > $o] :
( ( A @ D )
& ( D @ C ) ) ) ) )
=> ( ( B
= ( ^ [C: a] : $false ) )
| ( B
= ( ^ [C: a] : $true ) ) ) )
& ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ( ( A
= ( ^ [D: a] : $false ) )
| ( A
= ( ^ [D: a] : $true ) ) )
& ( ( B
= ( ^ [D: a] : $false ) )
| ( B
= ( ^ [D: a] : $true ) ) )
& ( C
= ( ^ [D: a] :
( ( A @ D )
& ( B @ D ) ) ) ) )
=> ( ( C
= ( ^ [D: a] : $false ) )
| ( C
= ( ^ [D: a] : $true ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
( sk1
| sk3
| ( sk7
= ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) ) )
| ~ sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(23,plain,
( ( sk7
= ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) ) )
| sk1
| sk3
| ~ sk5 ),
inference(lifteq,[status(thm)],[9]) ).
thf(18,plain,
( sk1
| ( sk4
= ( ^ [A: a] : $true ) )
| ~ sk3 ),
inference(cnf,[status(esa)],[3]) ).
thf(28,plain,
( ( sk4
= ( ^ [A: a] : $true ) )
| sk1
| ~ sk3 ),
inference(lifteq,[status(thm)],[18]) ).
thf(11,plain,
( ( sk2
= ( ^ [A: a] : $false ) )
| ~ sk1 ),
inference(cnf,[status(esa)],[3]) ).
thf(30,plain,
( ( sk2
= ( ^ [A: a] : $false ) )
| ~ sk1 ),
inference(lifteq,[status(thm)],[11]) ).
thf(17,plain,
( ( sk2
!= ( ^ [A: a] : $false ) )
| ~ sk1 ),
inference(cnf,[status(esa)],[3]) ).
thf(25,plain,
( ( sk2
!= ( ^ [A: a] : $false ) )
| ~ sk1 ),
inference(lifteq,[status(thm)],[17]) ).
thf(39,plain,
( ~ sk1
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[30,25]) ).
thf(40,plain,
~ sk1,
inference(pattern_uni,[status(thm)],[39:[]]) ).
thf(64,plain,
( ( sk4
= ( ^ [A: a] : $true ) )
| $false
| ~ sk3 ),
inference(rewrite,[status(thm)],[28,40]) ).
thf(65,plain,
( ( sk4
= ( ^ [A: a] : $true ) )
| ~ sk3 ),
inference(simp,[status(thm)],[64]) ).
thf(10,plain,
( sk1
| ( sk4
!= ( ^ [A: a] : $true ) )
| ~ sk3 ),
inference(cnf,[status(esa)],[3]) ).
thf(20,plain,
( ( sk4
!= ( ^ [A: a] : $true ) )
| sk1
| ~ sk3 ),
inference(lifteq,[status(thm)],[10]) ).
thf(47,plain,
( ( sk4
!= ( ^ [A: a] : $true ) )
| $false
| ~ sk3 ),
inference(rewrite,[status(thm)],[20,40]) ).
thf(48,plain,
( ( sk4
!= ( ^ [A: a] : $true ) )
| ~ sk3 ),
inference(simp,[status(thm)],[47]) ).
thf(67,plain,
( ~ sk3
| ( sk4 != sk4 ) ),
inference(paramod_ordered,[status(thm)],[65,48]) ).
thf(68,plain,
~ sk3,
inference(pattern_uni,[status(thm)],[67:[]]) ).
thf(91,plain,
( ( sk7
= ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) ) )
| $false
| $false
| ~ sk5 ),
inference(rewrite,[status(thm)],[23,68,40]) ).
thf(92,plain,
( ( sk7
= ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) ) )
| ~ sk5 ),
inference(simp,[status(thm)],[91]) ).
thf(16,plain,
( sk1
| sk3
| ( sk7
!= ( ^ [A: a] : $false ) )
| ~ sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(29,plain,
( ( sk7
!= ( ^ [A: a] : $false ) )
| sk1
| sk3
| ~ sk5 ),
inference(lifteq,[status(thm)],[16]) ).
thf(58,plain,
( ( sk7
!= ( ^ [A: a] : $false ) )
| $false
| sk3
| ~ sk5 ),
inference(rewrite,[status(thm)],[29,40]) ).
thf(59,plain,
( ( sk7
!= ( ^ [A: a] : $false ) )
| sk3
| ~ sk5 ),
inference(simp,[status(thm)],[58]) ).
thf(79,plain,
( ( sk7
!= ( ^ [A: a] : $false ) )
| $false
| ~ sk5 ),
inference(rewrite,[status(thm)],[59,68]) ).
thf(80,plain,
( ( sk7
!= ( ^ [A: a] : $false ) )
| ~ sk5 ),
inference(simp,[status(thm)],[79]) ).
thf(94,plain,
( ~ sk5
| ( ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ( sk7 != sk7 ) ),
inference(paramod_ordered,[status(thm)],[92,80]) ).
thf(95,plain,
( ~ sk5
| ( ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) )
!= ( ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[94:[]]) ).
thf(98,plain,
( ? [A: a > $o] :
( ( sk6 @ A )
& ( A @ sk20 ) )
| ~ sk5 ),
inference(func_ext,[status(esa)],[95]) ).
thf(102,plain,
( ~ sk5
| ( sk6 @ sk21 ) ),
inference(cnf,[status(esa)],[98]) ).
thf(5,plain,
( sk1
| sk3
| ( sk7
!= ( ^ [A: a] : $true ) )
| ~ sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(19,plain,
( ( sk7
!= ( ^ [A: a] : $true ) )
| sk1
| sk3
| ~ sk5 ),
inference(lifteq,[status(thm)],[5]) ).
thf(50,plain,
( ( sk7
!= ( ^ [A: a] : $true ) )
| $false
| sk3
| ~ sk5 ),
inference(rewrite,[status(thm)],[19,40]) ).
thf(51,plain,
( ( sk7
!= ( ^ [A: a] : $true ) )
| sk3
| ~ sk5 ),
inference(simp,[status(thm)],[50]) ).
thf(73,plain,
( ( sk7
!= ( ^ [A: a] : $true ) )
| $false
| ~ sk5 ),
inference(rewrite,[status(thm)],[51,68]) ).
thf(74,plain,
( ( sk7
!= ( ^ [A: a] : $true ) )
| ~ sk5 ),
inference(simp,[status(thm)],[73]) ).
thf(96,plain,
( ~ sk5
| ( ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) )
!= ( ^ [A: a] : $true ) )
| ( sk7 != sk7 ) ),
inference(paramod_ordered,[status(thm)],[92,74]) ).
thf(97,plain,
( ~ sk5
| ( ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) )
!= ( ^ [A: a] : $true ) ) ),
inference(pattern_uni,[status(thm)],[96:[]]) ).
thf(103,plain,
( ~ ? [A: a > $o] :
( ( sk6 @ A )
& ( A @ sk22 ) )
| ~ sk5 ),
inference(func_ext,[status(esa)],[97]) ).
thf(106,plain,
! [A: a > $o] :
( ~ sk5
| ~ ( sk6 @ A )
| ~ ( A @ sk22 ) ),
inference(cnf,[status(esa)],[103]) ).
thf(112,plain,
! [A: a > $o] :
( ~ sk5
| ~ ( sk6 @ A )
| ( ( sk6 @ sk21 )
!= ( A @ sk22 ) ) ),
inference(paramod_ordered,[status(thm)],[102,106]) ).
thf(141,plain,
( ~ sk5
| ~ ( sk6
@ ^ [A: a] : ( sk6 @ sk21 ) ) ),
inference(pre_uni,[status(thm)],[112:[bind(A,$thf( ^ [B: a] : ( sk6 @ sk21 ) ))]]) ).
thf(232,plain,
( ~ sk5
| ( ( sk6
@ ^ [A: a] : ( sk6 @ sk21 ) )
!= ( sk6 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[102,141]) ).
thf(239,plain,
( ~ sk5
| ( ( ^ [A: a] : ( sk6 @ sk21 ) )
!= sk21 ) ),
inference(simp,[status(thm)],[232]) ).
thf(601,plain,
( ( ( sk6 @ sk21 )
!= ( sk21 @ sk43 ) )
| ~ sk5 ),
inference(func_ext,[status(esa)],[239]) ).
thf(2333,plain,
( ~ sk5
| ~ ( sk21 @ sk43 )
| ( ( sk6 @ sk21 )
!= ( sk6 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[102,601]) ).
thf(2334,plain,
( ~ sk5
| ~ ( sk21 @ sk43 ) ),
inference(pattern_uni,[status(thm)],[2333:[]]) ).
thf(6,plain,
( sk1
| sk3
| sk5
| ( sk10
!= ( ^ [A: a] : $false ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(22,plain,
( ( sk10
!= ( ^ [A: a] : $false ) )
| sk1
| sk3
| sk5 ),
inference(lifteq,[status(thm)],[6]) ).
thf(81,plain,
( ( sk10
!= ( ^ [A: a] : $false ) )
| $false
| $false
| sk5 ),
inference(rewrite,[status(thm)],[22,68,40]) ).
thf(82,plain,
( ( sk10
!= ( ^ [A: a] : $false ) )
| sk5 ),
inference(simp,[status(thm)],[81]) ).
thf(83,plain,
( ( sk10 @ sk17 )
| sk5 ),
inference(func_ext,[status(esa)],[82]) ).
thf(8,plain,
( sk1
| sk3
| sk5
| ( sk10
= ( ^ [A: a] :
( ( sk8 @ A )
& ( sk9 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(31,plain,
( ( ( ^ [A: a] :
( ( sk8 @ A )
& ( sk9 @ A ) ) )
= sk10 )
| sk1
| sk3
| sk5 ),
inference(lifteq,[status(thm)],[8]) ).
thf(61,plain,
( ( ( ^ [A: a] :
( ( sk8 @ A )
& ( sk9 @ A ) ) )
= sk10 )
| $false
| sk3
| sk5 ),
inference(rewrite,[status(thm)],[31,40]) ).
thf(62,plain,
( ( ( ^ [A: a] :
( ( sk8 @ A )
& ( sk9 @ A ) ) )
= sk10 )
| sk3
| sk5 ),
inference(simp,[status(thm)],[61]) ).
thf(75,plain,
( ( ( ^ [A: a] :
( ( sk8 @ A )
& ( sk9 @ A ) ) )
= sk10 )
| $false
| sk5 ),
inference(rewrite,[status(thm)],[62,68]) ).
thf(76,plain,
( ( ( ^ [A: a] :
( ( sk8 @ A )
& ( sk9 @ A ) ) )
= sk10 )
| sk5 ),
inference(simp,[status(thm)],[75]) ).
thf(90,plain,
! [A: a] :
( ( ( ( sk8 @ A )
& ( sk9 @ A ) )
= ( sk10 @ A ) )
| sk5 ),
inference(func_ext,[status(esa)],[76]) ).
thf(248,plain,
! [A: a] :
( sk5
| ( ( sk8 @ A )
& ( sk9 @ A ) )
| ~ ( sk10 @ A ) ),
inference(bool_ext,[status(thm)],[90]) ).
thf(251,plain,
! [A: a] :
( ~ ( sk10 @ A )
| ( sk9 @ A )
| sk5 ),
inference(cnf,[status(esa)],[248]) ).
thf(1934,plain,
! [A: a] :
( sk5
| ( sk9 @ A )
| ( ( sk10 @ sk17 )
!= ( sk10 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[83,251]) ).
thf(1935,plain,
( sk5
| ( sk9 @ sk17 ) ),
inference(pattern_uni,[status(thm)],[1934:[bind(A,$thf( sk17 ))]]) ).
thf(1943,plain,
! [A: a] :
( sk5
| ( ( sk8 @ A )
= ( sk10 @ A ) )
| ( ( sk9 @ sk17 )
!= ( sk9 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1935,90]) ).
thf(1944,plain,
( sk5
| ( ( sk10 @ sk17 )
= ( sk8 @ sk17 ) ) ),
inference(pattern_uni,[status(thm)],[1943:[bind(A,$thf( sk17 ))]]) ).
thf(2061,plain,
( sk5
| ( sk8 @ sk17 )
| ( ( sk10 @ sk17 )
!= ( sk10 @ sk17 ) ) ),
inference(paramod_ordered,[status(thm)],[1944,83]) ).
thf(2062,plain,
( sk5
| ( sk8 @ sk17 ) ),
inference(pattern_uni,[status(thm)],[2061:[]]) ).
thf(12,plain,
( sk1
| sk3
| sk5
| ( sk8
= ( ^ [A: a] : $false ) )
| ( sk8
= ( ^ [A: a] : $true ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(26,plain,
( ( sk8
= ( ^ [A: a] : $false ) )
| ( sk8
= ( ^ [A: a] : $true ) )
| sk1
| sk3
| sk5 ),
inference(lifteq,[status(thm)],[12]) ).
thf(43,plain,
( ( sk8
= ( ^ [A: a] : $false ) )
| ( sk8
= ( ^ [A: a] : $true ) )
| $false
| sk3
| sk5 ),
inference(rewrite,[status(thm)],[26,40]) ).
thf(44,plain,
( ( sk8
= ( ^ [A: a] : $false ) )
| ( sk8
= ( ^ [A: a] : $true ) )
| sk3
| sk5 ),
inference(simp,[status(thm)],[43]) ).
thf(45,plain,
! [B: a,A: a] :
( ~ ( sk8 @ A )
| ( sk8 @ B )
| sk3
| sk5 ),
inference(func_ext,[status(esa)],[44]) ).
thf(263,plain,
! [B: a,A: a] :
( ~ ( sk8 @ A )
| ( sk8 @ B )
| $false
| sk5 ),
inference(rewrite,[status(thm)],[45,68]) ).
thf(264,plain,
! [B: a,A: a] :
( ~ ( sk8 @ A )
| ( sk8 @ B )
| sk5 ),
inference(simp,[status(thm)],[263]) ).
thf(2070,plain,
! [B: a,A: a] :
( sk5
| ( sk8 @ B )
| ( ( sk8 @ sk17 )
!= ( sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2062,264]) ).
thf(2071,plain,
! [A: a] :
( sk5
| ( sk8 @ A ) ),
inference(pattern_uni,[status(thm)],[2070:[bind(A,$thf( sk17 ))]]) ).
thf(2077,plain,
! [A: a] :
( sk5
| ( sk8 @ A ) ),
inference(simp,[status(thm)],[2071]) ).
thf(15,plain,
( sk1
| sk3
| sk5
| ( sk9
= ( ^ [A: a] : $false ) )
| ( sk9
= ( ^ [A: a] : $true ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(33,plain,
( ( sk9
= ( ^ [A: a] : $false ) )
| ( sk9
= ( ^ [A: a] : $true ) )
| sk1
| sk3
| sk5 ),
inference(lifteq,[status(thm)],[15]) ).
thf(172,plain,
( ( sk9
= ( ^ [A: a] : $false ) )
| ( sk9
= ( ^ [A: a] : $true ) )
| $false
| $false
| sk5 ),
inference(rewrite,[status(thm)],[33,68,40]) ).
thf(173,plain,
( ( sk9
= ( ^ [A: a] : $false ) )
| ( sk9
= ( ^ [A: a] : $true ) )
| sk5 ),
inference(simp,[status(thm)],[172]) ).
thf(174,plain,
! [B: a,A: a] :
( ~ ( sk9 @ A )
| ( sk9 @ B )
| sk5 ),
inference(func_ext,[status(esa)],[173]) ).
thf(1936,plain,
! [B: a,A: a] :
( sk5
| ( sk9 @ B )
| ( ( sk9 @ sk17 )
!= ( sk9 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1935,174]) ).
thf(1937,plain,
! [A: a] :
( sk5
| ( sk9 @ A ) ),
inference(pattern_uni,[status(thm)],[1936:[bind(A,$thf( sk17 ))]]) ).
thf(1945,plain,
! [A: a] :
( sk5
| ( sk9 @ A ) ),
inference(simp,[status(thm)],[1937]) ).
thf(3285,plain,
! [B: a,A: a] :
( sk5
| ( ( sk8 @ B )
= ( sk10 @ B ) )
| ( ( sk9 @ A )
!= ( sk9 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1945,90]) ).
thf(3286,plain,
! [A: a] :
( sk5
| ( ( sk10 @ A )
= ( sk8 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3285:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(13,plain,
( sk1
| sk3
| sk5
| ( sk10
!= ( ^ [A: a] : $true ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(24,plain,
( ( sk10
!= ( ^ [A: a] : $true ) )
| sk1
| sk3
| sk5 ),
inference(lifteq,[status(thm)],[13]) ).
thf(165,plain,
( ( sk10
!= ( ^ [A: a] : $true ) )
| $false
| $false
| sk5 ),
inference(rewrite,[status(thm)],[24,68,40]) ).
thf(166,plain,
( ( sk10
!= ( ^ [A: a] : $true ) )
| sk5 ),
inference(simp,[status(thm)],[165]) ).
thf(167,plain,
( ~ ( sk10 @ sk23 )
| sk5 ),
inference(func_ext,[status(esa)],[166]) ).
thf(4677,plain,
! [A: a] :
( sk5
| ~ ( sk8 @ A )
| ( ( sk10 @ A )
!= ( sk10 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[3286,167]) ).
thf(4678,plain,
( sk5
| ~ ( sk8 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[4677:[bind(A,$thf( sk23 ))]]) ).
thf(4692,plain,
! [A: a] :
( sk5
| ( ( sk8 @ A )
!= ( sk8 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[2077,4678]) ).
thf(4693,plain,
sk5,
inference(pattern_uni,[status(thm)],[4692:[bind(A,$thf( sk23 ))]]) ).
thf(5072,plain,
( ~ $true
| ~ ( sk21 @ sk43 ) ),
inference(rewrite,[status(thm)],[2334,4693]) ).
thf(5073,plain,
~ ( sk21 @ sk43 ),
inference(simp,[status(thm)],[5072]) ).
thf(101,plain,
( ~ sk5
| ( sk21 @ sk20 ) ),
inference(cnf,[status(esa)],[98]) ).
thf(4700,plain,
( ~ $true
| ( sk21 @ sk20 ) ),
inference(rewrite,[status(thm)],[101,4693]) ).
thf(4701,plain,
sk21 @ sk20,
inference(simp,[status(thm)],[4700]) ).
thf(4,plain,
! [A: a > $o] :
( sk1
| sk3
| ~ ( sk6 @ A )
| ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) )
| ~ sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(32,plain,
! [A: a > $o] :
( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) )
| sk1
| sk3
| ~ ( sk6 @ A )
| ~ sk5 ),
inference(lifteq,[status(thm)],[4]) ).
thf(177,plain,
! [A: a > $o] :
( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) )
| $false
| $false
| ~ ( sk6 @ A )
| ~ sk5 ),
inference(rewrite,[status(thm)],[32,68,40]) ).
thf(178,plain,
! [A: a > $o] :
( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) )
| ~ ( sk6 @ A )
| ~ sk5 ),
inference(simp,[status(thm)],[177]) ).
thf(202,plain,
! [A: a > $o] :
( ~ sk5
| ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) )
| ( ( sk6 @ sk21 )
!= ( sk6 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,178]) ).
thf(203,plain,
( ~ sk5
| ( sk21
= ( ^ [A: a] : $false ) )
| ( sk21
= ( ^ [A: a] : $true ) ) ),
inference(pattern_uni,[status(thm)],[202:[bind(A,$thf( sk21 ))]]) ).
thf(374,plain,
! [B: a,A: a] :
( ~ ( sk21 @ A )
| ( sk21 @ B )
| ~ sk5 ),
inference(func_ext,[status(esa)],[203]) ).
thf(7319,plain,
! [B: a,A: a] :
( ~ ( sk21 @ A )
| ( sk21 @ B )
| ~ $true ),
inference(rewrite,[status(thm)],[374,4693]) ).
thf(7320,plain,
! [B: a,A: a] :
( ~ ( sk21 @ A )
| ( sk21 @ B ) ),
inference(simp,[status(thm)],[7319]) ).
thf(7321,plain,
! [B: a,A: a] :
( ( sk21 @ B )
| ( ( sk21 @ sk20 )
!= ( sk21 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4701,7320]) ).
thf(7322,plain,
! [A: a] : ( sk21 @ A ),
inference(pattern_uni,[status(thm)],[7321:[bind(A,$thf( sk20 ))]]) ).
thf(7343,plain,
! [A: a] : ( sk21 @ A ),
inference(simp,[status(thm)],[7322]) ).
thf(7368,plain,
~ $true,
inference(rewrite,[status(thm)],[5073,7343]) ).
thf(7369,plain,
$false,
inference(simp,[status(thm)],[7368]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEV261^5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 19:20:39 EDT 2024
% 0.14/0.35 % CPUTime :
% 1.20/1.13 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.61/1.33 % [INFO] Parsing done (197ms).
% 1.61/1.34 % [INFO] Running in sequential loop mode.
% 2.36/1.81 % [INFO] eprover registered as external prover.
% 2.36/1.81 % [INFO] cvc4 registered as external prover.
% 2.36/1.82 % [INFO] Scanning for conjecture ...
% 2.63/1.94 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.63/1.98 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.63/1.98 % [INFO] Problem is higher-order (TPTP THF).
% 2.63/1.99 % [INFO] Type checking passed.
% 2.80/1.99 % [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 ...
% 67.47/11.14 % [INFO] Killing All external provers ...
% 67.47/11.16 % Time passed: 10610ms (effective reasoning time: 9790ms)
% 67.47/11.16 % 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)>
% 67.47/11.16 % Axioms used in derivation (0):
% 67.47/11.16 % No. of inferences in proof: 118
% 67.47/11.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10610 ms resp. 9790 ms w/o parsing
% 67.47/11.23 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 67.47/11.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------