TSTP Solution File: SET788+1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET788+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 03:06:59 EDT 2024
% Result : Theorem 277.90s 101.26s
% Output : Refutation 277.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 9
% Syntax : Number of formulae : 114 ( 8 unt; 8 typ; 0 def)
% Number of atoms : 396 ( 28 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1278 ( 100 ~; 200 |; 8 &; 944 @)
% ( 6 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 142 ( 0 ^ 142 !; 0 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
thf(equalish_type,type,
equalish: $i > $i > $o ).
thf(a_member_of_type,type,
a_member_of: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: $i > $i > $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(1,conjecture,
( ! [A: $i,B: $i] :
( ( equalish @ A @ B )
<=> ! [C: $i] :
( ( a_member_of @ C @ A )
<=> ( a_member_of @ C @ B ) ) )
=> ! [A: $i,B: $i] :
( ( equalish @ A @ B )
<=> ( equalish @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: $i] :
( ( equalish @ A @ B )
<=> ! [C: $i] :
( ( a_member_of @ C @ A )
<=> ( a_member_of @ C @ B ) ) )
=> ! [A: $i,B: $i] :
( ( equalish @ A @ B )
<=> ( equalish @ B @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( ( equalish @ A @ B )
=> ! [C: $i] :
( ( ( a_member_of @ C @ A )
=> ( a_member_of @ C @ B ) )
& ( ( a_member_of @ C @ B )
=> ( a_member_of @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( ( a_member_of @ C @ A )
=> ( a_member_of @ C @ B ) )
& ( ( a_member_of @ C @ B )
=> ( a_member_of @ C @ A ) ) )
=> ( equalish @ A @ B ) ) )
=> ! [A: $i,B: $i] :
( ( ( equalish @ A @ B )
=> ( equalish @ B @ A ) )
& ( ( equalish @ B @ A )
=> ( equalish @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ! [A: $i,B: $i] :
( ( equalish @ A @ B )
=> ( ! [C: $i] :
( ( a_member_of @ C @ A )
=> ( a_member_of @ C @ B ) )
& ! [C: $i] :
( ( a_member_of @ C @ B )
=> ( a_member_of @ C @ A ) ) ) )
& ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( a_member_of @ C @ A )
=> ( a_member_of @ C @ B ) )
& ! [C: $i] :
( ( a_member_of @ C @ B )
=> ( a_member_of @ C @ A ) ) )
=> ( equalish @ A @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( equalish @ A @ B )
=> ( equalish @ B @ A ) )
& ! [A: $i,B: $i] :
( ( equalish @ B @ A )
=> ( equalish @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(10,plain,
( ~ ( equalish @ sk4 @ sk3 )
| ( equalish @ sk6 @ sk5 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( a_member_of @ ( sk1 @ B @ A ) @ A )
| ( a_member_of @ ( sk2 @ B @ A ) @ B )
| ( equalish @ A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( a_member_of @ ( sk1 @ B @ A ) @ A )
| ( a_member_of @ ( sk2 @ B @ A ) @ B )
| ( equalish @ A @ B ) ),
inference(simp,[status(thm)],[9]) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( a_member_of @ C @ A )
| ( a_member_of @ C @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(88,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( a_member_of @ ( sk1 @ B @ A ) @ A )
| ( equalish @ A @ B )
| ~ ( equalish @ C @ D )
| ( a_member_of @ E @ D )
| ( ( a_member_of @ ( sk2 @ B @ A ) @ B )
!= ( a_member_of @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17,13]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ( a_member_of @ ( sk1 @ B @ C ) @ C )
| ( equalish @ C @ B )
| ~ ( equalish @ B @ A )
| ( a_member_of @ ( sk2 @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( D )),bind(E,$thf( sk2 @ F @ G ))]]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( a_member_of @ ( sk1 @ B @ C ) @ C )
| ( equalish @ C @ B )
| ~ ( equalish @ B @ A )
| ( a_member_of @ ( sk2 @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[89]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ sk4 @ sk3 )
| ( a_member_of @ ( sk1 @ B @ C ) @ C )
| ( equalish @ C @ B )
| ( a_member_of @ ( sk2 @ B @ C ) @ A )
| ( ( equalish @ sk6 @ sk5 )
!= ( equalish @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,96]) ).
thf(162,plain,
! [A: $i] :
( ~ ( equalish @ sk4 @ sk3 )
| ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
| ( equalish @ A @ sk6 )
| ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 ) ),
inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(167,plain,
! [A: $i] :
( ~ ( equalish @ sk4 @ sk3 )
| ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
| ( equalish @ A @ sk6 )
| ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 ) ),
inference(simp,[status(thm)],[162]) ).
thf(5,plain,
( ( equalish @ sk3 @ sk4 )
| ( equalish @ sk6 @ sk5 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ( equalish @ sk3 @ sk4 )
| ( a_member_of @ ( sk1 @ B @ C ) @ C )
| ( equalish @ C @ B )
| ( a_member_of @ ( sk2 @ B @ C ) @ A )
| ( ( equalish @ sk6 @ sk5 )
!= ( equalish @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5,96]) ).
thf(154,plain,
! [A: $i] :
( ( equalish @ sk3 @ sk4 )
| ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
| ( equalish @ A @ sk6 )
| ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 ) ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(169,plain,
! [A: $i] :
( ( equalish @ sk3 @ sk4 )
| ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
| ( equalish @ A @ sk6 )
| ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 ) ),
inference(simp,[status(thm)],[154]) ).
thf(6,plain,
! [B: $i,A: $i] :
( ( a_member_of @ ( sk1 @ B @ A ) @ A )
| ~ ( a_member_of @ ( sk2 @ B @ A ) @ A )
| ( equalish @ A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( a_member_of @ ( sk1 @ B @ A ) @ A )
| ~ ( a_member_of @ ( sk2 @ B @ A ) @ A )
| ( equalish @ A @ B ) ),
inference(simp,[status(thm)],[6]) ).
thf(219,plain,
! [C: $i,B: $i,A: $i] :
( ( equalish @ sk3 @ sk4 )
| ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
| ( equalish @ A @ sk6 )
| ( a_member_of @ ( sk1 @ C @ B ) @ B )
| ( equalish @ B @ C )
| ( ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 )
!= ( a_member_of @ ( sk2 @ C @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[169,16]) ).
thf(220,plain,
( ( equalish @ sk3 @ sk4 )
| ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
| ( equalish @ sk5 @ sk6 )
| ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
| ( equalish @ sk5 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[219:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 )),bind(C,$thf( sk6 ))]]) ).
thf(229,plain,
( ( equalish @ sk3 @ sk4 )
| ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
| ( equalish @ sk5 @ sk6 ) ),
inference(simp,[status(thm)],[220]) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( a_member_of @ C @ B )
| ( a_member_of @ C @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( a_member_of @ C @ B )
| ( a_member_of @ C @ A ) ),
inference(simp,[status(thm)],[7]) ).
thf(474,plain,
! [C: $i,B: $i,A: $i] :
( ( equalish @ sk3 @ sk4 )
| ~ ( a_member_of @ C @ B )
| ( a_member_of @ C @ A )
| ( ( equalish @ sk6 @ sk5 )
!= ( equalish @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5,19]) ).
thf(475,plain,
! [A: $i] :
( ( equalish @ sk3 @ sk4 )
| ~ ( a_member_of @ A @ sk5 )
| ( a_member_of @ A @ sk6 ) ),
inference(pattern_uni,[status(thm)],[474:[bind(A,$thf( sk6 )),bind(B,$thf( sk5 ))]]) ).
thf(536,plain,
! [A: $i] :
( ( equalish @ sk3 @ sk4 )
| ~ ( a_member_of @ A @ sk5 )
| ( a_member_of @ A @ sk6 ) ),
inference(simp,[status(thm)],[475]) ).
thf(1498,plain,
! [A: $i] :
( ( equalish @ sk3 @ sk4 )
| ( equalish @ sk5 @ sk6 )
| ( a_member_of @ A @ sk6 )
| ( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
!= ( a_member_of @ A @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[229,536]) ).
thf(1499,plain,
( ( equalish @ sk3 @ sk4 )
| ( equalish @ sk5 @ sk6 )
| ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk6 ) ),
inference(pattern_uni,[status(thm)],[1498:[bind(A,$thf( sk1 @ sk6 @ sk5 ))]]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ~ ( a_member_of @ ( sk1 @ B @ A ) @ B )
| ( a_member_of @ ( sk2 @ B @ A ) @ B )
| ( equalish @ A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ~ ( a_member_of @ ( sk1 @ B @ A ) @ B )
| ( a_member_of @ ( sk2 @ B @ A ) @ B )
| ( equalish @ A @ B ) ),
inference(simp,[status(thm)],[12]) ).
thf(1715,plain,
! [B: $i,A: $i] :
( ( equalish @ sk3 @ sk4 )
| ( equalish @ sk5 @ sk6 )
| ( a_member_of @ ( sk2 @ B @ A ) @ B )
| ( equalish @ A @ B )
| ( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk6 )
!= ( a_member_of @ ( sk1 @ B @ A ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1499,18]) ).
thf(1716,plain,
( ( equalish @ sk3 @ sk4 )
| ( equalish @ sk5 @ sk6 )
| ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk6 )
| ( equalish @ sk5 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[1715:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(1747,plain,
( ( equalish @ sk3 @ sk4 )
| ( equalish @ sk5 @ sk6 )
| ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk6 ) ),
inference(simp,[status(thm)],[1716]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( equalish @ sk3 @ sk4 )
| ~ ( a_member_of @ C @ A )
| ( a_member_of @ C @ B )
| ( ( equalish @ sk6 @ sk5 )
!= ( equalish @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5,13]) ).
thf(81,plain,
! [A: $i] :
( ( equalish @ sk3 @ sk4 )
| ~ ( a_member_of @ A @ sk6 )
| ( a_member_of @ A @ sk5 ) ),
inference(pattern_uni,[status(thm)],[80:[bind(A,$thf( sk6 )),bind(B,$thf( sk5 ))]]) ).
thf(92,plain,
! [A: $i] :
( ( equalish @ sk3 @ sk4 )
| ~ ( a_member_of @ A @ sk6 )
| ( a_member_of @ A @ sk5 ) ),
inference(simp,[status(thm)],[81]) ).
thf(1766,plain,
! [A: $i] :
( ( equalish @ sk3 @ sk4 )
| ( equalish @ sk5 @ sk6 )
| ( a_member_of @ A @ sk5 )
| ( ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk6 )
!= ( a_member_of @ A @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[1747,92]) ).
thf(1767,plain,
( ( equalish @ sk3 @ sk4 )
| ( equalish @ sk5 @ sk6 )
| ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk5 ) ),
inference(pattern_uni,[status(thm)],[1766:[bind(A,$thf( sk2 @ sk6 @ sk5 ))]]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ~ ( a_member_of @ ( sk1 @ B @ A ) @ B )
| ~ ( a_member_of @ ( sk2 @ B @ A ) @ A )
| ( equalish @ A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ~ ( a_member_of @ ( sk1 @ B @ A ) @ B )
| ~ ( a_member_of @ ( sk2 @ B @ A ) @ A )
| ( equalish @ A @ B ) ),
inference(simp,[status(thm)],[14]) ).
thf(1721,plain,
! [B: $i,A: $i] :
( ( equalish @ sk3 @ sk4 )
| ( equalish @ sk5 @ sk6 )
| ~ ( a_member_of @ ( sk2 @ B @ A ) @ A )
| ( equalish @ A @ B )
| ( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk6 )
!= ( a_member_of @ ( sk1 @ B @ A ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1499,15]) ).
thf(1722,plain,
( ( equalish @ sk3 @ sk4 )
| ( equalish @ sk5 @ sk6 )
| ~ ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk5 )
| ( equalish @ sk5 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[1721:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(1749,plain,
( ( equalish @ sk3 @ sk4 )
| ( equalish @ sk5 @ sk6 )
| ~ ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk5 ) ),
inference(simp,[status(thm)],[1722]) ).
thf(1903,plain,
( ( equalish @ sk3 @ sk4 )
| ( equalish @ sk5 @ sk6 )
| ( ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk5 )
!= ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[1767,1749]) ).
thf(1904,plain,
( ( equalish @ sk3 @ sk4 )
| ( equalish @ sk5 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[1903:[]]) ).
thf(8,plain,
( ( equalish @ sk3 @ sk4 )
| ~ ( equalish @ sk5 @ sk6 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(1966,plain,
( ( equalish @ sk3 @ sk4 )
| ( ( equalish @ sk5 @ sk6 )
!= ( equalish @ sk5 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[1904,8]) ).
thf(1967,plain,
equalish @ sk3 @ sk4,
inference(pattern_uni,[status(thm)],[1966:[]]) ).
thf(1998,plain,
! [C: $i,B: $i,A: $i] :
( ( a_member_of @ ( sk1 @ B @ C ) @ C )
| ( equalish @ C @ B )
| ( a_member_of @ ( sk2 @ B @ C ) @ A )
| ( ( equalish @ sk3 @ sk4 )
!= ( equalish @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1967,96]) ).
thf(1999,plain,
! [A: $i] :
( ( a_member_of @ ( sk1 @ sk3 @ A ) @ A )
| ( equalish @ A @ sk3 )
| ( a_member_of @ ( sk2 @ sk3 @ A ) @ sk4 ) ),
inference(pattern_uni,[status(thm)],[1998:[bind(A,$thf( sk4 )),bind(B,$thf( sk3 ))]]) ).
thf(2027,plain,
! [A: $i] :
( ( a_member_of @ ( sk1 @ sk3 @ A ) @ A )
| ( equalish @ A @ sk3 )
| ( a_member_of @ ( sk2 @ sk3 @ A ) @ sk4 ) ),
inference(simp,[status(thm)],[1999]) ).
thf(2058,plain,
! [C: $i,B: $i,A: $i] :
( ( a_member_of @ ( sk1 @ sk3 @ A ) @ A )
| ( equalish @ A @ sk3 )
| ( a_member_of @ ( sk1 @ C @ B ) @ B )
| ( equalish @ B @ C )
| ( ( a_member_of @ ( sk2 @ sk3 @ A ) @ sk4 )
!= ( a_member_of @ ( sk2 @ C @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2027,16]) ).
thf(2059,plain,
( ( a_member_of @ ( sk1 @ sk3 @ sk4 ) @ sk4 )
| ( equalish @ sk4 @ sk3 )
| ( a_member_of @ ( sk1 @ sk3 @ sk4 ) @ sk4 )
| ( equalish @ sk4 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[2058:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 )),bind(C,$thf( sk3 ))]]) ).
thf(2104,plain,
( ( a_member_of @ ( sk1 @ sk3 @ sk4 ) @ sk4 )
| ( equalish @ sk4 @ sk3 ) ),
inference(simp,[status(thm)],[2059]) ).
thf(1994,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( a_member_of @ C @ B )
| ( a_member_of @ C @ A )
| ( ( equalish @ sk3 @ sk4 )
!= ( equalish @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1967,19]) ).
thf(1995,plain,
! [A: $i] :
( ~ ( a_member_of @ A @ sk4 )
| ( a_member_of @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1994:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(2026,plain,
! [A: $i] :
( ~ ( a_member_of @ A @ sk4 )
| ( a_member_of @ A @ sk3 ) ),
inference(simp,[status(thm)],[1995]) ).
thf(2251,plain,
! [A: $i] :
( ( equalish @ sk4 @ sk3 )
| ( a_member_of @ A @ sk3 )
| ( ( a_member_of @ ( sk1 @ sk3 @ sk4 ) @ sk4 )
!= ( a_member_of @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[2104,2026]) ).
thf(2252,plain,
( ( equalish @ sk4 @ sk3 )
| ( a_member_of @ ( sk1 @ sk3 @ sk4 ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[2251:[bind(A,$thf( sk1 @ sk3 @ sk4 ))]]) ).
thf(2302,plain,
! [B: $i,A: $i] :
( ( equalish @ sk4 @ sk3 )
| ( a_member_of @ ( sk2 @ B @ A ) @ B )
| ( equalish @ A @ B )
| ( ( a_member_of @ ( sk1 @ sk3 @ sk4 ) @ sk3 )
!= ( a_member_of @ ( sk1 @ B @ A ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2252,18]) ).
thf(2303,plain,
( ( equalish @ sk4 @ sk3 )
| ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk3 )
| ( equalish @ sk4 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[2302:[bind(A,$thf( sk4 )),bind(B,$thf( sk3 ))]]) ).
thf(2327,plain,
( ( equalish @ sk4 @ sk3 )
| ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk3 ) ),
inference(simp,[status(thm)],[2303]) ).
thf(1989,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( a_member_of @ C @ A )
| ( a_member_of @ C @ B )
| ( ( equalish @ sk3 @ sk4 )
!= ( equalish @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1967,13]) ).
thf(1990,plain,
! [A: $i] :
( ~ ( a_member_of @ A @ sk3 )
| ( a_member_of @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[1989:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(2025,plain,
! [A: $i] :
( ~ ( a_member_of @ A @ sk3 )
| ( a_member_of @ A @ sk4 ) ),
inference(simp,[status(thm)],[1990]) ).
thf(2307,plain,
! [B: $i,A: $i] :
( ( equalish @ sk4 @ sk3 )
| ~ ( a_member_of @ ( sk2 @ B @ A ) @ A )
| ( equalish @ A @ B )
| ( ( a_member_of @ ( sk1 @ sk3 @ sk4 ) @ sk3 )
!= ( a_member_of @ ( sk1 @ B @ A ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2252,15]) ).
thf(2308,plain,
( ( equalish @ sk4 @ sk3 )
| ~ ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk4 )
| ( equalish @ sk4 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[2307:[bind(A,$thf( sk4 )),bind(B,$thf( sk3 ))]]) ).
thf(2318,plain,
( ( equalish @ sk4 @ sk3 )
| ~ ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk4 ) ),
inference(simp,[status(thm)],[2308]) ).
thf(2344,plain,
! [A: $i] :
( ~ ( a_member_of @ A @ sk3 )
| ( equalish @ sk4 @ sk3 )
| ( ( a_member_of @ A @ sk4 )
!= ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[2025,2318]) ).
thf(2345,plain,
( ~ ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk3 )
| ( equalish @ sk4 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[2344:[bind(A,$thf( sk2 @ sk3 @ sk4 ))]]) ).
thf(2471,plain,
( ( equalish @ sk4 @ sk3 )
| ( ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk3 )
!= ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[2327,2345]) ).
thf(2472,plain,
equalish @ sk4 @ sk3,
inference(pattern_uni,[status(thm)],[2471:[]]) ).
thf(2732,plain,
! [A: $i] :
( ~ $true
| ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
| ( equalish @ A @ sk6 )
| ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 ) ),
inference(rewrite,[status(thm)],[167,2472]) ).
thf(2733,plain,
! [A: $i] :
( ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
| ( equalish @ A @ sk6 )
| ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 ) ),
inference(simp,[status(thm)],[2732]) ).
thf(2736,plain,
! [C: $i,B: $i,A: $i] :
( ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
| ( equalish @ A @ sk6 )
| ( a_member_of @ ( sk1 @ C @ B ) @ B )
| ( equalish @ B @ C )
| ( ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 )
!= ( a_member_of @ ( sk2 @ C @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2733,16]) ).
thf(2737,plain,
( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
| ( equalish @ sk5 @ sk6 )
| ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
| ( equalish @ sk5 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[2736:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 )),bind(C,$thf( sk6 ))]]) ).
thf(2777,plain,
( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
| ( equalish @ sk5 @ sk6 ) ),
inference(simp,[status(thm)],[2737]) ).
thf(11,plain,
( ~ ( equalish @ sk4 @ sk3 )
| ~ ( equalish @ sk5 @ sk6 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(2510,plain,
( ~ $true
| ~ ( equalish @ sk5 @ sk6 ) ),
inference(rewrite,[status(thm)],[11,2472]) ).
thf(2511,plain,
~ ( equalish @ sk5 @ sk6 ),
inference(simp,[status(thm)],[2510]) ).
thf(2795,plain,
( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
| $false ),
inference(rewrite,[status(thm)],[2777,2511]) ).
thf(2796,plain,
a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5,
inference(simp,[status(thm)],[2795]) ).
thf(504,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ sk4 @ sk3 )
| ~ ( a_member_of @ C @ B )
| ( a_member_of @ C @ A )
| ( ( equalish @ sk6 @ sk5 )
!= ( equalish @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10,19]) ).
thf(505,plain,
! [A: $i] :
( ~ ( equalish @ sk4 @ sk3 )
| ~ ( a_member_of @ A @ sk5 )
| ( a_member_of @ A @ sk6 ) ),
inference(pattern_uni,[status(thm)],[504:[bind(A,$thf( sk6 )),bind(B,$thf( sk5 ))]]) ).
thf(535,plain,
! [A: $i] :
( ~ ( equalish @ sk4 @ sk3 )
| ~ ( a_member_of @ A @ sk5 )
| ( a_member_of @ A @ sk6 ) ),
inference(simp,[status(thm)],[505]) ).
thf(2516,plain,
! [A: $i] :
( ~ $true
| ~ ( a_member_of @ A @ sk5 )
| ( a_member_of @ A @ sk6 ) ),
inference(rewrite,[status(thm)],[535,2472]) ).
thf(2517,plain,
! [A: $i] :
( ~ ( a_member_of @ A @ sk5 )
| ( a_member_of @ A @ sk6 ) ),
inference(simp,[status(thm)],[2516]) ).
thf(2810,plain,
! [A: $i] :
( ( a_member_of @ A @ sk6 )
| ( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
!= ( a_member_of @ A @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[2796,2517]) ).
thf(2811,plain,
a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk6,
inference(pattern_uni,[status(thm)],[2810:[bind(A,$thf( sk1 @ sk6 @ sk5 ))]]) ).
thf(2854,plain,
! [B: $i,A: $i] :
( ~ ( a_member_of @ ( sk2 @ B @ A ) @ A )
| ( equalish @ A @ B )
| ( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk6 )
!= ( a_member_of @ ( sk1 @ B @ A ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2811,15]) ).
thf(2855,plain,
( ~ ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk5 )
| ( equalish @ sk5 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[2854:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(2846,plain,
! [B: $i,A: $i] :
( ( a_member_of @ ( sk2 @ B @ A ) @ B )
| ( equalish @ A @ B )
| ( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk6 )
!= ( a_member_of @ ( sk1 @ B @ A ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2811,18]) ).
thf(2847,plain,
( ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk6 )
| ( equalish @ sk5 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[2846:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(2875,plain,
( ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk6 )
| $false ),
inference(rewrite,[status(thm)],[2847,2511]) ).
thf(2876,plain,
a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk6,
inference(simp,[status(thm)],[2875]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ sk4 @ sk3 )
| ~ ( a_member_of @ C @ A )
| ( a_member_of @ C @ B )
| ( ( equalish @ sk6 @ sk5 )
!= ( equalish @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10,13]) ).
thf(83,plain,
! [A: $i] :
( ~ ( equalish @ sk4 @ sk3 )
| ~ ( a_member_of @ A @ sk6 )
| ( a_member_of @ A @ sk5 ) ),
inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( sk6 )),bind(B,$thf( sk5 ))]]) ).
thf(93,plain,
! [A: $i] :
( ~ ( equalish @ sk4 @ sk3 )
| ~ ( a_member_of @ A @ sk6 )
| ( a_member_of @ A @ sk5 ) ),
inference(simp,[status(thm)],[83]) ).
thf(2514,plain,
! [A: $i] :
( ~ $true
| ~ ( a_member_of @ A @ sk6 )
| ( a_member_of @ A @ sk5 ) ),
inference(rewrite,[status(thm)],[93,2472]) ).
thf(2515,plain,
! [A: $i] :
( ~ ( a_member_of @ A @ sk6 )
| ( a_member_of @ A @ sk5 ) ),
inference(simp,[status(thm)],[2514]) ).
thf(2883,plain,
! [A: $i] :
( ( a_member_of @ A @ sk5 )
| ( ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk6 )
!= ( a_member_of @ A @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[2876,2515]) ).
thf(2884,plain,
a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk5,
inference(pattern_uni,[status(thm)],[2883:[bind(A,$thf( sk2 @ sk6 @ sk5 ))]]) ).
thf(40970,plain,
( ~ $true
| $false ),
inference(rewrite,[status(thm)],[2855,2884,2511]) ).
thf(40971,plain,
$false,
inference(simp,[status(thm)],[40970]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SET788+1 : TPTP v8.2.0. Released v3.1.0.
% 0.05/0.11 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n013.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon May 20 13:21:24 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.89/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.04 % [INFO] Parsing done (141ms).
% 1.23/1.05 % [INFO] Running in sequential loop mode.
% 1.69/1.40 % [INFO] nitpick registered as external prover.
% 1.69/1.40 % [INFO] Scanning for conjecture ...
% 1.91/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.91/1.51 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.91/1.51 % [INFO] Problem is first-order (TPTP FOF).
% 1.91/1.52 % [INFO] Type checking passed.
% 1.91/1.52 % [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 ...
% 277.90/101.25 % [INFO] Killing All external provers ...
% 277.90/101.25 % Time passed: 100801ms (effective reasoning time: 100194ms)
% 277.90/101.25 % 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)>
% 277.90/101.26 % Axioms used in derivation (0):
% 277.90/101.26 % No. of inferences in proof: 106
% 277.90/101.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 100801 ms resp. 100194 ms w/o parsing
% 277.90/101.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 277.90/101.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------