TSTP Solution File: SEU689^2 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEU689^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n021.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 15:27:58 EDT 2024
% Result : Theorem 16.13s 4.55s
% Output : Refutation 16.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 88 ( 16 unt; 0 typ; 3 def)
% Number of atoms : 318 ( 90 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1236 ( 141 ~; 140 |; 0 &; 915 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 203 ( 25 ^ 178 !; 0 ?; 203 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(subsetI1_type,type,
subsetI1: $o ).
thf(subsetI1_def,definition,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ) ) ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(breln_type,type,
breln: $i > $i > $i > $o ).
thf(breln_def,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf(brelnall1_type,type,
brelnall1: $o ).
thf(brelnall1_def,definition,
( brelnall1
= ( ! [A: $i,B: $i,C: $i] :
( ( breln @ A @ B @ C )
=> ! [D: $i > $o] :
( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( D @ ( kpair @ E @ F ) ) ) ) )
=> ! [E: $i] :
( ( in @ E @ C )
=> ( D @ E ) ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: ( $i > $o ) > $i > $i > $i > $i ).
thf(sk3_type,type,
sk3: ( $i > $o ) > $i > $i > $i > $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(1,conjecture,
( subsetI1
=> ( brelnall1
=> ! [A: $i,B: $i,C: $i] :
( ( breln @ A @ B @ C )
=> ! [D: $i] :
( ( breln @ A @ B @ D )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( in @ ( kpair @ E @ F ) @ D ) ) ) )
=> ( subset @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subbreln) ).
thf(2,negated_conjecture,
~ ( subsetI1
=> ( brelnall1
=> ! [A: $i,B: $i,C: $i] :
( ( breln @ A @ B @ C )
=> ! [D: $i] :
( ( breln @ A @ B @ D )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( in @ ( kpair @ E @ F ) @ D ) ) ) )
=> ( subset @ C @ D ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ ( cartprod @ A @ B ) )
=> ! [D: $i > $o] :
( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( D @ ( kpair @ E @ F ) ) ) ) )
=> ! [E: $i] :
( ( in @ E @ C )
=> ( D @ E ) ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ ( cartprod @ A @ B ) )
=> ! [D: $i] :
( ( subset @ D @ ( cartprod @ A @ B ) )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( in @ ( kpair @ E @ F ) @ D ) ) ) )
=> ( subset @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
~ ( subset @ sk6 @ sk7 ),
inference(cnf,[status(esa)],[3]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( ( subset @ A @ B )
!= ( subset @ sk6 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[4,13]) ).
thf(57,plain,
~ ( in @ ( sk1 @ sk7 @ sk6 ) @ sk7 ),
inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( sk6 )),bind(B,$thf( sk7 ))]]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(54,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( subset @ C @ D )
| ( ( in @ ( sk1 @ B @ A ) @ A )
!= ( in @ ( sk1 @ D @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[9,4]) ).
thf(55,plain,
! [A: $i] :
( ( subset @ A @ A )
| ( subset @ A @ A ) ),
inference(pattern_uni,[status(thm)],[54:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(60,plain,
! [A: $i] : ( subset @ A @ A ),
inference(simp,[status(thm)],[55]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( ( subset @ A @ B )
!= ( subset @ sk6 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[9,13]) ).
thf(38,plain,
in @ ( sk1 @ sk7 @ sk6 ) @ sk6,
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( sk6 )),bind(B,$thf( sk7 ))]]) ).
thf(7,plain,
subset @ sk6 @ ( cartprod @ sk4 @ sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [E: $i,D: $i > $o,C: $i,B: $i,A: $i] :
( ~ ( subset @ C @ ( cartprod @ A @ B ) )
| ( in @ ( sk2 @ D @ C @ B @ A ) @ A )
| ~ ( in @ E @ C )
| ( D @ E ) ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
! [E: $i,D: $i > $o,C: $i,B: $i,A: $i] :
( ~ ( subset @ C @ ( cartprod @ A @ B ) )
| ( in @ ( sk2 @ D @ C @ B @ A ) @ A )
| ~ ( in @ E @ C )
| ( D @ E ) ),
inference(simp,[status(thm)],[6]) ).
thf(77,plain,
! [G: $i,F: $i > $o,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ~ ( subset @ E @ ( cartprod @ C @ D ) )
| ( in @ ( sk2 @ F @ E @ D @ C ) @ C )
| ( F @ G )
| ( ( in @ ( sk1 @ B @ A ) @ A )
!= ( in @ G @ E ) ) ),
inference(paramod_ordered,[status(thm)],[9,15]) ).
thf(78,plain,
! [E: $i,D: $i,C: $i > $o,B: $i,A: $i] :
( ( subset @ E @ D )
| ~ ( subset @ E @ ( cartprod @ A @ B ) )
| ( in @ ( sk2 @ C @ E @ B @ A ) @ A )
| ( C @ ( sk1 @ D @ E ) ) ),
inference(pattern_uni,[status(thm)],[77:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( I )),bind(F,$thf( F )),bind(G,$thf( sk1 @ H @ I ))]]) ).
thf(131,plain,
! [E: $i,D: $i,C: $i > $o,B: $i,A: $i] :
( ( subset @ E @ D )
| ~ ( subset @ E @ ( cartprod @ A @ B ) )
| ( in @ ( sk2 @ C @ E @ B @ A ) @ A )
| ( C @ ( sk1 @ D @ E ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(297,plain,
! [E: $i,D: $i,C: $i > $o,B: $i,A: $i] :
( ( subset @ E @ D )
| ( in @ ( sk2 @ C @ E @ B @ A ) @ A )
| ( C @ ( sk1 @ D @ E ) )
| ( ( subset @ sk6 @ ( cartprod @ sk4 @ sk5 ) )
!= ( subset @ E @ ( cartprod @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,131]) ).
thf(298,plain,
! [B: $i,A: $i > $o] :
( ( subset @ sk6 @ B )
| ( in @ ( sk2 @ A @ sk6 @ sk5 @ sk4 ) @ sk4 )
| ( A @ ( sk1 @ B @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( sk6 ))]]) ).
thf(379,plain,
! [B: $i,A: $i > $o] :
( ( subset @ sk6 @ B )
| ( in @ ( sk2 @ A @ sk6 @ sk5 @ sk4 ) @ sk4 )
| ( A @ ( sk1 @ B @ sk6 ) ) ),
inference(simp,[status(thm)],[298]) ).
thf(1026,plain,
! [B: $i,A: $i > $o] :
( ( subset @ sk6 @ B )
| ( in @ ( sk2 @ A @ sk6 @ sk5 @ sk4 ) @ sk4 )
| ( ( A @ ( sk1 @ B @ sk6 ) )
!= ( in @ ( sk1 @ sk7 @ sk6 ) @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[379,57]) ).
thf(1087,plain,
( ( subset @ sk6 @ sk7 )
| ( in
@ ( sk2
@ ^ [A: $i] : ( in @ A @ sk7 )
@ sk6
@ sk5
@ sk4 )
@ sk4 ) ),
inference(pre_uni,[status(thm)],[1026:[bind(A,$thf( ^ [C: $i] : ( in @ C @ sk7 ) )),bind(B,$thf( sk7 ))]]) ).
thf(1133,plain,
( $false
| ( in
@ ( sk2
@ ^ [A: $i] : ( in @ A @ sk7 )
@ sk6
@ sk5
@ sk4 )
@ sk4 ) ),
inference(rewrite,[status(thm)],[1087,13]) ).
thf(1134,plain,
( in
@ ( sk2
@ ^ [A: $i] : ( in @ A @ sk7 )
@ sk6
@ sk5
@ sk4 )
@ sk4 ),
inference(simp,[status(thm)],[1133]) ).
thf(8,plain,
! [E: $i,D: $i > $o,C: $i,B: $i,A: $i] :
( ~ ( subset @ C @ ( cartprod @ A @ B ) )
| ~ ( D @ ( kpair @ ( sk2 @ D @ C @ B @ A ) @ ( sk3 @ D @ C @ B @ A ) ) )
| ~ ( in @ E @ C )
| ( D @ E ) ),
inference(cnf,[status(esa)],[3]) ).
thf(18,plain,
! [E: $i,D: $i > $o,C: $i,B: $i,A: $i] :
( ~ ( subset @ C @ ( cartprod @ A @ B ) )
| ~ ( D @ ( kpair @ ( sk2 @ D @ C @ B @ A ) @ ( sk3 @ D @ C @ B @ A ) ) )
| ~ ( in @ E @ C )
| ( D @ E ) ),
inference(simp,[status(thm)],[8]) ).
thf(12,plain,
! [E: $i,D: $i > $o,C: $i,B: $i,A: $i] :
( ~ ( subset @ C @ ( cartprod @ A @ B ) )
| ( in @ ( sk3 @ D @ C @ B @ A ) @ B )
| ~ ( in @ E @ C )
| ( D @ E ) ),
inference(cnf,[status(esa)],[3]) ).
thf(16,plain,
! [E: $i,D: $i > $o,C: $i,B: $i,A: $i] :
( ~ ( subset @ C @ ( cartprod @ A @ B ) )
| ( in @ ( sk3 @ D @ C @ B @ A ) @ B )
| ~ ( in @ E @ C )
| ( D @ E ) ),
inference(simp,[status(thm)],[12]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( ( in @ ( sk1 @ B @ A ) @ A )
!= ( in @ ( sk1 @ sk7 @ sk6 ) @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[9,57]) ).
thf(167,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk7 @ sk6 ) )
| ( A != sk7 ) ),
inference(simp,[status(thm)],[164]) ).
thf(175,plain,
! [A: $i] :
( ( subset @ sk7 @ A )
| ( ( sk1 @ A @ sk7 )
!= ( sk1 @ sk7 @ sk6 ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(21,plain,
( ( subset @ sk6 @ ( cartprod @ sk4 @ sk5 ) )
!= ( subset @ sk6 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[7,13]) ).
thf(22,plain,
( ( sk6 != sk6 )
| ( ( cartprod @ sk4 @ sk5 )
!= sk7 ) ),
inference(simp,[status(thm)],[21]) ).
thf(23,plain,
( ( cartprod @ sk4 @ sk5 )
!= sk7 ),
inference(simp,[status(thm)],[22]) ).
thf(1139,plain,
( ( in
@ ( sk2
@ ^ [A: $i] : ( in @ A @ sk7 )
@ sk6
@ sk5
@ sk4 )
@ sk4 )
!= ( in @ ( sk1 @ sk7 @ sk6 ) @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[1134,57]) ).
thf(1158,plain,
( ( ( sk2
@ ^ [A: $i] : ( in @ A @ sk7 )
@ sk6
@ sk5
@ sk4 )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk7 != sk4 ) ),
inference(simp,[status(thm)],[1139]) ).
thf(5,plain,
subset @ sk7 @ ( cartprod @ sk4 @ sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ~ ( in @ B @ sk5 )
| ~ ( in @ ( kpair @ A @ B ) @ sk6 )
| ( in @ ( kpair @ A @ B ) @ sk7 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ~ ( in @ B @ sk5 )
| ~ ( in @ ( kpair @ A @ B ) @ sk6 )
| ( in @ ( kpair @ A @ B ) @ sk7 ) ),
inference(simp,[status(thm)],[10]) ).
thf(162,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ~ ( in @ B @ sk5 )
| ~ ( in @ ( kpair @ A @ B ) @ sk6 )
| ( ( in @ ( kpair @ A @ B ) @ sk7 )
!= ( in @ ( sk1 @ sk7 @ sk6 ) @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[14,57]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ~ ( in @ B @ sk5 )
| ~ ( in @ ( kpair @ A @ B ) @ sk6 )
| ( ( kpair @ A @ B )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk7 != sk7 ) ),
inference(simp,[status(thm)],[162]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ~ ( in @ B @ sk5 )
| ~ ( in @ ( kpair @ A @ B ) @ sk6 )
| ( ( kpair @ A @ B )
!= ( sk1 @ sk7 @ sk6 ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ~ ( in @ B @ sk5 )
| ( ( kpair @ A @ B )
!= ( sk1 @ sk7 @ sk6 ) )
| ( ( in @ ( sk1 @ sk7 @ sk6 ) @ sk6 )
!= ( in @ ( kpair @ A @ B ) @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[38,178]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ~ ( in @ B @ sk5 )
| ( ( kpair @ A @ B )
!= ( sk1 @ sk7 @ sk6 ) )
| ( ( sk1 @ sk7 @ sk6 )
!= ( kpair @ A @ B ) )
| ( sk6 != sk6 ) ),
inference(simp,[status(thm)],[193]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ~ ( in @ B @ sk5 )
| ( ( kpair @ A @ B )
!= ( sk1 @ sk7 @ sk6 ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ( ( kpair @ A @ B )
!= ( sk1 @ sk7 @ sk6 ) )
| ( ( in @ ( sk1 @ sk7 @ sk6 ) @ sk6 )
!= ( in @ B @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[38,241]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ( ( kpair @ A @ B )
!= ( sk1 @ sk7 @ sk6 ) )
| ( ( sk1 @ sk7 @ sk6 )
!= B )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[249]) ).
thf(269,plain,
! [A: $i] :
( ~ ( in @ A @ sk4 )
| ( ( kpair @ A @ ( sk1 @ sk7 @ sk6 ) )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[260]) ).
thf(1061,plain,
! [A: $i] :
( ( subset @ sk6 @ A )
| ( in
@ ( sk2
@ ^ [B: $i] : $false
@ sk6
@ sk5
@ sk4 )
@ sk4 )
| $false ),
inference(prim_subst,[status(thm)],[379:[bind(A,$thf( ^ [C: $i] : $false ))]]) ).
thf(1112,plain,
! [A: $i] :
( ( subset @ sk6 @ A )
| ( in
@ ( sk2
@ ^ [B: $i] : $false
@ sk6
@ sk5
@ sk4 )
@ sk4 ) ),
inference(simp,[status(thm)],[1061]) ).
thf(1182,plain,
! [A: $i] :
( ( in
@ ( sk2
@ ^ [B: $i] : $false
@ sk6
@ sk5
@ sk4 )
@ sk4 )
| ( ( subset @ sk6 @ A )
!= ( subset @ sk6 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[1112,13]) ).
thf(1183,plain,
( in
@ ( sk2
@ ^ [A: $i] : $false
@ sk6
@ sk5
@ sk4 )
@ sk4 ),
inference(pattern_uni,[status(thm)],[1182:[bind(A,$thf( sk7 ))]]) ).
thf(1576,plain,
! [A: $i] :
( ( ( kpair @ A @ ( sk1 @ sk7 @ sk6 ) )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk6 != sk5 )
| ( ( in
@ ( sk2
@ ^ [B: $i] : $false
@ sk6
@ sk5
@ sk4 )
@ sk4 )
!= ( in @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[1183,269]) ).
thf(1577,plain,
( ( ( kpair
@ ( sk2
@ ^ [A: $i] : $false
@ sk6
@ sk5
@ sk4 )
@ ( sk1 @ sk7 @ sk6 ) )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk6 != sk5 ) ),
inference(pattern_uni,[status(thm)],[1576:[bind(A,$thf( sk2 @ ^ [B: $i] : $false @ sk6 @ sk5 @ sk4 ))]]) ).
thf(163,plain,
( ( in @ ( sk1 @ sk7 @ sk6 ) @ sk7 )
!= ( in @ ( sk1 @ sk7 @ sk6 ) @ sk6 ) ),
inference(paramod_ordered,[status(thm)],[38,57]) ).
thf(174,plain,
( ( ( sk1 @ sk7 @ sk6 )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk7 != sk6 ) ),
inference(simp,[status(thm)],[163]) ).
thf(179,plain,
sk7 != sk6,
inference(simp,[status(thm)],[174]) ).
thf(553,plain,
! [A: $i] :
( ( ( kpair @ A @ ( sk1 @ sk7 @ sk6 ) )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk6 != sk5 )
| ( ( in @ ( sk1 @ sk7 @ sk6 ) @ sk6 )
!= ( in @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[38,269]) ).
thf(569,plain,
! [A: $i] :
( ( ( kpair @ A @ ( sk1 @ sk7 @ sk6 ) )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk6 != sk5 )
| ( ( sk1 @ sk7 @ sk6 )
!= A )
| ( sk6 != sk4 ) ),
inference(simp,[status(thm)],[553]) ).
thf(578,plain,
( ( ( kpair @ ( sk1 @ sk7 @ sk6 ) @ ( sk1 @ sk7 @ sk6 ) )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk6 != sk5 )
| ( sk6 != sk4 ) ),
inference(simp,[status(thm)],[569]) ).
thf(280,plain,
! [E: $i,D: $i,C: $i > $o,B: $i,A: $i] :
( ( subset @ E @ D )
| ( in @ ( sk2 @ C @ E @ B @ A ) @ A )
| ( C @ ( sk1 @ D @ E ) )
| ( ( subset @ sk7 @ ( cartprod @ sk4 @ sk5 ) )
!= ( subset @ E @ ( cartprod @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,131]) ).
thf(281,plain,
! [B: $i,A: $i > $o] :
( ( subset @ sk7 @ B )
| ( in @ ( sk2 @ A @ sk7 @ sk5 @ sk4 ) @ sk4 )
| ( A @ ( sk1 @ B @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( sk7 ))]]) ).
thf(371,plain,
! [B: $i,A: $i > $o] :
( ( subset @ sk7 @ B )
| ( in @ ( sk2 @ A @ sk7 @ sk5 @ sk4 ) @ sk4 )
| ( A @ ( sk1 @ B @ sk7 ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(649,plain,
! [A: $i] :
( ( subset @ sk7 @ A )
| ( in
@ ( sk2
@ ^ [B: $i] : $false
@ sk7
@ sk5
@ sk4 )
@ sk4 )
| $false ),
inference(prim_subst,[status(thm)],[371:[bind(A,$thf( ^ [C: $i] : $false ))]]) ).
thf(685,plain,
! [A: $i] :
( ( subset @ sk7 @ A )
| ( in
@ ( sk2
@ ^ [B: $i] : $false
@ sk7
@ sk5
@ sk4 )
@ sk4 ) ),
inference(simp,[status(thm)],[649]) ).
thf(717,plain,
! [A: $i] :
( ( subset @ sk7 @ A )
| ( ( in
@ ( sk2
@ ^ [B: $i] : $false
@ sk7
@ sk5
@ sk4 )
@ sk4 )
!= ( in @ ( sk1 @ sk7 @ sk6 ) @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[685,57]) ).
thf(745,plain,
! [A: $i] :
( ( subset @ sk7 @ A )
| ( ( sk2
@ ^ [B: $i] : $false
@ sk7
@ sk5
@ sk4 )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk7 != sk4 ) ),
inference(simp,[status(thm)],[717]) ).
thf(11,plain,
! [E: $i,D: $i > $o,C: $i,B: $i,A: $i] :
( ~ ( subset @ C @ ( cartprod @ A @ B ) )
| ( in @ ( kpair @ ( sk2 @ D @ C @ B @ A ) @ ( sk3 @ D @ C @ B @ A ) ) @ C )
| ~ ( in @ E @ C )
| ( D @ E ) ),
inference(cnf,[status(esa)],[3]) ).
thf(17,plain,
! [E: $i,D: $i > $o,C: $i,B: $i,A: $i] :
( ~ ( subset @ C @ ( cartprod @ A @ B ) )
| ( in @ ( kpair @ ( sk2 @ D @ C @ B @ A ) @ ( sk3 @ D @ C @ B @ A ) ) @ C )
| ~ ( in @ E @ C )
| ( D @ E ) ),
inference(simp,[status(thm)],[11]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ sk5 )
| ( ( kpair @ A @ B )
!= ( sk1 @ sk7 @ sk6 ) )
| ( ( in @ ( sk1 @ sk7 @ sk6 ) @ sk6 )
!= ( in @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[38,241]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ sk5 )
| ( ( kpair @ A @ B )
!= ( sk1 @ sk7 @ sk6 ) )
| ( ( sk1 @ sk7 @ sk6 )
!= A )
| ( sk6 != sk4 ) ),
inference(simp,[status(thm)],[248]) ).
thf(271,plain,
! [A: $i] :
( ~ ( in @ A @ sk5 )
| ( ( kpair @ ( sk1 @ sk7 @ sk6 ) @ A )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk6 != sk4 ) ),
inference(simp,[status(thm)],[262]) ).
thf(1143,plain,
! [A: $i] :
( ( ( kpair @ A @ ( sk1 @ sk7 @ sk6 ) )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk6 != sk5 )
| ( ( in
@ ( sk2
@ ^ [B: $i] : ( in @ B @ sk7 )
@ sk6
@ sk5
@ sk4 )
@ sk4 )
!= ( in @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[1134,269]) ).
thf(1144,plain,
( ( ( kpair
@ ( sk2
@ ^ [A: $i] : ( in @ A @ sk7 )
@ sk6
@ sk5
@ sk4 )
@ ( sk1 @ sk7 @ sk6 ) )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk6 != sk5 ) ),
inference(pattern_uni,[status(thm)],[1143:[bind(A,$thf( sk2 @ ^ [B: $i] : ( in @ B @ sk7 ) @ sk6 @ sk5 @ sk4 ))]]) ).
thf(1566,plain,
( ( in
@ ( sk2
@ ^ [A: $i] : $false
@ sk6
@ sk5
@ sk4 )
@ sk4 )
!= ( in @ ( sk1 @ sk7 @ sk6 ) @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[1183,57]) ).
thf(1594,plain,
( ( ( sk2
@ ^ [A: $i] : $false
@ sk6
@ sk5
@ sk4 )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk7 != sk4 ) ),
inference(simp,[status(thm)],[1566]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( ( in @ ( sk1 @ sk7 @ sk6 ) @ sk6 )
!= ( in @ ( sk1 @ B @ A ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[38,4]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( ( sk1 @ sk7 @ sk6 )
!= ( sk1 @ B @ A ) )
| ( sk6 != B ) ),
inference(simp,[status(thm)],[53]) ).
thf(62,plain,
! [A: $i] :
( ( subset @ A @ sk6 )
| ( ( sk1 @ sk7 @ sk6 )
!= ( sk1 @ sk6 @ A ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(1582,plain,
! [A: $i] :
( ( ( kpair @ ( sk1 @ sk7 @ sk6 ) @ A )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk6 != sk4 )
| ( ( in
@ ( sk2
@ ^ [B: $i] : $false
@ sk6
@ sk5
@ sk4 )
@ sk4 )
!= ( in @ A @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[1183,271]) ).
thf(1598,plain,
! [A: $i] :
( ( ( kpair @ ( sk1 @ sk7 @ sk6 ) @ A )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk6 != sk4 )
| ( ( sk2
@ ^ [B: $i] : $false
@ sk6
@ sk5
@ sk4 )
!= A )
| ( sk5 != sk4 ) ),
inference(simp,[status(thm)],[1582]) ).
thf(1621,plain,
( ( ( kpair @ ( sk1 @ sk7 @ sk6 )
@ ( sk2
@ ^ [A: $i] : $false
@ sk6
@ sk5
@ sk4 ) )
!= ( sk1 @ sk7 @ sk6 ) )
| ( sk6 != sk4 )
| ( sk5 != sk4 ) ),
inference(simp,[status(thm)],[1598]) ).
thf(1923,plain,
$false,
inference(e,[status(thm)],[57,60,38,1134,18,16,175,23,4,1158,5,379,269,14,1577,179,1183,578,9,13,371,745,17,271,7,1144,685,1594,3,241,131,15,62,1621]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU689^2 : TPTP v8.2.0. Released v3.7.0.
% 0.00/0.10 % Command : run_Leo-III %s %d THM
% 0.09/0.30 % Computer : n021.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Fri Jun 21 13:04:55 EDT 2024
% 0.09/0.30 % CPUTime :
% 1.00/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.28/1.09 % [INFO] Parsing done (145ms).
% 1.28/1.11 % [INFO] Running in sequential loop mode.
% 1.68/1.39 % [INFO] eprover registered as external prover.
% 1.79/1.40 % [INFO] Scanning for conjecture ...
% 2.02/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.09/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.09/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.09/1.56 % [INFO] Type checking passed.
% 2.09/1.57 % [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 ...
% 16.13/4.55 % External prover 'e' found a proof!
% 16.13/4.55 % [INFO] Killing All external provers ...
% 16.13/4.55 % Time passed: 4074ms (effective reasoning time: 3440ms)
% 16.13/4.55 % 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)>
% 16.13/4.55 % Axioms used in derivation (0):
% 16.13/4.55 % No. of inferences in proof: 85
% 16.13/4.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4074 ms resp. 3440 ms w/o parsing
% 16.13/4.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.13/4.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------