TSTP Solution File: LCL713^1 by Leo-III---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : LCL713^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n020.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 11:15:29 EDT 2024
% Result : Theorem 28.86s 7.01s
% Output : Refutation 28.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 87 ( 36 unt; 0 typ; 6 def)
% Number of atoms : 196 ( 37 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1174 ( 173 ~; 150 |; 2 &; 844 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 199 ( 42 ^ 157 !; 0 ?; 199 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(mforall_prop_type,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(mforall_prop_def,definition,
( mforall_prop
= ( ^ [A: ( $i > $o ) > $i > $o,B: $i] :
! [C: $i > $o] : ( A @ C @ B ) ) ) ).
thf(mbox_type,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
! [D: $i] :
( ~ ( A @ C @ D )
| ( B @ D ) ) ) ) ).
thf(mdia_type,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mdia_def,definition,
( mdia
= ( ^ [A: $i > $i > $o,B: $i > $o] : ( mnot @ ( mbox @ A @ ( mnot @ B ) ) ) ) ) ).
thf(meuclidean_type,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(meuclidean_def,definition,
( meuclidean
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ B @ D ) )
=> ( A @ C @ D ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(sk1_type,type,
sk1: $i > $i > $o ).
thf(sk2_type,type,
sk2: $i > ( $i > $o ) > $i > $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [B: $i > $o] : ( mimplies @ ( mdia @ A @ B ) @ ( mbox @ A @ ( mdia @ A @ B ) ) ) ) )
=> ( meuclidean @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [B: $i > $o] : ( mimplies @ ( mdia @ A @ B ) @ ( mbox @ A @ ( mdia @ A @ B ) ) ) ) )
=> ( meuclidean @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o] :
( ! [B: $i,C: $i > $o] :
( ! [D: $i] :
( ~ ( A @ B @ D )
| ~ ( C @ D ) )
| ! [D: $i] :
( ~ ( A @ B @ D )
| ~ ! [E: $i] :
( ~ ( A @ D @ E )
| ~ ( C @ E ) ) ) )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ B @ D ) )
=> ( A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
sk1 @ sk3 @ sk5,
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( sk1 @ A @ C )
| ~ ( B @ C )
| ~ ( sk1 @ A @ D )
| ( B @ ( sk2 @ D @ B @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(17,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( B @ C )
| ~ ( sk1 @ A @ D )
| ( B @ ( sk2 @ D @ B @ A ) )
| ( ( sk1 @ sk3 @ sk5 )
!= ( sk1 @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,5]) ).
thf(18,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ sk5 )
| ~ ( sk1 @ sk3 @ B )
| ( A @ ( sk2 @ B @ A @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(72,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ sk5 )
| ~ ( sk1 @ sk3 @ B )
| ( A @ ( sk2 @ B @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(227,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ sk5 )
| ( A @ ( sk2 @ B @ A @ sk3 ) )
| ( ( sk1 @ sk3 @ sk5 )
!= ( sk1 @ sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6,72]) ).
thf(228,plain,
! [A: $i > $o] :
( ~ ( A @ sk5 )
| ( A @ ( sk2 @ sk5 @ A @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[227:[bind(A,$thf( A )),bind(B,$thf( sk5 ))]]) ).
thf(309,plain,
! [A: $i > $o] :
( ~ ~ ( A @ sk5 )
| ~ ( A
@ ( sk2 @ sk5
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) ) ),
inference(prim_subst,[status(thm)],[228:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).
thf(346,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk2 @ sk5
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) )
| ( A @ sk5 ) ),
inference(cnf,[status(esa)],[309]) ).
thf(347,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk2 @ sk5
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) )
| ( A @ sk5 ) ),
inference(simp,[status(thm)],[346]) ).
thf(300,plain,
! [A: $i > $o] :
( ( A @ ( sk2 @ sk5 @ A @ sk3 ) )
| ( ( sk1 @ sk3 @ sk5 )
!= ( A @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[6,228]) ).
thf(324,plain,
sk1 @ sk3 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ),
inference(pre_uni,[status(thm)],[300:[bind(A,$thf( sk1 @ sk3 ))]]) ).
thf(515,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ sk5 )
| ( A @ ( sk2 @ B @ A @ sk3 ) )
| ( ( sk1 @ sk3 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) )
!= ( sk1 @ sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[324,72]) ).
thf(516,plain,
! [A: $i > $o] :
( ~ ( A @ sk5 )
| ( A @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[515:[bind(A,$thf( A )),bind(B,$thf( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ))]]) ).
thf(1317,plain,
! [A: $i > $o] :
( ( A @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) )
| ( ( sk1 @ sk3 @ sk5 )
!= ( A @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[6,516]) ).
thf(1388,plain,
sk1 @ sk3 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ),
inference(pre_uni,[status(thm)],[1317:[bind(A,$thf( sk1 @ sk3 ))]]) ).
thf(1998,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ sk5 )
| ( A @ ( sk2 @ B @ A @ sk3 ) )
| ( ( sk1 @ sk3 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) )
!= ( sk1 @ sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1388,72]) ).
thf(1999,plain,
! [A: $i > $o] :
( ~ ( A @ sk5 )
| ( A @ ( sk2 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[1998:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ))]]) ).
thf(32,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( sk1 @ A @ C )
| ~ ( B @ C )
| ~ ( sk1 @ A @ D )
| ( ( B @ ( sk2 @ D @ B @ A ) )
!= ( ~ ( B @ C ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[5]) ).
thf(42,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( sk1 @ A @ C )
| ~ ( B @ C )
| ~ ( sk1 @ A @ D )
| ( ( B @ ( sk2 @ D @ B @ A ) )
!= ( ~ ( B @ C ) ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(308,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( ( A @ sk5 )
| ( B @ sk5 ) )
| ( A
@ ( sk2 @ sk5
@ ^ [C: $i] :
( ( A @ C )
| ( B @ C ) )
@ sk3 ) )
| ( B
@ ( sk2 @ sk5
@ ^ [C: $i] :
( ( A @ C )
| ( B @ C ) )
@ sk3 ) ) ),
inference(prim_subst,[status(thm)],[228:[bind(A,$thf( ^ [D: $i] : ( ( B @ D ) | ( C @ D ) ) ))]]) ).
thf(342,plain,
! [B: $i > $o,A: $i > $o] :
( ( A
@ ( sk2 @ sk5
@ ^ [C: $i] :
( ( A @ C )
| ( B @ C ) )
@ sk3 ) )
| ( B
@ ( sk2 @ sk5
@ ^ [C: $i] :
( ( A @ C )
| ( B @ C ) )
@ sk3 ) )
| ~ ( A @ sk5 ) ),
inference(cnf,[status(esa)],[308]) ).
thf(344,plain,
! [B: $i > $o,A: $i > $o] :
( ( A
@ ( sk2 @ sk5
@ ^ [C: $i] :
( ( A @ C )
| ( B @ C ) )
@ sk3 ) )
| ( B
@ ( sk2 @ sk5
@ ^ [C: $i] :
( ( A @ C )
| ( B @ C ) )
@ sk3 ) )
| ~ ( A @ sk5 ) ),
inference(simp,[status(thm)],[342]) ).
thf(36,plain,
! [E: $i > $o,D: $i > $o,C: $i,B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( ( D @ B )
| ( E @ B ) )
| ~ ( sk1 @ A @ C )
| ( D
@ ( sk2 @ C
@ ^ [F: $i] :
( ( D @ F )
| ( E @ F ) )
@ A ) )
| ( E
@ ( sk2 @ C
@ ^ [F: $i] :
( ( D @ F )
| ( E @ F ) )
@ A ) ) ),
inference(prim_subst,[status(thm)],[5:[bind(A,$thf( A )),bind(B,$thf( ^ [G: $i] : ( ( E @ G ) | ( F @ G ) ) ))]]) ).
thf(59,plain,
! [E: $i > $o,D: $i > $o,C: $i,B: $i,A: $i] :
( ( D
@ ( sk2 @ C
@ ^ [F: $i] :
( ( D @ F )
| ( E @ F ) )
@ A ) )
| ( E
@ ( sk2 @ C
@ ^ [F: $i] :
( ( D @ F )
| ( E @ F ) )
@ A ) )
| ~ ( sk1 @ A @ C )
| ~ ( D @ B )
| ~ ( sk1 @ A @ B ) ),
inference(cnf,[status(esa)],[36]) ).
thf(61,plain,
! [E: $i > $o,D: $i > $o,C: $i,B: $i,A: $i] :
( ( D
@ ( sk2 @ C
@ ^ [F: $i] :
( ( D @ F )
| ( E @ F ) )
@ A ) )
| ( E
@ ( sk2 @ C
@ ^ [F: $i] :
( ( D @ F )
| ( E @ F ) )
@ A ) )
| ~ ( sk1 @ A @ C )
| ~ ( D @ B )
| ~ ( sk1 @ A @ B ) ),
inference(simp,[status(thm)],[59]) ).
thf(8,plain,
sk1 @ sk3 @ sk4,
inference(cnf,[status(esa)],[3]) ).
thf(230,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ sk5 )
| ( A @ ( sk2 @ B @ A @ sk3 ) )
| ( ( sk1 @ sk3 @ sk4 )
!= ( sk1 @ sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8,72]) ).
thf(231,plain,
! [A: $i > $o] :
( ~ ( A @ sk5 )
| ( A @ ( sk2 @ sk4 @ A @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[230:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(766,plain,
! [A: $i > $o] :
( ( A @ ( sk2 @ sk4 @ A @ sk3 ) )
| ( ( sk1 @ sk3 @ sk5 )
!= ( A @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[6,231]) ).
thf(815,plain,
sk1 @ sk3 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ),
inference(pre_uni,[status(thm)],[766:[bind(A,$thf( sk1 @ sk3 ))]]) ).
thf(1181,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ sk5 )
| ( A @ ( sk2 @ B @ A @ sk3 ) )
| ( ( sk1 @ sk3 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) )
!= ( sk1 @ sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[815,72]) ).
thf(1182,plain,
! [A: $i > $o] :
( ~ ( A @ sk5 )
| ( A @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[1181:[bind(A,$thf( A )),bind(B,$thf( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ))]]) ).
thf(2119,plain,
! [A: $i > $o] :
( ( A @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) )
| ( ( sk1 @ sk3 @ sk5 )
!= ( A @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[6,1182]) ).
thf(2208,plain,
sk1 @ sk3 @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ),
inference(pre_uni,[status(thm)],[2119:[bind(A,$thf( sk1 @ sk3 ))]]) ).
thf(2566,plain,
! [A: $i > $o] :
( ~ ~ ( A @ sk5 )
| ~ ( A
@ ( sk2 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 )
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) ) ),
inference(prim_subst,[status(thm)],[1999:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).
thf(2663,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk2 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 )
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) )
| ( A @ sk5 ) ),
inference(cnf,[status(esa)],[2566]) ).
thf(2664,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk2 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 )
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) )
| ( A @ sk5 ) ),
inference(simp,[status(thm)],[2663]) ).
thf(2406,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ sk5 )
| ( A @ ( sk2 @ B @ A @ sk3 ) )
| ( ( sk1 @ sk3 @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) )
!= ( sk1 @ sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2208,72]) ).
thf(2407,plain,
! [A: $i > $o] :
( ~ ( A @ sk5 )
| ( A @ ( sk2 @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[2406:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ))]]) ).
thf(4,plain,
~ ( sk1 @ sk4 @ sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(60,plain,
! [E: $i > $o,D: $i > $o,C: $i,B: $i,A: $i] :
( ( D
@ ( sk2 @ C
@ ^ [F: $i] :
( ( D @ F )
| ( E @ F ) )
@ A ) )
| ( E
@ ( sk2 @ C
@ ^ [F: $i] :
( ( D @ F )
| ( E @ F ) )
@ A ) )
| ~ ( sk1 @ A @ C )
| ~ ( E @ B )
| ~ ( sk1 @ A @ B ) ),
inference(cnf,[status(esa)],[36]) ).
thf(62,plain,
! [E: $i > $o,D: $i > $o,C: $i,B: $i,A: $i] :
( ( D
@ ( sk2 @ C
@ ^ [F: $i] :
( ( D @ F )
| ( E @ F ) )
@ A ) )
| ( E
@ ( sk2 @ C
@ ^ [F: $i] :
( ( D @ F )
| ( E @ F ) )
@ A ) )
| ~ ( sk1 @ A @ C )
| ~ ( E @ B )
| ~ ( sk1 @ A @ B ) ),
inference(simp,[status(thm)],[60]) ).
thf(1337,plain,
! [A: $i > $o] :
( ~ ~ ( A @ sk5 )
| ~ ( A
@ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 )
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) ) ),
inference(prim_subst,[status(thm)],[516:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).
thf(1416,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 )
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) )
| ( A @ sk5 ) ),
inference(cnf,[status(esa)],[1337]) ).
thf(1417,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 )
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) )
| ( A @ sk5 ) ),
inference(simp,[status(thm)],[1416]) ).
thf(28,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( B @ C )
| ~ ( sk1 @ A @ D )
| ( B @ ( sk2 @ D @ B @ A ) )
| ( ( sk1 @ A @ C )
!= ( sk1 @ A @ D ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[5]) ).
thf(51,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( B @ C )
| ~ ( sk1 @ A @ C )
| ( B @ ( sk2 @ C @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(2716,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( B @ C )
| ( B @ ( sk2 @ C @ B @ A ) )
| ( ( sk1 @ sk3 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) )
!= ( sk1 @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[815,51]) ).
thf(2717,plain,
! [A: $i > $o] :
( ~ ( A @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) )
| ( A @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[2716:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ))]]) ).
thf(2904,plain,
! [A: $i > $o] :
( ~ ( A @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) )
| ( A @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[2717]) ).
thf(15,plain,
! [H: $i,G: $i,F: $i > $o,E: $i,D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( sk1 @ A @ C )
| ~ ( B @ C )
| ~ ( sk1 @ A @ D )
| ~ ( sk1 @ E @ G )
| ~ ( sk1 @ E @ H )
| ( F @ ( sk2 @ H @ F @ E ) )
| ( ( B @ ( sk2 @ D @ B @ A ) )
!= ( F @ G ) ) ),
inference(paramod_ordered,[status(thm)],[5,5]) ).
thf(44,plain,
! [H: $i,G: $i,F: $i > $o,E: $i,D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( sk1 @ A @ C )
| ~ ( B @ C )
| ~ ( sk1 @ A @ D )
| ~ ( sk1 @ E @ G )
| ~ ( sk1 @ E @ H )
| ( F @ ( sk2 @ H @ F @ E ) )
| ( ( B @ ( sk2 @ D @ B @ A ) )
!= ( F @ G ) ) ),
inference(pre_uni,[status(thm)],[15:[]]) ).
thf(45,plain,
! [H: $i,G: $i,F: $i > $o,E: $i,D: $i,C: $i,B: $i > $o,A: $i] :
( ( F @ ( sk2 @ H @ F @ E ) )
| ~ ( sk1 @ E @ H )
| ~ ( sk1 @ E @ G )
| ~ ( sk1 @ A @ D )
| ~ ( B @ C )
| ~ ( sk1 @ A @ C )
| ( ( B @ ( sk2 @ D @ B @ A ) )
!= ( F @ G ) ) ),
inference(pre_uni,[status(thm)],[44:[]]) ).
thf(1336,plain,
! [A: $i > $o] :
( ~ ( A @ sk5 )
| ( ( A @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) )
!= ( ~ ( A @ sk5 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[516]) ).
thf(1389,plain,
! [A: $i > $o] :
( ~ ( A @ sk5 )
| ( ( A @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) )
!= ( ~ ( A @ sk5 ) ) ) ),
inference(simp,[status(thm)],[1336]) ).
thf(2153,plain,
! [A: $i > $o] :
( ~ ~ ( A @ sk5 )
| ~ ( A
@ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 )
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) ) ),
inference(prim_subst,[status(thm)],[1182:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).
thf(2256,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 )
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) )
| ( A @ sk5 ) ),
inference(cnf,[status(esa)],[2153]) ).
thf(2257,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 )
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) )
| ( A @ sk5 ) ),
inference(simp,[status(thm)],[2256]) ).
thf(7,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( sk1 @ A @ C )
| ~ ( B @ C )
| ~ ( sk1 @ A @ D )
| ( sk1 @ D @ ( sk2 @ D @ B @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(780,plain,
! [A: $i > $o] :
( ~ ( A @ sk5 )
| ( ( A @ ( sk2 @ sk4 @ A @ sk3 ) )
!= ( ~ ( A @ sk5 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[231]) ).
thf(823,plain,
! [A: $i > $o] :
( ~ ( A @ sk5 )
| ( ( A @ ( sk2 @ sk4 @ A @ sk3 ) )
!= ( ~ ( A @ sk5 ) ) ) ),
inference(simp,[status(thm)],[780]) ).
thf(3128,plain,
! [A: $i > $o] :
( ( A @ ( sk2 @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) )
| ( ( sk1 @ sk3 @ sk5 )
!= ( A @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[6,2407]) ).
thf(3273,plain,
sk1 @ sk3 @ ( sk2 @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ),
inference(pre_uni,[status(thm)],[3128:[bind(A,$thf( sk1 @ sk3 ))]]) ).
thf(306,plain,
! [A: $i > $o] :
( ~ ( A @ sk5 )
| ( ( A @ ( sk2 @ sk5 @ A @ sk3 ) )
!= ( ~ ( A @ sk5 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[228]) ).
thf(331,plain,
! [A: $i > $o] :
( ~ ( A @ sk5 )
| ( ( A @ ( sk2 @ sk5 @ A @ sk3 ) )
!= ( ~ ( A @ sk5 ) ) ) ),
inference(simp,[status(thm)],[306]) ).
thf(9,plain,
( ( sk1 @ sk4 @ sk5 )
!= ( sk1 @ sk3 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[6,4]) ).
thf(10,plain,
( ( sk4 != sk3 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[9]) ).
thf(11,plain,
sk4 != sk3,
inference(simp,[status(thm)],[10]) ).
thf(2529,plain,
! [A: $i > $o] :
( ( A @ ( sk2 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) )
| ( ( sk1 @ sk3 @ sk5 )
!= ( A @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[6,1999]) ).
thf(2584,plain,
sk1 @ sk3 @ ( sk2 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ),
inference(pre_uni,[status(thm)],[2529:[bind(A,$thf( sk1 @ sk3 ))]]) ).
thf(2719,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( B @ C )
| ( B @ ( sk2 @ C @ B @ A ) )
| ( ( sk1 @ sk3 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) )
!= ( sk1 @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[324,51]) ).
thf(2720,plain,
! [A: $i > $o] :
( ~ ( A @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) )
| ( A @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[2719:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ))]]) ).
thf(2907,plain,
! [A: $i > $o] :
( ~ ( A @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) )
| ( A @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[2720]) ).
thf(783,plain,
! [A: $i > $o] :
( ~ ~ ( A @ sk5 )
| ~ ( A
@ ( sk2 @ sk4
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) ) ),
inference(prim_subst,[status(thm)],[231:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).
thf(832,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk2 @ sk4
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) )
| ( A @ sk5 ) ),
inference(cnf,[status(esa)],[783]) ).
thf(833,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk2 @ sk4
@ ^ [B: $i] :
~ ( A @ B )
@ sk3 ) )
| ( A @ sk5 ) ),
inference(simp,[status(thm)],[832]) ).
thf(4696,plain,
$false,
inference(e,[status(thm)],[347,5,1999,42,344,228,61,6,815,324,1182,2208,2664,3,2407,8,4,62,1417,2904,45,1389,1388,2257,7,516,823,3273,331,11,72,2584,231,2907,833,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL713^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Jun 22 15:14:40 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.97/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.41/1.01 % [INFO] Parsing done (147ms).
% 1.41/1.02 % [INFO] Running in sequential loop mode.
% 1.91/1.24 % [INFO] eprover registered as external prover.
% 1.91/1.24 % [INFO] Scanning for conjecture ...
% 2.29/1.35 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.29/1.37 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.29/1.37 % [INFO] Problem is higher-order (TPTP THF).
% 2.29/1.37 % [INFO] Type checking passed.
% 2.29/1.37 % [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 ...
% 28.86/7.00 % External prover 'e' found a proof!
% 28.86/7.00 % [INFO] Killing All external provers ...
% 28.86/7.00 % Time passed: 6472ms (effective reasoning time: 5980ms)
% 28.86/7.00 % 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)>
% 28.86/7.01 % Axioms used in derivation (0):
% 28.86/7.01 % No. of inferences in proof: 81
% 28.86/7.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6472 ms resp. 5980 ms w/o parsing
% 28.86/7.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.86/7.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------