TSTP Solution File: SYN052^7 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SYN052^7 : TPTP v8.2.0. Released v5.5.0.
% 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 19:45:54 EDT 2024
% Result : Theorem 84.04s 20.06s
% Output : Refutation 84.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 12
% Syntax : Number of formulae : 170 ( 15 unt; 0 typ; 7 def)
% Number of atoms : 1333 ( 276 equ; 0 cnn)
% Maximal formula atoms : 35 ( 7 avg)
% Number of connectives : 3901 ( 923 ~; 969 |; 4 &;1997 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 12 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 13 con; 0-3 aty)
% Number of variables : 573 ( 15 ^ 556 !; 2 ?; 573 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mand_def,definition,
( mand
= ( ^ [A: $i > $o,B: $i > $o] : ( mnot @ ( mor @ ( mnot @ A ) @ ( mnot @ B ) ) ) ) ) ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(exists_in_world_type,type,
exists_in_world: mu > $i > $o ).
thf(mforall_ind_type,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(mforall_ind_def,definition,
( mforall_ind
= ( ^ [A: mu > $i > $o,B: $i] :
! [C: mu] :
( ( exists_in_world @ C @ B )
=> ( A @ C @ B ) ) ) ) ).
thf(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(mreflexive_def,definition,
( mreflexive
= ( ^ [A: $i > $i > $o] :
! [B: $i] : ( A @ B @ B ) ) ) ).
thf(mtransitive_type,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(mtransitive_def,definition,
( mtransitive
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(rel_s4_type,type,
rel_s4: $i > $i > $o ).
thf(mbox_s4_type,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(mbox_s4_def,definition,
( mbox_s4
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( A @ C ) ) ) ) ).
thf(p_type,type,
p: $i > $o ).
thf(big_f_type,type,
big_f: mu > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > mu > $i > $i ).
thf(sk4_type,type,
sk4: $i > mu > $i > $i ).
thf(sk5_type,type,
sk5: $o ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: mu ).
thf(sk9_type,type,
sk9: $i ).
thf(sk10_type,type,
sk10: $i ).
thf(sk11_type,type,
sk11: $i ).
thf(sk12_type,type,
sk12: $i > mu ).
thf(3,axiom,
! [A: $i] :
? [B: mu] : ( exists_in_world @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_ax) ).
thf(27,plain,
! [A: $i] :
? [B: mu] : ( exists_in_world @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,plain,
! [A: $i] : ( exists_in_world @ ( sk12 @ A ) @ A ),
inference(cnf,[status(esa)],[27]) ).
thf(1,conjecture,
( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_f @ A ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_f @ A ) ) @ ( mbox_s4 @ p ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ p )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mbox_s4 @ ( big_f @ A ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mbox_s4 @ ( big_f @ A ) ) ) )
@ ( mbox_s4 @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel22) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_f @ A ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_f @ A ) ) @ ( mbox_s4 @ p ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ p )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mbox_s4 @ ( big_f @ A ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mbox_s4 @ ( big_f @ A ) ) ) )
@ ( mbox_s4 @ p ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: $i,B: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ! [D: mu] :
( ( exists_in_world @ D @ C )
=> ~ ( ~ ! [E: $i] :
( ~ ( rel_s4 @ C @ E )
| ~ ! [F: $i] :
( ~ ( rel_s4 @ E @ F )
| ( p @ F ) )
| ! [F: $i] :
( ~ ( rel_s4 @ E @ F )
| ( big_f @ D @ F ) ) )
| ~ ! [E: $i] :
( ~ ( rel_s4 @ C @ E )
| ~ ! [F: $i] :
( ~ ( rel_s4 @ E @ F )
| ( big_f @ D @ F ) )
| ! [F: $i] :
( ~ ( rel_s4 @ E @ F )
| ( p @ F ) ) ) ) ) )
| ~ ( ~ ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ~ ! [D: $i] :
( ~ ( rel_s4 @ C @ D )
| ( p @ D ) )
| ! [D: $i] :
( ~ ( rel_s4 @ C @ D )
| ! [E: mu] :
( ( exists_in_world @ E @ D )
=> ! [F: $i] :
( ~ ( rel_s4 @ D @ F )
| ( big_f @ E @ F ) ) ) ) )
| ~ ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ~ ! [D: $i] :
( ~ ( rel_s4 @ C @ D )
| ! [E: mu] :
( ( exists_in_world @ E @ D )
=> ! [F: $i] :
( ~ ( rel_s4 @ D @ F )
| ( big_f @ E @ F ) ) ) )
| ! [D: $i] :
( ~ ( rel_s4 @ C @ D )
| ( p @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
rel_s4 @ sk1 @ sk2,
inference(cnf,[status(esa)],[7]) ).
thf(6,axiom,
! [A: mu,B: $i,C: $i] :
( ( ( exists_in_world @ A @ B )
& ( rel_s4 @ B @ C ) )
=> ( exists_in_world @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cumulative_ax) ).
thf(33,plain,
! [A: mu,B: $i,C: $i] :
( ( ( exists_in_world @ A @ B )
& ( rel_s4 @ B @ C ) )
=> ( exists_in_world @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(34,plain,
! [C: $i,B: $i,A: mu] :
( ~ ( exists_in_world @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ( exists_in_world @ A @ C ) ),
inference(cnf,[status(esa)],[33]) ).
thf(4178,plain,
! [C: $i,B: $i,A: mu] :
( ~ ( exists_in_world @ A @ B )
| ( exists_in_world @ A @ C )
| ( ( rel_s4 @ sk1 @ sk2 )
!= ( rel_s4 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16,34]) ).
thf(4179,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk1 )
| ( exists_in_world @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[4178:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).
thf(4289,plain,
! [B: mu,A: $i] :
( ( exists_in_world @ B @ sk2 )
| ( ( exists_in_world @ ( sk12 @ A ) @ A )
!= ( exists_in_world @ B @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[28,4179]) ).
thf(4290,plain,
exists_in_world @ ( sk12 @ sk1 ) @ sk2,
inference(pattern_uni,[status(thm)],[4289:[bind(A,$thf( sk1 )),bind(B,$thf( sk12 @ sk1 ))]]) ).
thf(5,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rel_s4 @ A @ B )
& ( rel_s4 @ B @ C ) )
=> ( rel_s4 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ( rel_s4 @ A @ C ) ),
inference(cnf,[status(esa)],[31]) ).
thf(19,plain,
( ~ sk5
| ( rel_s4 @ sk10 @ sk11 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(12,plain,
! [D: $i,C: $i,B: mu,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ~ ( p @ ( sk3 @ C @ B @ A ) )
| ~ ( rel_s4 @ C @ D )
| ( big_f @ B @ D ) ),
inference(cnf,[status(esa)],[7]) ).
thf(37,plain,
! [D: $i,C: $i,B: mu,A: $i] :
( ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ~ ( p @ ( sk3 @ C @ B @ A ) )
| ~ ( rel_s4 @ C @ D )
| ( big_f @ B @ D )
| ( ( rel_s4 @ sk2 @ A )
!= ( rel_s4 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[16,12]) ).
thf(51,plain,
! [D: $i,C: $i,B: mu,A: $i] :
( ( big_f @ B @ D )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ~ ( p @ ( sk3 @ C @ B @ A ) )
| ~ ( rel_s4 @ C @ D )
| ( sk2 != sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[37]) ).
thf(55,plain,
! [C: $i,B: $i,A: mu] :
( ( big_f @ A @ C )
| ~ ( exists_in_world @ A @ sk2 )
| ~ ( rel_s4 @ sk2 @ B )
| ~ ( p @ ( sk3 @ B @ A @ sk2 ) )
| ~ ( rel_s4 @ B @ C )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[51]) ).
thf(128,plain,
! [C: $i,B: $i,A: mu] :
( ~ sk5
| ( big_f @ A @ C )
| ~ ( exists_in_world @ A @ sk2 )
| ~ ( p @ ( sk3 @ B @ A @ sk2 ) )
| ~ ( rel_s4 @ B @ C )
| ( sk2 != sk1 )
| ( ( rel_s4 @ sk10 @ sk11 )
!= ( rel_s4 @ sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19,55]) ).
thf(131,plain,
! [C: $i,B: $i,A: mu] :
( ( big_f @ A @ C )
| ~ sk5
| ~ ( exists_in_world @ A @ sk2 )
| ~ ( p @ ( sk3 @ B @ A @ sk2 ) )
| ~ ( rel_s4 @ B @ C )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ( sk11 != B ) ),
inference(simp,[status(thm)],[128]) ).
thf(133,plain,
! [B: $i,A: mu] :
( ( big_f @ A @ B )
| ~ sk5
| ~ ( exists_in_world @ A @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ A @ sk2 ) )
| ~ ( rel_s4 @ sk11 @ B )
| ( sk2 != sk1 )
| ( sk10 != sk2 ) ),
inference(simp,[status(thm)],[131]) ).
thf(343,plain,
! [E: $i,D: mu,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ( big_f @ D @ E )
| ~ sk5
| ~ ( exists_in_world @ D @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ D @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ( ( rel_s4 @ A @ C )
!= ( rel_s4 @ sk11 @ E ) ) ),
inference(paramod_ordered,[status(thm)],[32,133]) ).
thf(344,plain,
! [C: mu,B: $i,A: $i] :
( ~ ( rel_s4 @ sk11 @ A )
| ~ ( rel_s4 @ A @ B )
| ( big_f @ C @ B )
| ~ sk5
| ~ ( exists_in_world @ C @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ C @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 ) ),
inference(pattern_uni,[status(thm)],[343:[bind(A,$thf( sk11 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( C ))]]) ).
thf(392,plain,
! [C: mu,B: $i,A: $i] :
( ~ ( rel_s4 @ sk11 @ A )
| ~ ( rel_s4 @ A @ B )
| ( big_f @ C @ B )
| ~ sk5
| ~ ( exists_in_world @ C @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ C @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 ) ),
inference(simp,[status(thm)],[344]) ).
thf(489,plain,
! [F: mu,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ D @ E )
| ( big_f @ F @ E )
| ~ sk5
| ~ ( exists_in_world @ F @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ F @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ( ( rel_s4 @ A @ C )
!= ( rel_s4 @ sk11 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[32,392]) ).
thf(490,plain,
! [D: mu,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk11 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ( big_f @ D @ C )
| ~ sk5
| ~ ( exists_in_world @ D @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ D @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 ) ),
inference(pattern_uni,[status(thm)],[489:[bind(A,$thf( sk11 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(511,plain,
! [D: mu,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk11 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ( big_f @ D @ C )
| ~ sk5
| ~ ( exists_in_world @ D @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ D @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 ) ),
inference(simp,[status(thm)],[490]) ).
thf(10,plain,
( ( exists_in_world @ sk8 @ sk7 )
| sk5 ),
inference(cnf,[status(esa)],[7]) ).
thf(14,plain,
( ( rel_s4 @ sk6 @ sk7 )
| sk5 ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
( ( rel_s4 @ sk7 @ sk9 )
| sk5 ),
inference(cnf,[status(esa)],[7]) ).
thf(355,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ B @ C )
| ( rel_s4 @ A @ C )
| ( ( rel_s4 @ sk1 @ sk2 )
!= ( rel_s4 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,32]) ).
thf(356,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ( rel_s4 @ sk1 @ A ) ),
inference(pattern_uni,[status(thm)],[355:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(396,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ( rel_s4 @ sk1 @ A ) ),
inference(simp,[status(thm)],[356]) ).
thf(777,plain,
! [A: $i] :
( sk5
| ( rel_s4 @ sk1 @ A )
| ( ( rel_s4 @ sk7 @ sk9 )
!= ( rel_s4 @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,396]) ).
thf(785,plain,
! [A: $i] :
( sk5
| ( rel_s4 @ sk1 @ A )
| ( sk7 != sk2 )
| ( sk9 != A ) ),
inference(simp,[status(thm)],[777]) ).
thf(789,plain,
( sk5
| ( rel_s4 @ sk1 @ sk9 )
| ( sk7 != sk2 ) ),
inference(simp,[status(thm)],[785]) ).
thf(357,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ( rel_s4 @ A @ C )
| ( ( rel_s4 @ sk1 @ sk2 )
!= ( rel_s4 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16,32]) ).
thf(358,plain,
! [A: $i] :
( ~ ( rel_s4 @ A @ sk1 )
| ( rel_s4 @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).
thf(437,plain,
! [A: $i] :
( ~ sk5
| ( rel_s4 @ A @ sk2 )
| ( ( rel_s4 @ sk10 @ sk11 )
!= ( rel_s4 @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[19,358]) ).
thf(441,plain,
! [A: $i] :
( ( rel_s4 @ A @ sk2 )
| ~ sk5
| ( sk10 != A )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[437]) ).
thf(455,plain,
( ( rel_s4 @ sk10 @ sk2 )
| ~ sk5
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[441]) ).
thf(18,plain,
! [D: $i,C: $i,B: mu,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ~ ( big_f @ B @ ( sk4 @ C @ B @ A ) )
| ~ ( rel_s4 @ C @ D )
| ( p @ D ) ),
inference(cnf,[status(esa)],[7]) ).
thf(23,plain,
! [D: $i,C: $i,B: mu,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ~ ( big_f @ B @ ( sk4 @ C @ B @ A ) )
| ~ ( rel_s4 @ C @ D )
| ( p @ D ) ),
inference(simp,[status(thm)],[18]) ).
thf(655,plain,
! [H: $i,G: $i,F: mu,E: $i,D: mu,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk11 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ sk5
| ~ ( exists_in_world @ D @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ D @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( rel_s4 @ sk2 @ E )
| ~ ( exists_in_world @ F @ E )
| ~ ( rel_s4 @ E @ G )
| ~ ( rel_s4 @ G @ H )
| ( p @ H )
| ( ( big_f @ D @ C )
!= ( big_f @ F @ ( sk4 @ G @ F @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[511,23]) ).
thf(656,plain,
! [F: $i,E: mu,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk11 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ ( sk4 @ D @ E @ F ) )
| ~ sk5
| ~ ( exists_in_world @ E @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ E @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( rel_s4 @ sk2 @ F )
| ~ ( exists_in_world @ E @ F )
| ~ ( rel_s4 @ F @ D )
| ~ ( rel_s4 @ D @ C )
| ( p @ C ) ),
inference(pattern_uni,[status(thm)],[655:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 @ I @ J @ K )),bind(D,$thf( J )),bind(E,$thf( K )),bind(F,$thf( J )),bind(G,$thf( I ))]]) ).
thf(743,plain,
! [F: $i,E: mu,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk11 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ ( sk4 @ D @ E @ F ) )
| ~ sk5
| ~ ( exists_in_world @ E @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ E @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( rel_s4 @ sk2 @ F )
| ~ ( exists_in_world @ E @ F )
| ~ ( rel_s4 @ F @ D )
| ~ ( rel_s4 @ D @ C )
| ( p @ C ) ),
inference(simp,[status(thm)],[656]) ).
thf(959,plain,
! [G: $i,F: mu,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ sk1 )
| ~ ( rel_s4 @ sk11 @ B )
| ~ ( rel_s4 @ B @ C )
| ~ sk5
| ~ ( exists_in_world @ F @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ F @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( rel_s4 @ sk2 @ G )
| ~ ( exists_in_world @ F @ G )
| ~ ( rel_s4 @ G @ E )
| ~ ( rel_s4 @ E @ D )
| ( p @ D )
| ( ( rel_s4 @ A @ sk2 )
!= ( rel_s4 @ C @ ( sk4 @ E @ F @ G ) ) ) ),
inference(paramod_ordered,[status(thm)],[358,743]) ).
thf(1073,plain,
! [G: $i,F: mu,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( p @ D )
| ~ ( rel_s4 @ A @ sk1 )
| ~ ( rel_s4 @ sk11 @ B )
| ~ ( rel_s4 @ B @ C )
| ~ sk5
| ~ ( exists_in_world @ F @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ F @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( rel_s4 @ sk2 @ G )
| ~ ( exists_in_world @ F @ G )
| ~ ( rel_s4 @ G @ E )
| ~ ( rel_s4 @ E @ D )
| ( A != C )
| ( ( sk4 @ E @ F @ G )
!= sk2 ) ),
inference(simp,[status(thm)],[959]) ).
thf(1114,plain,
! [F: $i,E: mu,D: $i,C: $i,B: $i,A: $i] :
( ( p @ C )
| ~ ( rel_s4 @ B @ sk1 )
| ~ ( rel_s4 @ sk11 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ sk5
| ~ ( exists_in_world @ E @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ E @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( rel_s4 @ sk2 @ F )
| ~ ( exists_in_world @ E @ F )
| ~ ( rel_s4 @ F @ D )
| ~ ( rel_s4 @ D @ C )
| ( ( sk4 @ D @ E @ F )
!= sk2 ) ),
inference(simp,[status(thm)],[1073]) ).
thf(1415,plain,
! [F: $i,E: mu,D: $i,C: $i,B: $i,A: $i] :
( ~ sk5
| ( sk11 != sk1 )
| ( p @ C )
| ~ ( rel_s4 @ B @ sk1 )
| ~ ( rel_s4 @ A @ B )
| ~ ( exists_in_world @ E @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ E @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( rel_s4 @ sk2 @ F )
| ~ ( exists_in_world @ E @ F )
| ~ ( rel_s4 @ F @ D )
| ~ ( rel_s4 @ D @ C )
| ( ( sk4 @ D @ E @ F )
!= sk2 )
| ( ( rel_s4 @ sk11 @ A )
!= ( rel_s4 @ sk10 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[455,1114]) ).
thf(1448,plain,
! [F: $i,E: mu,D: $i,C: $i,B: $i,A: $i] :
( ( p @ C )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ B @ sk1 )
| ~ ( rel_s4 @ A @ B )
| ~ ( exists_in_world @ E @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ E @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( rel_s4 @ sk2 @ F )
| ~ ( exists_in_world @ E @ F )
| ~ ( rel_s4 @ F @ D )
| ~ ( rel_s4 @ D @ C )
| ( ( sk4 @ D @ E @ F )
!= sk2 )
| ( sk11 != sk10 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[1415]) ).
thf(1472,plain,
! [E: $i,D: mu,C: $i,B: $i,A: $i] :
( ( p @ B )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ A @ sk1 )
| ~ ( rel_s4 @ sk2 @ A )
| ~ ( exists_in_world @ D @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ D @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( rel_s4 @ sk2 @ E )
| ~ ( exists_in_world @ D @ E )
| ~ ( rel_s4 @ E @ C )
| ~ ( rel_s4 @ C @ B )
| ( ( sk4 @ C @ D @ E )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[1448]) ).
thf(1791,plain,
! [H: $i,G: mu,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ( p @ E )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ D @ sk1 )
| ~ ( rel_s4 @ sk2 @ D )
| ~ ( exists_in_world @ G @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ G @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ G @ H )
| ~ ( rel_s4 @ H @ F )
| ~ ( rel_s4 @ F @ E )
| ( ( sk4 @ F @ G @ H )
!= sk2 )
| ( sk11 != sk10 )
| ( ( rel_s4 @ A @ C )
!= ( rel_s4 @ sk2 @ H ) ) ),
inference(paramod_ordered,[status(thm)],[32,1472]) ).
thf(1792,plain,
! [F: mu,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ( p @ D )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ C @ sk1 )
| ~ ( rel_s4 @ sk2 @ C )
| ~ ( exists_in_world @ F @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ F @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ F @ B )
| ~ ( rel_s4 @ B @ E )
| ~ ( rel_s4 @ E @ D )
| ( ( sk4 @ E @ F @ B )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(pattern_uni,[status(thm)],[1791:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( C ))]]) ).
thf(1883,plain,
! [F: mu,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ( p @ D )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ C @ sk1 )
| ~ ( rel_s4 @ sk2 @ C )
| ~ ( exists_in_world @ F @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ F @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ F @ B )
| ~ ( rel_s4 @ B @ E )
| ~ ( rel_s4 @ E @ D )
| ( ( sk4 @ E @ F @ B )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[1792]) ).
thf(2022,plain,
! [I: mu,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ D @ E )
| ( p @ G )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ F @ sk1 )
| ~ ( rel_s4 @ sk2 @ F )
| ~ ( exists_in_world @ I @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ I @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ I @ E )
| ~ ( rel_s4 @ E @ H )
| ~ ( rel_s4 @ H @ G )
| ( ( sk4 @ H @ I @ E )
!= sk2 )
| ( sk11 != sk10 )
| ( ( rel_s4 @ A @ C )
!= ( rel_s4 @ sk2 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[32,1883]) ).
thf(2023,plain,
! [G: mu,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ( p @ E )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ D @ sk1 )
| ~ ( rel_s4 @ sk2 @ D )
| ~ ( exists_in_world @ G @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ G @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ G @ C )
| ~ ( rel_s4 @ C @ F )
| ~ ( rel_s4 @ F @ E )
| ( ( sk4 @ F @ G @ C )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(pattern_uni,[status(thm)],[2022:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(2204,plain,
! [G: mu,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ( p @ E )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ D @ sk1 )
| ~ ( rel_s4 @ sk2 @ D )
| ~ ( exists_in_world @ G @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ G @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ G @ C )
| ~ ( rel_s4 @ C @ F )
| ~ ( rel_s4 @ F @ E )
| ( ( sk4 @ F @ G @ C )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[2023]) ).
thf(2981,plain,
! [J: mu,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ( p @ H )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ G @ sk1 )
| ~ ( rel_s4 @ sk2 @ G )
| ~ ( exists_in_world @ J @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ J @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ J @ F )
| ~ ( rel_s4 @ F @ I )
| ~ ( rel_s4 @ I @ H )
| ( ( sk4 @ I @ J @ F )
!= sk2 )
| ( sk11 != sk10 )
| ( ( rel_s4 @ A @ C )
!= ( rel_s4 @ sk2 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[32,2204]) ).
thf(2982,plain,
! [H: mu,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ C @ D )
| ( p @ F )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ E @ sk1 )
| ~ ( rel_s4 @ sk2 @ E )
| ~ ( exists_in_world @ H @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ H @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ H @ D )
| ~ ( rel_s4 @ D @ G )
| ~ ( rel_s4 @ G @ F )
| ( ( sk4 @ G @ H @ D )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(pattern_uni,[status(thm)],[2981:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(3213,plain,
! [H: mu,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ C @ D )
| ( p @ F )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ E @ sk1 )
| ~ ( rel_s4 @ sk2 @ E )
| ~ ( exists_in_world @ H @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ H @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ H @ D )
| ~ ( rel_s4 @ D @ G )
| ~ ( rel_s4 @ G @ F )
| ( ( sk4 @ G @ H @ D )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[2982]) ).
thf(3402,plain,
! [K: mu,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ~ ( rel_s4 @ F @ G )
| ( p @ I )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ H @ sk1 )
| ~ ( rel_s4 @ sk2 @ H )
| ~ ( exists_in_world @ K @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ K @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ K @ G )
| ~ ( rel_s4 @ G @ J )
| ~ ( rel_s4 @ J @ I )
| ( ( sk4 @ J @ K @ G )
!= sk2 )
| ( sk11 != sk10 )
| ( ( rel_s4 @ A @ C )
!= ( rel_s4 @ sk2 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[32,3213]) ).
thf(3403,plain,
! [I: mu,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ C @ D )
| ~ ( rel_s4 @ D @ E )
| ( p @ G )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ F @ sk1 )
| ~ ( rel_s4 @ sk2 @ F )
| ~ ( exists_in_world @ I @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ I @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ I @ E )
| ~ ( rel_s4 @ E @ H )
| ~ ( rel_s4 @ H @ G )
| ( ( sk4 @ H @ I @ E )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(pattern_uni,[status(thm)],[3402:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(3619,plain,
! [I: mu,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ C @ D )
| ~ ( rel_s4 @ D @ E )
| ( p @ G )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ F @ sk1 )
| ~ ( rel_s4 @ sk2 @ F )
| ~ ( exists_in_world @ I @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ I @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ I @ E )
| ~ ( rel_s4 @ E @ H )
| ~ ( rel_s4 @ H @ G )
| ( ( sk4 @ H @ I @ E )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[3403]) ).
thf(4639,plain,
! [L: mu,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ~ ( rel_s4 @ F @ G )
| ~ ( rel_s4 @ G @ H )
| ( p @ J )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ I @ sk1 )
| ~ ( rel_s4 @ sk2 @ I )
| ~ ( exists_in_world @ L @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ L @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ L @ H )
| ~ ( rel_s4 @ H @ K )
| ~ ( rel_s4 @ K @ J )
| ( ( sk4 @ K @ L @ H )
!= sk2 )
| ( sk11 != sk10 )
| ( ( rel_s4 @ A @ C )
!= ( rel_s4 @ sk2 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[32,3619]) ).
thf(4640,plain,
! [J: mu,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ C @ D )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ( p @ H )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ G @ sk1 )
| ~ ( rel_s4 @ sk2 @ G )
| ~ ( exists_in_world @ J @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ J @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ J @ F )
| ~ ( rel_s4 @ F @ I )
| ~ ( rel_s4 @ I @ H )
| ( ( sk4 @ I @ J @ F )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(pattern_uni,[status(thm)],[4639:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(4957,plain,
! [J: mu,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ C @ D )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ( p @ H )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ G @ sk1 )
| ~ ( rel_s4 @ sk2 @ G )
| ~ ( exists_in_world @ J @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ J @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ J @ F )
| ~ ( rel_s4 @ F @ I )
| ~ ( rel_s4 @ I @ H )
| ( ( sk4 @ I @ J @ F )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[4640]) ).
thf(5251,plain,
! [M: mu,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ~ ( rel_s4 @ F @ G )
| ~ ( rel_s4 @ G @ H )
| ~ ( rel_s4 @ H @ I )
| ( p @ K )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ J @ sk1 )
| ~ ( rel_s4 @ sk2 @ J )
| ~ ( exists_in_world @ M @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ M @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ M @ I )
| ~ ( rel_s4 @ I @ L )
| ~ ( rel_s4 @ L @ K )
| ( ( sk4 @ L @ M @ I )
!= sk2 )
| ( sk11 != sk10 )
| ( ( rel_s4 @ A @ C )
!= ( rel_s4 @ sk2 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[32,4957]) ).
thf(5252,plain,
! [K: mu,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ C @ D )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ~ ( rel_s4 @ F @ G )
| ( p @ I )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ H @ sk1 )
| ~ ( rel_s4 @ sk2 @ H )
| ~ ( exists_in_world @ K @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ K @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ K @ G )
| ~ ( rel_s4 @ G @ J )
| ~ ( rel_s4 @ J @ I )
| ( ( sk4 @ J @ K @ G )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(pattern_uni,[status(thm)],[5251:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(5630,plain,
! [K: mu,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ C @ D )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ~ ( rel_s4 @ F @ G )
| ( p @ I )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ H @ sk1 )
| ~ ( rel_s4 @ sk2 @ H )
| ~ ( exists_in_world @ K @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ K @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ K @ G )
| ~ ( rel_s4 @ G @ J )
| ~ ( rel_s4 @ J @ I )
| ( ( sk4 @ J @ K @ G )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[5252]) ).
thf(6300,plain,
! [N: mu,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ~ ( rel_s4 @ F @ G )
| ~ ( rel_s4 @ G @ H )
| ~ ( rel_s4 @ H @ I )
| ~ ( rel_s4 @ I @ J )
| ( p @ L )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ K @ sk1 )
| ~ ( rel_s4 @ sk2 @ K )
| ~ ( exists_in_world @ N @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ N @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ N @ J )
| ~ ( rel_s4 @ J @ M )
| ~ ( rel_s4 @ M @ L )
| ( ( sk4 @ M @ N @ J )
!= sk2 )
| ( sk11 != sk10 )
| ( ( rel_s4 @ A @ C )
!= ( rel_s4 @ sk2 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[32,5630]) ).
thf(6301,plain,
! [L: mu,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ C @ D )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ~ ( rel_s4 @ F @ G )
| ~ ( rel_s4 @ G @ H )
| ( p @ J )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ I @ sk1 )
| ~ ( rel_s4 @ sk2 @ I )
| ~ ( exists_in_world @ L @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ L @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ L @ H )
| ~ ( rel_s4 @ H @ K )
| ~ ( rel_s4 @ K @ J )
| ( ( sk4 @ K @ L @ H )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(pattern_uni,[status(thm)],[6300:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(6747,plain,
! [L: mu,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ C @ D )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ~ ( rel_s4 @ F @ G )
| ~ ( rel_s4 @ G @ H )
| ( p @ J )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ I @ sk1 )
| ~ ( rel_s4 @ sk2 @ I )
| ~ ( exists_in_world @ L @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ L @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ L @ H )
| ~ ( rel_s4 @ H @ K )
| ~ ( rel_s4 @ K @ J )
| ( ( sk4 @ K @ L @ H )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[6301]) ).
thf(4186,plain,
! [D: $i,C: $i,B: mu,A: $i] :
( ~ ( rel_s4 @ C @ D )
| ( exists_in_world @ B @ D )
| ( ( exists_in_world @ ( sk12 @ A ) @ A )
!= ( exists_in_world @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,34]) ).
thf(4187,plain,
! [B: $i,A: $i] :
( ~ ( rel_s4 @ B @ A )
| ( exists_in_world @ ( sk12 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[4186:[bind(A,$thf( E )),bind(B,$thf( sk12 @ E )),bind(C,$thf( E ))]]) ).
thf(4266,plain,
! [B: $i,A: $i] :
( ~ ( rel_s4 @ B @ A )
| ( exists_in_world @ ( sk12 @ B ) @ A ) ),
inference(simp,[status(thm)],[4187]) ).
thf(7863,plain,
! [B: $i,A: $i] :
( sk5
| ( exists_in_world @ ( sk12 @ B ) @ A )
| ( ( rel_s4 @ sk6 @ sk7 )
!= ( rel_s4 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14,4266]) ).
thf(7864,plain,
( sk5
| ( exists_in_world @ ( sk12 @ sk6 ) @ sk7 ) ),
inference(pattern_uni,[status(thm)],[7863:[bind(A,$thf( sk7 )),bind(B,$thf( sk6 ))]]) ).
thf(7087,plain,
! [O: mu,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ~ ( rel_s4 @ F @ G )
| ~ ( rel_s4 @ G @ H )
| ~ ( rel_s4 @ H @ I )
| ~ ( rel_s4 @ I @ J )
| ~ ( rel_s4 @ J @ K )
| ( p @ M )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ L @ sk1 )
| ~ ( rel_s4 @ sk2 @ L )
| ~ ( exists_in_world @ O @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ O @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ O @ K )
| ~ ( rel_s4 @ K @ N )
| ~ ( rel_s4 @ N @ M )
| ( ( sk4 @ N @ O @ K )
!= sk2 )
| ( sk11 != sk10 )
| ( ( rel_s4 @ A @ C )
!= ( rel_s4 @ sk2 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[32,6747]) ).
thf(7088,plain,
! [M: mu,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ C @ D )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ~ ( rel_s4 @ F @ G )
| ~ ( rel_s4 @ G @ H )
| ~ ( rel_s4 @ H @ I )
| ( p @ K )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ J @ sk1 )
| ~ ( rel_s4 @ sk2 @ J )
| ~ ( exists_in_world @ M @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ M @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ M @ I )
| ~ ( rel_s4 @ I @ L )
| ~ ( rel_s4 @ L @ K )
| ( ( sk4 @ L @ M @ I )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(pattern_uni,[status(thm)],[7087:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(7680,plain,
! [M: mu,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ C @ D )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ~ ( rel_s4 @ F @ G )
| ~ ( rel_s4 @ G @ H )
| ~ ( rel_s4 @ H @ I )
| ( p @ K )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ J @ sk1 )
| ~ ( rel_s4 @ sk2 @ J )
| ~ ( exists_in_world @ M @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ M @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ M @ I )
| ~ ( rel_s4 @ I @ L )
| ~ ( rel_s4 @ L @ K )
| ( ( sk4 @ L @ M @ I )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[7088]) ).
thf(11,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk6 @ A )
| ( p @ A )
| sk5 ),
inference(cnf,[status(esa)],[7]) ).
thf(24,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk6 @ A )
| ( p @ A )
| sk5 ),
inference(simp,[status(thm)],[11]) ).
thf(8,plain,
! [C: $i,B: mu,A: $i] :
( ~ sk5
| ~ ( rel_s4 @ sk10 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ( big_f @ B @ C ) ),
inference(cnf,[status(esa)],[7]) ).
thf(25,plain,
! [C: $i,B: mu,A: $i] :
( ~ sk5
| ~ ( rel_s4 @ sk10 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ( big_f @ B @ C ) ),
inference(simp,[status(thm)],[8]) ).
thf(20,plain,
! [D: $i,C: $i,B: mu,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ( rel_s4 @ C @ ( sk3 @ C @ B @ A ) )
| ~ ( rel_s4 @ C @ D )
| ( big_f @ B @ D ) ),
inference(cnf,[status(esa)],[7]) ).
thf(4,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(29,plain,
! [A: $i] : ( rel_s4 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,plain,
( ~ ( big_f @ sk8 @ sk9 )
| sk5 ),
inference(cnf,[status(esa)],[7]) ).
thf(22,plain,
( ( rel_s4 @ sk2 @ sk6 )
| sk5 ),
inference(cnf,[status(esa)],[7]) ).
thf(331,plain,
! [C: $i,B: $i,A: $i] :
( sk5
| ~ ( rel_s4 @ A @ B )
| ( rel_s4 @ A @ C )
| ( ( rel_s4 @ sk6 @ sk7 )
!= ( rel_s4 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[14,32]) ).
thf(332,plain,
! [A: $i] :
( sk5
| ~ ( rel_s4 @ A @ sk6 )
| ( rel_s4 @ A @ sk7 ) ),
inference(pattern_uni,[status(thm)],[331:[bind(A,$thf( A )),bind(B,$thf( sk6 )),bind(C,$thf( sk7 ))]]) ).
thf(3804,plain,
! [A: $i] :
( sk5
| ( rel_s4 @ A @ sk7 )
| ( ( rel_s4 @ sk2 @ sk6 )
!= ( rel_s4 @ A @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[22,332]) ).
thf(3805,plain,
( sk5
| ( rel_s4 @ sk2 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[3804:[bind(A,$thf( sk2 ))]]) ).
thf(7901,plain,
! [B: $i,A: $i] :
( sk5
| ( exists_in_world @ ( sk12 @ B ) @ A )
| ( ( rel_s4 @ sk2 @ sk7 )
!= ( rel_s4 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3805,4266]) ).
thf(7902,plain,
( sk5
| ( exists_in_world @ ( sk12 @ sk2 ) @ sk7 ) ),
inference(pattern_uni,[status(thm)],[7901:[bind(A,$thf( sk7 )),bind(B,$thf( sk2 ))]]) ).
thf(427,plain,
! [A: $i] :
( sk5
| ( rel_s4 @ A @ sk2 )
| ( ( rel_s4 @ sk7 @ sk9 )
!= ( rel_s4 @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[9,358]) ).
thf(442,plain,
! [A: $i] :
( sk5
| ( rel_s4 @ A @ sk2 )
| ( sk7 != A )
| ( sk9 != sk1 ) ),
inference(simp,[status(thm)],[427]) ).
thf(456,plain,
( sk5
| ( rel_s4 @ sk7 @ sk2 )
| ( sk9 != sk1 ) ),
inference(simp,[status(thm)],[442]) ).
thf(155,plain,
! [A: $i] :
( sk5
| ( p @ A )
| ( ( rel_s4 @ sk6 @ sk7 )
!= ( rel_s4 @ sk6 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14,24]) ).
thf(156,plain,
( sk5
| ( p @ sk7 ) ),
inference(pattern_uni,[status(thm)],[155:[bind(A,$thf( sk7 ))]]) ).
thf(17,plain,
( ~ sk5
| ( rel_s4 @ sk2 @ sk10 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(173,plain,
! [B: $i,A: mu] :
( ~ sk5
| ( big_f @ A @ B )
| ~ ( exists_in_world @ A @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ A @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ( ( rel_s4 @ sk11 @ B )
!= ( rel_s4 @ sk2 @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[17,133]) ).
thf(183,plain,
! [B: $i,A: mu] :
( ( big_f @ A @ B )
| ~ sk5
| ~ ( exists_in_world @ A @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ A @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ( sk11 != sk2 )
| ( B != sk10 ) ),
inference(simp,[status(thm)],[173]) ).
thf(188,plain,
! [A: mu] :
( ( big_f @ A @ sk10 )
| ~ sk5
| ~ ( exists_in_world @ A @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ A @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ( sk11 != sk2 ) ),
inference(simp,[status(thm)],[183]) ).
thf(402,plain,
! [B: $i,A: $i] :
( ~ ( rel_s4 @ A @ sk1 )
| ( p @ B )
| sk5
| ( ( rel_s4 @ A @ sk2 )
!= ( rel_s4 @ sk6 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[358,24]) ).
thf(403,plain,
( ~ ( rel_s4 @ sk6 @ sk1 )
| ( p @ sk2 )
| sk5 ),
inference(pattern_uni,[status(thm)],[402:[bind(A,$thf( sk6 )),bind(B,$thf( sk2 ))]]) ).
thf(7897,plain,
! [B: $i,A: $i] :
( ~ sk5
| ( exists_in_world @ ( sk12 @ B ) @ A )
| ( ( rel_s4 @ sk10 @ sk11 )
!= ( rel_s4 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19,4266]) ).
thf(7898,plain,
( ~ sk5
| ( exists_in_world @ ( sk12 @ sk10 ) @ sk11 ) ),
inference(pattern_uni,[status(thm)],[7897:[bind(A,$thf( sk11 )),bind(B,$thf( sk10 ))]]) ).
thf(4370,plain,
! [C: $i,B: $i,A: mu] :
( ~ ( rel_s4 @ B @ C )
| ( exists_in_world @ A @ C )
| ( ( exists_in_world @ ( sk12 @ sk1 ) @ sk2 )
!= ( exists_in_world @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4290,34]) ).
thf(4371,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ( exists_in_world @ ( sk12 @ sk1 ) @ A ) ),
inference(pattern_uni,[status(thm)],[4370:[bind(A,$thf( sk12 @ sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( C ))]]) ).
thf(4398,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ( exists_in_world @ ( sk12 @ sk1 ) @ A ) ),
inference(simp,[status(thm)],[4371]) ).
thf(4424,plain,
! [A: $i] :
( sk5
| ( exists_in_world @ ( sk12 @ sk1 ) @ A )
| ( ( rel_s4 @ sk2 @ sk6 )
!= ( rel_s4 @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[22,4398]) ).
thf(4425,plain,
( sk5
| ( exists_in_world @ ( sk12 @ sk1 ) @ sk6 ) ),
inference(pattern_uni,[status(thm)],[4424:[bind(A,$thf( sk6 ))]]) ).
thf(4420,plain,
! [A: $i] :
( ~ sk5
| ( exists_in_world @ ( sk12 @ sk1 ) @ A )
| ( ( rel_s4 @ sk2 @ sk10 )
!= ( rel_s4 @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17,4398]) ).
thf(4421,plain,
( ~ sk5
| ( exists_in_world @ ( sk12 @ sk1 ) @ sk10 ) ),
inference(pattern_uni,[status(thm)],[4420:[bind(A,$thf( sk10 ))]]) ).
thf(622,plain,
( sk5
| ( p @ sk2 )
| ( ( rel_s4 @ sk6 @ sk7 )
!= ( rel_s4 @ sk6 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[14,403]) ).
thf(635,plain,
( sk5
| ( p @ sk2 )
| ( sk6 != sk6 )
| ( sk7 != sk1 ) ),
inference(simp,[status(thm)],[622]) ).
thf(642,plain,
( sk5
| ( p @ sk2 )
| ( sk7 != sk1 ) ),
inference(simp,[status(thm)],[635]) ).
thf(404,plain,
! [A: $i] :
( sk5
| ( rel_s4 @ A @ sk2 )
| ( ( rel_s4 @ sk6 @ sk7 )
!= ( rel_s4 @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[14,358]) ).
thf(443,plain,
! [A: $i] :
( sk5
| ( rel_s4 @ A @ sk2 )
| ( sk6 != A )
| ( sk7 != sk1 ) ),
inference(simp,[status(thm)],[404]) ).
thf(457,plain,
( sk5
| ( rel_s4 @ sk6 @ sk2 )
| ( sk7 != sk1 ) ),
inference(simp,[status(thm)],[443]) ).
thf(13,plain,
( ~ sk5
| ~ ( p @ sk11 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(40,plain,
! [D: $i,C: $i,B: mu,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ~ ( p @ ( sk3 @ C @ B @ A ) )
| ( big_f @ B @ D )
| ( ( rel_s4 @ sk1 @ sk2 )
!= ( rel_s4 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[16,12]) ).
thf(41,plain,
! [B: mu,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ sk1 )
| ~ ( p @ ( sk3 @ sk1 @ B @ A ) )
| ( big_f @ B @ sk2 ) ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind(D,$thf( sk2 ))]]) ).
thf(784,plain,
! [A: $i] :
( ~ sk5
| ( rel_s4 @ sk1 @ A )
| ( ( rel_s4 @ sk10 @ sk11 )
!= ( rel_s4 @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19,396]) ).
thf(787,plain,
! [A: $i] :
( ( rel_s4 @ sk1 @ A )
| ~ sk5
| ( sk10 != sk2 )
| ( sk11 != A ) ),
inference(simp,[status(thm)],[784]) ).
thf(792,plain,
( ( rel_s4 @ sk1 @ sk11 )
| ~ sk5
| ( sk10 != sk2 ) ),
inference(simp,[status(thm)],[787]) ).
thf(772,plain,
! [A: $i] :
( sk5
| ( rel_s4 @ sk1 @ A )
| ( ( rel_s4 @ sk2 @ sk6 )
!= ( rel_s4 @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[22,396]) ).
thf(773,plain,
( sk5
| ( rel_s4 @ sk1 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[772:[bind(A,$thf( sk6 ))]]) ).
thf(4437,plain,
! [A: $i] :
( sk5
| ( exists_in_world @ ( sk12 @ sk1 ) @ A )
| ( ( rel_s4 @ sk2 @ sk7 )
!= ( rel_s4 @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3805,4398]) ).
thf(4438,plain,
( sk5
| ( exists_in_world @ ( sk12 @ sk1 ) @ sk7 ) ),
inference(pattern_uni,[status(thm)],[4437:[bind(A,$thf( sk7 ))]]) ).
thf(3795,plain,
! [A: $i] :
( sk5
| ( rel_s4 @ A @ sk7 )
| ( ( rel_s4 @ sk1 @ sk6 )
!= ( rel_s4 @ A @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[773,332]) ).
thf(3796,plain,
( sk5
| ( rel_s4 @ sk1 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[3795:[bind(A,$thf( sk1 ))]]) ).
thf(8366,plain,
! [P: mu,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ~ ( rel_s4 @ F @ G )
| ~ ( rel_s4 @ G @ H )
| ~ ( rel_s4 @ H @ I )
| ~ ( rel_s4 @ I @ J )
| ~ ( rel_s4 @ J @ K )
| ~ ( rel_s4 @ K @ L )
| ( p @ N )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ M @ sk1 )
| ~ ( rel_s4 @ sk2 @ M )
| ~ ( exists_in_world @ P @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ P @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ P @ L )
| ~ ( rel_s4 @ L @ O )
| ~ ( rel_s4 @ O @ N )
| ( ( sk4 @ O @ P @ L )
!= sk2 )
| ( sk11 != sk10 )
| ( ( rel_s4 @ A @ C )
!= ( rel_s4 @ sk2 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[32,7680]) ).
thf(8367,plain,
! [N: mu,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ C @ D )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ~ ( rel_s4 @ F @ G )
| ~ ( rel_s4 @ G @ H )
| ~ ( rel_s4 @ H @ I )
| ~ ( rel_s4 @ I @ J )
| ( p @ L )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ K @ sk1 )
| ~ ( rel_s4 @ sk2 @ K )
| ~ ( exists_in_world @ N @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ N @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ N @ J )
| ~ ( rel_s4 @ J @ M )
| ~ ( rel_s4 @ M @ L )
| ( ( sk4 @ M @ N @ J )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(pattern_uni,[status(thm)],[8366:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(8986,plain,
! [N: mu,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ~ ( rel_s4 @ C @ D )
| ~ ( rel_s4 @ D @ E )
| ~ ( rel_s4 @ E @ F )
| ~ ( rel_s4 @ F @ G )
| ~ ( rel_s4 @ G @ H )
| ~ ( rel_s4 @ H @ I )
| ~ ( rel_s4 @ I @ J )
| ( p @ L )
| ~ sk5
| ( sk11 != sk1 )
| ~ ( rel_s4 @ K @ sk1 )
| ~ ( rel_s4 @ sk2 @ K )
| ~ ( exists_in_world @ N @ sk2 )
| ~ ( p @ ( sk3 @ sk11 @ N @ sk2 ) )
| ( sk2 != sk1 )
| ( sk10 != sk2 )
| ~ ( exists_in_world @ N @ J )
| ~ ( rel_s4 @ J @ M )
| ~ ( rel_s4 @ M @ L )
| ( ( sk4 @ M @ N @ J )
!= sk2 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[8367]) ).
thf(157,plain,
! [A: $i] :
( sk5
| ( p @ A )
| ( ( rel_s4 @ sk7 @ sk9 )
!= ( rel_s4 @ sk6 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,24]) ).
thf(164,plain,
! [A: $i] :
( sk5
| ( p @ A )
| ( sk7 != sk6 )
| ( sk9 != A ) ),
inference(simp,[status(thm)],[157]) ).
thf(167,plain,
( sk5
| ( p @ sk9 )
| ( sk7 != sk6 ) ),
inference(simp,[status(thm)],[164]) ).
thf(7883,plain,
! [B: $i,A: $i] :
( sk5
| ( exists_in_world @ ( sk12 @ B ) @ A )
| ( ( rel_s4 @ sk2 @ sk6 )
!= ( rel_s4 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[22,4266]) ).
thf(7884,plain,
( sk5
| ( exists_in_world @ ( sk12 @ sk2 ) @ sk6 ) ),
inference(pattern_uni,[status(thm)],[7883:[bind(A,$thf( sk6 )),bind(B,$thf( sk2 ))]]) ).
thf(30,plain,
! [A: $i] : ( rel_s4 @ A @ A ),
inference(cnf,[status(esa)],[29]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( p @ B )
| sk5
| ( ( rel_s4 @ A @ A )
!= ( rel_s4 @ sk6 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[30,24]) ).
thf(162,plain,
( ( p @ sk6 )
| sk5 ),
inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( sk6 )),bind(B,$thf( sk6 ))]]) ).
thf(7871,plain,
! [B: $i,A: $i] :
( sk5
| ( exists_in_world @ ( sk12 @ B ) @ A )
| ( ( rel_s4 @ sk7 @ sk9 )
!= ( rel_s4 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,4266]) ).
thf(7872,plain,
( sk5
| ( exists_in_world @ ( sk12 @ sk7 ) @ sk9 ) ),
inference(pattern_uni,[status(thm)],[7871:[bind(A,$thf( sk9 )),bind(B,$thf( sk7 ))]]) ).
thf(15,plain,
! [D: $i,C: $i,B: mu,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ( rel_s4 @ C @ ( sk4 @ C @ B @ A ) )
| ~ ( rel_s4 @ C @ D )
| ( p @ D ) ),
inference(cnf,[status(esa)],[7]) ).
thf(26,plain,
! [D: $i,C: $i,B: mu,A: $i] :
( ~ ( rel_s4 @ sk2 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ( rel_s4 @ C @ ( sk4 @ C @ B @ A ) )
| ~ ( rel_s4 @ C @ D )
| ( p @ D ) ),
inference(simp,[status(thm)],[15]) ).
thf(780,plain,
! [A: $i] :
( ~ sk5
| ( rel_s4 @ sk1 @ A )
| ( ( rel_s4 @ sk2 @ sk10 )
!= ( rel_s4 @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17,396]) ).
thf(781,plain,
( ~ sk5
| ( rel_s4 @ sk1 @ sk10 ) ),
inference(pattern_uni,[status(thm)],[780:[bind(A,$thf( sk10 ))]]) ).
thf(160,plain,
! [A: $i] :
( ( p @ A )
| sk5
| ( ( rel_s4 @ sk6 @ A )
!= ( rel_s4 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[16,24]) ).
thf(165,plain,
! [A: $i] :
( ( p @ A )
| sk5
| ( sk6 != sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[160]) ).
thf(168,plain,
( ( p @ sk2 )
| sk5
| ( sk6 != sk1 ) ),
inference(simp,[status(thm)],[165]) ).
thf(7879,plain,
! [B: $i,A: $i] :
( ~ sk5
| ( exists_in_world @ ( sk12 @ B ) @ A )
| ( ( rel_s4 @ sk2 @ sk10 )
!= ( rel_s4 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17,4266]) ).
thf(7880,plain,
( ~ sk5
| ( exists_in_world @ ( sk12 @ sk2 ) @ sk10 ) ),
inference(pattern_uni,[status(thm)],[7879:[bind(A,$thf( sk10 )),bind(B,$thf( sk2 ))]]) ).
thf(46,plain,
! [E: $i,D: $i,C: mu,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ B )
| ~ ( exists_in_world @ C @ B )
| ~ ( rel_s4 @ B @ D )
| ~ ( p @ ( sk3 @ D @ C @ B ) )
| ( big_f @ C @ E )
| ( ( rel_s4 @ A @ A )
!= ( rel_s4 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[30,12]) ).
thf(47,plain,
! [C: mu,B: $i,A: $i] :
( ~ ( rel_s4 @ sk2 @ B )
| ~ ( exists_in_world @ C @ B )
| ~ ( rel_s4 @ B @ A )
| ~ ( p @ ( sk3 @ A @ C @ B ) )
| ( big_f @ C @ A ) ),
inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( A ))]]) ).
thf(38876,plain,
$false,
inference(e,[status(thm)],[4290,511,10,14,789,2204,6747,7864,7680,4266,24,25,20,4179,29,396,133,5630,28,392,21,33,1883,7902,456,4957,156,188,403,9,7898,4425,4421,642,1114,457,13,41,792,773,4438,17,32,34,22,743,27,3213,3796,12,3619,7,8986,455,167,7884,162,1472,4398,16,31,7872,26,55,781,23,168,30,19,358,3805,332,7880,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN052^7 : TPTP v8.2.0. Released v5.5.0.
% 0.03/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Jun 23 20:44:25 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.95/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.47/1.01 % [INFO] Parsing done (141ms).
% 1.47/1.02 % [INFO] Running in sequential loop mode.
% 1.88/1.22 % [INFO] eprover registered as external prover.
% 1.88/1.22 % [INFO] Scanning for conjecture ...
% 1.99/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.28/1.35 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.28/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 2.28/1.36 % [INFO] Type checking passed.
% 2.28/1.36 % [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 ...
% 84.04/20.06 % External prover 'e' found a proof!
% 84.04/20.06 % [INFO] Killing All external provers ...
% 84.04/20.06 % Time passed: 19524ms (effective reasoning time: 19038ms)
% 84.04/20.06 % 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)>
% 84.04/20.06 % Axioms used in derivation (4): nonempty_ax, cumulative_ax, a2, a1
% 84.04/20.06 % No. of inferences in proof: 163
% 84.04/20.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19524 ms resp. 19038 ms w/o parsing
% 84.04/20.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 84.04/20.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------