TSTP Solution File: SYN397^7 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SYN397^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% 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 19:54:25 EDT 2024
% Result : Theorem 95.86s 14.78s
% Output : Refutation 96.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 13
% Syntax : Number of formulae : 86 ( 19 unt; 0 typ; 9 def)
% Number of atoms : 356 ( 23 equ; 0 cnn)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 926 ( 182 ~; 152 |; 4 &; 575 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 12 con; 0-3 aty)
% Number of variables : 137 ( 21 ^ 116 !; 0 ?; 137 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: $i > $o,B: $i] :
~ ( A @ B ) ) ) ).
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(mexists_ind_type,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(mexists_ind_def,definition,
( mexists_ind
= ( ^ [A: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [B: mu] : ( mnot @ ( A @ 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(f_type,type,
f: mu > $i > $o ).
thf(sk1_type,type,
sk1: $o ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: mu > $i > $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: mu ).
thf(sk7_type,type,
sk7: $i ).
thf(sk9_type,type,
sk9: $i ).
thf(sk10_type,type,
sk10: $i > mu > $i > $i ).
thf(sk11_type,type,
sk11: $i ).
thf(sk12_type,type,
sk12: mu ).
thf(1,conjecture,
( mvalid
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [A: mu] : ( mbox_s4 @ ( f @ A ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ A ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ A ) ) ) ) ) )
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [A: mu] : ( mbox_s4 @ ( f @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish204) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [A: mu] : ( mbox_s4 @ ( f @ A ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ A ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ A ) ) ) ) ) )
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [A: mu] : ( mbox_s4 @ ( f @ A ) ) ) ) ) ) ) ) ),
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 @ D @ E ) ) ) )
| ! [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 )
| ( f @ D @ F ) ) ) ) ) )
| ~ ! [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 )
| ( f @ D @ F ) ) ) ) )
| ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ! [D: mu] :
( ( exists_in_world @ D @ C )
=> ~ ! [E: $i] :
( ~ ( rel_s4 @ C @ E )
| ( f @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,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 @ D @ E ) ) ) )
| ! [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 )
| ( f @ D @ F ) ) ) ) ) )
| ~ ! [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 )
| ( f @ D @ F ) ) ) ) )
| ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ! [D: mu] :
( ( exists_in_world @ D @ C )
=> ~ ! [E: $i] :
( ~ ( rel_s4 @ C @ E )
| ( f @ D @ E ) ) ) ) ) ),
inference(miniscope,[status(thm)],[7]) ).
thf(21,plain,
! [B: mu,A: $i] :
( ~ ( rel_s4 @ sk3 @ A )
| ~ ( exists_in_world @ B @ A )
| ( rel_s4 @ A @ ( sk4 @ B @ A ) )
| sk1 ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
( ~ sk1
| ( exists_in_world @ sk12 @ sk11 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(12,plain,
( ~ sk1
| ( rel_s4 @ sk9 @ sk11 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(18,plain,
! [C: $i,B: mu,A: $i] :
( ~ sk1
| ~ ( rel_s4 @ sk9 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ( rel_s4 @ C @ ( sk10 @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(23,plain,
! [C: $i,B: mu,A: $i] :
( ~ sk1
| ~ ( rel_s4 @ sk9 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ( rel_s4 @ C @ ( sk10 @ C @ B @ A ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(15,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_s4 @ sk11 @ A )
| ( f @ sk12 @ A ) ),
inference(cnf,[status(esa)],[8]) ).
thf(25,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_s4 @ sk11 @ A )
| ( f @ sk12 @ A ) ),
inference(simp,[status(thm)],[15]) ).
thf(4,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(28,plain,
! [A: $i] : ( rel_s4 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,plain,
! [A: $i] : ( rel_s4 @ A @ A ),
inference(cnf,[status(esa)],[28]) ).
thf(19,plain,
! [C: $i,B: mu,A: $i] :
( ~ sk1
| ~ ( rel_s4 @ sk9 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ~ ( f @ B @ ( sk10 @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(24,plain,
! [C: $i,B: mu,A: $i] :
( ~ sk1
| ~ ( rel_s4 @ sk9 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ~ ( f @ B @ ( sk10 @ C @ B @ A ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(34,plain,
! [C: $i,B: mu,A: $i] :
( ~ sk1
| ~ ( rel_s4 @ sk9 @ A )
| ~ ( rel_s4 @ A @ C )
| ~ ( f @ B @ ( sk10 @ C @ B @ A ) )
| ( ( exists_in_world @ sk12 @ sk11 )
!= ( exists_in_world @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,24]) ).
thf(35,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_s4 @ sk9 @ sk11 )
| ~ ( rel_s4 @ sk11 @ A )
| ~ ( f @ sk12 @ ( sk10 @ A @ sk12 @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( sk11 )),bind(B,$thf( sk12 ))]]) ).
thf(46,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_s4 @ sk9 @ sk11 )
| ~ ( rel_s4 @ sk11 @ A )
| ~ ( f @ sk12 @ ( sk10 @ A @ sk12 @ sk11 ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ~ sk1
| ~ ( rel_s4 @ sk9 @ sk11 )
| ~ ( f @ sk12 @ ( sk10 @ B @ sk12 @ sk11 ) )
| ( ( rel_s4 @ A @ A )
!= ( rel_s4 @ sk11 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29,46]) ).
thf(57,plain,
( ~ sk1
| ~ ( rel_s4 @ sk9 @ sk11 )
| ~ ( f @ sk12 @ ( sk10 @ sk11 @ sk12 @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( sk11 )),bind(B,$thf( sk11 ))]]) ).
thf(124,plain,
( ~ sk1
| ~ ( f @ sk12 @ ( sk10 @ sk11 @ sk12 @ sk11 ) )
| ( ( rel_s4 @ sk9 @ sk11 )
!= ( rel_s4 @ sk9 @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[12,57]) ).
thf(125,plain,
( ~ sk1
| ~ ( f @ sk12 @ ( sk10 @ sk11 @ sk12 @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[124:[]]) ).
thf(383,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_s4 @ sk11 @ A )
| ( ( f @ sk12 @ A )
!= ( f @ sk12 @ ( sk10 @ sk11 @ sk12 @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,125]) ).
thf(384,plain,
( ~ sk1
| ~ ( rel_s4 @ sk11 @ ( sk10 @ sk11 @ sk12 @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[383:[bind(A,$thf( sk10 @ sk11 @ sk12 @ sk11 ))]]) ).
thf(419,plain,
! [C: $i,B: mu,A: $i] :
( ~ sk1
| ~ ( rel_s4 @ sk9 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( rel_s4 @ A @ C )
| ( ( rel_s4 @ C @ ( sk10 @ C @ B @ A ) )
!= ( rel_s4 @ sk11 @ ( sk10 @ sk11 @ sk12 @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,384]) ).
thf(420,plain,
( ~ sk1
| ~ ( rel_s4 @ sk9 @ sk11 )
| ~ ( exists_in_world @ sk12 @ sk11 )
| ~ ( rel_s4 @ sk11 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[419:[bind(A,$thf( sk11 )),bind(B,$thf( sk12 )),bind(C,$thf( sk11 ))]]) ).
thf(567,plain,
( ~ sk1
| ~ ( rel_s4 @ sk9 @ sk11 )
| ~ ( exists_in_world @ sk12 @ sk11 )
| ~ $true ),
inference(rewrite,[status(thm)],[420,29]) ).
thf(568,plain,
( ~ sk1
| ~ ( rel_s4 @ sk9 @ sk11 )
| ~ ( exists_in_world @ sk12 @ sk11 ) ),
inference(simp,[status(thm)],[567]) ).
thf(571,plain,
( ~ sk1
| ~ ( exists_in_world @ sk12 @ sk11 )
| ( ( rel_s4 @ sk9 @ sk11 )
!= ( rel_s4 @ sk9 @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[12,568]) ).
thf(572,plain,
( ~ sk1
| ~ ( exists_in_world @ sk12 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[571:[]]) ).
thf(649,plain,
( ~ sk1
| ( ( exists_in_world @ sk12 @ sk11 )
!= ( exists_in_world @ sk12 @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[10,572]) ).
thf(650,plain,
~ sk1,
inference(pattern_uni,[status(thm)],[649:[]]) ).
thf(659,plain,
! [B: mu,A: $i] :
( ~ ( rel_s4 @ sk3 @ A )
| ~ ( exists_in_world @ B @ A )
| ( rel_s4 @ A @ ( sk4 @ B @ A ) )
| $false ),
inference(rewrite,[status(thm)],[21,650]) ).
thf(660,plain,
! [B: mu,A: $i] :
( ~ ( rel_s4 @ sk3 @ A )
| ~ ( exists_in_world @ B @ A )
| ( rel_s4 @ A @ ( sk4 @ B @ A ) ) ),
inference(simp,[status(thm)],[659]) ).
thf(13,plain,
( ( rel_s4 @ sk3 @ sk5 )
| sk1 ),
inference(cnf,[status(esa)],[8]) ).
thf(661,plain,
( ( rel_s4 @ sk3 @ sk5 )
| $false ),
inference(rewrite,[status(thm)],[13,650]) ).
thf(662,plain,
rel_s4 @ sk3 @ sk5,
inference(simp,[status(thm)],[661]) ).
thf(17,plain,
( ( rel_s4 @ sk5 @ sk7 )
| sk1 ),
inference(cnf,[status(esa)],[8]) ).
thf(5,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(30,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(31,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ( rel_s4 @ A @ C ) ),
inference(cnf,[status(esa)],[30]) ).
thf(491,plain,
! [C: $i,B: $i,A: $i] :
( sk1
| ~ ( rel_s4 @ A @ B )
| ( rel_s4 @ A @ C )
| ( ( rel_s4 @ sk5 @ sk7 )
!= ( rel_s4 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17,31]) ).
thf(492,plain,
! [A: $i] :
( sk1
| ~ ( rel_s4 @ A @ sk5 )
| ( rel_s4 @ A @ sk7 ) ),
inference(pattern_uni,[status(thm)],[491:[bind(A,$thf( A )),bind(B,$thf( sk5 )),bind(C,$thf( sk7 ))]]) ).
thf(1041,plain,
! [A: $i] :
( $false
| ~ ( rel_s4 @ A @ sk5 )
| ( rel_s4 @ A @ sk7 ) ),
inference(rewrite,[status(thm)],[492,650]) ).
thf(1042,plain,
! [A: $i] :
( ~ ( rel_s4 @ A @ sk5 )
| ( rel_s4 @ A @ sk7 ) ),
inference(simp,[status(thm)],[1041]) ).
thf(1069,plain,
! [A: $i] :
( ( rel_s4 @ A @ sk7 )
| ( ( rel_s4 @ sk3 @ sk5 )
!= ( rel_s4 @ A @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[662,1042]) ).
thf(1070,plain,
rel_s4 @ sk3 @ sk7,
inference(pattern_uni,[status(thm)],[1069:[bind(A,$thf( sk3 ))]]) ).
thf(9,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk7 @ A )
| ( f @ sk6 @ A )
| sk1 ),
inference(cnf,[status(esa)],[8]) ).
thf(22,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk7 @ A )
| ( f @ sk6 @ A )
| sk1 ),
inference(simp,[status(thm)],[9]) ).
thf(11,plain,
! [B: mu,A: $i] :
( ~ ( rel_s4 @ sk3 @ A )
| ~ ( exists_in_world @ B @ A )
| ~ ( f @ B @ ( sk4 @ B @ A ) )
| sk1 ),
inference(cnf,[status(esa)],[8]) ).
thf(140,plain,
! [C: mu,B: $i,A: $i] :
( ~ ( rel_s4 @ sk7 @ A )
| sk1
| ~ ( rel_s4 @ sk3 @ B )
| ~ ( exists_in_world @ C @ B )
| ( ( f @ sk6 @ A )
!= ( f @ C @ ( sk4 @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[22,11]) ).
thf(141,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk7 @ ( sk4 @ sk6 @ A ) )
| sk1
| ~ ( rel_s4 @ sk3 @ A )
| ~ ( exists_in_world @ sk6 @ A ) ),
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( sk4 @ sk6 @ E )),bind(B,$thf( E )),bind(C,$thf( sk6 ))]]) ).
thf(153,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk7 @ ( sk4 @ sk6 @ A ) )
| sk1
| ~ ( rel_s4 @ sk3 @ A )
| ~ ( exists_in_world @ sk6 @ A ) ),
inference(simp,[status(thm)],[141]) ).
thf(2877,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk7 @ ( sk4 @ sk6 @ A ) )
| $false
| ~ ( rel_s4 @ sk3 @ A )
| ~ ( exists_in_world @ sk6 @ A ) ),
inference(rewrite,[status(thm)],[153,650]) ).
thf(2878,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk7 @ ( sk4 @ sk6 @ A ) )
| ~ ( rel_s4 @ sk3 @ A )
| ~ ( exists_in_world @ sk6 @ A ) ),
inference(simp,[status(thm)],[2877]) ).
thf(2947,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk7 @ ( sk4 @ sk6 @ A ) )
| ~ ( exists_in_world @ sk6 @ A )
| ( ( rel_s4 @ sk3 @ sk7 )
!= ( rel_s4 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1070,2878]) ).
thf(2948,plain,
( ~ ( rel_s4 @ sk7 @ ( sk4 @ sk6 @ sk7 ) )
| ~ ( exists_in_world @ sk6 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[2947:[bind(A,$thf( sk7 ))]]) ).
thf(683,plain,
( ( rel_s4 @ sk5 @ sk7 )
| $false ),
inference(rewrite,[status(thm)],[17,650]) ).
thf(684,plain,
rel_s4 @ sk5 @ sk7,
inference(simp,[status(thm)],[683]) ).
thf(14,plain,
( ( exists_in_world @ sk6 @ sk5 )
| sk1 ),
inference(cnf,[status(esa)],[8]) ).
thf(657,plain,
( ( exists_in_world @ sk6 @ sk5 )
| $false ),
inference(rewrite,[status(thm)],[14,650]) ).
thf(658,plain,
exists_in_world @ sk6 @ sk5,
inference(simp,[status(thm)],[657]) ).
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(32,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(33,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)],[32]) ).
thf(701,plain,
! [C: $i,B: $i,A: mu] :
( ~ ( rel_s4 @ B @ C )
| ( exists_in_world @ A @ C )
| ( ( exists_in_world @ sk6 @ sk5 )
!= ( exists_in_world @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[658,33]) ).
thf(702,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk5 @ A )
| ( exists_in_world @ sk6 @ A ) ),
inference(pattern_uni,[status(thm)],[701:[bind(A,$thf( sk6 )),bind(B,$thf( sk5 ))]]) ).
thf(703,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk5 @ A )
| ( exists_in_world @ sk6 @ A ) ),
inference(simp,[status(thm)],[702]) ).
thf(3729,plain,
! [A: $i] :
( ( exists_in_world @ sk6 @ A )
| ( ( rel_s4 @ sk5 @ sk7 )
!= ( rel_s4 @ sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[684,703]) ).
thf(3730,plain,
exists_in_world @ sk6 @ sk7,
inference(pattern_uni,[status(thm)],[3729:[bind(A,$thf( sk7 ))]]) ).
thf(6380,plain,
( ~ ( rel_s4 @ sk7 @ ( sk4 @ sk6 @ sk7 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[2948,3730]) ).
thf(6381,plain,
~ ( rel_s4 @ sk7 @ ( sk4 @ sk6 @ sk7 ) ),
inference(simp,[status(thm)],[6380]) ).
thf(15718,plain,
! [B: mu,A: $i] :
( ~ ( rel_s4 @ sk3 @ A )
| ~ ( exists_in_world @ B @ A )
| ( ( rel_s4 @ A @ ( sk4 @ B @ A ) )
!= ( rel_s4 @ sk7 @ ( sk4 @ sk6 @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[660,6381]) ).
thf(15719,plain,
( ~ ( rel_s4 @ sk3 @ sk7 )
| ~ ( exists_in_world @ sk6 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[15718:[bind(A,$thf( sk7 )),bind(B,$thf( sk6 ))]]) ).
thf(16141,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[15719,3730,1070]) ).
thf(16142,plain,
$false,
inference(simp,[status(thm)],[16141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN397^7 : TPTP v8.2.0. Released v5.5.0.
% 0.03/0.12 % Command : run_Leo-III %s %d SAT
% 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 : Sun Jun 23 21:47:25 EDT 2024
% 0.12/0.33 % CPUTime :
% 1.14/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.53/1.17 % [INFO] Parsing done (191ms).
% 1.68/1.18 % [INFO] Running in sequential loop mode.
% 2.14/1.45 % [INFO] nitpick registered as external prover.
% 2.14/1.45 % [INFO] Scanning for conjecture ...
% 2.51/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.51/1.60 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.51/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.51/1.60 % [INFO] Type checking passed.
% 2.51/1.61 % [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 ...
% 95.86/14.77 % [INFO] Killing All external provers ...
% 95.86/14.78 % Time passed: 14245ms (effective reasoning time: 13592ms)
% 95.86/14.78 % 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)>
% 95.86/14.78 % Axioms used in derivation (3): a1, a2, cumulative_ax
% 95.86/14.78 % No. of inferences in proof: 77
% 95.86/14.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 14245 ms resp. 13592 ms w/o parsing
% 96.06/14.89 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 96.06/14.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------