TSTP Solution File: SET575^7 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : SET575^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 08:07:29 EDT 2024
% Result : Theorem 9.65s 3.12s
% Output : Refutation 9.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 37
% Syntax : Number of formulae : 116 ( 20 unt; 22 typ; 8 def)
% Number of atoms : 390 ( 83 equ; 0 cnn)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 1110 ( 169 ~; 155 |; 4 &; 768 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 11 con; 0-3 aty)
% Number of variables : 120 ( 23 ^ 95 !; 2 ?; 120 :)
% 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(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(member_type,type,
member: mu > mu > $i > $o ).
thf(intersect_type,type,
intersect: mu > mu > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: mu ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: mu ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: mu > $i ).
thf(sk8_type,type,
sk8: mu > $i ).
thf(sk9_type,type,
sk9: $i > mu ).
thf(1,conjecture,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] :
( mbox_s4
@ ( mimplies @ ( mbox_s4 @ ( intersect @ A @ B ) )
@ ( mexists_ind
@ ^ [C: mu] : ( mand @ ( mbox_s4 @ ( member @ C @ A ) ) @ ( mbox_s4 @ ( member @ C @ B ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th15) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] :
( mbox_s4
@ ( mimplies @ ( mbox_s4 @ ( intersect @ A @ B ) )
@ ( mexists_ind
@ ^ [C: mu] : ( mand @ ( mbox_s4 @ ( member @ C @ A ) ) @ ( mbox_s4 @ ( member @ C @ B ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i,B: $i] :
( ~ ( rel_s4 @ A @ B )
| ! [C: mu] :
( ( exists_in_world @ C @ B )
=> ! [D: $i] :
( ~ ( rel_s4 @ B @ D )
| ! [E: mu] :
( ( exists_in_world @ E @ D )
=> ! [F: $i] :
( ~ ( rel_s4 @ D @ F )
| ~ ! [G: $i] :
( ~ ( rel_s4 @ F @ G )
| ( intersect @ C @ E @ G ) )
| ~ ! [G: mu] :
( ( exists_in_world @ G @ F )
=> ( ~ ! [H: $i] :
( ~ ( rel_s4 @ F @ H )
| ( member @ G @ C @ H ) )
| ~ ! [H: $i] :
( ~ ( rel_s4 @ F @ H )
| ( member @ G @ E @ H ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
exists_in_world @ sk3 @ sk2,
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk6 )
| ~ ( member @ A @ sk3 @ ( sk7 @ A ) )
| ~ ( member @ A @ sk5 @ ( sk8 @ A ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(22,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk6 )
| ~ ( member @ A @ sk3 @ ( sk7 @ A ) )
| ~ ( member @ A @ sk5 @ ( sk8 @ A ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(61,plain,
! [A: mu] :
( ~ ( member @ A @ sk3 @ ( sk7 @ A ) )
| ~ ( member @ A @ sk5 @ ( sk8 @ A ) )
| ( ( exists_in_world @ sk3 @ sk2 )
!= ( exists_in_world @ A @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[18,22]) ).
thf(62,plain,
! [A: mu] :
( ~ ( member @ A @ sk3 @ ( sk7 @ A ) )
| ~ ( member @ A @ sk5 @ ( sk8 @ A ) )
| ( sk3 != A )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[61]) ).
thf(63,plain,
( ~ ( member @ sk3 @ sk3 @ ( sk7 @ sk3 ) )
| ~ ( member @ sk3 @ sk5 @ ( sk8 @ sk3 ) )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[62]) ).
thf(85,plain,
( ~ ( member @ sk3 @ sk3 @ ( sk7 @ sk3 ) )
| ( sk6 != sk2 )
| ( ( member @ sk3 @ sk5 @ ( sk8 @ sk3 ) )
!= ( member @ sk3 @ sk3 @ ( sk7 @ sk3 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[63]) ).
thf(87,plain,
( ~ ( member @ sk3 @ sk3 @ ( sk7 @ sk3 ) )
| ( sk6 != sk2 )
| ( sk3 != sk3 )
| ( sk5 != sk3 )
| ( ( sk8 @ sk3 )
!= ( sk7 @ sk3 ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(88,plain,
( ~ ( member @ sk3 @ sk3 @ ( sk7 @ sk3 ) )
| ( sk6 != sk2 )
| ( sk5 != sk3 )
| ( ( sk8 @ sk3 )
!= ( sk7 @ sk3 ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(3,axiom,
! [A: $i] :
? [B: mu] : ( exists_in_world @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_ax) ).
thf(24,plain,
! [A: $i] :
? [B: mu] : ( exists_in_world @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,plain,
! [A: $i] : ( exists_in_world @ ( sk9 @ A ) @ A ),
inference(cnf,[status(esa)],[24]) ).
thf(83,plain,
! [B: mu,A: $i] :
( ~ ( member @ B @ sk3 @ ( sk7 @ B ) )
| ~ ( member @ B @ sk5 @ ( sk8 @ B ) )
| ( ( exists_in_world @ ( sk9 @ A ) @ A )
!= ( exists_in_world @ B @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[25,22]) ).
thf(84,plain,
( ~ ( member @ ( sk9 @ sk6 ) @ sk3 @ ( sk7 @ ( sk9 @ sk6 ) ) )
| ~ ( member @ ( sk9 @ sk6 ) @ sk5 @ ( sk8 @ ( sk9 @ sk6 ) ) ) ),
inference(pattern_uni,[status(thm)],[83:[bind(A,$thf( sk6 )),bind(B,$thf( sk9 @ sk6 ))]]) ).
thf(17,plain,
rel_s4 @ sk1 @ sk2,
inference(cnf,[status(esa)],[9]) ).
thf(5,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(28,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(29,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ( rel_s4 @ A @ C ) ),
inference(cnf,[status(esa)],[28]) ).
thf(146,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)],[17,29]) ).
thf(147,plain,
! [A: $i] :
( ~ ( rel_s4 @ A @ sk1 )
| ( rel_s4 @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).
thf(19,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk6 )
| ( rel_s4 @ sk6 @ ( sk7 @ A ) )
| ( rel_s4 @ sk6 @ ( sk8 @ A ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(23,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk6 )
| ( rel_s4 @ sk6 @ ( sk7 @ A ) )
| ( rel_s4 @ sk6 @ ( sk8 @ A ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(89,plain,
! [B: mu,A: $i] :
( ( rel_s4 @ sk6 @ ( sk7 @ B ) )
| ( rel_s4 @ sk6 @ ( sk8 @ B ) )
| ( ( exists_in_world @ ( sk9 @ A ) @ A )
!= ( exists_in_world @ B @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[25,23]) ).
thf(90,plain,
( ( rel_s4 @ sk6 @ ( sk7 @ ( sk9 @ sk6 ) ) )
| ( rel_s4 @ sk6 @ ( sk8 @ ( sk9 @ sk6 ) ) ) ),
inference(pattern_uni,[status(thm)],[89:[bind(A,$thf( sk6 )),bind(B,$thf( sk9 @ sk6 ))]]) ).
thf(106,plain,
( ( rel_s4 @ sk6 @ ( sk7 @ ( sk9 @ sk6 ) ) )
| ( ( rel_s4 @ sk6 @ ( sk8 @ ( sk9 @ sk6 ) ) )
!= ( rel_s4 @ sk6 @ ( sk7 @ ( sk9 @ sk6 ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[90]) ).
thf(108,plain,
( ( rel_s4 @ sk6 @ ( sk7 @ ( sk9 @ sk6 ) ) )
| ( sk6 != sk6 )
| ( ( sk8 @ ( sk9 @ sk6 ) )
!= ( sk7 @ ( sk9 @ sk6 ) ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(109,plain,
( ( rel_s4 @ sk6 @ ( sk7 @ ( sk9 @ sk6 ) ) )
| ( ( sk8 @ ( sk9 @ sk6 ) )
!= ( sk7 @ ( sk9 @ sk6 ) ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(14,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk6 @ A )
| ( intersect @ sk3 @ sk5 @ A ) ),
inference(cnf,[status(esa)],[9]) ).
thf(104,plain,
! [A: $i] :
( ( rel_s4 @ sk6 @ ( sk7 @ ( sk9 @ sk6 ) ) )
| ( intersect @ sk3 @ sk5 @ A )
| ( ( rel_s4 @ sk6 @ ( sk8 @ ( sk9 @ sk6 ) ) )
!= ( rel_s4 @ sk6 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[90,14]) ).
thf(105,plain,
( ( rel_s4 @ sk6 @ ( sk7 @ ( sk9 @ sk6 ) ) )
| ( intersect @ sk3 @ sk5 @ ( sk8 @ ( sk9 @ sk6 ) ) ) ),
inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( sk8 @ ( sk9 @ sk6 ) ))]]) ).
thf(4,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(26,plain,
! [A: $i] : ( rel_s4 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,plain,
! [A: $i] : ( rel_s4 @ A @ A ),
inference(cnf,[status(esa)],[26]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( intersect @ sk3 @ sk5 @ B )
| ( ( rel_s4 @ A @ A )
!= ( rel_s4 @ sk6 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27,14]) ).
thf(80,plain,
intersect @ sk3 @ sk5 @ sk6,
inference(pattern_uni,[status(thm)],[79:[bind(A,$thf( sk6 )),bind(B,$thf( sk6 ))]]) ).
thf(120,plain,
( ~ ( member @ ( sk9 @ sk6 ) @ sk3 @ ( sk7 @ ( sk9 @ sk6 ) ) )
| ( ( member @ ( sk9 @ sk6 ) @ sk5 @ ( sk8 @ ( sk9 @ sk6 ) ) )
!= ( member @ ( sk9 @ sk6 ) @ sk3 @ ( sk7 @ ( sk9 @ sk6 ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[84]) ).
thf(122,plain,
( ~ ( member @ ( sk9 @ sk6 ) @ sk3 @ ( sk7 @ ( sk9 @ sk6 ) ) )
| ( ( sk9 @ sk6 )
!= ( sk9 @ sk6 ) )
| ( sk5 != sk3 )
| ( ( sk8 @ ( sk9 @ sk6 ) )
!= ( sk7 @ ( sk9 @ sk6 ) ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(123,plain,
( ~ ( member @ ( sk9 @ sk6 ) @ sk3 @ ( sk7 @ ( sk9 @ sk6 ) ) )
| ( sk5 != sk3 )
| ( ( sk8 @ ( sk9 @ sk6 ) )
!= ( sk7 @ ( sk9 @ sk6 ) ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(12,plain,
rel_s4 @ sk2 @ sk4,
inference(cnf,[status(esa)],[9]) ).
thf(66,plain,
! [A: $i] :
( ( intersect @ sk3 @ sk5 @ A )
| ( ( rel_s4 @ sk6 @ A )
!= ( rel_s4 @ sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[12,14]) ).
thf(69,plain,
! [A: $i] :
( ( intersect @ sk3 @ sk5 @ A )
| ( sk6 != sk2 )
| ( A != sk4 ) ),
inference(simp,[status(thm)],[66]) ).
thf(72,plain,
( ( intersect @ sk3 @ sk5 @ sk4 )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[69]) ).
thf(13,plain,
rel_s4 @ sk4 @ sk6,
inference(cnf,[status(esa)],[9]) ).
thf(211,plain,
! [A: $i] :
( ( rel_s4 @ A @ sk2 )
| ( ( rel_s4 @ sk4 @ sk6 )
!= ( rel_s4 @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[13,147]) ).
thf(226,plain,
! [A: $i] :
( ( rel_s4 @ A @ sk2 )
| ( sk4 != A )
| ( sk6 != sk1 ) ),
inference(simp,[status(thm)],[211]) ).
thf(231,plain,
( ( rel_s4 @ sk4 @ sk2 )
| ( sk6 != sk1 ) ),
inference(simp,[status(thm)],[226]) ).
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(30,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(15,plain,
exists_in_world @ sk5 @ sk4,
inference(cnf,[status(esa)],[9]) ).
thf(93,plain,
! [A: mu] :
( ( rel_s4 @ sk6 @ ( sk7 @ A ) )
| ( rel_s4 @ sk6 @ ( sk8 @ A ) )
| ( ( exists_in_world @ sk5 @ sk4 )
!= ( exists_in_world @ A @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[15,23]) ).
thf(96,plain,
! [A: mu] :
( ( rel_s4 @ sk6 @ ( sk7 @ A ) )
| ( rel_s4 @ sk6 @ ( sk8 @ A ) )
| ( sk5 != A )
| ( sk6 != sk4 ) ),
inference(simp,[status(thm)],[93]) ).
thf(100,plain,
( ( rel_s4 @ sk6 @ ( sk7 @ sk5 ) )
| ( rel_s4 @ sk6 @ ( sk8 @ sk5 ) )
| ( sk6 != sk4 ) ),
inference(simp,[status(thm)],[96]) ).
thf(124,plain,
! [A: $i] :
( ( rel_s4 @ sk6 @ ( sk7 @ sk5 ) )
| ( sk6 != sk4 )
| ( intersect @ sk3 @ sk5 @ A )
| ( ( rel_s4 @ sk6 @ ( sk8 @ sk5 ) )
!= ( rel_s4 @ sk6 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[100,14]) ).
thf(125,plain,
( ( rel_s4 @ sk6 @ ( sk7 @ sk5 ) )
| ( sk6 != sk4 )
| ( intersect @ sk3 @ sk5 @ ( sk8 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[124:[bind(A,$thf( sk8 @ sk5 ))]]) ).
thf(10,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk6 )
| ~ ( member @ A @ sk3 @ ( sk7 @ A ) )
| ( rel_s4 @ sk6 @ ( sk8 @ A ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(20,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk6 )
| ~ ( member @ A @ sk3 @ ( sk7 @ A ) )
| ( rel_s4 @ sk6 @ ( sk8 @ A ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(50,plain,
! [A: mu] :
( ~ ( member @ A @ sk3 @ ( sk7 @ A ) )
| ~ ( member @ A @ sk5 @ ( sk8 @ A ) )
| ( ( exists_in_world @ sk5 @ sk4 )
!= ( exists_in_world @ A @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[15,22]) ).
thf(52,plain,
! [A: mu] :
( ~ ( member @ A @ sk3 @ ( sk7 @ A ) )
| ~ ( member @ A @ sk5 @ ( sk8 @ A ) )
| ( sk5 != A )
| ( sk6 != sk4 ) ),
inference(simp,[status(thm)],[50]) ).
thf(55,plain,
( ~ ( member @ sk5 @ sk3 @ ( sk7 @ sk5 ) )
| ~ ( member @ sk5 @ sk5 @ ( sk8 @ sk5 ) )
| ( sk6 != sk4 ) ),
inference(simp,[status(thm)],[52]) ).
thf(57,plain,
( ~ ( member @ sk5 @ sk3 @ ( sk7 @ sk5 ) )
| ( sk6 != sk4 )
| ( ( member @ sk5 @ sk5 @ ( sk8 @ sk5 ) )
!= ( member @ sk5 @ sk3 @ ( sk7 @ sk5 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[55]) ).
thf(59,plain,
( ~ ( member @ sk5 @ sk3 @ ( sk7 @ sk5 ) )
| ( sk6 != sk4 )
| ( sk5 != sk5 )
| ( sk5 != sk3 )
| ( ( sk8 @ sk5 )
!= ( sk7 @ sk5 ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(60,plain,
( ~ ( member @ sk5 @ sk3 @ ( sk7 @ sk5 ) )
| ( sk6 != sk4 )
| ( sk5 != sk3 )
| ( ( sk8 @ sk5 )
!= ( sk7 @ sk5 ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(94,plain,
! [A: mu] :
( ( rel_s4 @ sk6 @ ( sk7 @ A ) )
| ( rel_s4 @ sk6 @ ( sk8 @ A ) )
| ( ( exists_in_world @ sk3 @ sk2 )
!= ( exists_in_world @ A @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[18,23]) ).
thf(99,plain,
! [A: mu] :
( ( rel_s4 @ sk6 @ ( sk7 @ A ) )
| ( rel_s4 @ sk6 @ ( sk8 @ A ) )
| ( sk3 != A )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[94]) ).
thf(102,plain,
( ( rel_s4 @ sk6 @ ( sk7 @ sk3 ) )
| ( rel_s4 @ sk6 @ ( sk8 @ sk3 ) )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[99]) ).
thf(16,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk6 )
| ( rel_s4 @ sk6 @ ( sk7 @ A ) )
| ~ ( member @ A @ sk5 @ ( sk8 @ A ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(21,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk6 )
| ( rel_s4 @ sk6 @ ( sk7 @ A ) )
| ~ ( member @ A @ sk5 @ ( sk8 @ A ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(126,plain,
( ( rel_s4 @ sk6 @ ( sk7 @ sk5 ) )
| ( sk6 != sk4 )
| ( ( rel_s4 @ sk6 @ ( sk8 @ sk5 ) )
!= ( rel_s4 @ sk6 @ ( sk7 @ sk5 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[100]) ).
thf(128,plain,
( ( rel_s4 @ sk6 @ ( sk7 @ sk5 ) )
| ( sk6 != sk4 )
| ( sk6 != sk6 )
| ( ( sk8 @ sk5 )
!= ( sk7 @ sk5 ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(129,plain,
( ( rel_s4 @ sk6 @ ( sk7 @ sk5 ) )
| ( sk6 != sk4 )
| ( ( sk8 @ sk5 )
!= ( sk7 @ sk5 ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(7,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] :
( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ ( intersect @ A @ B ) )
@ ( mexists_ind
@ ^ [C: mu] : ( mand @ ( mbox_s4 @ ( member @ C @ A ) ) @ ( mbox_s4 @ ( member @ C @ B ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [C: mu] : ( mand @ ( mbox_s4 @ ( member @ C @ A ) ) @ ( mbox_s4 @ ( member @ C @ B ) ) ) )
@ ( mbox_s4 @ ( intersect @ A @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
thf(32,plain,
! [A: $i,B: $i] :
( ~ ( rel_s4 @ A @ B )
| ! [C: mu] :
( ( exists_in_world @ C @ B )
=> ! [D: $i] :
( ~ ( rel_s4 @ B @ D )
| ! [E: mu] :
( ( exists_in_world @ E @ D )
=> ~ ( ~ ! [F: $i] :
( ~ ( rel_s4 @ D @ F )
| ~ ! [G: $i] :
( ~ ( rel_s4 @ F @ G )
| ( intersect @ C @ E @ G ) )
| ~ ! [G: mu] :
( ( exists_in_world @ G @ F )
=> ( ~ ! [H: $i] :
( ~ ( rel_s4 @ F @ H )
| ( member @ G @ C @ H ) )
| ~ ! [H: $i] :
( ~ ( rel_s4 @ F @ H )
| ( member @ G @ E @ H ) ) ) ) )
| ~ ! [F: $i] :
( ~ ( rel_s4 @ D @ F )
| ! [G: mu] :
( ( exists_in_world @ G @ F )
=> ( ~ ! [H: $i] :
( ~ ( rel_s4 @ F @ H )
| ( member @ G @ C @ H ) )
| ~ ! [H: $i] :
( ~ ( rel_s4 @ F @ H )
| ( member @ G @ E @ H ) ) ) )
| ! [G: $i] :
( ~ ( rel_s4 @ F @ G )
| ( intersect @ C @ E @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(65,plain,
! [A: $i] :
( ( intersect @ sk3 @ sk5 @ A )
| ( ( rel_s4 @ sk6 @ A )
!= ( rel_s4 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[17,14]) ).
thf(68,plain,
! [A: $i] :
( ( intersect @ sk3 @ sk5 @ A )
| ( sk6 != sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[65]) ).
thf(71,plain,
( ( intersect @ sk3 @ sk5 @ sk2 )
| ( sk6 != sk1 ) ),
inference(simp,[status(thm)],[68]) ).
thf(58,plain,
( ~ ( member @ sk5 @ sk3 @ ( sk7 @ sk5 ) )
| ( sk6 != sk4 )
| ( ( member @ sk5 @ sk5 @ ( sk8 @ sk5 ) )
!= ( member @ sk5 @ sk3 @ ( sk7 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(81,plain,
! [B: mu,A: $i] :
( ~ ( member @ B @ sk3 @ ( sk7 @ B ) )
| ( rel_s4 @ sk6 @ ( sk8 @ B ) )
| ( ( exists_in_world @ ( sk9 @ A ) @ A )
!= ( exists_in_world @ B @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[25,20]) ).
thf(82,plain,
( ~ ( member @ ( sk9 @ sk6 ) @ sk3 @ ( sk7 @ ( sk9 @ sk6 ) ) )
| ( rel_s4 @ sk6 @ ( sk8 @ ( sk9 @ sk6 ) ) ) ),
inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( sk6 )),bind(B,$thf( sk9 @ sk6 ))]]) ).
thf(8,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( intersect @ A @ B ) ) @ ( mbox_s4 @ ( intersect @ B @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
thf(47,plain,
! [A: $i,B: $i] :
( ~ ( rel_s4 @ A @ B )
| ! [C: mu] :
( ( exists_in_world @ C @ B )
=> ! [D: $i] :
( ~ ( rel_s4 @ B @ D )
| ! [E: mu] :
( ( exists_in_world @ E @ D )
=> ! [F: $i] :
( ~ ( rel_s4 @ D @ F )
| ~ ! [G: $i] :
( ~ ( rel_s4 @ F @ G )
| ( intersect @ C @ E @ G ) )
| ! [G: $i] :
( ~ ( rel_s4 @ F @ G )
| ( intersect @ E @ C @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(110,plain,
! [B: mu,A: $i] :
( ( rel_s4 @ sk6 @ ( sk7 @ B ) )
| ~ ( member @ B @ sk5 @ ( sk8 @ B ) )
| ( ( exists_in_world @ ( sk9 @ A ) @ A )
!= ( exists_in_world @ B @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[25,21]) ).
thf(111,plain,
( ( rel_s4 @ sk6 @ ( sk7 @ ( sk9 @ sk6 ) ) )
| ~ ( member @ ( sk9 @ sk6 ) @ sk5 @ ( sk8 @ ( sk9 @ sk6 ) ) ) ),
inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( sk6 )),bind(B,$thf( sk9 @ sk6 ))]]) ).
thf(642,plain,
$false,
inference(cvc4,[status(thm)],[88,84,147,9,109,105,80,123,72,231,30,24,25,14,125,20,29,60,102,28,21,13,129,32,17,22,27,71,12,63,18,26,55,23,58,82,47,15,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET575^7 : TPTP v8.1.2. Released v5.5.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n008.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 13:09:54 EDT 2024
% 0.16/0.36 % CPUTime :
% 1.07/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.42/1.14 % [INFO] Parsing done (189ms).
% 1.42/1.15 % [INFO] Running in sequential loop mode.
% 2.01/1.46 % [INFO] eprover registered as external prover.
% 2.01/1.47 % [INFO] cvc4 registered as external prover.
% 2.17/1.47 % [INFO] Scanning for conjecture ...
% 2.32/1.60 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 2.56/1.62 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.56/1.63 % [INFO] Problem is higher-order (TPTP THF).
% 2.56/1.63 % [INFO] Type checking passed.
% 2.56/1.64 % [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 ...
% 9.65/3.11 % External prover 'cvc4' found a proof!
% 9.65/3.11 % [INFO] Killing All external provers ...
% 9.65/3.11 % Time passed: 2577ms (effective reasoning time: 1959ms)
% 9.65/3.11 % 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)>
% 9.65/3.12 % Axioms used in derivation (6): intersect_defn, cumulative_ax, a1, nonempty_ax, symmetry_of_intersect, a2
% 9.65/3.12 % No. of inferences in proof: 86
% 9.65/3.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2577 ms resp. 1959 ms w/o parsing
% 9.65/3.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.65/3.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------