TSTP Solution File: GEG003^1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : GEG003^1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 May 20 19:56:58 EDT 2024
% Result : Theorem 73.18s 11.12s
% Output : Refutation 73.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 39
% Syntax : Number of formulae : 125 ( 28 unt; 24 typ; 8 def)
% Number of atoms : 311 ( 81 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 793 ( 130 ~; 96 |; 32 &; 513 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 15 con; 0-3 aty)
% Number of variables : 146 ( 25 ^ 105 !; 16 ?; 146 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(mforall_prop_type,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(mforall_prop_def,definition,
( mforall_prop
= ( ^ [A: ( $i > $o ) > $i > $o,B: $i] :
! [C: $i > $o] : ( A @ C @ B ) ) ) ).
thf(mbox_type,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
! [D: $i] :
( ~ ( A @ C @ D )
| ( B @ D ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(reg_type,type,
reg: $tType ).
thf(c_type,type,
c: reg > reg > $o ).
thf(dc_type,type,
dc: reg > reg > $o ).
thf(dc_def,definition,
( dc
= ( ^ [A: reg,B: reg] :
~ ( c @ A @ B ) ) ) ).
thf(ec_type,type,
ec: reg > reg > $o ).
thf(ec_def,definition,
( ec
= ( ^ [A: reg,B: reg] :
( ( c @ A @ B )
& ~ ( o @ A @ B ) ) ) ) ).
thf(tpp_type,type,
tpp: reg > reg > $o ).
thf(tpp_def,definition,
( tpp
= ( ^ [A: reg,B: reg] :
( ( pp @ A @ B )
& ? [C: reg] :
( ( ec @ C @ A )
& ( ec @ C @ B ) ) ) ) ) ).
thf(ntpp_type,type,
ntpp: reg > reg > $o ).
thf(ntpp_def,definition,
( ntpp
= ( ^ [A: reg,B: reg] :
( ( pp @ A @ B )
& ~ ? [C: reg] :
( ( ec @ C @ A )
& ( ec @ C @ B ) ) ) ) ) ).
thf(catalunya_type,type,
catalunya: reg ).
thf(france_type,type,
france: reg ).
thf(spain_type,type,
spain: reg ).
thf(paris_type,type,
paris: reg ).
thf(a_type,type,
a: $i > $i > $o ).
thf(fool_type,type,
fool: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: ( $i > $o ) > $i > $i ).
thf(sk4_type,type,
sk4: reg ).
thf(sk5_type,type,
sk5: reg ).
thf(sk8_type,type,
sk8: reg > reg ).
thf(sk9_type,type,
sk9: reg > reg ).
thf(1,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [A: $i] :
( ( dc @ catalunya @ paris )
& ( dc @ spain @ paris ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [A: $i] :
( ( dc @ catalunya @ paris )
& ( dc @ spain @ paris ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i,B: $i] :
( ~ ( a @ A @ B )
| ( ~ ( c @ catalunya @ paris )
& ~ ( c @ spain @ paris ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
~ ( ~ ? [A: $i,B: $i] : ( a @ A @ B )
| ( ~ ( c @ catalunya @ paris )
& ~ ( c @ spain @ paris ) ) ),
inference(miniscope,[status(thm)],[9]) ).
thf(12,plain,
a @ sk1 @ sk2,
inference(cnf,[status(esa)],[10]) ).
thf(6,axiom,
( mvalid
@ ( mbox @ a
@ ^ [A: $i] : ( tpp @ catalunya @ spain ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(20,plain,
! [A: $i,B: $i] :
( ~ ( a @ A @ B )
| ( ! [C: reg] :
( ( c @ C @ catalunya )
=> ( c @ C @ spain ) )
& ~ ! [C: reg] :
( ( c @ C @ spain )
=> ( c @ C @ catalunya ) )
& ? [C: reg] :
( ( c @ C @ catalunya )
& ~ ? [D: reg] :
( ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ C ) )
& ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ catalunya ) ) )
& ( c @ C @ spain )
& ~ ? [D: reg] :
( ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ C ) )
& ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ spain ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,plain,
( ~ ? [A: $i,B: $i] : ( a @ A @ B )
| ( ! [A: reg] :
( ( c @ A @ catalunya )
=> ( c @ A @ spain ) )
& ~ ! [A: reg] :
( ( c @ A @ spain )
=> ( c @ A @ catalunya ) )
& ? [A: reg] :
( ( c @ A @ catalunya )
& ~ ? [B: reg] :
( ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ A ) )
& ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ catalunya ) ) )
& ( c @ A @ spain )
& ~ ? [B: reg] :
( ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ A ) )
& ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ spain ) ) ) ) ) ),
inference(miniscope,[status(thm)],[20]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( a @ A @ B )
| ~ ( c @ sk4 @ catalunya ) ),
inference(cnf,[status(esa)],[21]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ~ ( c @ sk4 @ catalunya )
| ( ( a @ sk1 @ sk2 )
!= ( a @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,32]) ).
thf(69,plain,
~ ( c @ sk4 @ catalunya ),
inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(30,plain,
! [C: reg,B: $i,A: $i] :
( ~ ( a @ A @ B )
| ( c @ ( sk8 @ C ) @ C )
| ( c @ ( sk9 @ C ) @ C ) ),
inference(cnf,[status(esa)],[21]) ).
thf(37,plain,
! [C: reg,B: $i,A: $i] :
( ~ ( a @ A @ B )
| ( c @ ( sk8 @ C ) @ C )
| ( c @ ( sk9 @ C ) @ C ) ),
inference(simp,[status(thm)],[30]) ).
thf(3,axiom,
! [A: reg] : ( c @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_reflexive) ).
thf(13,plain,
! [A: reg] : ( c @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
! [A: reg] : ( c @ A @ A ),
inference(cnf,[status(esa)],[13]) ).
thf(5,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ ( mbox @ a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_axiom_for_fool_a) ).
thf(17,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( fool @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( a @ A @ C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( fool @ A @ ( sk3 @ B @ A ) )
| ~ ( a @ A @ C )
| ( B @ C ) ),
inference(cnf,[status(esa)],[17]) ).
thf(157,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( fool @ A @ ( sk3 @ B @ A ) )
| ( B @ C )
| ( ( a @ sk1 @ sk2 )
!= ( a @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12,18]) ).
thf(158,plain,
! [A: $i > $o] :
( ( fool @ sk1 @ ( sk3 @ A @ sk1 ) )
| ( A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(195,plain,
! [A: $i > $o] :
( ( fool @ sk1 @ ( sk3 @ A @ sk1 ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[158]) ).
thf(222,plain,
( ( fool @ sk1
@ ( sk3
@ ^ [A: $i] : $false
@ sk1 ) )
| $false ),
inference(prim_subst,[status(thm)],[195:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).
thf(238,plain,
( fool @ sk1
@ ( sk3
@ ^ [A: $i] : $false
@ sk1 ) ),
inference(simp,[status(thm)],[222]) ).
thf(11,plain,
( ( c @ catalunya @ paris )
| ( c @ spain @ paris ) ),
inference(cnf,[status(esa)],[10]) ).
thf(63,plain,
( ( c @ catalunya @ paris )
| ( ( c @ spain @ paris )
!= ( c @ catalunya @ paris ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11]) ).
thf(65,plain,
( ( c @ catalunya @ paris )
| ( spain != catalunya )
| ( paris != paris ) ),
inference(simp,[status(thm)],[63]) ).
thf(66,plain,
( ( c @ catalunya @ paris )
| ( spain != catalunya ) ),
inference(simp,[status(thm)],[65]) ).
thf(4,axiom,
! [A: reg,B: reg] :
( ( c @ A @ B )
=> ( c @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_symmetric) ).
thf(15,plain,
! [A: reg,B: reg] :
( ( c @ A @ B )
=> ( c @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
! [B: reg,A: reg] :
( ~ ( c @ A @ B )
| ( c @ B @ A ) ),
inference(cnf,[status(esa)],[15]) ).
thf(93,plain,
! [B: reg,A: reg] :
( ~ ( c @ A @ B )
| ( ( c @ B @ A )
!= ( c @ sk4 @ catalunya ) ) ),
inference(paramod_ordered,[status(thm)],[16,69]) ).
thf(94,plain,
~ ( c @ catalunya @ sk4 ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( catalunya )),bind(B,$thf( sk4 ))]]) ).
thf(108,plain,
( ( spain != catalunya )
| ( ( c @ catalunya @ sk4 )
!= ( c @ catalunya @ paris ) ) ),
inference(paramod_ordered,[status(thm)],[66,94]) ).
thf(113,plain,
( ( spain != catalunya )
| ( catalunya != catalunya )
| ( sk4 != paris ) ),
inference(simp,[status(thm)],[108]) ).
thf(116,plain,
( ( spain != catalunya )
| ( sk4 != paris ) ),
inference(simp,[status(thm)],[113]) ).
thf(19,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( B @ ( sk3 @ B @ A ) )
| ~ ( a @ A @ C )
| ( B @ C ) ),
inference(cnf,[status(esa)],[17]) ).
thf(263,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( B @ ( sk3 @ B @ A ) )
| ( B @ C )
| ( ( a @ sk1 @ sk2 )
!= ( a @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12,19]) ).
thf(264,plain,
! [A: $i > $o] :
( ~ ( A @ ( sk3 @ A @ sk1 ) )
| ( A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[263:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(331,plain,
! [A: $i > $o] :
( ~ ( A @ ( sk3 @ A @ sk1 ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[264]) ).
thf(412,plain,
! [A: $i > $o] :
( ~ ~ ( A
@ ( sk3
@ ^ [B: $i] :
~ ( A @ B )
@ sk1 ) )
| ~ ( A @ sk2 ) ),
inference(prim_subst,[status(thm)],[331:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).
thf(451,plain,
! [A: $i > $o] :
( ~ ( A @ sk2 )
| ( A
@ ( sk3
@ ^ [B: $i] :
~ ( A @ B )
@ sk1 ) ) ),
inference(cnf,[status(esa)],[412]) ).
thf(452,plain,
! [A: $i > $o] :
( ~ ( A @ sk2 )
| ( A
@ ( sk3
@ ^ [B: $i] :
~ ( A @ B )
@ sk1 ) ) ),
inference(simp,[status(thm)],[451]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ ( a @ A @ B )
| ( c @ sk5 @ catalunya ) ),
inference(cnf,[status(esa)],[21]) ).
thf(470,plain,
! [B: $i,A: $i] :
( ( c @ sk5 @ catalunya )
| ( ( a @ sk1 @ sk2 )
!= ( a @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,25]) ).
thf(471,plain,
c @ sk5 @ catalunya,
inference(pattern_uni,[status(thm)],[470:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(84,plain,
! [C: reg,B: $i,A: $i] :
( ( c @ ( sk8 @ C ) @ C )
| ( c @ ( sk9 @ C ) @ C )
| ( ( a @ sk1 @ sk2 )
!= ( a @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,37]) ).
thf(85,plain,
! [A: reg] :
( ( c @ ( sk8 @ A ) @ A )
| ( c @ ( sk9 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(90,plain,
! [A: reg] :
( ( c @ ( sk8 @ A ) @ A )
| ( c @ ( sk9 @ A ) @ A ) ),
inference(simp,[status(thm)],[85]) ).
thf(137,plain,
! [A: reg] :
( ( c @ ( sk8 @ A ) @ A )
| ( ( c @ ( sk9 @ A ) @ A )
!= ( c @ catalunya @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[90,94]) ).
thf(140,plain,
! [A: reg] :
( ( c @ ( sk8 @ A ) @ A )
| ( ( sk9 @ A )
!= catalunya )
| ( A != sk4 ) ),
inference(simp,[status(thm)],[137]) ).
thf(145,plain,
( ( c @ ( sk8 @ sk4 ) @ sk4 )
| ( ( sk9 @ sk4 )
!= catalunya ) ),
inference(simp,[status(thm)],[140]) ).
thf(204,plain,
! [B: reg,A: reg] :
( ( ( sk9 @ sk4 )
!= catalunya )
| ( c @ B @ A )
| ( ( c @ ( sk8 @ sk4 ) @ sk4 )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[145,16]) ).
thf(205,plain,
( ( ( sk9 @ sk4 )
!= catalunya )
| ( c @ sk4 @ ( sk8 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[204:[bind(A,$thf( sk8 @ sk4 )),bind(B,$thf( sk4 ))]]) ).
thf(78,plain,
( ( c @ catalunya @ paris )
| ( ( c @ sk4 @ catalunya )
!= ( c @ spain @ paris ) ) ),
inference(paramod_ordered,[status(thm)],[11,69]) ).
thf(81,plain,
( ( c @ catalunya @ paris )
| ( sk4 != spain )
| ( paris != catalunya ) ),
inference(simp,[status(thm)],[78]) ).
thf(404,plain,
! [B: $i > $o,A: $i > $o] :
( ( A @ sk2 )
| ( B @ sk2 )
| ( ( fool @ sk1 @ ( sk3 @ A @ sk1 ) )
!= ( B @ ( sk3 @ B @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[195,331]) ).
thf(417,plain,
( ( fool @ sk1 @ sk2 )
| ( fool @ sk1 @ sk2 ) ),
inference(pre_uni,[status(thm)],[404:[bind(A,$thf( fool @ sk1 )),bind(B,$thf( fool @ sk1 ))]]) ).
thf(455,plain,
fool @ sk1 @ sk2,
inference(simp,[status(thm)],[417]) ).
thf(103,plain,
! [B: reg,A: reg] :
( ( c @ catalunya @ paris )
| ( c @ B @ A )
| ( ( c @ spain @ paris )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11,16]) ).
thf(104,plain,
( ( c @ catalunya @ paris )
| ( c @ paris @ spain ) ),
inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( spain )),bind(B,$thf( paris ))]]) ).
thf(76,plain,
! [A: reg] :
( ( c @ A @ A )
!= ( c @ sk4 @ catalunya ) ),
inference(paramod_ordered,[status(thm)],[14,69]) ).
thf(79,plain,
! [A: reg] :
( ( A != sk4 )
| ( A != catalunya ) ),
inference(simp,[status(thm)],[76]) ).
thf(82,plain,
sk4 != catalunya,
inference(simp,[status(thm)],[79]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( a @ A @ B )
| ( c @ sk5 @ spain ) ),
inference(cnf,[status(esa)],[21]) ).
thf(613,plain,
! [B: $i,A: $i] :
( ( c @ sk5 @ spain )
| ( ( a @ sk1 @ sk2 )
!= ( a @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,28]) ).
thf(614,plain,
c @ sk5 @ spain,
inference(pattern_uni,[status(thm)],[613:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(134,plain,
! [A: reg] :
( ( c @ ( sk8 @ A ) @ A )
| ( ( c @ ( sk9 @ A ) @ A )
!= ( c @ sk4 @ catalunya ) ) ),
inference(paramod_ordered,[status(thm)],[90,69]) ).
thf(139,plain,
! [A: reg] :
( ( c @ ( sk8 @ A ) @ A )
| ( ( sk9 @ A )
!= sk4 )
| ( A != catalunya ) ),
inference(simp,[status(thm)],[134]) ).
thf(144,plain,
( ( c @ ( sk8 @ catalunya ) @ catalunya )
| ( ( sk9 @ catalunya )
!= sk4 ) ),
inference(simp,[status(thm)],[139]) ).
thf(196,plain,
( ( ( sk9 @ catalunya )
!= sk4 )
| ( ( c @ ( sk8 @ catalunya ) @ catalunya )
!= ( c @ sk4 @ catalunya ) ) ),
inference(paramod_ordered,[status(thm)],[144,69]) ).
thf(200,plain,
( ( ( sk9 @ catalunya )
!= sk4 )
| ( ( sk8 @ catalunya )
!= sk4 )
| ( catalunya != catalunya ) ),
inference(simp,[status(thm)],[196]) ).
thf(202,plain,
( ( ( sk9 @ catalunya )
!= sk4 )
| ( ( sk8 @ catalunya )
!= sk4 ) ),
inference(simp,[status(thm)],[200]) ).
thf(482,plain,
! [B: reg,A: reg] :
( ( c @ B @ A )
| ( ( c @ sk5 @ catalunya )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[471,16]) ).
thf(483,plain,
c @ catalunya @ sk5,
inference(pattern_uni,[status(thm)],[482:[bind(A,$thf( sk5 )),bind(B,$thf( catalunya ))]]) ).
thf(197,plain,
! [B: reg,A: reg] :
( ( ( sk9 @ catalunya )
!= sk4 )
| ( c @ B @ A )
| ( ( c @ ( sk8 @ catalunya ) @ catalunya )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[144,16]) ).
thf(198,plain,
( ( ( sk9 @ catalunya )
!= sk4 )
| ( c @ catalunya @ ( sk8 @ catalunya ) ) ),
inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( sk8 @ catalunya )),bind(B,$thf( catalunya ))]]) ).
thf(479,plain,
( ( c @ sk5 @ catalunya )
!= ( c @ sk4 @ catalunya ) ),
inference(paramod_ordered,[status(thm)],[471,69]) ).
thf(487,plain,
( ( sk5 != sk4 )
| ( catalunya != catalunya ) ),
inference(simp,[status(thm)],[479]) ).
thf(490,plain,
sk5 != sk4,
inference(simp,[status(thm)],[487]) ).
thf(206,plain,
( ( ( sk9 @ sk4 )
!= catalunya )
| ( ( c @ ( sk8 @ sk4 ) @ sk4 )
!= ( c @ catalunya @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[145,94]) ).
thf(208,plain,
( ( ( sk9 @ sk4 )
!= catalunya )
| ( ( sk8 @ sk4 )
!= catalunya )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[206]) ).
thf(209,plain,
( ( ( sk9 @ sk4 )
!= catalunya )
| ( ( sk8 @ sk4 )
!= catalunya ) ),
inference(simp,[status(thm)],[208]) ).
thf(8,axiom,
( mvalid
@ ( mbox @ a
@ ^ [A: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(50,plain,
! [A: $i,B: $i] :
( ~ ( a @ A @ B )
| ( ! [C: reg] :
( ( c @ C @ paris )
=> ( c @ C @ france ) )
& ~ ! [C: reg] :
( ( c @ C @ france )
=> ( c @ C @ paris ) )
& ~ ? [C: reg] :
( ( c @ C @ paris )
& ~ ? [D: reg] :
( ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ C ) )
& ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ paris ) ) )
& ( c @ C @ france )
& ~ ? [D: reg] :
( ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ C ) )
& ! [E: reg] :
( ( c @ E @ D )
=> ( c @ E @ france ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(150,plain,
( ( sk4 != spain )
| ( paris != catalunya )
| ( ( c @ catalunya @ sk4 )
!= ( c @ catalunya @ paris ) ) ),
inference(paramod_ordered,[status(thm)],[81,94]) ).
thf(152,plain,
( ( sk4 != spain )
| ( paris != catalunya )
| ( catalunya != catalunya )
| ( sk4 != paris ) ),
inference(simp,[status(thm)],[150]) ).
thf(154,plain,
( ( sk4 != spain )
| ( paris != catalunya )
| ( sk4 != paris ) ),
inference(simp,[status(thm)],[152]) ).
thf(7,axiom,
( mvalid
@ ( mbox @ fool
@ ^ [A: $i] : ( ec @ spain @ france ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(43,plain,
! [A: $i,B: $i] :
( ~ ( fool @ A @ B )
| ( ( c @ spain @ france )
& ~ ? [C: reg] :
( ! [D: reg] :
( ( c @ D @ C )
=> ( c @ D @ spain ) )
& ! [D: reg] :
( ( c @ D @ C )
=> ( c @ D @ france ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(99,plain,
! [B: reg,A: reg] :
( ( spain != catalunya )
| ( c @ B @ A )
| ( ( c @ catalunya @ paris )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[66,16]) ).
thf(100,plain,
( ( spain != catalunya )
| ( c @ paris @ catalunya ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( catalunya )),bind(B,$thf( paris ))]]) ).
thf(26295,plain,
$false,
inference(e,[status(thm)],[69,37,14,20,238,116,452,9,471,13,205,17,81,455,18,104,82,19,15,614,202,12,144,483,66,198,490,209,145,50,331,16,154,11,43,195,94,90,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEG003^1 : TPTP v8.2.0. Released v4.1.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n028.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 : Sat May 18 21:54:09 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.83/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.99 % [INFO] Parsing done (145ms).
% 1.23/1.00 % [INFO] Running in sequential loop mode.
% 1.83/1.20 % [INFO] eprover registered as external prover.
% 1.83/1.20 % [INFO] cvc4 registered as external prover.
% 1.83/1.20 % [INFO] Scanning for conjecture ...
% 2.02/1.31 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.30/1.33 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.30/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 2.30/1.34 % [INFO] Type checking passed.
% 2.30/1.34 % [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 ...
% 73.18/11.11 % External prover 'e' found a proof!
% 73.18/11.11 % [INFO] Killing All external provers ...
% 73.18/11.12 % Time passed: 10597ms (effective reasoning time: 10110ms)
% 73.18/11.12 % 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)>
% 73.18/11.12 % Axioms used in derivation (6): ax1, ax2, c_symmetric, i_axiom_for_fool_a, ax3, c_reflexive
% 73.18/11.12 % No. of inferences in proof: 93
% 73.18/11.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10597 ms resp. 10110 ms w/o parsing
% 73.18/11.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 73.18/11.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------