TSTP Solution File: GEO083+1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : GEO083+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n017.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 06:17:59 EDT 2024
% Result : Theorem 47.78s 10.60s
% Output : Refutation 47.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 35
% Syntax : Number of formulae : 135 ( 13 unt; 18 typ; 0 def)
% Number of atoms : 441 ( 79 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1417 ( 137 ~; 140 |; 85 &; 978 @)
% ( 9 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 266 ( 0 ^ 241 !; 25 ?; 266 :)
% Comments :
%------------------------------------------------------------------------------
thf(part_of_type,type,
part_of: $i > $i > $o ).
thf(meet_type,type,
meet: $i > $i > $i > $o ).
thf(sum_type,type,
sum: $i > $i > $i ).
thf(incident_c_type,type,
incident_c: $i > $i > $o ).
thf(open_type,type,
open: $i > $o ).
thf(end_point_type,type,
end_point: $i > $i > $o ).
thf(inner_point_type,type,
inner_point: $i > $i > $o ).
thf(closed_type,type,
closed: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i > $i > $i ).
thf(sk6_type,type,
sk6: $i > $i > $i ).
thf(sk7_type,type,
sk7: $i > $i ).
thf(sk9_type,type,
sk9: $i > $i ).
thf(sk10_type,type,
sk10: $i > $i ).
thf(sk20_type,type,
sk20: $i > $i > $i ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( end_point @ A @ B )
<=> ( ( incident_c @ A @ B )
& ! [C: $i,D: $i] :
( ( ( part_of @ C @ B )
& ( part_of @ D @ B )
& ( incident_c @ A @ C )
& ( incident_c @ A @ D ) )
=> ( ( part_of @ C @ D )
| ( part_of @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( ( end_point @ A @ B )
=> ( ( incident_c @ A @ B )
& ! [C: $i,D: $i] :
( ( ( part_of @ C @ B )
& ( part_of @ D @ B )
& ( incident_c @ A @ C )
& ( incident_c @ A @ D ) )
=> ( ( part_of @ C @ D )
| ( part_of @ D @ C ) ) ) ) )
& ( ( ( incident_c @ A @ B )
& ! [C: $i,D: $i] :
( ( ( part_of @ C @ B )
& ( part_of @ D @ B )
& ( incident_c @ A @ C )
& ( incident_c @ A @ D ) )
=> ( ( part_of @ C @ D )
| ( part_of @ D @ C ) ) ) )
=> ( end_point @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(93,plain,
( ! [A: $i,B: $i] :
( ( end_point @ A @ B )
=> ( ( incident_c @ A @ B )
& ! [C: $i,D: $i] :
( ( ( part_of @ C @ B )
& ( part_of @ D @ B )
& ( incident_c @ A @ C )
& ( incident_c @ A @ D ) )
=> ( ( part_of @ C @ D )
| ( part_of @ D @ C ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( incident_c @ A @ B )
& ! [C: $i,D: $i] :
( ( ( part_of @ C @ B )
& ( part_of @ D @ B )
& ( incident_c @ A @ C )
& ( incident_c @ A @ D ) )
=> ( ( part_of @ C @ D )
| ( part_of @ D @ C ) ) ) )
=> ( end_point @ A @ B ) ) ),
inference(miniscope,[status(thm)],[92]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( incident_c @ A @ B ) ),
inference(cnf,[status(esa)],[93]) ).
thf(8,axiom,
! [A: $i] :
( ( closed @ A )
<=> ~ ? [B: $i] : ( end_point @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closed_defn) ).
thf(53,plain,
! [A: $i] :
( ( ( closed @ A )
=> ~ ? [B: $i] : ( end_point @ B @ A ) )
& ( ~ ? [B: $i] : ( end_point @ B @ A )
=> ( closed @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(54,plain,
( ! [A: $i] :
( ( closed @ A )
=> ~ ? [B: $i] : ( end_point @ B @ A ) )
& ! [A: $i] :
( ~ ? [B: $i] : ( end_point @ B @ A )
=> ( closed @ A ) ) ),
inference(miniscope,[status(thm)],[53]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ~ ( closed @ A )
| ~ ( end_point @ B @ A ) ),
inference(cnf,[status(esa)],[54]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( incident_c @ C @ A )
<=> ( incident_c @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c9) ).
thf(25,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( incident_c @ C @ A )
=> ( incident_c @ C @ B ) )
& ( ( incident_c @ C @ B )
=> ( incident_c @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( incident_c @ C @ A )
=> ( incident_c @ C @ B ) )
& ! [C: $i] :
( ( incident_c @ C @ B )
=> ( incident_c @ C @ A ) ) )
=> ( A = B ) ),
inference(miniscope,[status(thm)],[25]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( sk5 @ B @ A ) @ B )
| ( incident_c @ ( sk6 @ B @ A ) @ B )
| ( A = B ) ),
inference(cnf,[status(esa)],[26]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( incident_c @ ( sk5 @ B @ A ) @ B )
| ( incident_c @ ( sk6 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( part_of @ B @ C )
& ( meet @ D @ A @ B )
& ( meet @ D @ A @ C ) )
=> ( part_of @ ( sum @ A @ B ) @ ( sum @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_6_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( part_of @ B @ C )
& ( meet @ D @ A @ B )
& ( meet @ D @ A @ C ) )
=> ( part_of @ ( sum @ A @ B ) @ ( sum @ A @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( part_of @ B @ C )
& ( meet @ D @ A @ B )
& ( meet @ D @ A @ C ) )
=> ( part_of @ ( sum @ A @ B ) @ ( sum @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( part_of @ B @ C )
& ? [D: $i] :
( ( meet @ D @ A @ B )
& ( meet @ D @ A @ C ) ) )
=> ( part_of @ ( sum @ A @ B ) @ ( sum @ A @ C ) ) ),
inference(miniscope,[status(thm)],[19]) ).
thf(24,plain,
part_of @ sk2 @ sk3,
inference(cnf,[status(esa)],[20]) ).
thf(541,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( sk5 @ B @ A ) @ B )
| ( incident_c @ ( sk6 @ B @ A ) @ B )
| ( part_of @ A @ sk3 )
| ( B != sk2 ) ),
inference(paramod_ordered,[status(thm)],[32,24]) ).
thf(542,plain,
! [A: $i] :
( ~ ( incident_c @ ( sk5 @ sk2 @ A ) @ sk2 )
| ( incident_c @ ( sk6 @ sk2 @ A ) @ sk2 )
| ( part_of @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[541:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(55,plain,
! [A: $i] :
( ( end_point @ ( sk9 @ A ) @ A )
| ( closed @ A ) ),
inference(cnf,[status(esa)],[54]) ).
thf(57,plain,
! [A: $i] :
( ( end_point @ ( sk9 @ A ) @ A )
| ( closed @ A ) ),
inference(simp,[status(thm)],[55]) ).
thf(9,axiom,
! [A: $i] :
? [B: $i] : ( inner_point @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3) ).
thf(58,plain,
! [A: $i] :
? [B: $i] : ( inner_point @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(59,plain,
! [A: $i] : ( inner_point @ ( sk10 @ A ) @ A ),
inference(cnf,[status(esa)],[58]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( inner_point @ A @ B )
<=> ( ( incident_c @ A @ B )
& ~ ( end_point @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_point_defn) ).
thf(47,plain,
! [A: $i,B: $i] :
( ( ( inner_point @ A @ B )
=> ( ( incident_c @ A @ B )
& ~ ( end_point @ A @ B ) ) )
& ( ( ( incident_c @ A @ B )
& ~ ( end_point @ A @ B ) )
=> ( inner_point @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(48,plain,
( ! [A: $i,B: $i] :
( ( inner_point @ A @ B )
=> ( ( incident_c @ A @ B )
& ~ ( end_point @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( ( incident_c @ A @ B )
& ~ ( end_point @ A @ B ) )
=> ( inner_point @ A @ B ) ) ),
inference(miniscope,[status(thm)],[47]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ~ ( end_point @ A @ B ) ),
inference(cnf,[status(esa)],[48]) ).
thf(933,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( end_point @ B @ C )
| ( ( inner_point @ ( sk10 @ A ) @ A )
!= ( inner_point @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[59,51]) ).
thf(934,plain,
! [A: $i] :
~ ( end_point @ ( sk10 @ A ) @ A ),
inference(pattern_uni,[status(thm)],[933:[bind(A,$thf( D )),bind(B,$thf( sk10 @ D )),bind(C,$thf( D ))]]) ).
thf(937,plain,
! [A: $i] :
~ ( end_point @ ( sk10 @ A ) @ A ),
inference(simp,[status(thm)],[934]) ).
thf(4,axiom,
! [A: $i] :
( ( open @ A )
<=> ? [B: $i] : ( end_point @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',open_defn) ).
thf(35,plain,
! [A: $i] :
( ( ( open @ A )
=> ? [B: $i] : ( end_point @ B @ A ) )
& ( ? [B: $i] : ( end_point @ B @ A )
=> ( open @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(36,plain,
( ! [A: $i] :
( ( open @ A )
=> ? [B: $i] : ( end_point @ B @ A ) )
& ! [A: $i] :
( ? [B: $i] : ( end_point @ B @ A )
=> ( open @ A ) ) ),
inference(miniscope,[status(thm)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ B @ A )
| ( open @ A ) ),
inference(cnf,[status(esa)],[36]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ B @ A )
| ( open @ A ) ),
inference(simp,[status(thm)],[37]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( part_of @ B @ A )
<=> ! [C: $i] :
( ( incident_c @ C @ B )
=> ( incident_c @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn) ).
thf(123,plain,
! [A: $i,B: $i] :
( ( ( part_of @ B @ A )
=> ! [C: $i] :
( ( incident_c @ C @ B )
=> ( incident_c @ C @ A ) ) )
& ( ! [C: $i] :
( ( incident_c @ C @ B )
=> ( incident_c @ C @ A ) )
=> ( part_of @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( end_point @ B @ A )
=> ? [C: $i] :
( ( end_point @ C @ A )
& ( B != C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c6) ).
thf(43,plain,
! [A: $i,B: $i] :
( ( end_point @ B @ A )
=> ? [C: $i] :
( ( end_point @ C @ A )
& ( B != C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(277,plain,
! [C: $i,B: $i,A: $i] :
( ( closed @ A )
| ( open @ B )
| ( ( end_point @ ( sk9 @ A ) @ A )
!= ( end_point @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57,39]) ).
thf(278,plain,
! [A: $i] :
( ( closed @ A )
| ( open @ A ) ),
inference(pattern_uni,[status(thm)],[277:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk9 @ D ))]]) ).
thf(283,plain,
! [A: $i] :
( ( closed @ A )
| ( open @ A ) ),
inference(simp,[status(thm)],[278]) ).
thf(929,plain,
! [C: $i,B: $i,A: $i] :
( ( closed @ A )
| ~ ( inner_point @ B @ C )
| ( ( end_point @ ( sk9 @ A ) @ A )
!= ( end_point @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[57,51]) ).
thf(930,plain,
! [A: $i] :
( ( closed @ A )
| ~ ( inner_point @ ( sk9 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[929:[bind(A,$thf( D )),bind(B,$thf( sk9 @ D )),bind(C,$thf( D ))]]) ).
thf(935,plain,
! [A: $i] :
( ( closed @ A )
| ~ ( inner_point @ ( sk9 @ A ) @ A ) ),
inference(simp,[status(thm)],[930]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( meet @ C @ A @ B )
=> ? [C: $i] :
( C
= ( sum @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c8) ).
thf(120,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( meet @ C @ A @ B )
=> ? [C: $i] :
( C
= ( sum @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( sk5 @ B @ A ) @ B )
| ~ ( incident_c @ ( sk6 @ B @ A ) @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[26]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( incident_c @ ( sk5 @ B @ A ) @ B )
| ~ ( incident_c @ ( sk6 @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(21,plain,
~ ( part_of @ ( sum @ sk1 @ sk2 ) @ ( sum @ sk1 @ sk3 ) ),
inference(cnf,[status(esa)],[20]) ).
thf(138,plain,
( ( part_of @ ( sum @ sk1 @ sk2 ) @ ( sum @ sk1 @ sk3 ) )
!= ( part_of @ sk2 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[24,21]) ).
thf(139,plain,
( ( ( sum @ sk1 @ sk2 )
!= sk2 )
| ( ( sum @ sk1 @ sk3 )
!= sk3 ) ),
inference(simp,[status(thm)],[138]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( sk5 @ B @ A ) @ B )
| ~ ( incident_c @ ( sk6 @ B @ A ) @ A )
| ( A != sk2 )
| ( ( sum @ sk1 @ sk3 )
!= sk3 )
| ( B
!= ( sum @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[31,139]) ).
thf(218,plain,
! [A: $i] :
( ~ ( incident_c @ ( sk5 @ ( sum @ sk1 @ sk2 ) @ A ) @ ( sum @ sk1 @ sk2 ) )
| ~ ( incident_c @ ( sk6 @ ( sum @ sk1 @ sk2 ) @ A ) @ A )
| ( A != sk2 )
| ( ( sum @ sk1 @ sk3 )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[217:[bind(A,$thf( A )),bind(B,$thf( sum @ sk1 @ sk2 ))]]) ).
thf(269,plain,
( ~ ( incident_c @ ( sk5 @ ( sum @ sk1 @ sk2 ) @ sk2 ) @ ( sum @ sk1 @ sk2 ) )
| ~ ( incident_c @ ( sk6 @ ( sum @ sk1 @ sk2 ) @ sk2 ) @ sk2 )
| ( ( sum @ sk1 @ sk3 )
!= sk3 ) ),
inference(simp,[status(thm)],[218]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( incident_c @ A @ B ) ),
inference(cnf,[status(esa)],[48]) ).
thf(291,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ B @ C )
| ( ( inner_point @ ( sk10 @ A ) @ A )
!= ( inner_point @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[59,50]) ).
thf(292,plain,
! [A: $i] : ( incident_c @ ( sk10 @ A ) @ A ),
inference(pattern_uni,[status(thm)],[291:[bind(A,$thf( D )),bind(B,$thf( sk10 @ D )),bind(C,$thf( D ))]]) ).
thf(293,plain,
! [A: $i] : ( incident_c @ ( sk10 @ A ) @ A ),
inference(simp,[status(thm)],[292]) ).
thf(1038,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( sk6 @ sk2 @ B ) @ sk2 )
| ( part_of @ B @ sk3 )
| ( ( incident_c @ ( sk10 @ A ) @ A )
!= ( incident_c @ ( sk5 @ sk2 @ B ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[293,542]) ).
thf(1110,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( sk6 @ sk2 @ B ) @ sk2 )
| ( part_of @ B @ sk3 )
| ( ( sk10 @ A )
!= ( sk5 @ sk2 @ B ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[1038]) ).
thf(1127,plain,
! [A: $i] :
( ( incident_c @ ( sk6 @ sk2 @ A ) @ sk2 )
| ( part_of @ A @ sk3 )
| ( ( sk5 @ sk2 @ A )
!= ( sk10 @ sk2 ) ) ),
inference(simp,[status(thm)],[1110]) ).
thf(1609,plain,
! [C: $i,B: $i,A: $i] :
( ( closed @ A )
| ( incident_c @ B @ C )
| ( ( end_point @ ( sk9 @ A ) @ A )
!= ( end_point @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[57,101]) ).
thf(1610,plain,
! [A: $i] :
( ( closed @ A )
| ( incident_c @ ( sk9 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[1609:[bind(A,$thf( D )),bind(B,$thf( sk9 @ D )),bind(C,$thf( D ))]]) ).
thf(1613,plain,
! [A: $i] :
( ( closed @ A )
| ( incident_c @ ( sk9 @ A ) @ A ) ),
inference(simp,[status(thm)],[1610]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( closed @ A )
& ( meet @ D @ B @ C )
& ( A
= ( sum @ B @ C ) ) )
=> ! [E: $i] :
( ( end_point @ E @ B )
=> ( meet @ E @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c7) ).
thf(133,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( closed @ A )
& ( meet @ D @ B @ C )
& ( A
= ( sum @ B @ C ) ) )
=> ! [E: $i] :
( ( end_point @ E @ B )
=> ( meet @ E @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( part_of @ B @ A )
& ( part_of @ C @ A )
& ( part_of @ D @ A )
& ? [E: $i] :
( ( end_point @ E @ B )
& ( end_point @ E @ C )
& ( end_point @ E @ D ) ) )
=> ( ( part_of @ C @ D )
| ( part_of @ D @ C )
| ( part_of @ B @ C )
| ( part_of @ C @ B )
| ( part_of @ B @ D )
| ( part_of @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2) ).
thf(60,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( part_of @ B @ A )
& ( part_of @ C @ A )
& ( part_of @ D @ A )
& ? [E: $i] :
( ( end_point @ E @ B )
& ( end_point @ E @ C )
& ( end_point @ E @ D ) ) )
=> ( ( part_of @ C @ D )
| ( part_of @ D @ C )
| ( part_of @ B @ C )
| ( part_of @ C @ B )
| ( part_of @ B @ D )
| ( part_of @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( sk5 @ B @ A ) @ B )
| ~ ( incident_c @ ( sk6 @ B @ A ) @ A )
| ( ( sum @ sk1 @ sk2 )
!= sk2 )
| ( A != sk3 )
| ( B
!= ( sum @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[31,139]) ).
thf(224,plain,
! [A: $i] :
( ~ ( incident_c @ ( sk5 @ ( sum @ sk1 @ sk3 ) @ A ) @ ( sum @ sk1 @ sk3 ) )
| ~ ( incident_c @ ( sk6 @ ( sum @ sk1 @ sk3 ) @ A ) @ A )
| ( ( sum @ sk1 @ sk2 )
!= sk2 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[223:[bind(A,$thf( A )),bind(B,$thf( sum @ sk1 @ sk3 ))]]) ).
thf(270,plain,
( ~ ( incident_c @ ( sk5 @ ( sum @ sk1 @ sk3 ) @ sk3 ) @ ( sum @ sk1 @ sk3 ) )
| ~ ( incident_c @ ( sk6 @ ( sum @ sk1 @ sk3 ) @ sk3 ) @ sk3 )
| ( ( sum @ sk1 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[224]) ).
thf(938,plain,
! [B: $i,A: $i] :
( ( closed @ A )
| ( ( end_point @ ( sk9 @ A ) @ A )
!= ( end_point @ ( sk10 @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57,937]) ).
thf(948,plain,
! [B: $i,A: $i] :
( ( closed @ A )
| ( ( sk9 @ A )
!= ( sk10 @ B ) )
| ( A != B ) ),
inference(simp,[status(thm)],[938]) ).
thf(952,plain,
! [A: $i] :
( ( closed @ A )
| ( ( sk10 @ A )
!= ( sk9 @ A ) ) ),
inference(simp,[status(thm)],[948]) ).
thf(38,plain,
! [A: $i] :
( ~ ( open @ A )
| ( end_point @ ( sk7 @ A ) @ A ) ),
inference(cnf,[status(esa)],[36]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( sk5 @ B @ A ) @ A )
| ~ ( incident_c @ ( sk6 @ B @ A ) @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[26]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( incident_c @ ( sk5 @ B @ A ) @ A )
| ~ ( incident_c @ ( sk6 @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(124,plain,
( ! [A: $i,B: $i] :
( ( part_of @ B @ A )
=> ! [C: $i] :
( ( incident_c @ C @ B )
=> ( incident_c @ C @ A ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ( incident_c @ C @ B )
=> ( incident_c @ C @ A ) )
=> ( part_of @ B @ A ) ) ),
inference(miniscope,[status(thm)],[123]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( sk20 @ B @ A ) @ B )
| ( part_of @ B @ A ) ),
inference(cnf,[status(esa)],[124]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( sk20 @ B @ A ) @ B )
| ( part_of @ B @ A ) ),
inference(simp,[status(thm)],[125]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( sk5 @ B @ A ) @ B )
| ~ ( incident_c @ ( sk6 @ B @ A ) @ A )
| ( ( sum @ sk1 @ sk2 )
!= sk2 )
| ( B != sk3 )
| ( A
!= ( sum @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[31,139]) ).
thf(212,plain,
! [A: $i] :
( ~ ( incident_c @ ( sk5 @ A @ ( sum @ sk1 @ sk3 ) ) @ A )
| ~ ( incident_c @ ( sk6 @ A @ ( sum @ sk1 @ sk3 ) ) @ ( sum @ sk1 @ sk3 ) )
| ( ( sum @ sk1 @ sk2 )
!= sk2 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[211:[bind(A,$thf( sum @ sk1 @ sk3 )),bind(B,$thf( B ))]]) ).
thf(266,plain,
( ~ ( incident_c @ ( sk5 @ sk3 @ ( sum @ sk1 @ sk3 ) ) @ sk3 )
| ~ ( incident_c @ ( sk6 @ sk3 @ ( sum @ sk1 @ sk3 ) ) @ ( sum @ sk1 @ sk3 ) )
| ( ( sum @ sk1 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[212]) ).
thf(943,plain,
! [B: $i,A: $i] :
( ~ ( open @ A )
| ( ( end_point @ ( sk7 @ A ) @ A )
!= ( end_point @ ( sk10 @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[38,937]) ).
thf(949,plain,
! [B: $i,A: $i] :
( ~ ( open @ A )
| ( ( sk7 @ A )
!= ( sk10 @ B ) )
| ( A != B ) ),
inference(simp,[status(thm)],[943]) ).
thf(953,plain,
! [A: $i] :
( ~ ( open @ A )
| ( ( sk10 @ A )
!= ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[949]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( sk5 @ B @ A ) @ A )
| ( incident_c @ ( sk6 @ B @ A ) @ B )
| ( A = B ) ),
inference(cnf,[status(esa)],[26]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( incident_c @ ( sk5 @ B @ A ) @ A )
| ( incident_c @ ( sk6 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(22,plain,
meet @ sk4 @ sk1 @ sk3,
inference(cnf,[status(esa)],[20]) ).
thf(931,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( open @ A )
| ~ ( inner_point @ B @ C )
| ( ( end_point @ ( sk7 @ A ) @ A )
!= ( end_point @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[38,51]) ).
thf(932,plain,
! [A: $i] :
( ~ ( open @ A )
| ~ ( inner_point @ ( sk7 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[931:[bind(A,$thf( D )),bind(B,$thf( sk7 @ D )),bind(C,$thf( D ))]]) ).
thf(936,plain,
! [A: $i] :
( ~ ( open @ A )
| ~ ( inner_point @ ( sk7 @ A ) @ A ) ),
inference(simp,[status(thm)],[932]) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( open @ A )
| ~ ( closed @ B )
| ( ( end_point @ ( sk7 @ A ) @ A )
!= ( end_point @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[38,56]) ).
thf(141,plain,
! [A: $i] :
( ~ ( open @ A )
| ~ ( closed @ A ) ),
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk7 @ D ))]]) ).
thf(144,plain,
! [A: $i] :
( ~ ( open @ A )
| ~ ( closed @ A ) ),
inference(simp,[status(thm)],[141]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( A
= ( sum @ B @ C ) )
<=> ! [D: $i] :
( ( incident_c @ D @ A )
<=> ( ( incident_c @ D @ B )
| ( incident_c @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_defn) ).
thf(66,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( sum @ B @ C ) )
=> ! [D: $i] :
( ( ( incident_c @ D @ A )
=> ( ( incident_c @ D @ B )
| ( incident_c @ D @ C ) ) )
& ( ( ( incident_c @ D @ B )
| ( incident_c @ D @ C ) )
=> ( incident_c @ D @ A ) ) ) )
& ( ! [D: $i] :
( ( ( incident_c @ D @ A )
=> ( ( incident_c @ D @ B )
| ( incident_c @ D @ C ) ) )
& ( ( ( incident_c @ D @ B )
| ( incident_c @ D @ C ) )
=> ( incident_c @ D @ A ) ) )
=> ( A
= ( sum @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( meet @ A @ B @ C )
<=> ( ( incident_c @ A @ B )
& ( incident_c @ A @ C )
& ! [D: $i] :
( ( ( incident_c @ D @ B )
& ( incident_c @ D @ C ) )
=> ( ( end_point @ D @ B )
& ( end_point @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_defn) ).
thf(108,plain,
! [A: $i,B: $i,C: $i] :
( ( ( meet @ A @ B @ C )
=> ( ( incident_c @ A @ B )
& ( incident_c @ A @ C )
& ! [D: $i] :
( ( ( incident_c @ D @ B )
& ( incident_c @ D @ C ) )
=> ( ( end_point @ D @ B )
& ( end_point @ D @ C ) ) ) ) )
& ( ( ( incident_c @ A @ B )
& ( incident_c @ A @ C )
& ! [D: $i] :
( ( ( incident_c @ D @ B )
& ( incident_c @ D @ C ) )
=> ( ( end_point @ D @ B )
& ( end_point @ D @ C ) ) ) )
=> ( meet @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( part_of @ B @ A )
& ( B != A ) )
=> ( open @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c1) ).
thf(130,plain,
! [A: $i,B: $i] :
( ( ( part_of @ B @ A )
& ( B != A ) )
=> ( open @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( sk5 @ B @ A ) @ B )
| ~ ( incident_c @ ( sk6 @ B @ A ) @ A )
| ( part_of @ A @ sk3 )
| ( B != sk2 ) ),
inference(paramod_ordered,[status(thm)],[31,24]) ).
thf(150,plain,
! [A: $i] :
( ~ ( incident_c @ ( sk5 @ sk2 @ A ) @ sk2 )
| ~ ( incident_c @ ( sk6 @ sk2 @ A ) @ A )
| ( part_of @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( sk5 @ B @ A ) @ B )
| ~ ( incident_c @ ( sk6 @ B @ A ) @ A )
| ( B != sk2 )
| ( ( sum @ sk1 @ sk3 )
!= sk3 )
| ( A
!= ( sum @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[31,139]) ).
thf(206,plain,
! [A: $i] :
( ~ ( incident_c @ ( sk5 @ A @ ( sum @ sk1 @ sk2 ) ) @ A )
| ~ ( incident_c @ ( sk6 @ A @ ( sum @ sk1 @ sk2 ) ) @ ( sum @ sk1 @ sk2 ) )
| ( A != sk2 )
| ( ( sum @ sk1 @ sk3 )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( sum @ sk1 @ sk2 )),bind(B,$thf( B ))]]) ).
thf(263,plain,
( ~ ( incident_c @ ( sk5 @ sk2 @ ( sum @ sk1 @ sk2 ) ) @ sk2 )
| ~ ( incident_c @ ( sk6 @ sk2 @ ( sum @ sk1 @ sk2 ) ) @ ( sum @ sk1 @ sk2 ) )
| ( ( sum @ sk1 @ sk3 )
!= sk3 ) ),
inference(simp,[status(thm)],[206]) ).
thf(543,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( sk5 @ B @ A ) @ B )
| ( incident_c @ ( sk6 @ B @ A ) @ B )
| ( part_of @ sk2 @ A )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[32,24]) ).
thf(544,plain,
! [A: $i] :
( ~ ( incident_c @ ( sk5 @ sk3 @ A ) @ sk3 )
| ( incident_c @ ( sk6 @ sk3 @ A ) @ sk3 )
| ( part_of @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[543:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( end_point @ B @ A )
& ( end_point @ C @ A )
& ( end_point @ D @ A ) )
=> ( ( B = C )
| ( B = D )
| ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c5) ).
thf(40,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( end_point @ B @ A )
& ( end_point @ C @ A )
& ( end_point @ D @ A ) )
=> ( ( B = C )
| ( B = D )
| ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,plain,
meet @ sk4 @ sk1 @ sk2,
inference(cnf,[status(esa)],[20]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( inner_point @ B @ A )
=> ? [C: $i,D: $i] :
( ( meet @ B @ C @ D )
& ( A
= ( sum @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c4) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( inner_point @ B @ A )
=> ? [C: $i,D: $i] :
( ( meet @ B @ C @ D )
& ( A
= ( sum @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19474,plain,
$false,
inference(e,[status(thm)],[101,56,542,57,937,92,53,39,123,43,58,283,935,120,269,1127,24,1613,25,293,133,60,270,952,38,21,33,128,266,953,32,34,22,59,936,144,66,108,130,35,150,263,50,544,31,40,139,23,51,19,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO083+1 : TPTP v8.2.0. Released v2.4.0.
% 0.04/0.13 % Command : run_Leo-III %s %d THM
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 21 10:44:40 EDT 2024
% 0.12/0.34 % CPUTime :
% 1.00/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.38/1.03 % [INFO] Parsing done (136ms).
% 1.38/1.04 % [INFO] Running in sequential loop mode.
% 1.81/1.27 % [INFO] eprover registered as external prover.
% 1.81/1.27 % [INFO] Scanning for conjecture ...
% 1.97/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.15/1.37 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.15/1.41 % [INFO] Problem is first-order (TPTP FOF).
% 2.15/1.42 % [INFO] Type checking passed.
% 2.15/1.42 % [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 ...
% 47.78/10.59 % External prover 'e' found a proof!
% 47.78/10.59 % [INFO] Killing All external provers ...
% 47.78/10.59 % Time passed: 10055ms (effective reasoning time: 9551ms)
% 47.78/10.59 % 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)>
% 47.78/10.60 % Axioms used in derivation (16): end_point_defn, c8, meet_defn, part_of_defn, c9, sum_defn, closed_defn, c7, inner_point_defn, c3, c4, c5, c2, c1, c6, open_defn
% 47.78/10.60 % No. of inferences in proof: 117
% 47.78/10.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10055 ms resp. 9551 ms w/o parsing
% 47.78/10.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 47.78/10.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------