TSTP Solution File: GEO087-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO087-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 : Fri May 19 11:09:17 EDT 2023
% Result : Unsatisfiable 7.83s 2.77s
% Output : Refutation 7.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 74
% Syntax : Number of formulae : 198 ( 19 unt; 24 typ; 0 def)
% Number of atoms : 511 ( 80 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1778 ( 264 ~; 303 |; 0 &;1211 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 5 con; 0-3 aty)
% Number of variables : 381 ( 0 ^; 381 !; 0 ?; 381 :)
% Comments :
%------------------------------------------------------------------------------
thf(part_of_type,type,
part_of: $i > $i > $o ).
thf(sk14_type,type,
sk14: $i ).
thf(sk15_type,type,
sk15: $i ).
thf(meet_type,type,
meet: $i > $i > $i > $o ).
thf(sk16_type,type,
sk16: $i ).
thf(end_point_type,type,
end_point: $i > $i > $o ).
thf(ax0_sk11_type,type,
ax0_sk11: $i > $i > $i ).
thf(incident_c_type,type,
incident_c: $i > $i > $o ).
thf(ax0_sk2_type,type,
ax0_sk2: $i > $i > $i > $i ).
thf(sum_type,type,
sum: $i > $i > $i ).
thf(ax0_sk13_type,type,
ax0_sk13: $i > $i > $i ).
thf(closed_type,type,
closed: $i > $o ).
thf(inner_point_type,type,
inner_point: $i > $i > $o ).
thf(ax0_sk3_type,type,
ax0_sk3: $i > $i > $i ).
thf(ax0_sk8_type,type,
ax0_sk8: $i > $i ).
thf(open_type,type,
open: $i > $o ).
thf(ax0_sk9_type,type,
ax0_sk9: $i > $i > $i ).
thf(ax0_sk10_type,type,
ax0_sk10: $i > $i > $i ).
thf(ax0_sk4_type,type,
ax0_sk4: $i > $i > $i ).
thf(ax0_sk7_type,type,
ax0_sk7: $i > $i ).
thf(ax0_sk6_type,type,
ax0_sk6: $i > $i ).
thf(ax0_sk5_type,type,
ax0_sk5: $i > $i > $i > $i ).
thf(ax0_sk1_type,type,
ax0_sk1: $i > $i > $i ).
thf(ax0_sk12_type,type,
ax0_sk12: $i > $i > $i ).
thf(29,axiom,
! [A: $i] :
( ~ ( open @ A )
| ( end_point @ ( ax0_sk7 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_defn_33) ).
thf(115,plain,
! [A: $i] :
( ~ ( open @ A )
| ( end_point @ ( ax0_sk7 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( A
!= ( ax0_sk11 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c6_42) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( A
!= ( ax0_sk11 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk1 @ A @ B ) @ B )
| ( part_of @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn_3) ).
thf(134,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk1 @ A @ B ) @ B )
| ( part_of @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( end_point @ A @ B )
| ( inner_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn_23) ).
thf(80,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( end_point @ A @ B )
| ( inner_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ~ ( incident_c @ C @ A )
| ( incident_c @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn_1) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ~ ( incident_c @ C @ A )
| ( incident_c @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ( A = B )
| ( open @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c1_35) ).
thf(154,plain,
! [B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ( A = B )
| ( open @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( A
!= ( ax0_sk11 @ A @ B ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( ax0_sk11 @ A @ B )
!= A )
| ~ ( end_point @ A @ B ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( closed @ A )
| ~ ( end_point @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_defn_31) ).
thf(69,plain,
! [B: $i,A: $i] :
( ~ ( closed @ A )
| ~ ( end_point @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( part_of @ ( ax0_sk4 @ B @ A ) @ B )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_16) ).
thf(138,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( part_of @ ( ax0_sk4 @ B @ A ) @ B )
| ( end_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( open @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_defn_34) ).
thf(88,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( open @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ B )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A )
| ( C
= ( sum @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_10) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ B )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A )
| ( C
= ( sum @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ~ ( incident_c @ D @ B )
| ~ ( incident_c @ D @ C )
| ( end_point @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_27) ).
thf(142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ~ ( incident_c @ D @ B )
| ~ ( incident_c @ D @ C )
| ( end_point @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(2,negated_conjecture,
meet @ sk16 @ sk14 @ sk15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_9_68) ).
thf(52,plain,
meet @ sk16 @ sk14 @ sk15,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A )
| ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C )
| ( C
= ( sum @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_12) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A )
| ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C )
| ( C
= ( sum @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(16,axiom,
! [A: $i] : ( inner_point @ ( ax0_sk8 @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c3_37) ).
thf(84,plain,
! [A: $i] : ( inner_point @ ( ax0_sk8 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( incident_c @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn_21) ).
thf(108,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( incident_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( incident_c @ A @ B ) ),
inference(cnf,[status(esa)],[108]) ).
thf(764,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ B @ C )
| ( ( inner_point @ ( ax0_sk8 @ A ) @ A )
!= ( inner_point @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[84,109]) ).
thf(765,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ A ) @ A ),
inference(pattern_uni,[status(thm)],[764:[bind(A,$thf( D )),bind(B,$thf( ax0_sk8 @ D )),bind(C,$thf( D ))]]) ).
thf(766,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ A ) @ A ),
inference(simp,[status(thm)],[765]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ B @ C ) )
| ~ ( incident_c @ D @ B )
| ( incident_c @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_5) ).
thf(65,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ B @ C ) )
| ~ ( incident_c @ D @ B )
| ( incident_c @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(66,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ B @ C ) )
| ~ ( incident_c @ D @ B )
| ( incident_c @ D @ A ) ),
inference(cnf,[status(esa)],[65]) ).
thf(67,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ B @ C ) )
| ~ ( incident_c @ D @ B )
| ( incident_c @ D @ A ) ),
inference(lifteq,[status(thm)],[66]) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ C @ A )
| ( incident_c @ C @ ( sum @ A @ B ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(769,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ D @ ( sum @ B @ C ) )
| ( ( incident_c @ ( ax0_sk8 @ A ) @ A )
!= ( incident_c @ D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[766,68]) ).
thf(770,plain,
! [B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ B @ A ) ),
inference(pattern_uni,[status(thm)],[769:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( ax0_sk8 @ E ))]]) ).
thf(793,plain,
! [B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ B @ A ) ),
inference(simp,[status(thm)],[770]) ).
thf(808,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ B @ A ) )
!= ( incident_c @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[793,68]) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ ( sum @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[808:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( sum @ G @ H )),bind(D,$thf( D )),bind(E,$thf( ax0_sk8 @ G ))]]) ).
thf(838,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ ( sum @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[809]) ).
thf(34,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ~ ( part_of @ C @ B )
| ~ ( part_of @ D @ B )
| ~ ( end_point @ E @ A )
| ~ ( end_point @ E @ C )
| ~ ( end_point @ E @ D )
| ( part_of @ C @ D )
| ( part_of @ D @ C )
| ( part_of @ A @ C )
| ( part_of @ C @ A )
| ( part_of @ A @ D )
| ( part_of @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2_36) ).
thf(125,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ~ ( part_of @ C @ B )
| ~ ( part_of @ D @ B )
| ~ ( end_point @ E @ A )
| ~ ( end_point @ E @ C )
| ~ ( end_point @ E @ D )
| ( part_of @ C @ D )
| ( part_of @ D @ C )
| ( part_of @ A @ C )
| ( part_of @ C @ A )
| ( part_of @ A @ D )
| ( part_of @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( part_of @ ( ax0_sk4 @ B @ A ) @ ( ax0_sk3 @ B @ A ) )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_20) ).
thf(157,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( part_of @ ( ax0_sk4 @ B @ A ) @ ( ax0_sk3 @ B @ A ) )
| ( end_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ B )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A )
| ( C
= ( sum @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_7) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ B )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A )
| ( C
= ( sum @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c9_48) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( B = A ) ),
inference(cnf,[status(esa)],[59]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B ) ),
inference(lifteq,[status(thm)],[60]) ).
thf(1,negated_conjecture,
part_of @ sk14 @ sk15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_9_67) ).
thf(51,plain,
part_of @ sk14 @ sk15,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(283,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( part_of @ sk14 @ A )
| ( B != sk15 ) ),
inference(paramod_ordered,[status(thm)],[61,51]) ).
thf(284,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ sk15 ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ sk15 ) @ sk15 )
| ( part_of @ sk14 @ A ) ),
inference(pattern_uni,[status(thm)],[283:[bind(A,$thf( A )),bind(B,$thf( sk15 ))]]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( incident_c @ A @ C )
| ( incident_c @ ( ax0_sk5 @ C @ B @ A ) @ B )
| ( meet @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_28) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( incident_c @ A @ C )
| ( incident_c @ ( ax0_sk5 @ C @ B @ A ) @ B )
| ( meet @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(116,plain,
! [A: $i] :
( ~ ( open @ A )
| ( end_point @ ( ax0_sk7 @ A ) @ A ) ),
inference(cnf,[status(esa)],[115]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ~ ( end_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn_22) ).
thf(106,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ~ ( end_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ~ ( end_point @ A @ B ) ),
inference(cnf,[status(esa)],[106]) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( end_point @ B @ C )
| ( ( inner_point @ ( ax0_sk8 @ A ) @ A )
!= ( inner_point @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[84,107]) ).
thf(164,plain,
! [A: $i] :
~ ( end_point @ ( ax0_sk8 @ A ) @ A ),
inference(pattern_uni,[status(thm)],[163:[bind(A,$thf( D )),bind(B,$thf( ax0_sk8 @ D )),bind(C,$thf( D ))]]) ).
thf(165,plain,
! [A: $i] :
~ ( end_point @ ( ax0_sk8 @ A ) @ A ),
inference(simp,[status(thm)],[164]) ).
thf(188,plain,
! [B: $i,A: $i] :
( ~ ( open @ A )
| ( ( end_point @ ( ax0_sk7 @ A ) @ A )
!= ( end_point @ ( ax0_sk8 @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[116,165]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ~ ( open @ A )
| ( ( ax0_sk7 @ A )
!= ( ax0_sk8 @ B ) )
| ( A != B ) ),
inference(simp,[status(thm)],[188]) ).
thf(195,plain,
! [A: $i] :
( ~ ( open @ A )
| ( ( ax0_sk7 @ A )
!= ( ax0_sk8 @ A ) ) ),
inference(simp,[status(thm)],[191]) ).
thf(293,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ~ ( open @ C )
| ( A
!= ( ax0_sk8 @ C ) )
| ( B
!= ( ax0_sk7 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[61,195]) ).
thf(294,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ ( ax0_sk7 @ B ) ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ ( ax0_sk7 @ B ) ) @ ( ax0_sk7 @ B ) )
| ~ ( open @ B )
| ( A
!= ( ax0_sk8 @ B ) ) ),
inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( A )),bind(B,$thf( ax0_sk7 @ D )),bind(C,$thf( D ))]]) ).
thf(316,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ A ) @ ( ax0_sk7 @ A ) ) @ ( ax0_sk8 @ A ) )
| ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ A ) @ ( ax0_sk7 @ A ) ) @ ( ax0_sk7 @ A ) )
| ~ ( open @ A ) ),
inference(simp,[status(thm)],[294]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( incident_c @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_13) ).
thf(63,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( incident_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( incident_c @ A @ B ) ),
inference(cnf,[status(esa)],[63]) ).
thf(474,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( open @ A )
| ( incident_c @ B @ C )
| ( ( end_point @ ( ax0_sk7 @ A ) @ A )
!= ( end_point @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[116,64]) ).
thf(475,plain,
! [A: $i] :
( ~ ( open @ A )
| ( incident_c @ ( ax0_sk7 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[474:[bind(A,$thf( D )),bind(B,$thf( ax0_sk7 @ D )),bind(C,$thf( D ))]]) ).
thf(485,plain,
! [A: $i] :
( ~ ( open @ A )
| ( incident_c @ ( ax0_sk7 @ A ) @ A ) ),
inference(simp,[status(thm)],[475]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( part_of @ ( ax0_sk3 @ B @ A ) @ ( ax0_sk4 @ B @ A ) )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_19) ).
thf(121,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( part_of @ ( ax0_sk3 @ B @ A ) @ ( ax0_sk4 @ B @ A ) )
| ( end_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ~ ( incident_c @ D @ B )
| ~ ( incident_c @ D @ C )
| ( end_point @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_26) ).
thf(132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ~ ( incident_c @ D @ B )
| ~ ( incident_c @ D @ C )
| ( end_point @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( open @ B ) ),
inference(cnf,[status(esa)],[88]) ).
thf(30,axiom,
! [A: $i] :
( ( end_point @ ( ax0_sk6 @ A ) @ A )
| ( closed @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_defn_32) ).
thf(117,plain,
! [A: $i] :
( ( end_point @ ( ax0_sk6 @ A ) @ A )
| ( closed @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c9_45) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ B @ C ) )
| ~ ( incident_c @ D @ C )
| ( incident_c @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_6) ).
thf(102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ B @ C ) )
| ~ ( incident_c @ D @ C )
| ( incident_c @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ~ ( closed @ A )
| ~ ( end_point @ B @ A ) ),
inference(cnf,[status(esa)],[69]) ).
thf(180,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( open @ A )
| ( ( ax0_sk11 @ B @ C )
!= B )
| ( ( end_point @ ( ax0_sk7 @ A ) @ A )
!= ( end_point @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[116,55]) ).
thf(181,plain,
! [A: $i] :
( ~ ( open @ A )
| ( ( ax0_sk11 @ ( ax0_sk7 @ A ) @ A )
!= ( ax0_sk7 @ A ) ) ),
inference(pattern_uni,[status(thm)],[180:[bind(A,$thf( D )),bind(B,$thf( ax0_sk7 @ D )),bind(C,$thf( D ))]]) ).
thf(192,plain,
! [A: $i] :
( ~ ( open @ A )
| ( ( ax0_sk11 @ ( ax0_sk7 @ A ) @ A )
!= ( ax0_sk7 @ A ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c9_46) ).
thf(92,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(118,plain,
! [A: $i] :
( ( end_point @ ( ax0_sk6 @ A ) @ A )
| ( closed @ A ) ),
inference(cnf,[status(esa)],[117]) ).
thf(174,plain,
! [C: $i,B: $i,A: $i] :
( ( closed @ A )
| ( open @ C )
| ( ( end_point @ ( ax0_sk6 @ A ) @ A )
!= ( end_point @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[118,89]) ).
thf(175,plain,
! [A: $i] :
( ( closed @ A )
| ( open @ A ) ),
inference(pattern_uni,[status(thm)],[174:[bind(A,$thf( D )),bind(B,$thf( ax0_sk6 @ D )),bind(C,$thf( D ))]]) ).
thf(176,plain,
! [A: $i] :
( ( closed @ A )
| ( open @ A ) ),
inference(simp,[status(thm)],[175]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( closed @ A )
| ( end_point @ ( ax0_sk7 @ B ) @ B )
| ( ( open @ A )
!= ( open @ B ) ) ),
inference(paramod_ordered,[status(thm)],[176,116]) ).
thf(190,plain,
! [A: $i] :
( ( closed @ A )
| ( end_point @ ( ax0_sk7 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[189:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(478,plain,
! [C: $i,B: $i,A: $i] :
( ( closed @ A )
| ( incident_c @ B @ C )
| ( ( end_point @ ( ax0_sk7 @ A ) @ A )
!= ( end_point @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[190,64]) ).
thf(479,plain,
! [A: $i] :
( ( closed @ A )
| ( incident_c @ ( ax0_sk7 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[478:[bind(A,$thf( D )),bind(B,$thf( ax0_sk7 @ D )),bind(C,$thf( D ))]]) ).
thf(488,plain,
! [A: $i] :
( ( closed @ A )
| ( incident_c @ ( ax0_sk7 @ A ) @ A ) ),
inference(simp,[status(thm)],[479]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk1 @ A @ B ) @ A )
| ( part_of @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn_2) ).
thf(123,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk1 @ A @ B ) @ A )
| ( part_of @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk1 @ A @ B ) @ A )
| ( part_of @ A @ B ) ),
inference(cnf,[status(esa)],[123]) ).
thf(182,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( open @ A )
| ~ ( inner_point @ B @ C )
| ( ( end_point @ ( ax0_sk7 @ A ) @ A )
!= ( end_point @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[116,107]) ).
thf(183,plain,
! [A: $i] :
( ~ ( open @ A )
| ~ ( inner_point @ ( ax0_sk7 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[182:[bind(A,$thf( D )),bind(B,$thf( ax0_sk7 @ D )),bind(C,$thf( D ))]]) ).
thf(193,plain,
! [A: $i] :
( ~ ( open @ A )
| ~ ( inner_point @ ( ax0_sk7 @ A ) @ A ) ),
inference(simp,[status(thm)],[183]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( B
= ( sum @ ( ax0_sk9 @ A @ B ) @ ( ax0_sk10 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c4_39) ).
thf(96,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( B
= ( sum @ ( ax0_sk9 @ A @ B ) @ ( ax0_sk10 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( closed @ A )
| ( ( end_point @ ( ax0_sk6 @ A ) @ A )
!= ( end_point @ ( ax0_sk8 @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[118,165]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( closed @ A )
| ( ( ax0_sk6 @ A )
!= ( ax0_sk8 @ B ) )
| ( A != B ) ),
inference(simp,[status(thm)],[170]) ).
thf(173,plain,
! [A: $i] :
( ( closed @ A )
| ( ( ax0_sk6 @ A )
!= ( ax0_sk8 @ A ) ) ),
inference(simp,[status(thm)],[171]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( ( ax0_sk12 @ C @ B )
= ( sum @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c8_44) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( ( ax0_sk12 @ C @ B )
= ( sum @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( incident_c @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_24) ).
thf(148,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( incident_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ~ ( 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/sandbox/benchmark/theBenchmark.p',end_point_defn_14) ).
thf(161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ~ ( part_of @ C @ B )
| ~ ( part_of @ D @ B )
| ~ ( incident_c @ A @ C )
| ~ ( incident_c @ A @ D )
| ( part_of @ C @ D )
| ( part_of @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ B @ C ) )
| ~ ( incident_c @ D @ A )
| ( incident_c @ D @ B )
| ( incident_c @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_4) ).
thf(71,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ B @ C ) )
| ~ ( incident_c @ D @ A )
| ( incident_c @ D @ B )
| ( incident_c @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(43,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( closed @ A )
| ~ ( meet @ B @ C @ D )
| ( A
!= ( sum @ C @ D ) )
| ~ ( end_point @ E @ C )
| ( meet @ E @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c7_43) ).
thf(144,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( closed @ A )
| ~ ( meet @ B @ C @ D )
| ( A
!= ( sum @ C @ D ) )
| ~ ( end_point @ E @ C )
| ( meet @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( incident_c @ A @ C )
| ( incident_c @ ( ax0_sk5 @ C @ B @ A ) @ C )
| ( meet @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_29) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( incident_c @ A @ C )
| ( incident_c @ ( ax0_sk5 @ C @ B @ A ) @ C )
| ( meet @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(166,plain,
! [C: $i,B: $i,A: $i] :
( ( closed @ A )
| ~ ( inner_point @ B @ C )
| ( ( end_point @ ( ax0_sk6 @ A ) @ A )
!= ( end_point @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[118,107]) ).
thf(167,plain,
! [A: $i] :
( ( closed @ A )
| ~ ( inner_point @ ( ax0_sk6 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( D )),bind(B,$thf( ax0_sk6 @ D )),bind(C,$thf( D ))]]) ).
thf(172,plain,
! [A: $i] :
( ( closed @ A )
| ~ ( inner_point @ ( ax0_sk6 @ A ) @ A ) ),
inference(simp,[status(thm)],[167]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( incident_c @ A @ ( ax0_sk4 @ B @ A ) )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_18) ).
thf(113,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( incident_c @ A @ ( ax0_sk4 @ B @ A ) )
| ( end_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ~ ( end_point @ C @ B )
| ~ ( end_point @ D @ B )
| ( A = C )
| ( A = D )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c5_40) ).
thf(76,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ~ ( end_point @ C @ B )
| ~ ( end_point @ D @ B )
| ( A = C )
| ( A = D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(295,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ~ ( open @ C )
| ( B
!= ( ax0_sk8 @ C ) )
| ( A
!= ( ax0_sk7 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[61,195]) ).
thf(296,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ B ) @ A ) @ ( ax0_sk7 @ B ) )
| ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ B ) @ A ) @ A )
| ~ ( open @ B )
| ( A
!= ( ax0_sk8 @ B ) ) ),
inference(pattern_uni,[status(thm)],[295:[bind(A,$thf( ax0_sk7 @ D )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(318,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ A ) @ ( ax0_sk8 @ A ) ) @ ( ax0_sk7 @ A ) )
| ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ A ) @ ( ax0_sk8 @ A ) ) @ ( ax0_sk8 @ A ) )
| ~ ( open @ A ) ),
inference(simp,[status(thm)],[296]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( incident_c @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_25) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( incident_c @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( open @ A )
| ~ ( closed @ B )
| ( ( end_point @ ( ax0_sk7 @ A ) @ A )
!= ( end_point @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[116,70]) ).
thf(187,plain,
! [A: $i] :
( ~ ( open @ A )
| ~ ( closed @ A ) ),
inference(pattern_uni,[status(thm)],[186:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( ax0_sk7 @ D ))]]) ).
thf(194,plain,
! [A: $i] :
( ~ ( open @ A )
| ~ ( closed @ A ) ),
inference(simp,[status(thm)],[187]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( part_of @ A @ sk15 )
| ( B != sk14 ) ),
inference(paramod_ordered,[status(thm)],[61,51]) ).
thf(282,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ sk14 ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ sk14 ) @ sk14 )
| ( part_of @ A @ sk15 ) ),
inference(pattern_uni,[status(thm)],[281:[bind(A,$thf( A )),bind(B,$thf( sk14 ))]]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( meet @ A @ ( ax0_sk9 @ A @ B ) @ ( ax0_sk10 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c4_38) ).
thf(150,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( meet @ A @ ( ax0_sk9 @ A @ B ) @ ( ax0_sk10 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ B )
| ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C )
| ( C
= ( sum @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_11) ).
thf(99,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ B )
| ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C )
| ( C
= ( sum @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( closed @ A )
| ~ ( inner_point @ ( ax0_sk7 @ B ) @ B )
| ( ( open @ A )
!= ( open @ B ) ) ),
inference(paramod_ordered,[status(thm)],[176,193]) ).
thf(203,plain,
! [A: $i] :
( ( closed @ A )
| ~ ( inner_point @ ( ax0_sk7 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[202:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ B )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ B )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A )
| ( C
= ( sum @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_9) ).
thf(75,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( incident_c @ A @ C )
| ~ ( end_point @ ( ax0_sk5 @ C @ B @ A ) @ B )
| ~ ( end_point @ ( ax0_sk5 @ C @ B @ A ) @ C )
| ( meet @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_30) ).
thf(119,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( incident_c @ A @ C )
| ~ ( end_point @ ( ax0_sk5 @ C @ B @ A ) @ B )
| ~ ( end_point @ ( ax0_sk5 @ C @ B @ A ) @ C )
| ( meet @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( closed @ A )
| ( ( ax0_sk7 @ B )
!= ( ax0_sk8 @ B ) )
| ( ( open @ A )
!= ( open @ B ) ) ),
inference(paramod_ordered,[status(thm)],[176,195]) ).
thf(207,plain,
! [A: $i] :
( ( closed @ A )
| ( ( ax0_sk7 @ A )
!= ( ax0_sk8 @ A ) ) ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( incident_c @ A @ ( ax0_sk3 @ B @ A ) )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_17) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( incident_c @ A @ ( ax0_sk3 @ B @ A ) )
| ( end_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( part_of @ ( ax0_sk3 @ B @ A ) @ B )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_15) ).
thf(136,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( part_of @ ( ax0_sk3 @ B @ A ) @ B )
| ( end_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c9_47) ).
thf(79,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C )
| ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C )
| ( C
= ( sum @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_8) ).
thf(62,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( end_point @ ( ax0_sk11 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c6_41) ).
thf(90,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( end_point @ ( ax0_sk11 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(476,plain,
! [C: $i,B: $i,A: $i] :
( ( closed @ A )
| ( incident_c @ B @ C )
| ( ( end_point @ ( ax0_sk6 @ A ) @ A )
!= ( end_point @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[118,64]) ).
thf(477,plain,
! [A: $i] :
( ( closed @ A )
| ( incident_c @ ( ax0_sk6 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[476:[bind(A,$thf( D )),bind(B,$thf( ax0_sk6 @ D )),bind(C,$thf( D ))]]) ).
thf(486,plain,
! [A: $i] :
( ( closed @ A )
| ( incident_c @ ( ax0_sk6 @ A ) @ A ) ),
inference(simp,[status(thm)],[477]) ).
thf(1104,plain,
$false,
inference(cvc4,[status(thm)],[115,53,134,80,127,154,55,69,138,88,56,142,52,110,838,125,157,93,284,152,316,485,106,121,84,766,61,132,89,116,117,793,85,102,70,192,165,92,65,109,488,124,193,96,173,129,148,161,64,176,59,118,71,144,159,172,113,76,318,140,108,123,194,63,282,150,99,203,75,119,207,82,51,190,107,136,79,195,68,62,90,486]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO087-1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n027.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 : Fri May 19 04:40:52 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.90/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/0.99 % [INFO] Parsing done (142ms).
% 1.42/1.00 % [INFO] Running in sequential loop mode.
% 1.89/1.21 % [INFO] eprover registered as external prover.
% 1.89/1.21 % [INFO] cvc4 registered as external prover.
% 1.89/1.21 % [INFO] Scanning for conjecture ...
% 1.89/1.27 % [INFO] Found a conjecture and 48 axioms. Running axiom selection ...
% 2.10/1.32 % [INFO] Axiom selection finished. Selected 48 axioms (removed 0 axioms).
% 2.10/1.37 % [INFO] Problem is propositional (TPTP CNF).
% 2.10/1.38 % [INFO] Type checking passed.
% 2.10/1.38 % [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 ...
% 7.83/2.77 % External prover 'cvc4' found a proof!
% 7.83/2.77 % [INFO] Killing All external provers ...
% 7.83/2.77 % Time passed: 2249ms (effective reasoning time: 1764ms)
% 7.83/2.77 % 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)>
% 7.83/2.77 % Axioms used in derivation (48): c6_41, part_of_defn_3, inner_point_defn_22, c7_43, meet_defn_30, c9_48, sum_defn_6, part_of_defn_2, c5_40, meet_defn_25, sum_defn_11, closed_defn_32, sum_defn_8, end_point_defn_19, end_point_defn_15, c9_46, c4_39, c1_35, sum_defn_5, c2_36, c9_47, c8_44, end_point_defn_18, inner_point_defn_21, sum_defn_4, c3_37, sum_defn_9, end_point_defn_14, closed_defn_31, meet_defn_28, end_point_defn_20, meet_defn_24, sum_defn_10, end_point_defn_17, meet_defn_29, end_point_defn_13, open_defn_33, meet_defn_27, meet_defn_26, part_of_defn_1, end_point_defn_16, c9_45, open_defn_34, sum_defn_12, inner_point_defn_23, sum_defn_7, c4_38, c6_42
% 7.83/2.77 % No. of inferences in proof: 174
% 7.83/2.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2249 ms resp. 1764 ms w/o parsing
% 7.83/2.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.83/2.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------