TSTP Solution File: GEO094-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO094-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 11:09:19 EDT 2023
% Result : Unsatisfiable 119.58s 36.94s
% Output : Refutation 120.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 77
% Syntax : Number of formulae : 717 ( 212 unt; 25 typ; 0 def)
% Number of atoms : 1801 ( 529 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 7684 ( 836 ~; 785 |; 0 &;6063 @)
% ( 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 : 28 ( 25 usr; 6 con; 0-3 aty)
% Number of variables : 1486 ( 0 ^;1486 !; 0 ?;1486 :)
% Comments :
%------------------------------------------------------------------------------
thf(meet_type,type,
meet: $i > $i > $i > $o ).
thf(sk17_type,type,
sk17: $i ).
thf(sk15_type,type,
sk15: $i ).
thf(sk16_type,type,
sk16: $i ).
thf(part_of_type,type,
part_of: $i > $i > $o ).
thf(sk14_type,type,
sk14: $i ).
thf(end_point_type,type,
end_point: $i > $i > $o ).
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(inner_point_type,type,
inner_point: $i > $i > $o ).
thf(ax0_sk8_type,type,
ax0_sk8: $i > $i ).
thf(ax0_sk9_type,type,
ax0_sk9: $i > $i > $i ).
thf(ax0_sk10_type,type,
ax0_sk10: $i > $i > $i ).
thf(ax0_sk5_type,type,
ax0_sk5: $i > $i > $i > $i ).
thf(ax0_sk3_type,type,
ax0_sk3: $i > $i > $i ).
thf(ax0_sk4_type,type,
ax0_sk4: $i > $i > $i ).
thf(ax0_sk1_type,type,
ax0_sk1: $i > $i > $i ).
thf(open_type,type,
open: $i > $o ).
thf(ax0_sk12_type,type,
ax0_sk12: $i > $i > $i ).
thf(ax0_sk6_type,type,
ax0_sk6: $i > $i ).
thf(closed_type,type,
closed: $i > $o ).
thf(ax0_sk11_type,type,
ax0_sk11: $i > $i > $i ).
thf(ax0_sk7_type,type,
ax0_sk7: $i > $i ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c9_45) ).
thf(69,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)],[10]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( B = A ) ),
inference(cnf,[status(esa)],[69]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ A ) ),
inference(lifteq,[status(thm)],[70]) ).
thf(9,axiom,
! [A: $i] : ( inner_point @ ( ax0_sk8 @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3_37) ).
thf(68,plain,
! [A: $i] : ( inner_point @ ( ax0_sk8 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,negated_conjecture,
end_point @ sk17 @ sk14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',proposition_2_14_3_70) ).
thf(56,plain,
end_point @ sk17 @ sk14,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ~ ( end_point @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_point_defn_22) ).
thf(113,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ~ ( end_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ~ ( end_point @ A @ B ) ),
inference(cnf,[status(esa)],[113]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( ( end_point @ sk17 @ sk14 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56,114]) ).
thf(288,plain,
~ ( inner_point @ sk17 @ sk14 ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( sk17 )),bind(B,$thf( sk14 ))]]) ).
thf(321,plain,
! [A: $i] :
( ( inner_point @ ( ax0_sk8 @ A ) @ A )
!= ( inner_point @ sk17 @ sk14 ) ),
inference(paramod_ordered,[status(thm)],[68,288]) ).
thf(330,plain,
! [A: $i] :
( ( ( ax0_sk8 @ A )
!= sk17 )
| ( A != sk14 ) ),
inference(simp,[status(thm)],[321]) ).
thf(333,plain,
( ( ax0_sk8 @ sk14 )
!= sk17 ),
inference(simp,[status(thm)],[330]) ).
thf(558,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( B != sk17 )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[71,333]) ).
thf(559,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ A ) @ A )
| ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ A ) @ ( ax0_sk8 @ sk14 ) )
| ( A != sk17 ) ),
inference(pattern_uni,[status(thm)],[558:[bind(A,$thf( ax0_sk8 @ sk14 )),bind(B,$thf( B ))]]) ).
thf(833,plain,
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[559]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ B @ C ) )
| ~ ( incident_c @ D @ B )
| ( incident_c @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_defn_5) ).
thf(74,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)],[13]) ).
thf(75,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)],[74]) ).
thf(76,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)],[75]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ C @ A )
| ( incident_c @ C @ ( sum @ A @ B ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(1319,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( incident_c @ C @ ( sum @ A @ B ) )
| ( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) )
!= ( incident_c @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[833,77]) ).
thf(1320,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( sum @ ( ax0_sk8 @ sk14 ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[1319:[bind(A,$thf( ax0_sk8 @ sk14 )),bind(B,$thf( B )),bind(C,$thf( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ))]]) ).
thf(1337,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( sum @ ( ax0_sk8 @ sk14 ) @ A ) ) ),
inference(simp,[status(thm)],[1320]) ).
thf(40,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/sandbox2/benchmark/theBenchmark.p',c7_43) ).
thf(138,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)],[40]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk1 @ A @ B ) @ A )
| ( part_of @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn_2) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk1 @ A @ B ) @ A )
| ( part_of @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( B
= ( sum @ ( ax0_sk9 @ A @ B ) @ ( ax0_sk10 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c4_39) ).
thf(81,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)],[15]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( B
= ( sum @ ( ax0_sk9 @ A @ B ) @ ( ax0_sk10 @ A @ B ) ) ) ),
inference(cnf,[status(esa)],[81]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( ( sum @ ( ax0_sk9 @ A @ B ) @ ( ax0_sk10 @ A @ B ) )
= B )
| ~ ( inner_point @ A @ B ) ),
inference(lifteq,[status(thm)],[82]) ).
thf(2808,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sum @ ( ax0_sk9 @ B @ C ) @ ( ax0_sk10 @ B @ C ) )
= C )
| ( ( inner_point @ ( ax0_sk8 @ A ) @ A )
!= ( inner_point @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[68,83]) ).
thf(2809,plain,
! [A: $i] :
( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[2808:[bind(A,$thf( D )),bind(B,$thf( ax0_sk8 @ D )),bind(C,$thf( D ))]]) ).
thf(2837,plain,
! [A: $i] :
( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
= A ),
inference(simp,[status(thm)],[2809]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( incident_c @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_point_defn_21) ).
thf(92,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( incident_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( incident_c @ A @ B ) ),
inference(cnf,[status(esa)],[92]) ).
thf(2101,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)],[68,93]) ).
thf(2102,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ A ) @ A ),
inference(pattern_uni,[status(thm)],[2101:[bind(A,$thf( D )),bind(B,$thf( ax0_sk8 @ D )),bind(C,$thf( D ))]]) ).
thf(2103,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ A ) @ A ),
inference(simp,[status(thm)],[2102]) ).
thf(2106,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)],[2103,77]) ).
thf(2107,plain,
! [B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ B @ A ) ),
inference(pattern_uni,[status(thm)],[2106:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( ax0_sk8 @ E ))]]) ).
thf(2155,plain,
! [B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ B @ A ) ),
inference(simp,[status(thm)],[2107]) ).
thf(2981,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk8 @ C ) @ A )
| ( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( sum @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2837,2155]) ).
thf(2982,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) ) @ A ),
inference(pattern_uni,[status(thm)],[2981:[bind(A,$thf( H )),bind(B,$thf( ax0_sk10 @ ( ax0_sk8 @ H ) @ H )),bind(C,$thf( ax0_sk9 @ ( ax0_sk8 @ H ) @ H ))]]) ).
thf(3020,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) ) @ A ),
inference(simp,[status(thm)],[2982]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c9_48) ).
thf(60,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)],[6]) ).
thf(61,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)],[60]) ).
thf(62,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)],[61]) ).
thf(334,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( A != sk17 )
| ( B
!= ( ax0_sk8 @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[62,333]) ).
thf(335,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ ( ax0_sk8 @ sk14 ) ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( A != sk17 ) ),
inference(pattern_uni,[status(thm)],[334:[bind(A,$thf( A )),bind(B,$thf( ax0_sk8 @ sk14 ))]]) ).
thf(344,plain,
( ~ ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ~ ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[335]) ).
thf(2105,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( incident_c @ ( ax0_sk8 @ A ) @ A )
!= ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2103,344]) ).
thf(2139,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( ax0_sk8 @ A )
!= ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[2105]) ).
thf(2156,plain,
( ~ ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(simp,[status(thm)],[2139]) ).
thf(3297,plain,
! [A: $i] :
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) ) @ A )
!= ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 ) ) ),
inference(paramod_ordered,[status(thm)],[3020,2156]) ).
thf(3337,plain,
! [A: $i] :
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) )
!= ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) )
| ( A != sk17 ) ),
inference(simp,[status(thm)],[3297]) ).
thf(3354,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ sk17 ) @ sk17 ) )
!= ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(simp,[status(thm)],[3337]) ).
thf(34754,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ sk17 ) @ sk17 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[3354]) ).
thf(34755,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ sk17 ) @ sk17 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(simp,[status(thm)],[34754]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ B @ C ) )
| ~ ( incident_c @ D @ C )
| ( incident_c @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_defn_6) ).
thf(88,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)],[18]) ).
thf(89,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ B @ C ) )
| ~ ( incident_c @ D @ C )
| ( incident_c @ D @ A ) ),
inference(cnf,[status(esa)],[88]) ).
thf(90,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ B @ C ) )
| ~ ( incident_c @ D @ C )
| ( incident_c @ D @ A ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ C @ B )
| ( incident_c @ C @ ( sum @ A @ B ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(5140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ D @ ( sum @ B @ C ) )
| ( ( incident_c @ ( ax0_sk8 @ A ) @ A )
!= ( incident_c @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2103,91]) ).
thf(5141,plain,
! [B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ A @ B ) ),
inference(pattern_uni,[status(thm)],[5140:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( ax0_sk8 @ E ))]]) ).
thf(5227,plain,
! [B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ A @ B ) ),
inference(simp,[status(thm)],[5141]) ).
thf(5275,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk8 @ C ) @ A )
| ( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( sum @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2837,5227]) ).
thf(5276,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) ) @ A ),
inference(pattern_uni,[status(thm)],[5275:[bind(A,$thf( H )),bind(B,$thf( ax0_sk9 @ ( ax0_sk8 @ H ) @ H )),bind(C,$thf( ax0_sk10 @ ( ax0_sk8 @ H ) @ H ))]]) ).
thf(5352,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) ) @ A ),
inference(simp,[status(thm)],[5276]) ).
thf(5397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ D @ ( sum @ B @ C ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) ) @ A )
!= ( incident_c @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5352,91]) ).
thf(5398,plain,
! [B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ A @ B ) ),
inference(pattern_uni,[status(thm)],[5397:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ G ) @ G ) ))]]) ).
thf(5452,plain,
! [B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ A @ B ) ),
inference(simp,[status(thm)],[5398]) ).
thf(7181,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ A @ B ) )
!= ( incident_c @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5452,77]) ).
thf(7182,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ ( sum @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[7181:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( sum @ J @ K )),bind(D,$thf( D )),bind(E,$thf( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ K ) @ K ) ))]]) ).
thf(7285,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ ( sum @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[7182]) ).
thf(5196,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 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[2155,91]) ).
thf(5197,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ A @ ( sum @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[5196:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( sum @ G @ H )),bind(E,$thf( ax0_sk8 @ G ))]]) ).
thf(5246,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ A @ ( sum @ B @ C ) ) ),
inference(simp,[status(thm)],[5197]) ).
thf(5524,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ F @ ( sum @ D @ E ) )
| ( ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ A @ ( sum @ B @ C ) ) )
!= ( incident_c @ F @ E ) ) ),
inference(paramod_ordered,[status(thm)],[5246,91]) ).
thf(5525,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ A @ ( sum @ B @ ( sum @ C @ D ) ) ) ),
inference(pattern_uni,[status(thm)],[5524:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( sum @ H @ ( sum @ J @ K ) )),bind(F,$thf( ax0_sk8 @ J ))]]) ).
thf(5582,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ A @ ( sum @ B @ ( sum @ C @ D ) ) ) ),
inference(simp,[status(thm)],[5525]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( open @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',open_defn_34) ).
thf(149,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( open @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( open @ B ) ),
inference(cnf,[status(esa)],[149]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( open @ B )
| ( ( end_point @ sk17 @ sk14 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56,150]) ).
thf(170,plain,
open @ sk14,
inference(pattern_uni,[status(thm)],[169:[bind(A,$thf( sk17 )),bind(B,$thf( sk14 ))]]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( ( ax0_sk12 @ C @ B )
= ( sum @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c8_44) ).
thf(115,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)],[29]) ).
thf(5301,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ A @ B ) )
!= ( incident_c @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[5227,91]) ).
thf(5302,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ A @ ( sum @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[5301:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( sum @ G @ H )),bind(E,$thf( ax0_sk8 @ H ))]]) ).
thf(5360,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ A @ ( sum @ B @ C ) ) ),
inference(simp,[status(thm)],[5302]) ).
thf(6885,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ F @ ( sum @ D @ E ) )
| ( ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ A @ ( sum @ B @ C ) ) )
!= ( incident_c @ F @ D ) ) ),
inference(paramod_ordered,[status(thm)],[5360,77]) ).
thf(6886,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ B @ ( sum @ C @ D ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[6885:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( sum @ H @ ( sum @ J @ K ) )),bind(E,$thf( E )),bind(F,$thf( ax0_sk8 @ K ))]]) ).
thf(7008,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ B @ ( sum @ C @ D ) ) @ A ) ),
inference(simp,[status(thm)],[6886]) ).
thf(1,negated_conjecture,
meet @ sk17 @ sk15 @ sk16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',proposition_2_14_3_67) ).
thf(53,plain,
meet @ sk17 @ sk15 @ sk16,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( incident_c @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_defn_24) ).
thf(142,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( incident_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( incident_c @ A @ B ) ),
inference(cnf,[status(esa)],[142]) ).
thf(52995,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ A @ B )
| ( ( meet @ sk17 @ sk15 @ sk16 )
!= ( meet @ A @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[53,143]) ).
thf(52996,plain,
incident_c @ sk17 @ sk15,
inference(pattern_uni,[status(thm)],[52995:[bind(A,$thf( sk17 )),bind(B,$thf( sk15 )),bind(C,$thf( sk16 ))]]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk1 @ A @ B ) @ B )
| ( part_of @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn_3) ).
thf(120,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk1 @ A @ B ) @ B )
| ( part_of @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(2,negated_conjecture,
part_of @ sk15 @ sk14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',proposition_2_14_3_68) ).
thf(54,plain,
part_of @ sk15 @ sk14,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ( A = B )
| ( open @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c1_35) ).
thf(108,plain,
! [B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ( A = B )
| ( open @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ( A = B )
| ( open @ A ) ),
inference(cnf,[status(esa)],[108]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( part_of @ A @ B )
| ( open @ A ) ),
inference(lifteq,[status(thm)],[109]) ).
thf(22579,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( open @ A )
| ( ( part_of @ sk15 @ sk14 )
!= ( part_of @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54,110]) ).
thf(22580,plain,
( ( sk14 = sk15 )
| ( open @ sk15 ) ),
inference(pattern_uni,[status(thm)],[22579:[bind(A,$thf( sk15 )),bind(B,$thf( sk14 ))]]) ).
thf(25998,plain,
( ( open @ sk15 )
| ( sk14 != sk14 ) ),
inference(paramod_ordered,[status(thm)],[22580,170]) ).
thf(25999,plain,
open @ sk15,
inference(pattern_uni,[status(thm)],[25998:[]]) ).
thf(52,axiom,
! [A: $i] :
( ~ ( open @ A )
| ( end_point @ ( ax0_sk7 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',open_defn_33) ).
thf(165,plain,
! [A: $i] :
( ~ ( open @ A )
| ( end_point @ ( ax0_sk7 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(166,plain,
! [A: $i] :
( ~ ( open @ A )
| ( end_point @ ( ax0_sk7 @ A ) @ A ) ),
inference(cnf,[status(esa)],[165]) ).
thf(26313,plain,
! [A: $i] :
( ( end_point @ ( ax0_sk7 @ A ) @ A )
| ( ( open @ sk15 )
!= ( open @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25999,166]) ).
thf(26314,plain,
end_point @ ( ax0_sk7 @ sk15 ) @ sk15,
inference(pattern_uni,[status(thm)],[26313:[bind(A,$thf( sk15 ))]]) ).
thf(268,plain,
! [A: $i] :
( ( end_point @ ( ax0_sk7 @ A ) @ A )
| ( ( open @ sk14 )
!= ( open @ A ) ) ),
inference(paramod_ordered,[status(thm)],[170,166]) ).
thf(269,plain,
end_point @ ( ax0_sk7 @ sk14 ) @ sk14,
inference(pattern_uni,[status(thm)],[268:[bind(A,$thf( sk14 ))]]) ).
thf(5268,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ A @ B ) )
!= ( incident_c @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5227,77]) ).
thf(5269,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ ( sum @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[5268:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( sum @ G @ H )),bind(D,$thf( D )),bind(E,$thf( ax0_sk8 @ H ))]]) ).
thf(5348,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ ( sum @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[5269]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( incident_c @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_defn_25) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( incident_c @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(135,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( incident_c @ A @ C ) ),
inference(cnf,[status(esa)],[134]) ).
thf(45879,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ A @ C )
| ( ( meet @ sk17 @ sk15 @ sk16 )
!= ( meet @ A @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[53,135]) ).
thf(45880,plain,
incident_c @ sk17 @ sk16,
inference(pattern_uni,[status(thm)],[45879:[bind(A,$thf( sk17 )),bind(B,$thf( sk15 )),bind(C,$thf( sk16 ))]]) ).
thf(45939,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ C @ ( sum @ A @ B ) )
| ( ( incident_c @ sk17 @ sk16 )
!= ( incident_c @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[45880,91]) ).
thf(45940,plain,
! [A: $i] : ( incident_c @ sk17 @ ( sum @ A @ sk16 ) ),
inference(pattern_uni,[status(thm)],[45939:[bind(A,$thf( A )),bind(B,$thf( sk16 )),bind(C,$thf( sk17 ))]]) ).
thf(46134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ D @ ( sum @ B @ C ) )
| ( ( incident_c @ sk17 @ ( sum @ A @ sk16 ) )
!= ( incident_c @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[45940,91]) ).
thf(46135,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ A @ ( sum @ B @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[46134:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( sum @ E @ sk16 )),bind(D,$thf( sk17 ))]]) ).
thf(46276,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ A @ ( sum @ B @ sk16 ) ) ),
inference(simp,[status(thm)],[46135]) ).
thf(48347,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ sk17 @ ( sum @ A @ ( sum @ B @ sk16 ) ) )
!= ( incident_c @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[46276,77]) ).
thf(48348,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ ( sum @ B @ ( sum @ C @ sk16 ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[48347:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( sum @ F @ ( sum @ H @ sk16 ) )),bind(D,$thf( D )),bind(E,$thf( sk17 ))]]) ).
thf(48621,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ ( sum @ B @ ( sum @ C @ sk16 ) ) @ A ) ),
inference(simp,[status(thm)],[48348]) ).
thf(5481,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ F @ ( sum @ D @ E ) )
| ( ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ A @ ( sum @ B @ C ) ) )
!= ( incident_c @ F @ D ) ) ),
inference(paramod_ordered,[status(thm)],[5246,77]) ).
thf(5482,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ ( sum @ B @ ( sum @ C @ D ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[5481:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( sum @ H @ ( sum @ J @ K ) )),bind(E,$thf( E )),bind(F,$thf( ax0_sk8 @ J ))]]) ).
thf(5589,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ ( sum @ B @ ( sum @ C @ D ) ) @ A ) ),
inference(simp,[status(thm)],[5482]) ).
thf(5650,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ F @ ( sum @ D @ E ) )
| ( ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ ( sum @ B @ C ) @ A ) )
!= ( incident_c @ F @ E ) ) ),
inference(paramod_ordered,[status(thm)],[5348,91]) ).
thf(5651,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ ( sum @ C @ D ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[5650:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( sum @ ( sum @ J @ K ) @ I )),bind(F,$thf( ax0_sk8 @ K ))]]) ).
thf(5708,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ ( sum @ C @ D ) @ B ) ) ),
inference(simp,[status(thm)],[5651]) ).
thf(9142,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ ( sum @ C @ D ) @ B ) ) )
!= ( incident_c @ G @ F ) ) ),
inference(paramod_ordered,[status(thm)],[5708,91]) ).
thf(9143,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ A @ ( sum @ B @ ( sum @ ( sum @ D @ E ) @ C ) ) ) ),
inference(pattern_uni,[status(thm)],[9142:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( sum @ I @ ( sum @ ( sum @ M @ N ) @ L ) )),bind(G,$thf( ax0_sk8 @ N ))]]) ).
thf(9233,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ A @ ( sum @ B @ ( sum @ ( sum @ D @ E ) @ C ) ) ) ),
inference(simp,[status(thm)],[9143]) ).
thf(5401,plain,
! [A: $i] :
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) ) @ A )
!= ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 ) ) ),
inference(paramod_ordered,[status(thm)],[5352,2156]) ).
thf(5428,plain,
! [A: $i] :
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) )
| ( A != sk17 ) ),
inference(simp,[status(thm)],[5401]) ).
thf(5467,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ sk17 ) @ sk17 ) )
!= ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(simp,[status(thm)],[5428]) ).
thf(43629,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ sk17 ) @ sk17 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[5467]) ).
thf(43630,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ sk17 ) @ sk17 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(simp,[status(thm)],[43629]) ).
thf(37,axiom,
! [A: $i] :
( ( end_point @ ( ax0_sk6 @ A ) @ A )
| ( closed @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closed_defn_32) ).
thf(132,plain,
! [A: $i] :
( ( end_point @ ( ax0_sk6 @ A ) @ A )
| ( closed @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(133,plain,
! [A: $i] :
( ( end_point @ ( ax0_sk6 @ A ) @ A )
| ( closed @ A ) ),
inference(cnf,[status(esa)],[132]) ).
thf(293,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)],[68,114]) ).
thf(294,plain,
! [A: $i] :
~ ( end_point @ ( ax0_sk8 @ A ) @ A ),
inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( D )),bind(B,$thf( ax0_sk8 @ D )),bind(C,$thf( D ))]]) ).
thf(297,plain,
! [A: $i] :
~ ( end_point @ ( ax0_sk8 @ A ) @ A ),
inference(simp,[status(thm)],[294]) ).
thf(383,plain,
! [B: $i,A: $i] :
( ( closed @ A )
| ( ( end_point @ ( ax0_sk6 @ A ) @ A )
!= ( end_point @ ( ax0_sk8 @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[133,297]) ).
thf(389,plain,
! [B: $i,A: $i] :
( ( closed @ A )
| ( ( ax0_sk6 @ A )
!= ( ax0_sk8 @ B ) )
| ( A != B ) ),
inference(simp,[status(thm)],[383]) ).
thf(395,plain,
! [A: $i] :
( ( closed @ A )
| ( ( ax0_sk6 @ A )
!= ( ax0_sk8 @ A ) ) ),
inference(simp,[status(thm)],[389]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ~ ( closed @ A )
| ~ ( end_point @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closed_defn_31) ).
thf(155,plain,
! [B: $i,A: $i] :
( ~ ( closed @ A )
| ~ ( end_point @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ~ ( closed @ A )
| ~ ( end_point @ B @ A ) ),
inference(cnf,[status(esa)],[155]) ).
thf(167,plain,
! [B: $i,A: $i] :
( ~ ( closed @ A )
| ( ( end_point @ sk17 @ sk14 )
!= ( end_point @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[56,156]) ).
thf(168,plain,
~ ( closed @ sk14 ),
inference(pattern_uni,[status(thm)],[167:[bind(A,$thf( sk14 )),bind(B,$thf( sk17 ))]]) ).
thf(917,plain,
! [A: $i] :
( ( ( ax0_sk6 @ A )
!= ( ax0_sk8 @ A ) )
| ( ( closed @ A )
!= ( closed @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[395,168]) ).
thf(918,plain,
( ( ax0_sk6 @ sk14 )
!= ( ax0_sk8 @ sk14 ) ),
inference(pattern_uni,[status(thm)],[917:[bind(A,$thf( sk14 ))]]) ).
thf(932,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( B
!= ( ax0_sk8 @ sk14 ) )
| ( A
!= ( ax0_sk6 @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[71,918]) ).
thf(933,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk6 @ sk14 ) @ A ) @ A )
| ( incident_c @ ( ax0_sk13 @ ( ax0_sk6 @ sk14 ) @ A ) @ ( ax0_sk6 @ sk14 ) )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[932:[bind(A,$thf( ax0_sk6 @ sk14 )),bind(B,$thf( B ))]]) ).
thf(945,plain,
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk6 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( incident_c @ ( ax0_sk13 @ ( ax0_sk6 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk6 @ sk14 ) ) ),
inference(simp,[status(thm)],[933]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( incident_c @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn_13) ).
thf(153,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( incident_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(8701,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ A @ ( sum @ B @ ( sum @ C @ D ) ) ) )
!= ( incident_c @ G @ E ) ) ),
inference(paramod_ordered,[status(thm)],[5582,77]) ).
thf(8702,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ B @ ( sum @ C @ ( sum @ D @ E ) ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[8701:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( sum @ I @ ( sum @ K @ ( sum @ M @ N ) ) )),bind(F,$thf( F )),bind(G,$thf( ax0_sk8 @ M ))]]) ).
thf(8881,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ B @ ( sum @ C @ ( sum @ D @ E ) ) ) @ A ) ),
inference(simp,[status(thm)],[8702]) ).
thf(554,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( A != sk17 )
| ( B
!= ( ax0_sk8 @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[71,333]) ).
thf(555,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( incident_c @ ( ax0_sk13 @ A @ ( ax0_sk8 @ sk14 ) ) @ A )
| ( A != sk17 ) ),
inference(pattern_uni,[status(thm)],[554:[bind(A,$thf( A )),bind(B,$thf( ax0_sk8 @ sk14 ))]]) ).
thf(829,plain,
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 ) ),
inference(simp,[status(thm)],[555]) ).
thf(5607,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ F @ ( sum @ D @ E ) )
| ( ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ ( sum @ B @ C ) @ A ) )
!= ( incident_c @ F @ D ) ) ),
inference(paramod_ordered,[status(thm)],[5348,77]) ).
thf(5608,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ ( sum @ C @ D ) @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[5607:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( sum @ ( sum @ J @ K ) @ I )),bind(E,$thf( E )),bind(F,$thf( ax0_sk8 @ K ))]]) ).
thf(5715,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ ( sum @ C @ D ) @ B ) @ A ) ),
inference(simp,[status(thm)],[5608]) ).
thf(9267,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ ( sum @ A @ C ) @ B ) )
| ( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( sum @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[2837,5715]) ).
thf(9268,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ ( sum @ C @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[9267:[bind(A,$thf( J )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( ax0_sk9 @ ( ax0_sk8 @ J ) @ J )),bind(E,$thf( ax0_sk10 @ ( ax0_sk8 @ J ) @ J ))]]) ).
thf(9424,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ ( sum @ C @ B ) @ A ) ),
inference(simp,[status(thm)],[9268]) ).
thf(8760,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ A @ ( sum @ B @ ( sum @ C @ D ) ) ) )
!= ( incident_c @ G @ F ) ) ),
inference(paramod_ordered,[status(thm)],[5582,91]) ).
thf(8761,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ B @ ( sum @ C @ ( sum @ D @ E ) ) ) ) ),
inference(pattern_uni,[status(thm)],[8760:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( sum @ I @ ( sum @ K @ ( sum @ M @ N ) ) )),bind(G,$thf( ax0_sk8 @ M ))]]) ).
thf(8851,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ B @ ( sum @ C @ ( sum @ D @ E ) ) ) ) ),
inference(simp,[status(thm)],[8761]) ).
thf(2163,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)],[2155,77]) ).
thf(2164,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ ( sum @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[2163:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( sum @ G @ H )),bind(D,$thf( D )),bind(E,$thf( ax0_sk8 @ G ))]]) ).
thf(2222,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ ( sum @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[2164]) ).
thf(5136,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ F @ ( sum @ D @ E ) )
| ( ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ ( sum @ B @ C ) @ A ) )
!= ( incident_c @ F @ E ) ) ),
inference(paramod_ordered,[status(thm)],[2222,91]) ).
thf(5137,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ A @ ( sum @ ( sum @ C @ D ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[5136:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( sum @ ( sum @ J @ K ) @ I )),bind(F,$thf( ax0_sk8 @ J ))]]) ).
thf(5226,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ A @ ( sum @ ( sum @ C @ D ) @ B ) ) ),
inference(simp,[status(thm)],[5137]) ).
thf(7955,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ A @ ( sum @ ( sum @ C @ D ) @ B ) ) )
!= ( incident_c @ G @ E ) ) ),
inference(paramod_ordered,[status(thm)],[5226,77]) ).
thf(7956,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ B @ ( sum @ ( sum @ D @ E ) @ C ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[7955:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( sum @ I @ ( sum @ ( sum @ M @ N ) @ L ) )),bind(F,$thf( F )),bind(G,$thf( ax0_sk8 @ M ))]]) ).
thf(8086,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ B @ ( sum @ ( sum @ D @ E ) @ C ) ) @ A ) ),
inference(simp,[status(thm)],[7956]) ).
thf(338,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( B != sk17 )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[62,333]) ).
thf(339,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ A ) @ ( ax0_sk8 @ sk14 ) )
| ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ A ) @ A )
| ( A != sk17 ) ),
inference(pattern_uni,[status(thm)],[338:[bind(A,$thf( ax0_sk8 @ sk14 )),bind(B,$thf( B ))]]) ).
thf(342,plain,
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) )
| ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 ) ),
inference(simp,[status(thm)],[339]) ).
thf(2122,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( ( incident_c @ ( ax0_sk8 @ A ) @ A )
!= ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2103,342]) ).
thf(2140,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( ( ax0_sk8 @ A )
!= ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[2122]) ).
thf(2157,plain,
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(simp,[status(thm)],[2140]) ).
thf(3444,plain,
! [A: $i] :
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) ) @ A )
!= ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 ) ) ),
inference(paramod_ordered,[status(thm)],[3020,2157]) ).
thf(3494,plain,
! [A: $i] :
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) )
!= ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) )
| ( A != sk17 ) ),
inference(simp,[status(thm)],[3444]) ).
thf(3513,plain,
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ sk17 ) @ sk17 ) )
!= ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) ) ),
inference(simp,[status(thm)],[3494]) ).
thf(5194,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( incident_c @ C @ ( sum @ A @ B ) )
| ( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) )
!= ( incident_c @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[833,91]) ).
thf(5195,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( sum @ A @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(pattern_uni,[status(thm)],[5194:[bind(A,$thf( A )),bind(B,$thf( ax0_sk8 @ sk14 )),bind(C,$thf( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ))]]) ).
thf(45904,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ C @ ( sum @ A @ B ) )
| ( ( incident_c @ sk17 @ sk16 )
!= ( incident_c @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45880,77]) ).
thf(45905,plain,
! [A: $i] : ( incident_c @ sk17 @ ( sum @ sk16 @ A ) ),
inference(pattern_uni,[status(thm)],[45904:[bind(A,$thf( sk16 )),bind(B,$thf( B )),bind(C,$thf( sk17 ))]]) ).
thf(46055,plain,
! [A: $i] : ( incident_c @ sk17 @ ( sum @ sk16 @ A ) ),
inference(simp,[status(thm)],[45905]) ).
thf(46341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ D @ ( sum @ B @ C ) )
| ( ( incident_c @ sk17 @ ( sum @ sk16 @ A ) )
!= ( incident_c @ D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[46055,77]) ).
thf(46342,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ ( sum @ sk16 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[46341:[bind(A,$thf( F )),bind(B,$thf( sum @ sk16 @ F )),bind(C,$thf( C )),bind(D,$thf( sk17 ))]]) ).
thf(46505,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ ( sum @ sk16 @ B ) @ A ) ),
inference(simp,[status(thm)],[46342]) ).
thf(2959,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ A @ B ) )
| ( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( sum @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[2837,2222]) ).
thf(2960,plain,
! [B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ B @ A ) ),
inference(pattern_uni,[status(thm)],[2959:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( ax0_sk9 @ ( ax0_sk8 @ I ) @ I )),bind(D,$thf( ax0_sk10 @ ( ax0_sk8 @ I ) @ I ))]]) ).
thf(3009,plain,
! [B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ B @ A ) ),
inference(simp,[status(thm)],[2960]) ).
thf(3131,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ B @ A ) )
!= ( incident_c @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[3009,77]) ).
thf(3132,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ ( sum @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[3131:[bind(A,$thf( K )),bind(B,$thf( J )),bind(C,$thf( sum @ J @ K )),bind(D,$thf( D )),bind(E,$thf( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ J ) @ J ) ))]]) ).
thf(3232,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ ( sum @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[3132]) ).
thf(4465,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ F @ ( sum @ D @ E ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ ( sum @ B @ C ) @ A ) )
!= ( incident_c @ F @ D ) ) ),
inference(paramod_ordered,[status(thm)],[3232,77]) ).
thf(4466,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ ( sum @ ( sum @ C @ D ) @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[4465:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( sum @ ( sum @ M @ N ) @ L )),bind(E,$thf( E )),bind(F,$thf( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ M ) @ M ) ))]]) ).
thf(4618,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ ( sum @ ( sum @ C @ D ) @ B ) @ A ) ),
inference(simp,[status(thm)],[4466]) ).
thf(272,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)],[166,156]) ).
thf(273,plain,
! [A: $i] :
( ~ ( open @ A )
| ~ ( closed @ A ) ),
inference(pattern_uni,[status(thm)],[272:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( ax0_sk7 @ D ))]]) ).
thf(280,plain,
! [A: $i] :
( ~ ( open @ A )
| ~ ( closed @ A ) ),
inference(simp,[status(thm)],[273]) ).
thf(909,plain,
! [B: $i,A: $i] :
( ( ( ax0_sk6 @ A )
!= ( ax0_sk8 @ A ) )
| ~ ( open @ B )
| ( ( closed @ A )
!= ( closed @ B ) ) ),
inference(paramod_ordered,[status(thm)],[395,280]) ).
thf(910,plain,
! [A: $i] :
( ( ( ax0_sk6 @ A )
!= ( ax0_sk8 @ A ) )
| ~ ( open @ A ) ),
inference(pattern_uni,[status(thm)],[909:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(26310,plain,
! [A: $i] :
( ( ( ax0_sk6 @ A )
!= ( ax0_sk8 @ A ) )
| ( ( open @ sk15 )
!= ( open @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25999,910]) ).
thf(26311,plain,
( ( ax0_sk6 @ sk15 )
!= ( ax0_sk8 @ sk15 ) ),
inference(pattern_uni,[status(thm)],[26310:[bind(A,$thf( sk15 ))]]) ).
thf(2123,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) )
| ( ( incident_c @ ( ax0_sk8 @ A ) @ A )
!= ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 ) ) ),
inference(paramod_ordered,[status(thm)],[2103,342]) ).
thf(2137,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk8 @ A )
!= ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) )
| ( A != sk17 ) ),
inference(simp,[status(thm)],[2123]) ).
thf(2153,plain,
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ sk17 ) ) ),
inference(simp,[status(thm)],[2137]) ).
thf(2244,plain,
! [A: $i] :
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ sk17 ) )
| ( ( incident_c @ ( ax0_sk8 @ A ) @ A )
!= ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2103,2153]) ).
thf(2339,plain,
! [A: $i] :
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ sk17 ) )
| ( ( ax0_sk8 @ A )
!= ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[2244]) ).
thf(2358,plain,
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ sk17 ) )
| ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(simp,[status(thm)],[2339]) ).
thf(4865,plain,
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ sk17 ) )
| ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) )
| ( ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ sk17 ) ) ),
inference(eqfactor_ordered,[status(thm)],[2358]) ).
thf(4866,plain,
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ sk17 ) )
| ( ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ sk17 ) ) ),
inference(simp,[status(thm)],[4865]) ).
thf(3,negated_conjecture,
part_of @ sk16 @ sk14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',proposition_2_14_3_69) ).
thf(55,plain,
part_of @ sk16 @ sk14,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23349,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( open @ A )
| ( ( part_of @ sk16 @ sk14 )
!= ( part_of @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[55,110]) ).
thf(23350,plain,
( ( sk14 = sk16 )
| ( open @ sk16 ) ),
inference(pattern_uni,[status(thm)],[23349:[bind(A,$thf( sk16 )),bind(B,$thf( sk14 ))]]) ).
thf(27063,plain,
( ( open @ sk16 )
| ( sk14 != sk14 ) ),
inference(paramod_ordered,[status(thm)],[23350,170]) ).
thf(27064,plain,
open @ sk16,
inference(pattern_uni,[status(thm)],[27063:[]]) ).
thf(27361,plain,
! [A: $i] :
( ~ ( closed @ A )
| ( ( open @ sk16 )
!= ( open @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27064,280]) ).
thf(27362,plain,
~ ( closed @ sk16 ),
inference(pattern_uni,[status(thm)],[27361:[bind(A,$thf( sk16 ))]]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( end_point @ ( ax0_sk11 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c6_41) ).
thf(151,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( end_point @ ( ax0_sk11 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( end_point @ ( ax0_sk11 @ A @ B ) @ B ) ),
inference(cnf,[status(esa)],[151]) ).
thf(57099,plain,
! [B: $i,A: $i] :
( ( end_point @ ( ax0_sk11 @ A @ B ) @ B )
| ( ( end_point @ ( ax0_sk7 @ sk14 ) @ sk14 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[269,152]) ).
thf(57100,plain,
end_point @ ( ax0_sk11 @ ( ax0_sk7 @ sk14 ) @ sk14 ) @ sk14,
inference(pattern_uni,[status(thm)],[57099:[bind(A,$thf( ax0_sk7 @ sk14 )),bind(B,$thf( sk14 ))]]) ).
thf(60558,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( ( end_point @ ( ax0_sk11 @ ( ax0_sk7 @ sk14 ) @ sk14 ) @ sk14 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57100,114]) ).
thf(60559,plain,
~ ( inner_point @ ( ax0_sk11 @ ( ax0_sk7 @ sk14 ) @ sk14 ) @ sk14 ),
inference(pattern_uni,[status(thm)],[60558:[bind(A,$thf( ax0_sk11 @ ( ax0_sk7 @ sk14 ) @ sk14 )),bind(B,$thf( sk14 ))]]) ).
thf(10526,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ B @ ( sum @ C @ D ) ) @ A ) )
!= ( incident_c @ G @ F ) ) ),
inference(paramod_ordered,[status(thm)],[7008,91]) ).
thf(10527,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ A @ ( sum @ ( sum @ C @ ( sum @ D @ E ) ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[10526:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( sum @ ( sum @ K @ ( sum @ M @ N ) ) @ J )),bind(G,$thf( ax0_sk8 @ N ))]]) ).
thf(10606,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ A @ ( sum @ ( sum @ C @ ( sum @ D @ E ) ) @ B ) ) ),
inference(simp,[status(thm)],[10527]) ).
thf(116,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( ( ax0_sk12 @ C @ B )
= ( sum @ B @ C ) ) ),
inference(cnf,[status(esa)],[115]) ).
thf(117,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ax0_sk12 @ C @ B )
= ( sum @ B @ C ) )
| ~ ( meet @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[116]) ).
thf(27441,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ax0_sk12 @ C @ B )
= ( sum @ B @ C ) )
| ( ( meet @ sk17 @ sk15 @ sk16 )
!= ( meet @ A @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[53,117]) ).
thf(27442,plain,
( ( ax0_sk12 @ sk16 @ sk15 )
= ( sum @ sk15 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[27441:[bind(A,$thf( sk17 )),bind(B,$thf( sk15 )),bind(C,$thf( sk16 ))]]) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',meet_defn_28) ).
thf(157,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)],[48]) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',end_point_defn_14) ).
thf(124,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)],[33]) ).
thf(125,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(cnf,[status(esa)],[124]) ).
thf(46087,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ D @ ( sum @ B @ C ) )
| ( ( incident_c @ sk17 @ ( sum @ A @ sk16 ) )
!= ( incident_c @ D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[45940,77]) ).
thf(46088,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ ( sum @ B @ sk16 ) @ A ) ),
inference(pattern_uni,[status(thm)],[46087:[bind(A,$thf( E )),bind(B,$thf( sum @ E @ sk16 )),bind(C,$thf( C )),bind(D,$thf( sk17 ))]]) ).
thf(46252,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ ( sum @ B @ sk16 ) @ A ) ),
inference(simp,[status(thm)],[46088]) ).
thf(46659,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ sk17 @ ( sum @ ( sum @ B @ sk16 ) @ A ) )
!= ( incident_c @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[46252,91]) ).
thf(46660,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ A @ ( sum @ ( sum @ C @ sk16 ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[46659:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( sum @ ( sum @ H @ sk16 ) @ G )),bind(E,$thf( sk17 ))]]) ).
thf(46817,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ A @ ( sum @ ( sum @ C @ sk16 ) @ B ) ) ),
inference(simp,[status(thm)],[46660]) ).
thf(57097,plain,
! [B: $i,A: $i] :
( ( end_point @ ( ax0_sk11 @ A @ B ) @ B )
| ( ( end_point @ ( ax0_sk7 @ sk15 ) @ sk15 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[26314,152]) ).
thf(57098,plain,
end_point @ ( ax0_sk11 @ ( ax0_sk7 @ sk15 ) @ sk15 ) @ sk15,
inference(pattern_uni,[status(thm)],[57097:[bind(A,$thf( ax0_sk7 @ sk15 )),bind(B,$thf( sk15 ))]]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( incident_c @ A @ B ) ),
inference(cnf,[status(esa)],[153]) ).
thf(58117,plain,
! [B: $i,A: $i] :
( ( incident_c @ A @ B )
| ( ( end_point @ ( ax0_sk11 @ ( ax0_sk7 @ sk15 ) @ sk15 ) @ sk15 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57098,154]) ).
thf(58118,plain,
incident_c @ ( ax0_sk11 @ ( ax0_sk7 @ sk15 ) @ sk15 ) @ sk15,
inference(pattern_uni,[status(thm)],[58117:[bind(A,$thf( ax0_sk11 @ ( ax0_sk7 @ sk15 ) @ sk15 )),bind(B,$thf( sk15 ))]]) ).
thf(45896,plain,
( ~ ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
!= ( incident_c @ sk17 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[45880,344]) ).
thf(46004,plain,
( ~ ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= sk17 )
| ( ( ax0_sk8 @ sk14 )
!= sk16 ) ),
inference(simp,[status(thm)],[45896]) ).
thf(45942,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
!= ( incident_c @ sk17 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[45880,2156]) ).
thf(46010,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= sk17 )
| ( sk16 != sk17 ) ),
inference(simp,[status(thm)],[45942]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',sum_defn_10) ).
thf(57,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)],[5]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',sum_defn_7) ).
thf(78,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)],[14]) ).
thf(37912,plain,
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ sk17 ) @ sk17 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) ) ),
inference(eqfactor_ordered,[status(thm)],[3513]) ).
thf(37913,plain,
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ sk17 ) @ sk17 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(simp,[status(thm)],[37912]) ).
thf(21747,plain,
! [B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ( open @ A )
| ( A != sk17 )
| ( B
!= ( ax0_sk8 @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[110,333]) ).
thf(21748,plain,
! [A: $i] :
( ~ ( part_of @ A @ ( ax0_sk8 @ sk14 ) )
| ( open @ A )
| ( A != sk17 ) ),
inference(pattern_uni,[status(thm)],[21747:[bind(A,$thf( A )),bind(B,$thf( ax0_sk8 @ sk14 ))]]) ).
thf(23960,plain,
( ~ ( part_of @ sk17 @ ( ax0_sk8 @ sk14 ) )
| ( open @ sk17 ) ),
inference(simp,[status(thm)],[21748]) ).
thf(5200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ D @ ( sum @ B @ C ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) ) @ A )
!= ( incident_c @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[3020,91]) ).
thf(5201,plain,
! [B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ A @ B ) ),
inference(pattern_uni,[status(thm)],[5200:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ G ) @ G ) ))]]) ).
thf(5248,plain,
! [B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ A @ B ) ),
inference(simp,[status(thm)],[5201]) ).
thf(7076,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ A @ B ) )
!= ( incident_c @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[5248,91]) ).
thf(7077,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ A @ ( sum @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[7076:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( sum @ J @ K )),bind(E,$thf( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ K ) @ K ) ))]]) ).
thf(7144,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ A @ ( sum @ B @ C ) ) ),
inference(simp,[status(thm)],[7077]) ).
thf(2290,plain,
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ sk17 ) )
| ( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) )
!= ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[833,2153]) ).
thf(2291,plain,
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ sk17 ) ) ),
inference(pattern_uni,[status(thm)],[2290:[]]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',sum_defn_11) ).
thf(84,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)],[16]) ).
thf(57101,plain,
! [B: $i,A: $i] :
( ( end_point @ ( ax0_sk11 @ A @ B ) @ B )
| ( ( end_point @ sk17 @ sk14 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56,152]) ).
thf(57102,plain,
end_point @ ( ax0_sk11 @ sk17 @ sk14 ) @ sk14,
inference(pattern_uni,[status(thm)],[57101:[bind(A,$thf( sk17 )),bind(B,$thf( sk14 ))]]) ).
thf(57231,plain,
! [A: $i] :
( ( end_point @ ( ax0_sk11 @ sk17 @ sk14 ) @ sk14 )
!= ( end_point @ ( ax0_sk8 @ A ) @ A ) ),
inference(paramod_ordered,[status(thm)],[57102,297]) ).
thf(57353,plain,
! [A: $i] :
( ( ( ax0_sk11 @ sk17 @ sk14 )
!= ( ax0_sk8 @ A ) )
| ( sk14 != A ) ),
inference(simp,[status(thm)],[57231]) ).
thf(57362,plain,
( ( ax0_sk11 @ sk17 @ sk14 )
!= ( ax0_sk8 @ sk14 ) ),
inference(simp,[status(thm)],[57353]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( end_point @ A @ B )
| ( inner_point @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_point_defn_23) ).
thf(122,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)],[32]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( end_point @ A @ B )
| ( inner_point @ A @ B ) ),
inference(cnf,[status(esa)],[122]) ).
thf(53072,plain,
! [B: $i,A: $i] :
( ( end_point @ A @ B )
| ( inner_point @ A @ B )
| ( ( incident_c @ sk17 @ sk15 )
!= ( incident_c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[52996,123]) ).
thf(53073,plain,
( ( end_point @ sk17 @ sk15 )
| ( inner_point @ sk17 @ sk15 ) ),
inference(pattern_uni,[status(thm)],[53072:[bind(A,$thf( sk17 )),bind(B,$thf( sk15 ))]]) ).
thf(56017,plain,
( ( end_point @ sk17 @ sk15 )
| ( ( inner_point @ sk17 @ sk14 )
!= ( inner_point @ sk17 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[53073,288]) ).
thf(56088,plain,
( ( end_point @ sk17 @ sk15 )
| ( sk17 != sk17 )
| ( sk14 != sk15 ) ),
inference(simp,[status(thm)],[56017]) ).
thf(56100,plain,
( ( end_point @ sk17 @ sk15 )
| ( sk14 != sk15 ) ),
inference(simp,[status(thm)],[56088]) ).
thf(56126,plain,
! [A: $i] :
( ( sk14 != sk15 )
| ( ( end_point @ ( ax0_sk8 @ A ) @ A )
!= ( end_point @ sk17 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[56100,297]) ).
thf(56222,plain,
! [A: $i] :
( ( sk14 != sk15 )
| ( ( ax0_sk8 @ A )
!= sk17 )
| ( A != sk15 ) ),
inference(simp,[status(thm)],[56126]) ).
thf(56234,plain,
( ( sk14 != sk15 )
| ( ( ax0_sk8 @ sk15 )
!= sk17 ) ),
inference(simp,[status(thm)],[56222]) ).
thf(8014,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ A @ ( sum @ ( sum @ C @ D ) @ B ) ) )
!= ( incident_c @ G @ F ) ) ),
inference(paramod_ordered,[status(thm)],[5226,91]) ).
thf(8015,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ B @ ( sum @ ( sum @ D @ E ) @ C ) ) ) ),
inference(pattern_uni,[status(thm)],[8014:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( sum @ I @ ( sum @ ( sum @ M @ N ) @ L ) )),bind(G,$thf( ax0_sk8 @ M ))]]) ).
thf(8109,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ B @ ( sum @ ( sum @ D @ E ) @ C ) ) ) ),
inference(simp,[status(thm)],[8015]) ).
thf(56162,plain,
! [B: $i,A: $i] :
( ( sk14 != sk15 )
| ~ ( inner_point @ A @ B )
| ( ( end_point @ sk17 @ sk15 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56100,114]) ).
thf(56163,plain,
( ( sk14 != sk15 )
| ~ ( inner_point @ sk17 @ sk15 ) ),
inference(pattern_uni,[status(thm)],[56162:[bind(A,$thf( sk17 )),bind(B,$thf( sk15 ))]]) ).
thf(47304,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= sk17 )
| ( ( ax0_sk8 @ sk14 )
!= sk16 )
| ( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
!= ( incident_c @ sk17 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[45880,46004]) ).
thf(47632,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= sk17 )
| ( ( ax0_sk8 @ sk14 )
!= sk16 )
| ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= sk17 )
| ( sk16 != sk17 ) ),
inference(simp,[status(thm)],[47304]) ).
thf(47689,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= sk17 )
| ( ( ax0_sk8 @ sk14 )
!= sk16 )
| ( sk16 != sk17 ) ),
inference(simp,[status(thm)],[47632]) ).
thf(121,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk1 @ A @ B ) @ B )
| ( part_of @ A @ B ) ),
inference(cnf,[status(esa)],[120]) ).
thf(381,plain,
! [B: $i,A: $i] :
( ~ ( open @ A )
| ( ( end_point @ ( ax0_sk7 @ A ) @ A )
!= ( end_point @ ( ax0_sk8 @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[166,297]) ).
thf(391,plain,
! [B: $i,A: $i] :
( ~ ( open @ A )
| ( ( ax0_sk7 @ A )
!= ( ax0_sk8 @ B ) )
| ( A != B ) ),
inference(simp,[status(thm)],[381]) ).
thf(397,plain,
! [A: $i] :
( ~ ( open @ A )
| ( ( ax0_sk7 @ A )
!= ( ax0_sk8 @ A ) ) ),
inference(simp,[status(thm)],[391]) ).
thf(53027,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ C @ ( sum @ A @ B ) )
| ( ( incident_c @ sk17 @ sk15 )
!= ( incident_c @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[52996,77]) ).
thf(53028,plain,
! [A: $i] : ( incident_c @ sk17 @ ( sum @ sk15 @ A ) ),
inference(pattern_uni,[status(thm)],[53027:[bind(A,$thf( sk15 )),bind(B,$thf( B )),bind(C,$thf( sk17 ))]]) ).
thf(53172,plain,
! [A: $i] : ( incident_c @ sk17 @ ( sum @ sk15 @ A ) ),
inference(simp,[status(thm)],[53028]) ).
thf(53487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ D @ ( sum @ B @ C ) )
| ( ( incident_c @ sk17 @ ( sum @ sk15 @ A ) )
!= ( incident_c @ D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[53172,77]) ).
thf(53488,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ ( sum @ sk15 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[53487:[bind(A,$thf( F )),bind(B,$thf( sum @ sk15 @ F )),bind(C,$thf( C )),bind(D,$thf( sk17 ))]]) ).
thf(53711,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ ( sum @ sk15 @ B ) @ A ) ),
inference(simp,[status(thm)],[53488]) ).
thf(2104,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( ( incident_c @ ( ax0_sk8 @ A ) @ A )
!= ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 ) ) ),
inference(paramod_ordered,[status(thm)],[2103,344]) ).
thf(2138,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk8 @ A )
!= ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) )
| ( A != sk17 ) ),
inference(simp,[status(thm)],[2104]) ).
thf(2154,plain,
( ~ ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ sk17 ) ) ),
inference(simp,[status(thm)],[2138]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk1 @ A @ B ) @ A )
| ( part_of @ A @ B ) ),
inference(cnf,[status(esa)],[101]) ).
thf(60550,plain,
! [B: $i,A: $i] :
( ( incident_c @ A @ B )
| ( ( end_point @ ( ax0_sk11 @ ( ax0_sk7 @ sk14 ) @ sk14 ) @ sk14 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57100,154]) ).
thf(60551,plain,
incident_c @ ( ax0_sk11 @ ( ax0_sk7 @ sk14 ) @ sk14 ) @ sk14,
inference(pattern_uni,[status(thm)],[60550:[bind(A,$thf( ax0_sk11 @ ( ax0_sk7 @ sk14 ) @ sk14 )),bind(B,$thf( sk14 ))]]) ).
thf(5409,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) ) @ A )
!= ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 ) ) ),
inference(paramod_ordered,[status(thm)],[5352,342]) ).
thf(5440,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) )
| ( A != sk17 ) ),
inference(simp,[status(thm)],[5409]) ).
thf(5443,plain,
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ sk17 ) @ sk17 ) )
!= ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) ) ),
inference(simp,[status(thm)],[5440]) ).
thf(5364,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ D @ ( sum @ B @ C ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) ) @ A )
!= ( incident_c @ D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5352,77]) ).
thf(5365,plain,
! [B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ B @ A ) ),
inference(pattern_uni,[status(thm)],[5364:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ G ) @ G ) ))]]) ).
thf(5468,plain,
! [B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ B @ A ) ),
inference(simp,[status(thm)],[5365]) ).
thf(7327,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ C ) @ C ) ) @ A )
| ( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( sum @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2837,5468]) ).
thf(7328,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) ) @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) ) ) @ A ),
inference(pattern_uni,[status(thm)],[7327:[bind(A,$thf( H )),bind(B,$thf( ax0_sk10 @ ( ax0_sk8 @ H ) @ H )),bind(C,$thf( ax0_sk9 @ ( ax0_sk8 @ H ) @ H ))]]) ).
thf(7439,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) ) @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) ) ) @ A ),
inference(simp,[status(thm)],[7328]) ).
thf(27363,plain,
! [A: $i] :
( ( ( ax0_sk6 @ A )
!= ( ax0_sk8 @ A ) )
| ( ( open @ sk16 )
!= ( open @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27064,910]) ).
thf(27364,plain,
( ( ax0_sk6 @ sk16 )
!= ( ax0_sk8 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[27363:[bind(A,$thf( sk16 ))]]) ).
thf(2845,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ F @ ( sum @ D @ E ) )
| ( ( incident_c @ ( ax0_sk8 @ B ) @ ( sum @ ( sum @ B @ C ) @ A ) )
!= ( incident_c @ F @ D ) ) ),
inference(paramod_ordered,[status(thm)],[2222,77]) ).
thf(2846,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ ( sum @ ( sum @ C @ D ) @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[2845:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( sum @ ( sum @ J @ K ) @ I )),bind(E,$thf( E )),bind(F,$thf( ax0_sk8 @ J ))]]) ).
thf(2923,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ ( sum @ ( sum @ C @ D ) @ B ) @ A ) ),
inference(simp,[status(thm)],[2846]) ).
thf(4312,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ ( sum @ ( sum @ C @ D ) @ B ) @ A ) )
!= ( incident_c @ G @ E ) ) ),
inference(paramod_ordered,[status(thm)],[2923,77]) ).
thf(4313,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ ( sum @ ( sum @ D @ E ) @ C ) @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[4312:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( sum @ ( sum @ ( sum @ M @ N ) @ L ) @ J )),bind(F,$thf( F )),bind(G,$thf( ax0_sk8 @ M ))]]) ).
thf(4449,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ ( sum @ ( sum @ D @ E ) @ C ) @ B ) @ A ) ),
inference(simp,[status(thm)],[4313]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',meet_defn_27) ).
thf(136,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)],[39]) ).
thf(137,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(cnf,[status(esa)],[136]) ).
thf(53062,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ C @ ( sum @ A @ B ) )
| ( ( incident_c @ sk17 @ sk15 )
!= ( incident_c @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[52996,91]) ).
thf(53063,plain,
! [A: $i] : ( incident_c @ sk17 @ ( sum @ A @ sk15 ) ),
inference(pattern_uni,[status(thm)],[53062:[bind(A,$thf( A )),bind(B,$thf( sk15 )),bind(C,$thf( sk17 ))]]) ).
thf(53221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ D @ ( sum @ B @ C ) )
| ( ( incident_c @ sk17 @ ( sum @ A @ sk15 ) )
!= ( incident_c @ D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[53063,77]) ).
thf(53222,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ ( sum @ B @ sk15 ) @ A ) ),
inference(pattern_uni,[status(thm)],[53221:[bind(A,$thf( E )),bind(B,$thf( sum @ E @ sk15 )),bind(C,$thf( C )),bind(D,$thf( sk17 ))]]) ).
thf(53436,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ ( sum @ B @ sk15 ) @ A ) ),
inference(simp,[status(thm)],[53222]) ).
thf(302,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( ( end_point @ ( ax0_sk7 @ sk14 ) @ sk14 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[269,114]) ).
thf(303,plain,
~ ( inner_point @ ( ax0_sk7 @ sk14 ) @ sk14 ),
inference(pattern_uni,[status(thm)],[302:[bind(A,$thf( ax0_sk7 @ sk14 )),bind(B,$thf( sk14 ))]]) ).
thf(351,plain,
! [A: $i] :
( ( inner_point @ ( ax0_sk8 @ A ) @ A )
!= ( inner_point @ ( ax0_sk7 @ sk14 ) @ sk14 ) ),
inference(paramod_ordered,[status(thm)],[68,303]) ).
thf(364,plain,
! [A: $i] :
( ( ( ax0_sk8 @ A )
!= ( ax0_sk7 @ sk14 ) )
| ( A != sk14 ) ),
inference(simp,[status(thm)],[351]) ).
thf(368,plain,
( ( ax0_sk7 @ sk14 )
!= ( ax0_sk8 @ sk14 ) ),
inference(simp,[status(thm)],[364]) ).
thf(373,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( B
!= ( ax0_sk8 @ sk14 ) )
| ( A
!= ( ax0_sk7 @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[62,368]) ).
thf(374,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ A ) @ ( ax0_sk7 @ sk14 ) )
| ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ A ) @ A )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[373:[bind(A,$thf( ax0_sk7 @ sk14 )),bind(B,$thf( B ))]]) ).
thf(378,plain,
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) )
| ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[374]) ).
thf(2112,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( ( incident_c @ ( ax0_sk8 @ A ) @ A )
!= ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2103,378]) ).
thf(2131,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk8 @ A )
!= ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) )
| ( A
!= ( ax0_sk7 @ sk14 ) ) ),
inference(simp,[status(thm)],[2112]) ).
thf(2147,plain,
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk7 @ sk14 ) ) ) ),
inference(simp,[status(thm)],[2131]) ).
thf(49,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/sandbox2/benchmark/theBenchmark.p',end_point_defn_20) ).
thf(159,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)],[49]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( part_of @ ( ax0_sk4 @ B @ A ) @ ( ax0_sk3 @ B @ A ) )
| ( end_point @ A @ B ) ),
inference(cnf,[status(esa)],[159]) ).
thf(7948,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ B @ ( sum @ A @ C ) ) )
| ( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( sum @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[2837,5226]) ).
thf(7949,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ A @ ( sum @ C @ B ) ) ),
inference(pattern_uni,[status(thm)],[7948:[bind(A,$thf( J )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( ax0_sk9 @ ( ax0_sk8 @ J ) @ J )),bind(E,$thf( ax0_sk10 @ ( ax0_sk8 @ J ) @ J ))]]) ).
thf(8085,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ A @ ( sum @ C @ B ) ) ),
inference(simp,[status(thm)],[7949]) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',meet_defn_30) ).
thf(97,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)],[21]) ).
thf(27359,plain,
! [A: $i] :
( ( ( ax0_sk7 @ A )
!= ( ax0_sk8 @ A ) )
| ( ( open @ sk16 )
!= ( open @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27064,397]) ).
thf(27360,plain,
( ( ax0_sk7 @ sk16 )
!= ( ax0_sk8 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[27359:[bind(A,$thf( sk16 ))]]) ).
thf(5944,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( sum @ ( ax0_sk8 @ sk14 ) @ A ) )
!= ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1337]) ).
thf(5962,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) )
| ( ( sum @ ( ax0_sk8 @ sk14 ) @ A )
!= sk17 ) ),
inference(simp,[status(thm)],[5944]) ).
thf(5993,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( ( sum @ ( ax0_sk8 @ sk14 ) @ A )
!= sk17 ) ),
inference(simp,[status(thm)],[5962]) ).
thf(1305,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( incident_c @ C @ ( sum @ A @ B ) )
| ( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
!= ( incident_c @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[829,77]) ).
thf(1306,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( sum @ ( ax0_sk8 @ sk14 ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[1305:[bind(A,$thf( ax0_sk8 @ sk14 )),bind(B,$thf( B )),bind(C,$thf( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ))]]) ).
thf(1350,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( sum @ ( ax0_sk8 @ sk14 ) @ A ) ) ),
inference(simp,[status(thm)],[1306]) ).
thf(940,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( B
!= ( ax0_sk8 @ sk14 ) )
| ( A
!= ( ax0_sk6 @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[62,918]) ).
thf(941,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk6 @ sk14 ) @ A ) @ ( ax0_sk6 @ sk14 ) )
| ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk6 @ sk14 ) @ A ) @ A )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[940:[bind(A,$thf( ax0_sk6 @ sk14 )),bind(B,$thf( B ))]]) ).
thf(948,plain,
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk6 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk6 @ sk14 ) )
| ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk6 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[941]) ).
thf(5171,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ ( sum @ ( sum @ C @ D ) @ B ) @ A ) )
!= ( incident_c @ G @ F ) ) ),
inference(paramod_ordered,[status(thm)],[2923,91]) ).
thf(5172,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ ( sum @ ( sum @ D @ E ) @ C ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[5171:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( sum @ ( sum @ ( sum @ M @ N ) @ L ) @ J )),bind(G,$thf( ax0_sk8 @ M ))]]) ).
thf(5238,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ ( sum @ ( sum @ D @ E ) @ C ) @ B ) ) ),
inference(simp,[status(thm)],[5172]) ).
thf(139,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(cnf,[status(esa)],[138]) ).
thf(140,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ C @ D ) )
| ~ ( closed @ A )
| ~ ( meet @ B @ C @ D )
| ~ ( end_point @ E @ C )
| ( meet @ E @ C @ D ) ),
inference(lifteq,[status(thm)],[139]) ).
thf(141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( closed @ ( sum @ B @ C ) )
| ~ ( meet @ A @ B @ C )
| ~ ( end_point @ D @ B )
| ( meet @ D @ B @ C ) ),
inference(simp,[status(thm)],[140]) ).
thf(9578,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( sum @ A @ ( ax0_sk8 @ sk14 ) ) )
!= ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[5195]) ).
thf(9600,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) )
| ( ( sum @ A @ ( ax0_sk8 @ sk14 ) )
!= sk17 ) ),
inference(simp,[status(thm)],[9578]) ).
thf(9603,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( ( sum @ A @ ( ax0_sk8 @ sk14 ) )
!= sk17 ) ),
inference(simp,[status(thm)],[9600]) ).
thf(45949,plain,
! [B: $i,A: $i] :
( ( end_point @ A @ B )
| ( inner_point @ A @ B )
| ( ( incident_c @ sk17 @ sk16 )
!= ( incident_c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[45880,123]) ).
thf(45950,plain,
( ( end_point @ sk17 @ sk16 )
| ( inner_point @ sk17 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[45949:[bind(A,$thf( sk17 )),bind(B,$thf( sk16 ))]]) ).
thf(46388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ D @ ( sum @ B @ C ) )
| ( ( incident_c @ sk17 @ ( sum @ sk16 @ A ) )
!= ( incident_c @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[46055,91]) ).
thf(46389,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ A @ ( sum @ sk16 @ B ) ) ),
inference(pattern_uni,[status(thm)],[46388:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( sum @ sk16 @ F )),bind(D,$thf( sk17 ))]]) ).
thf(46529,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ A @ ( sum @ sk16 @ B ) ) ),
inference(simp,[status(thm)],[46389]) ).
thf(37914,plain,
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk9 @ ( ax0_sk8 @ sk17 ) @ sk17 )
!= ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[37912]) ).
thf(20,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/sandbox2/benchmark/theBenchmark.p',sum_defn_12) ).
thf(94,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)],[20]) ).
thf(95,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(cnf,[status(esa)],[94]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( sum @ B @ A ) )
| ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A )
| ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C ) ),
inference(lifteq,[status(thm)],[95]) ).
thf(2391,plain,
! [A: $i] :
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ sk17 ) )
| ( ( incident_c @ ( ax0_sk8 @ A ) @ A )
!= ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2103,2154]) ).
thf(2484,plain,
! [A: $i] :
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ sk17 ) )
| ( ( ax0_sk8 @ A )
!= ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[2391]) ).
thf(2504,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ sk17 ) )
| ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(simp,[status(thm)],[2484]) ).
thf(5817,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ sk17 ) )
| ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ sk17 ) ) ),
inference(eqfactor_ordered,[status(thm)],[2504]) ).
thf(5818,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ sk17 ) )
| ( ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ sk17 ) ) ),
inference(simp,[status(thm)],[5817]) ).
thf(52757,plain,
( ( end_point @ sk17 @ sk16 )
| ( ( inner_point @ sk17 @ sk14 )
!= ( inner_point @ sk17 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[45950,288]) ).
thf(52823,plain,
( ( end_point @ sk17 @ sk16 )
| ( sk17 != sk17 )
| ( sk14 != sk16 ) ),
inference(simp,[status(thm)],[52757]) ).
thf(52834,plain,
( ( end_point @ sk17 @ sk16 )
| ( sk14 != sk16 ) ),
inference(simp,[status(thm)],[52823]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( part_of @ ( ax0_sk3 @ B @ A ) @ B )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn_15) ).
thf(128,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)],[35]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( part_of @ ( ax0_sk3 @ B @ A ) @ B )
| ( end_point @ A @ B ) ),
inference(cnf,[status(esa)],[128]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c9_46) ).
thf(73,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',c5_40) ).
thf(105,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)],[25]) ).
thf(26306,plain,
! [A: $i] :
( ( ( ax0_sk7 @ A )
!= ( ax0_sk8 @ A ) )
| ( ( open @ sk15 )
!= ( open @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25999,397]) ).
thf(26307,plain,
( ( ax0_sk7 @ sk15 )
!= ( ax0_sk8 @ sk15 ) ),
inference(pattern_uni,[status(thm)],[26306:[bind(A,$thf( sk15 ))]]) ).
thf(52861,plain,
! [A: $i] :
( ( sk14 != sk16 )
| ( ( end_point @ ( ax0_sk8 @ A ) @ A )
!= ( end_point @ sk17 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[52834,297]) ).
thf(52956,plain,
! [A: $i] :
( ( sk14 != sk16 )
| ( ( ax0_sk8 @ A )
!= sk17 )
| ( A != sk16 ) ),
inference(simp,[status(thm)],[52861]) ).
thf(52987,plain,
( ( sk14 != sk16 )
| ( ( ax0_sk8 @ sk16 )
!= sk17 ) ),
inference(simp,[status(thm)],[52956]) ).
thf(58021,plain,
! [B: $i,A: $i] :
( ( incident_c @ A @ B )
| ( ( end_point @ ( ax0_sk7 @ sk14 ) @ sk14 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[269,154]) ).
thf(58022,plain,
incident_c @ ( ax0_sk7 @ sk14 ) @ sk14,
inference(pattern_uni,[status(thm)],[58021:[bind(A,$thf( ax0_sk7 @ sk14 )),bind(B,$thf( sk14 ))]]) ).
thf(369,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( A
!= ( ax0_sk8 @ sk14 ) )
| ( B
!= ( ax0_sk7 @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[62,368]) ).
thf(370,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ ( ax0_sk7 @ sk14 ) ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[369:[bind(A,$thf( A )),bind(B,$thf( ax0_sk7 @ sk14 ))]]) ).
thf(377,plain,
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) ) ),
inference(simp,[status(thm)],[370]) ).
thf(2121,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( ( incident_c @ ( ax0_sk8 @ A ) @ A )
!= ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2103,377]) ).
thf(2133,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk8 @ A )
!= ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) )
| ( A
!= ( ax0_sk7 @ sk14 ) ) ),
inference(simp,[status(thm)],[2121]) ).
thf(2149,plain,
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk7 @ sk14 ) ) ) ),
inference(simp,[status(thm)],[2133]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( A
!= ( ax0_sk11 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c6_42) ).
thf(146,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( A
!= ( ax0_sk11 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( A
!= ( ax0_sk11 @ A @ B ) ) ),
inference(cnf,[status(esa)],[146]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( ( ax0_sk11 @ A @ B )
!= A )
| ~ ( end_point @ A @ B ) ),
inference(lifteq,[status(thm)],[147]) ).
thf(50,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/sandbox2/benchmark/theBenchmark.p',meet_defn_29) ).
thf(161,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)],[50]) ).
thf(291,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)],[133,114]) ).
thf(292,plain,
! [A: $i] :
( ( closed @ A )
| ~ ( inner_point @ ( ax0_sk6 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[291:[bind(A,$thf( D )),bind(B,$thf( ax0_sk6 @ D )),bind(C,$thf( D ))]]) ).
thf(296,plain,
! [A: $i] :
( ( closed @ A )
| ~ ( inner_point @ ( ax0_sk6 @ A ) @ A ) ),
inference(simp,[status(thm)],[292]) ).
thf(3036,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) ) @ A )
!= ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 ) ) ),
inference(paramod_ordered,[status(thm)],[3020,344]) ).
thf(3091,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) )
!= ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) )
| ( A != sk17 ) ),
inference(simp,[status(thm)],[3036]) ).
thf(3111,plain,
( ~ ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ sk17 ) @ sk17 ) )
!= ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(simp,[status(thm)],[3091]) ).
thf(7333,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ B @ A ) )
!= ( incident_c @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5468,77]) ).
thf(7334,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ ( sum @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[7333:[bind(A,$thf( K )),bind(B,$thf( J )),bind(C,$thf( sum @ J @ K )),bind(D,$thf( D )),bind(E,$thf( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ J ) @ J ) ))]]) ).
thf(7440,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ ( sum @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[7334]) ).
thf(30,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/sandbox2/benchmark/theBenchmark.p',meet_defn_26) ).
thf(118,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)],[30]) ).
thf(7592,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( sum @ ( ax0_sk8 @ sk14 ) @ A ) )
!= ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1350]) ).
thf(7594,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( sum @ ( ax0_sk8 @ sk14 ) @ A )
!= sk17 ) ),
inference(simp,[status(thm)],[7592]) ).
thf(7632,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( sum @ ( ax0_sk8 @ sk14 ) @ A )
!= sk17 ) ),
inference(simp,[status(thm)],[7594]) ).
thf(9659,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( A != sk17 )
| ( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( sum @ ( ax0_sk8 @ sk14 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2837,7632]) ).
thf(9810,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( ax0_sk9 @ ( ax0_sk8 @ sk17 ) @ sk17 )
!= ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk10 @ ( ax0_sk8 @ sk17 ) @ sk17 )
!= A ) ),
inference(simp,[status(thm)],[9659]) ).
thf(9852,plain,
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( ax0_sk9 @ ( ax0_sk8 @ sk17 ) @ sk17 )
!= ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[9810]) ).
thf(34756,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk9 @ ( ax0_sk8 @ sk17 ) @ sk17 )
!= ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[34754]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( meet @ A @ ( ax0_sk9 @ A @ B ) @ ( ax0_sk10 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c4_38) ).
thf(144,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)],[42]) ).
thf(56274,plain,
! [B: $i,A: $i] :
( ( sk14 != sk16 )
| ( ( ax0_sk11 @ A @ B )
!= A )
| ( ( end_point @ sk17 @ sk16 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[52834,148]) ).
thf(56275,plain,
( ( sk14 != sk16 )
| ( ( ax0_sk11 @ sk17 @ sk16 )
!= sk17 ) ),
inference(pattern_uni,[status(thm)],[56274:[bind(A,$thf( sk17 )),bind(B,$thf( sk16 ))]]) ).
thf(936,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( A
!= ( ax0_sk8 @ sk14 ) )
| ( B
!= ( ax0_sk6 @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[62,918]) ).
thf(937,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ ( ax0_sk6 @ sk14 ) ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ ( ax0_sk6 @ sk14 ) ) @ ( ax0_sk6 @ sk14 ) )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[936:[bind(A,$thf( A )),bind(B,$thf( ax0_sk6 @ sk14 ))]]) ).
thf(947,plain,
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk6 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk6 @ sk14 ) ) @ ( ax0_sk6 @ sk14 ) ) ),
inference(simp,[status(thm)],[937]) ).
thf(85,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(cnf,[status(esa)],[84]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( sum @ B @ A ) )
| ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ B )
| ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C ) ),
inference(lifteq,[status(thm)],[85]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( open @ A )
| ( B != sk14 ) ),
inference(paramod_ordered,[status(thm)],[62,170]) ).
thf(172,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ sk14 ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ sk14 ) @ sk14 )
| ( open @ A ) ),
inference(pattern_uni,[status(thm)],[171:[bind(A,$thf( A )),bind(B,$thf( sk14 ))]]) ).
thf(2113,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) )
| ( ( incident_c @ ( ax0_sk8 @ A ) @ A )
!= ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2103,378]) ).
thf(2135,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) )
| ( ( ax0_sk8 @ A )
!= ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[2113]) ).
thf(2151,plain,
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) )
| ( ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(simp,[status(thm)],[2135]) ).
thf(5186,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ B @ A ) )
!= ( incident_c @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[3009,91]) ).
thf(5187,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ A @ ( sum @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[5186:[bind(A,$thf( K )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( sum @ J @ K )),bind(E,$thf( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ J ) @ J ) ))]]) ).
thf(5244,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ A @ ( sum @ B @ C ) ) ),
inference(simp,[status(thm)],[5187]) ).
thf(3069,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) ) @ A )
!= ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 ) ) ),
inference(paramod_ordered,[status(thm)],[3020,342]) ).
thf(3086,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) )
!= ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) )
| ( A != sk17 ) ),
inference(simp,[status(thm)],[3069]) ).
thf(3106,plain,
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ sk17 ) @ sk17 ) )
!= ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) ) ),
inference(simp,[status(thm)],[3086]) ).
thf(56264,plain,
! [B: $i,A: $i] :
( ( ( ax0_sk11 @ A @ B )
!= A )
| ( ( end_point @ sk17 @ sk14 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56,148]) ).
thf(56265,plain,
( ( ax0_sk11 @ sk17 @ sk14 )
!= sk17 ),
inference(pattern_uni,[status(thm)],[56264:[bind(A,$thf( sk17 )),bind(B,$thf( sk14 ))]]) ).
thf(659,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( A
!= ( ax0_sk8 @ sk14 ) )
| ( B
!= ( ax0_sk7 @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[71,368]) ).
thf(660,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) )
| ( incident_c @ ( ax0_sk13 @ A @ ( ax0_sk7 @ sk14 ) ) @ A )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[659:[bind(A,$thf( A )),bind(B,$thf( ax0_sk7 @ sk14 ))]]) ).
thf(863,plain,
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) )
| ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[660]) ).
thf(98,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(cnf,[status(esa)],[97]) ).
thf(7228,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ A @ B ) )
!= ( incident_c @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[5452,91]) ).
thf(7229,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ A @ ( sum @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[7228:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( sum @ J @ K )),bind(E,$thf( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ K ) @ K ) ))]]) ).
thf(7302,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ A @ ( sum @ B @ C ) ) ),
inference(simp,[status(thm)],[7229]) ).
thf(9083,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ ( sum @ C @ D ) @ B ) ) )
!= ( incident_c @ G @ E ) ) ),
inference(paramod_ordered,[status(thm)],[5708,77]) ).
thf(9084,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ ( sum @ B @ ( sum @ ( sum @ D @ E ) @ C ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[9083:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( sum @ I @ ( sum @ ( sum @ M @ N ) @ L ) )),bind(F,$thf( F )),bind(G,$thf( ax0_sk8 @ N ))]]) ).
thf(9263,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ ( sum @ B @ ( sum @ ( sum @ D @ E ) @ C ) ) @ A ) ),
inference(simp,[status(thm)],[9084]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',sum_defn_4) ).
thf(63,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)],[7]) ).
thf(64,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(cnf,[status(esa)],[63]) ).
thf(65,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(lifteq,[status(thm)],[64]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ C @ ( sum @ A @ B ) )
| ( incident_c @ C @ A )
| ( incident_c @ C @ B ) ),
inference(simp,[status(thm)],[65]) ).
thf(56262,plain,
! [B: $i,A: $i] :
( ( ( ax0_sk11 @ A @ B )
!= A )
| ( ( end_point @ ( ax0_sk7 @ sk14 ) @ sk14 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[269,148]) ).
thf(56263,plain,
( ( ax0_sk11 @ ( ax0_sk7 @ sk14 ) @ sk14 )
!= ( ax0_sk7 @ sk14 ) ),
inference(pattern_uni,[status(thm)],[56262:[bind(A,$thf( ax0_sk7 @ sk14 )),bind(B,$thf( sk14 ))]]) ).
thf(46600,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ sk17 @ ( sum @ ( sum @ B @ sk16 ) @ A ) )
!= ( incident_c @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[46252,77]) ).
thf(46601,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ ( sum @ ( sum @ C @ sk16 ) @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[46600:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( sum @ ( sum @ H @ sk16 ) @ G )),bind(D,$thf( D )),bind(E,$thf( sk17 ))]]) ).
thf(46797,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ ( sum @ ( sum @ C @ sk16 ) @ B ) @ A ) ),
inference(simp,[status(thm)],[46601]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',c2_36) ).
thf(103,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)],[24]) ).
thf(1544,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( incident_c @ C @ ( sum @ A @ B ) )
| ( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) )
!= ( incident_c @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[863,77]) ).
thf(1545,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( sum @ ( ax0_sk7 @ sk14 ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[1544:[bind(A,$thf( ax0_sk7 @ sk14 )),bind(B,$thf( B )),bind(C,$thf( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ))]]) ).
thf(1630,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( sum @ ( ax0_sk7 @ sk14 ) @ A ) ) ),
inference(simp,[status(thm)],[1545]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( part_of @ ( ax0_sk4 @ B @ A ) @ B )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn_16) ).
thf(130,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)],[36]) ).
thf(6928,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ F @ ( sum @ D @ E ) )
| ( ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ A @ ( sum @ B @ C ) ) )
!= ( incident_c @ F @ E ) ) ),
inference(paramod_ordered,[status(thm)],[5360,91]) ).
thf(6929,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ B @ ( sum @ C @ D ) ) ) ),
inference(pattern_uni,[status(thm)],[6928:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( sum @ H @ ( sum @ J @ K ) )),bind(F,$thf( ax0_sk8 @ K ))]]) ).
thf(6985,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ B @ ( sum @ C @ D ) ) ) ),
inference(simp,[status(thm)],[6929]) ).
thf(10335,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ B @ ( sum @ C @ D ) ) ) )
!= ( incident_c @ G @ F ) ) ),
inference(paramod_ordered,[status(thm)],[6985,91]) ).
thf(10336,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ A @ ( sum @ B @ ( sum @ C @ ( sum @ D @ E ) ) ) ) ),
inference(pattern_uni,[status(thm)],[10335:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( sum @ I @ ( sum @ K @ ( sum @ M @ N ) ) )),bind(G,$thf( ax0_sk8 @ N ))]]) ).
thf(10444,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ A @ ( sum @ B @ ( sum @ C @ ( sum @ D @ E ) ) ) ) ),
inference(simp,[status(thm)],[10336]) ).
thf(9333,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ ( sum @ C @ D ) @ B ) @ A ) )
!= ( incident_c @ G @ F ) ) ),
inference(paramod_ordered,[status(thm)],[5715,91]) ).
thf(9334,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ A @ ( sum @ ( sum @ ( sum @ D @ E ) @ C ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[9333:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( sum @ ( sum @ ( sum @ M @ N ) @ L ) @ J )),bind(G,$thf( ax0_sk8 @ N ))]]) ).
thf(9450,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ A @ ( sum @ ( sum @ ( sum @ D @ E ) @ C ) @ B ) ) ),
inference(simp,[status(thm)],[9334]) ).
thf(30134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( part_of @ A @ B )
| ( part_of @ C @ D )
| ( ( incident_c @ ( ax0_sk1 @ A @ B ) @ A )
!= ( incident_c @ ( ax0_sk1 @ C @ D ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[102,121]) ).
thf(30135,plain,
! [A: $i] :
( ( part_of @ A @ A )
| ( part_of @ A @ A ) ),
inference(pattern_uni,[status(thm)],[30134:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(30316,plain,
! [A: $i] : ( part_of @ A @ A ),
inference(simp,[status(thm)],[30135]) ).
thf(2389,plain,
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ sk17 ) )
| ( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
!= ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[829,2154]) ).
thf(2390,plain,
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ sk17 ) ) ),
inference(pattern_uni,[status(thm)],[2389:[]]) ).
thf(79,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(cnf,[status(esa)],[78]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( sum @ B @ A ) )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ B )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A ) ),
inference(lifteq,[status(thm)],[79]) ).
thf(27366,plain,
! [A: $i] :
( ( end_point @ ( ax0_sk7 @ A ) @ A )
| ( ( open @ sk16 )
!= ( open @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27064,166]) ).
thf(27367,plain,
end_point @ ( ax0_sk7 @ sk16 ) @ sk16,
inference(pattern_uni,[status(thm)],[27366:[bind(A,$thf( sk16 ))]]) ).
thf(57136,plain,
! [B: $i,A: $i] :
( ( end_point @ ( ax0_sk11 @ A @ B ) @ B )
| ( ( end_point @ ( ax0_sk7 @ sk16 ) @ sk16 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27367,152]) ).
thf(57137,plain,
end_point @ ( ax0_sk11 @ ( ax0_sk7 @ sk16 ) @ sk16 ) @ sk16,
inference(pattern_uni,[status(thm)],[57136:[bind(A,$thf( ax0_sk7 @ sk16 )),bind(B,$thf( sk16 ))]]) ).
thf(60769,plain,
! [B: $i,A: $i] :
( ( incident_c @ A @ B )
| ( ( end_point @ ( ax0_sk11 @ ( ax0_sk7 @ sk16 ) @ sk16 ) @ sk16 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57137,154]) ).
thf(60770,plain,
incident_c @ ( ax0_sk11 @ ( ax0_sk7 @ sk16 ) @ sk16 ) @ sk16,
inference(pattern_uni,[status(thm)],[60769:[bind(A,$thf( ax0_sk11 @ ( ax0_sk7 @ sk16 ) @ sk16 )),bind(B,$thf( sk16 ))]]) ).
thf(928,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( A
!= ( ax0_sk8 @ sk14 ) )
| ( B
!= ( ax0_sk6 @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[71,918]) ).
thf(929,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ ( ax0_sk6 @ sk14 ) ) @ ( ax0_sk6 @ sk14 ) )
| ( incident_c @ ( ax0_sk13 @ A @ ( ax0_sk6 @ sk14 ) ) @ A )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[928:[bind(A,$thf( A )),bind(B,$thf( ax0_sk6 @ sk14 ))]]) ).
thf(944,plain,
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk6 @ sk14 ) ) @ ( ax0_sk6 @ sk14 ) )
| ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk6 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[929]) ).
thf(247,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)],[133,150]) ).
thf(248,plain,
! [A: $i] :
( ( closed @ A )
| ( open @ A ) ),
inference(pattern_uni,[status(thm)],[247:[bind(A,$thf( D )),bind(B,$thf( ax0_sk6 @ D )),bind(C,$thf( D ))]]) ).
thf(255,plain,
! [A: $i] :
( ( closed @ A )
| ( open @ A ) ),
inference(simp,[status(thm)],[248]) ).
thf(5132,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( incident_c @ C @ ( sum @ A @ B ) )
| ( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
!= ( incident_c @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[829,91]) ).
thf(5133,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( sum @ A @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(pattern_uni,[status(thm)],[5132:[bind(A,$thf( A )),bind(B,$thf( ax0_sk8 @ sk14 )),bind(C,$thf( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ))]]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( meet @ A @ ( ax0_sk9 @ A @ B ) @ ( ax0_sk10 @ A @ B ) ) ),
inference(cnf,[status(esa)],[144]) ).
thf(8951,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ ( sum @ B @ ( sum @ C @ D ) ) @ A ) )
!= ( incident_c @ G @ F ) ) ),
inference(paramod_ordered,[status(thm)],[5589,91]) ).
thf(8952,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ ( sum @ C @ ( sum @ D @ E ) ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[8951:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( sum @ ( sum @ K @ ( sum @ M @ N ) ) @ J )),bind(G,$thf( ax0_sk8 @ M ))]]) ).
thf(9069,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ ( sum @ C @ ( sum @ D @ E ) ) @ B ) ) ),
inference(simp,[status(thm)],[8952]) ).
thf(9076,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ B @ ( sum @ A @ C ) ) )
| ( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( sum @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[2837,5708]) ).
thf(9077,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ A @ ( sum @ C @ B ) ) ),
inference(pattern_uni,[status(thm)],[9076:[bind(A,$thf( J )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( ax0_sk9 @ ( ax0_sk8 @ J ) @ J )),bind(E,$thf( ax0_sk10 @ ( ax0_sk8 @ J ) @ J ))]]) ).
thf(9259,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ A @ ( sum @ C @ B ) ) ),
inference(simp,[status(thm)],[9077]) ).
thf(8331,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( A != sk17 )
| ( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( sum @ ( ax0_sk8 @ sk14 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2837,5993]) ).
thf(8478,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( ( ax0_sk9 @ ( ax0_sk8 @ sk17 ) @ sk17 )
!= ( ax0_sk8 @ sk14 ) )
| ( ( ax0_sk10 @ ( ax0_sk8 @ sk17 ) @ sk17 )
!= A ) ),
inference(simp,[status(thm)],[8331]) ).
thf(8505,plain,
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( ( ax0_sk9 @ ( ax0_sk8 @ sk17 ) @ sk17 )
!= ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[8478]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ~ ( incident_c @ C @ A )
| ( incident_c @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn_1) ).
thf(111,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)],[27]) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ~ ( incident_c @ C @ A )
| ( incident_c @ C @ B ) ),
inference(cnf,[status(esa)],[111]) ).
thf(289,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)],[166,114]) ).
thf(290,plain,
! [A: $i] :
( ~ ( open @ A )
| ~ ( inner_point @ ( ax0_sk7 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[289:[bind(A,$thf( D )),bind(B,$thf( ax0_sk7 @ D )),bind(C,$thf( D ))]]) ).
thf(295,plain,
! [A: $i] :
( ~ ( open @ A )
| ~ ( inner_point @ ( ax0_sk7 @ A ) @ A ) ),
inference(simp,[status(thm)],[290]) ).
thf(3150,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ C ) @ C ) ) @ A )
| ( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( sum @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2837,3009]) ).
thf(3151,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) ) @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) ) ) @ A ),
inference(pattern_uni,[status(thm)],[3150:[bind(A,$thf( H )),bind(B,$thf( ax0_sk10 @ ( ax0_sk8 @ H ) @ H )),bind(C,$thf( ax0_sk9 @ ( ax0_sk8 @ H ) @ H ))]]) ).
thf(3214,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) ) @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) ) ) @ A ),
inference(simp,[status(thm)],[3151]) ).
thf(52897,plain,
! [B: $i,A: $i] :
( ( sk14 != sk16 )
| ~ ( inner_point @ A @ B )
| ( ( end_point @ sk17 @ sk16 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[52834,114]) ).
thf(52898,plain,
( ( sk14 != sk16 )
| ~ ( inner_point @ sk17 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[52897:[bind(A,$thf( sk17 )),bind(B,$thf( sk16 ))]]) ).
thf(7023,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ C ) @ C ) ) @ A )
| ( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( sum @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2837,5248]) ).
thf(7024,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) ) ) @ A ),
inference(pattern_uni,[status(thm)],[7023:[bind(A,$thf( H )),bind(B,$thf( ax0_sk9 @ ( ax0_sk8 @ H ) @ H )),bind(C,$thf( ax0_sk10 @ ( ax0_sk8 @ H ) @ H ))]]) ).
thf(7166,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) ) ) @ A ),
inference(simp,[status(thm)],[7024]) ).
thf(26308,plain,
! [A: $i] :
( ~ ( closed @ A )
| ( ( open @ sk15 )
!= ( open @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25999,280]) ).
thf(26309,plain,
~ ( closed @ sk15 ),
inference(pattern_uni,[status(thm)],[26308:[bind(A,$thf( sk15 ))]]) ).
thf(10467,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ B @ ( sum @ C @ D ) ) @ A ) )
!= ( incident_c @ G @ E ) ) ),
inference(paramod_ordered,[status(thm)],[7008,77]) ).
thf(10468,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ ( sum @ ( sum @ C @ ( sum @ D @ E ) ) @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[10467:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( sum @ ( sum @ K @ ( sum @ M @ N ) ) @ J )),bind(F,$thf( F )),bind(G,$thf( ax0_sk8 @ N ))]]) ).
thf(10636,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ ( sum @ ( sum @ C @ ( sum @ D @ E ) ) @ B ) @ A ) ),
inference(simp,[status(thm)],[10468]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',sum_defn_9) ).
thf(67,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( incident_c @ A @ ( ax0_sk3 @ B @ A ) )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn_17) ).
thf(126,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)],[34]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( incident_c @ A @ ( ax0_sk3 @ B @ A ) )
| ( end_point @ A @ B ) ),
inference(cnf,[status(esa)],[126]) ).
thf(56286,plain,
! [B: $i,A: $i] :
( ( ( ax0_sk11 @ A @ B )
!= A )
| ( ( end_point @ ( ax0_sk7 @ sk16 ) @ sk16 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27367,148]) ).
thf(56287,plain,
( ( ax0_sk11 @ ( ax0_sk7 @ sk16 ) @ sk16 )
!= ( ax0_sk7 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[56286:[bind(A,$thf( ax0_sk7 @ sk16 )),bind(B,$thf( sk16 ))]]) ).
thf(45947,plain,
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ ( ax0_sk8 @ sk14 ) )
!= ( incident_c @ sk17 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[45880,342]) ).
thf(46012,plain,
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
| ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= sk17 )
| ( ( ax0_sk8 @ sk14 )
!= sk16 ) ),
inference(simp,[status(thm)],[45947]) ).
thf(51991,plain,
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= sk17 )
| ( ( ax0_sk8 @ sk14 )
!= sk16 )
| ( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
!= ( incident_c @ sk17 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[45880,46012]) ).
thf(52339,plain,
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= sk17 )
| ( ( ax0_sk8 @ sk14 )
!= sk16 )
| ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= sk17 )
| ( sk16 != sk17 ) ),
inference(simp,[status(thm)],[51991]) ).
thf(52417,plain,
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= sk17 )
| ( ( ax0_sk8 @ sk14 )
!= sk16 )
| ( sk16 != sk17 ) ),
inference(simp,[status(thm)],[52339]) ).
thf(60501,plain,
! [A: $i] :
( ( end_point @ ( ax0_sk11 @ ( ax0_sk7 @ sk14 ) @ sk14 ) @ sk14 )
!= ( end_point @ ( ax0_sk8 @ A ) @ A ) ),
inference(paramod_ordered,[status(thm)],[57100,297]) ).
thf(60650,plain,
! [A: $i] :
( ( ( ax0_sk11 @ ( ax0_sk7 @ sk14 ) @ sk14 )
!= ( ax0_sk8 @ A ) )
| ( sk14 != A ) ),
inference(simp,[status(thm)],[60501]) ).
thf(60690,plain,
( ( ax0_sk11 @ ( ax0_sk7 @ sk14 ) @ sk14 )
!= ( ax0_sk8 @ sk14 ) ),
inference(simp,[status(thm)],[60650]) ).
thf(663,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( B
!= ( ax0_sk8 @ sk14 ) )
| ( A
!= ( ax0_sk7 @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[71,368]) ).
thf(664,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ A ) @ A )
| ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ A ) @ ( ax0_sk7 @ sk14 ) )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[663:[bind(A,$thf( ax0_sk7 @ sk14 )),bind(B,$thf( B ))]]) ).
thf(864,plain,
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) ) ),
inference(simp,[status(thm)],[664]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',sum_defn_8) ).
thf(72,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8250,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ ( sum @ A @ ( ax0_sk8 @ sk14 ) ) )
!= ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[5133]) ).
thf(8259,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( sum @ A @ ( ax0_sk8 @ sk14 ) )
!= sk17 ) ),
inference(simp,[status(thm)],[8250]) ).
thf(8299,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( sum @ A @ ( ax0_sk8 @ sk14 ) )
!= sk17 ) ),
inference(simp,[status(thm)],[8259]) ).
thf(48671,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ sk17 @ ( sum @ ( sum @ sk16 @ B ) @ A ) )
!= ( incident_c @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[46505,77]) ).
thf(48672,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ ( sum @ ( sum @ sk16 @ C ) @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[48671:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( sum @ ( sum @ sk16 @ I ) @ G )),bind(D,$thf( D )),bind(E,$thf( sk17 ))]]) ).
thf(48880,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ ( sum @ ( sum @ sk16 @ C ) @ B ) @ A ) ),
inference(simp,[status(thm)],[48672]) ).
thf(43631,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk10 @ ( ax0_sk8 @ sk17 ) @ sk17 )
!= ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[43629]) ).
thf(8892,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ C ) @ ( sum @ ( sum @ B @ ( sum @ C @ D ) ) @ A ) )
!= ( incident_c @ G @ E ) ) ),
inference(paramod_ordered,[status(thm)],[5589,77]) ).
thf(8893,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ ( sum @ C @ ( sum @ D @ E ) ) @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[8892:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( sum @ ( sum @ K @ ( sum @ M @ N ) ) @ J )),bind(F,$thf( F )),bind(G,$thf( ax0_sk8 @ M ))]]) ).
thf(9046,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ ( sum @ C @ ( sum @ D @ E ) ) @ B ) @ A ) ),
inference(simp,[status(thm)],[8893]) ).
thf(27374,plain,
! [A: $i] :
( ~ ( inner_point @ ( ax0_sk7 @ A ) @ A )
| ( ( open @ sk16 )
!= ( open @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27064,295]) ).
thf(27375,plain,
~ ( inner_point @ ( ax0_sk7 @ sk16 ) @ sk16 ),
inference(pattern_uni,[status(thm)],[27374:[bind(A,$thf( sk16 ))]]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c9_47) ).
thf(87,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(104,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(cnf,[status(esa)],[103]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',end_point_defn_19) ).
thf(99,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)],[22]) ).
thf(58075,plain,
! [B: $i,A: $i] :
( ( incident_c @ A @ B )
| ( ( end_point @ ( ax0_sk11 @ sk17 @ sk14 ) @ sk14 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57102,154]) ).
thf(58076,plain,
incident_c @ ( ax0_sk11 @ sk17 @ sk14 ) @ sk14,
inference(pattern_uni,[status(thm)],[58075:[bind(A,$thf( ax0_sk11 @ sk17 @ sk14 )),bind(B,$thf( sk14 ))]]) ).
thf(58023,plain,
! [B: $i,A: $i] :
( ( incident_c @ A @ B )
| ( ( end_point @ sk17 @ sk14 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56,154]) ).
thf(58024,plain,
incident_c @ sk17 @ sk14,
inference(pattern_uni,[status(thm)],[58023:[bind(A,$thf( sk17 )),bind(B,$thf( sk14 ))]]) ).
thf(158,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(cnf,[status(esa)],[157]) ).
thf(7029,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ A @ B ) )
!= ( incident_c @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5248,77]) ).
thf(7030,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ ( sum @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[7029:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( sum @ J @ K )),bind(D,$thf( D )),bind(E,$thf( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ K ) @ K ) ))]]) ).
thf(7167,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ ( sum @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[7030]) ).
thf(2120,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) )
| ( ( incident_c @ ( ax0_sk8 @ A ) @ A )
!= ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2103,377]) ).
thf(2136,plain,
! [A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) )
| ( ( ax0_sk8 @ A )
!= ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) )
| ( A
!= ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[2120]) ).
thf(2152,plain,
( ~ ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) )
| ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ ( ax0_sk7 @ sk14 ) )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(simp,[status(thm)],[2136]) ).
thf(4322,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ A @ C ) @ B ) )
| ( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( sum @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[2837,2923]) ).
thf(4323,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ ( sum @ C @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[4322:[bind(A,$thf( J )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( ax0_sk9 @ ( ax0_sk8 @ J ) @ J )),bind(E,$thf( ax0_sk10 @ ( ax0_sk8 @ J ) @ J ))]]) ).
thf(4451,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk9 @ ( ax0_sk8 @ C ) @ C ) ) @ ( sum @ ( sum @ C @ B ) @ A ) ),
inference(simp,[status(thm)],[4323]) ).
thf(53268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ D @ ( sum @ B @ C ) )
| ( ( incident_c @ sk17 @ ( sum @ A @ sk15 ) )
!= ( incident_c @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[53063,91]) ).
thf(53269,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ A @ ( sum @ B @ sk15 ) ) ),
inference(pattern_uni,[status(thm)],[53268:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( sum @ E @ sk15 )),bind(D,$thf( sk17 ))]]) ).
thf(53392,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ A @ ( sum @ B @ sk15 ) ) ),
inference(simp,[status(thm)],[53269]) ).
thf(45901,plain,
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( incident_c @ ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 ) @ sk17 )
!= ( incident_c @ sk17 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[45880,2157]) ).
thf(46000,plain,
( ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= ( ax0_sk8 @ ( ax0_sk8 @ sk14 ) ) )
| ( ( ax0_sk13 @ ( ax0_sk8 @ sk14 ) @ sk17 )
!= sk17 )
| ( sk16 != sk17 ) ),
inference(simp,[status(thm)],[45901]) ).
thf(9274,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ ( sum @ ( sum @ C @ D ) @ B ) @ A ) )
!= ( incident_c @ G @ E ) ) ),
inference(paramod_ordered,[status(thm)],[5715,77]) ).
thf(9275,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ ( sum @ ( sum @ ( sum @ D @ E ) @ C ) @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[9274:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( sum @ ( sum @ ( sum @ M @ N ) @ L ) @ J )),bind(F,$thf( F )),bind(G,$thf( ax0_sk8 @ N ))]]) ).
thf(9427,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ ( sum @ ( sum @ ( sum @ D @ E ) @ C ) @ B ) @ A ) ),
inference(simp,[status(thm)],[9275]) ).
thf(119,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(cnf,[status(esa)],[118]) ).
thf(57825,plain,
! [A: $i] :
( ( end_point @ ( ax0_sk11 @ ( ax0_sk7 @ sk15 ) @ sk15 ) @ sk15 )
!= ( end_point @ ( ax0_sk8 @ A ) @ A ) ),
inference(paramod_ordered,[status(thm)],[57098,297]) ).
thf(57971,plain,
! [A: $i] :
( ( ( ax0_sk11 @ ( ax0_sk7 @ sk15 ) @ sk15 )
!= ( ax0_sk8 @ A ) )
| ( sk15 != A ) ),
inference(simp,[status(thm)],[57825]) ).
thf(58012,plain,
( ( ax0_sk11 @ ( ax0_sk7 @ sk15 ) @ sk15 )
!= ( ax0_sk8 @ sk15 ) ),
inference(simp,[status(thm)],[57971]) ).
thf(58019,plain,
! [B: $i,A: $i] :
( ( incident_c @ A @ B )
| ( ( end_point @ ( ax0_sk7 @ sk15 ) @ sk15 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[26314,154]) ).
thf(58020,plain,
incident_c @ ( ax0_sk7 @ sk15 ) @ sk15,
inference(pattern_uni,[status(thm)],[58019:[bind(A,$thf( ax0_sk7 @ sk15 )),bind(B,$thf( sk15 ))]]) ).
thf(53534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ D @ ( sum @ B @ C ) )
| ( ( incident_c @ sk17 @ ( sum @ sk15 @ A ) )
!= ( incident_c @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[53172,91]) ).
thf(53535,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ A @ ( sum @ sk15 @ B ) ) ),
inference(pattern_uni,[status(thm)],[53534:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( sum @ sk15 @ F )),bind(D,$thf( sk17 ))]]) ).
thf(53667,plain,
! [B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ A @ ( sum @ sk15 @ B ) ) ),
inference(simp,[status(thm)],[53535]) ).
thf(56260,plain,
! [B: $i,A: $i] :
( ( ( ax0_sk11 @ A @ B )
!= A )
| ( ( end_point @ ( ax0_sk7 @ sk15 ) @ sk15 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[26314,148]) ).
thf(56261,plain,
( ( ax0_sk11 @ ( ax0_sk7 @ sk15 ) @ sk15 )
!= ( ax0_sk7 @ sk15 ) ),
inference(pattern_uni,[status(thm)],[56260:[bind(A,$thf( ax0_sk7 @ sk15 )),bind(B,$thf( sk15 ))]]) ).
thf(58107,plain,
! [B: $i,A: $i] :
( ( incident_c @ A @ B )
| ( ( end_point @ ( ax0_sk7 @ sk16 ) @ sk16 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27367,154]) ).
thf(58108,plain,
incident_c @ ( ax0_sk7 @ sk16 ) @ sk16,
inference(pattern_uni,[status(thm)],[58107:[bind(A,$thf( ax0_sk7 @ sk16 )),bind(B,$thf( sk16 ))]]) ).
thf(260,plain,
! [C: $i,B: $i,A: $i] :
( ( open @ A )
| ~ ( end_point @ C @ B )
| ( ( closed @ A )
!= ( closed @ B ) ) ),
inference(paramod_ordered,[status(thm)],[255,156]) ).
thf(261,plain,
! [B: $i,A: $i] :
( ( open @ A )
| ~ ( end_point @ B @ A ) ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ( open @ A )
| ~ ( end_point @ B @ A ) ),
inference(simp,[status(thm)],[261]) ).
thf(106,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(cnf,[status(esa)],[105]) ).
thf(107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( A = D )
| ( C = D )
| ~ ( end_point @ A @ B )
| ~ ( end_point @ C @ B )
| ~ ( end_point @ D @ B ) ),
inference(lifteq,[status(thm)],[106]) ).
thf(26321,plain,
! [A: $i] :
( ~ ( inner_point @ ( ax0_sk7 @ A ) @ A )
| ( ( open @ sk15 )
!= ( open @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25999,295]) ).
thf(26322,plain,
~ ( inner_point @ ( ax0_sk7 @ sk15 ) @ sk15 ),
inference(pattern_uni,[status(thm)],[26321:[bind(A,$thf( sk15 ))]]) ).
thf(2520,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( incident_c @ C @ ( sum @ A @ B ) )
| ( ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk7 @ sk14 ) )
!= ( incident_c @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[864,77]) ).
thf(2521,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( sum @ ( ax0_sk7 @ sk14 ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[2520:[bind(A,$thf( ax0_sk7 @ sk14 )),bind(B,$thf( B )),bind(C,$thf( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ))]]) ).
thf(2619,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( ax0_sk8 @ sk14 ) )
| ( incident_c @ ( ax0_sk13 @ ( ax0_sk7 @ sk14 ) @ ( ax0_sk8 @ sk14 ) ) @ ( sum @ ( ax0_sk7 @ sk14 ) @ A ) ) ),
inference(simp,[status(thm)],[2521]) ).
thf(53015,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= sk17 )
| ( ( ax0_sk8 @ sk14 )
!= sk16 )
| ( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
!= ( incident_c @ sk17 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[52996,46004]) ).
thf(53131,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= sk17 )
| ( ( ax0_sk8 @ sk14 )
!= sk16 )
| ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= sk17 )
| ( sk15 != sk17 ) ),
inference(simp,[status(thm)],[53015]) ).
thf(53159,plain,
( ( ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) )
!= sk17 )
| ( ( ax0_sk8 @ sk14 )
!= sk16 )
| ( sk15 != sk17 ) ),
inference(simp,[status(thm)],[53131]) ).
thf(10276,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ G @ ( sum @ E @ F ) )
| ( ( incident_c @ ( ax0_sk8 @ D ) @ ( sum @ A @ ( sum @ B @ ( sum @ C @ D ) ) ) )
!= ( incident_c @ G @ E ) ) ),
inference(paramod_ordered,[status(thm)],[6985,77]) ).
thf(10277,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ ( sum @ B @ ( sum @ C @ ( sum @ D @ E ) ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[10276:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( sum @ I @ ( sum @ K @ ( sum @ M @ N ) ) )),bind(F,$thf( F )),bind(G,$thf( ax0_sk8 @ N ))]]) ).
thf(10421,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ E ) @ ( sum @ ( sum @ B @ ( sum @ C @ ( sum @ D @ E ) ) ) @ A ) ),
inference(simp,[status(thm)],[10277]) ).
thf(57279,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( ( end_point @ ( ax0_sk11 @ sk17 @ sk14 ) @ sk14 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57102,114]) ).
thf(57280,plain,
~ ( inner_point @ ( ax0_sk11 @ sk17 @ sk14 ) @ sk14 ),
inference(pattern_uni,[status(thm)],[57279:[bind(A,$thf( ax0_sk11 @ sk17 @ sk14 )),bind(B,$thf( sk14 ))]]) ).
thf(7380,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ B @ A ) )
!= ( incident_c @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[5468,91]) ).
thf(7381,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ A @ ( sum @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[7380:[bind(A,$thf( K )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( sum @ J @ K )),bind(E,$thf( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ J ) @ J ) ))]]) ).
thf(7457,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ B ) @ B ) ) @ ( sum @ A @ ( sum @ B @ C ) ) ),
inference(simp,[status(thm)],[7381]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( part_of @ ( ax0_sk4 @ B @ A ) @ B )
| ( end_point @ A @ B ) ),
inference(cnf,[status(esa)],[130]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( incident_c @ A @ ( ax0_sk4 @ B @ A ) )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn_18) ).
thf(163,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)],[51]) ).
thf(48730,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ sk17 @ ( sum @ ( sum @ sk16 @ B ) @ A ) )
!= ( incident_c @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[46505,91]) ).
thf(48731,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ A @ ( sum @ ( sum @ sk16 @ C ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[48730:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( sum @ ( sum @ sk16 @ I ) @ G )),bind(E,$thf( sk17 ))]]) ).
thf(48900,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ A @ ( sum @ ( sum @ sk16 @ C ) @ B ) ) ),
inference(simp,[status(thm)],[48731]) ).
thf(9876,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( A != sk17 )
| ( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( sum @ B @ ( ax0_sk8 @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2837,8299]) ).
thf(10027,plain,
! [A: $i] :
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( ax0_sk9 @ ( ax0_sk8 @ sk17 ) @ sk17 )
!= A )
| ( ( ax0_sk10 @ ( ax0_sk8 @ sk17 ) @ sk17 )
!= ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[9876]) ).
thf(10060,plain,
( ( incident_c @ ( ax0_sk13 @ sk17 @ ( ax0_sk8 @ sk14 ) ) @ sk17 )
| ( ( ax0_sk10 @ ( ax0_sk8 @ sk17 ) @ sk17 )
!= ( ax0_sk8 @ sk14 ) ) ),
inference(simp,[status(thm)],[10027]) ).
thf(7175,plain,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ C ) @ C ) ) @ A )
| ( ( sum @ ( ax0_sk9 @ ( ax0_sk8 @ A ) @ A ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) )
!= ( sum @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2837,5452]) ).
thf(7176,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) ) ) @ A ),
inference(pattern_uni,[status(thm)],[7175:[bind(A,$thf( H )),bind(B,$thf( ax0_sk9 @ ( ax0_sk8 @ H ) @ H )),bind(C,$thf( ax0_sk10 @ ( ax0_sk8 @ H ) @ H ))]]) ).
thf(7284,plain,
! [A: $i] : ( incident_c @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) ) @ ( ax0_sk10 @ ( ax0_sk8 @ A ) @ A ) ) ) @ A ),
inference(simp,[status(thm)],[7176]) ).
thf(48406,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_c @ E @ ( sum @ C @ D ) )
| ( ( incident_c @ sk17 @ ( sum @ A @ ( sum @ B @ sk16 ) ) )
!= ( incident_c @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[46276,91]) ).
thf(48407,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ A @ ( sum @ B @ ( sum @ C @ sk16 ) ) ) ),
inference(pattern_uni,[status(thm)],[48406:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( sum @ F @ ( sum @ H @ sk16 ) )),bind(E,$thf( sk17 ))]]) ).
thf(48551,plain,
! [C: $i,B: $i,A: $i] : ( incident_c @ sk17 @ ( sum @ A @ ( sum @ B @ ( sum @ C @ sk16 ) ) ) ),
inference(simp,[status(thm)],[48407]) ).
thf(56288,plain,
! [B: $i,A: $i] :
( ( sk14 != sk15 )
| ( ( ax0_sk11 @ A @ B )
!= A )
| ( ( end_point @ sk17 @ sk15 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56100,148]) ).
thf(56289,plain,
( ( sk14 != sk15 )
| ( ( ax0_sk11 @ sk17 @ sk15 )
!= sk17 ) ),
inference(pattern_uni,[status(thm)],[56288:[bind(A,$thf( sk17 )),bind(B,$thf( sk15 ))]]) ).
thf(57880,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( ( end_point @ ( ax0_sk11 @ ( ax0_sk7 @ sk15 ) @ sk15 ) @ sk15 )
!= ( end_point @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57098,114]) ).
thf(57881,plain,
~ ( inner_point @ ( ax0_sk11 @ ( ax0_sk7 @ sk15 ) @ sk15 ) @ sk15 ),
inference(pattern_uni,[status(thm)],[57880:[bind(A,$thf( ax0_sk11 @ ( ax0_sk7 @ sk15 ) @ sk15 )),bind(B,$thf( sk15 ))]]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( part_of @ ( ax0_sk3 @ B @ A ) @ ( ax0_sk4 @ B @ A ) )
| ( end_point @ A @ B ) ),
inference(cnf,[status(esa)],[99]) ).
thf(128720,plain,
$false,
inference(cvc4,[status(thm)],[69,1337,138,101,333,34755,7285,5582,88,170,115,7008,52996,120,2837,26314,269,5348,48621,56,5589,9233,142,43630,945,153,5708,8881,829,9424,8851,5227,8086,288,5352,3513,5195,46505,4618,26311,4866,45940,27362,110,60559,10606,27442,157,125,344,46817,93,58118,152,46004,46010,57,78,37913,23960,7144,2291,84,5360,57362,56234,8109,2222,56163,47689,121,397,53711,280,132,5246,133,2103,74,57100,2154,102,60,117,60551,5443,7439,910,27364,297,4449,137,165,53436,2147,160,92,8085,97,27360,5993,1350,2157,948,5238,156,53,141,9603,45950,77,46529,37914,96,5818,124,2504,52834,3354,2153,45880,129,73,128,105,53063,134,26307,52987,58022,2149,166,148,161,5715,149,296,3111,46055,53073,7440,118,57102,9852,71,54,34756,144,56275,27064,947,2358,86,159,172,113,2151,5244,81,377,3106,56265,863,98,7632,303,7302,9263,91,66,2923,56263,155,108,46797,103,1630,46252,130,10444,9450,5248,30316,135,2390,2156,80,3009,60770,944,255,27367,5133,145,9069,9259,8505,112,342,123,5452,295,150,3214,53172,57098,52898,63,7166,26309,10636,67,5467,25999,127,56287,52417,60690,154,57137,864,72,5226,46012,143,8299,48880,43631,9046,27375,87,104,368,6985,99,58076,58024,158,7167,2152,4451,55,114,53392,46000,9427,119,378,58012,56100,151,58020,53667,146,56261,2155,3232,833,58108,168,262,107,26322,2619,94,126,918,136,53159,10421,57280,7457,3020,131,163,62,395,48900,5468,68,10060,122,83,7284,48551,56289,57881,100,46276,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO094-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n021.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 19 04:07:29 EDT 2023
% 0.16/0.37 % CPUTime :
% 1.02/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/1.05 % [INFO] Parsing done (148ms).
% 1.30/1.06 % [INFO] Running in sequential loop mode.
% 1.92/1.27 % [INFO] eprover registered as external prover.
% 1.92/1.27 % [INFO] cvc4 registered as external prover.
% 1.92/1.27 % [INFO] Scanning for conjecture ...
% 2.16/1.33 % [INFO] Found a conjecture and 48 axioms. Running axiom selection ...
% 2.16/1.38 % [INFO] Axiom selection finished. Selected 48 axioms (removed 0 axioms).
% 2.33/1.43 % [INFO] Problem is propositional (TPTP CNF).
% 2.33/1.44 % [INFO] Type checking passed.
% 2.33/1.44 % [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 ...
% 119.58/36.93 % External prover 'cvc4' found a proof!
% 119.58/36.93 % [INFO] Killing All external provers ...
% 119.58/36.93 % Time passed: 36391ms (effective reasoning time: 35872ms)
% 119.58/36.93 % 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)>
% 119.58/36.94 % 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
% 119.58/36.94 % No. of inferences in proof: 692
% 119.58/36.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 36391 ms resp. 35872 ms w/o parsing
% 120.01/37.07 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 120.01/37.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------