%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO112-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:12:22 AM UTC 2026
% Result : Unsatisfiable 36.57s 8.55s
% Output : Refutation 31.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 46
% Syntax : Number of formulae : 181 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 588 ( 94 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1854 ( 323 ~; 343 |; 0 &;1188 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 6 con; 0-4 aty)
% Number of variables : 429 ( 0 ^; 429 !; 0 ?; 429 :)
% Comments :
%------------------------------------------------------------------------------
thf(between_c_decl,type,
between_c: $i > $i > $i > $i > $o ).
thf(sk15_decl,type,
sk15: $i ).
thf(sk16_decl,type,
sk16: $i ).
thf(sk17_decl,type,
sk17: $i ).
thf(sk18_decl,type,
sk18: $i ).
thf(meet_decl,type,
meet: $i > $i > $i > $o ).
thf(incident_c_decl,type,
incident_c: $i > $i > $o ).
thf(end_point_decl,type,
end_point: $i > $i > $o ).
thf(closed_decl,type,
closed: $i > $o ).
thf(sum_decl,type,
sum: $i > $i > $i ).
thf(ax0_sk5_decl,type,
ax0_sk5: $i > $i > $i > $i ).
thf(ax0_sk12_decl,type,
ax0_sk12: $i > $i > $i ).
thf(ax0_sk4_decl,type,
ax0_sk4: $i > $i > $i ).
thf(ax0_sk3_decl,type,
ax0_sk3: $i > $i > $i ).
thf(ax0_sk1_decl,type,
ax0_sk1: $i > $i > $i ).
thf(part_of_decl,type,
part_of: $i > $i > $o ).
thf(inner_point_decl,type,
inner_point: $i > $i > $o ).
thf(ax0_sk9_decl,type,
ax0_sk9: $i > $i > $i ).
thf(ax0_sk10_decl,type,
ax0_sk10: $i > $i > $i ).
thf(open_decl,type,
open: $i > $o ).
thf(ax0_sk11_decl,type,
ax0_sk11: $i > $i > $i ).
thf(ax0_sk7_decl,type,
ax0_sk7: $i > $i ).
thf(ax0_sk6_decl,type,
ax0_sk6: $i > $i ).
thf(ax0_sk8_decl,type,
ax0_sk8: $i > $i ).
thf(ax1_sk1_decl,type,
ax1_sk1: $i > $i > $i > $i > $i ).
thf(39,axiom,
! [A: $i] :
( ( A @ closed )
| ( A @ ( A @ ax0_sk6 @ end_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closed_defn_32) ).
thf(135,plain,
! [A: $i] :
( ( A @ closed )
| ( A @ ( A @ ax0_sk6 @ end_point ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(136,plain,
! [A: $i] :
( ( A @ closed )
| ( A @ ( A @ ax0_sk6 @ end_point ) ) ),
inference(cnf,[status(esa)],[135]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ end_point ) )
| ~ ( B @ ( A @ inner_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_point_defn_22) ).
thf(102,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ end_point ) )
| ~ ( B @ ( A @ inner_point ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ end_point ) )
| ~ ( B @ ( A @ inner_point ) ) ),
inference(cnf,[status(esa)],[102]) ).
thf(197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk6 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ~ $true
| ~ ( C @ ( B @ inner_point ) )
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[136,103]) ).
thf(198,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk6 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ~ ( C @ ( B @ inner_point ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[197]) ).
thf(199,plain,
! [A: $i] :
( ~ ( A @ ( A @ ax0_sk6 @ inner_point ) )
| ( A @ closed ) ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( D )),bind(B,$thf( D @ ax0_sk6 )),bind(C,$thf( D ))]]) ).
thf(202,plain,
! [A: $i] :
( ~ ( A @ ( A @ ax0_sk6 @ inner_point ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[199]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ax1_sk1 ) ) ) @ ( C @ inner_point ) )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',between_c_defn_5) ).
thf(142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ax1_sk1 ) ) ) @ ( C @ inner_point ) )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(40,axiom,
! [A: $i] : ( A @ ( A @ ax0_sk8 @ inner_point ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3_37) ).
thf(137,plain,
! [A: $i] : ( A @ ( A @ ax0_sk8 @ inner_point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( A @ open )
| ( A = B )
| ~ ( B @ ( A @ part_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c1_35) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( A @ open )
| ( A = B )
| ~ ( B @ ( A @ part_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ ( A @ ax0_sk7 @ end_point ) )
| ~ ( A @ open ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',open_defn_33) ).
thf(133,plain,
! [A: $i] :
( ( A @ ( A @ ax0_sk7 @ end_point ) )
| ~ ( A @ open ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(134,plain,
! [A: $i] :
( ( A @ ( A @ ax0_sk7 @ end_point ) )
| ~ ( A @ open ) ),
inference(cnf,[status(esa)],[133]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ( A @ ( B @ ax0_sk4 ) @ ( A @ incident_c ) )
| ~ ( B @ ( A @ incident_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn_18) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ( A @ ( B @ ax0_sk4 ) @ ( A @ incident_c ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( A @ ax0_sk11 ) ) )
| ~ ( B @ ( A @ end_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c6_42) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( A @ ax0_sk11 ) ) )
| ~ ( B @ ( A @ end_point ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ax1_sk1 ) ) ) @ ( D @ end_point ) )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',between_c_defn_4) ).
thf(138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ax1_sk1 ) ) ) @ ( D @ end_point ) )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ part_of ) )
| ( A @ ( B @ ( A @ ax0_sk1 ) @ incident_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn_2) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ part_of ) )
| ( A @ ( B @ ( A @ ax0_sk1 ) @ incident_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ part_of ) )
| ( A @ ( B @ ( A @ ax0_sk1 ) @ incident_c ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ end_point ) )
| ~ ( C @ ( D @ incident_c ) )
| ~ ( B @ ( D @ incident_c ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_defn_27) ).
thf(52,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ end_point ) )
| ~ ( C @ ( D @ incident_c ) )
| ~ ( B @ ( D @ incident_c ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ( B @ ( A @ ( B @ ax0_sk4 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn_16) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ( B @ ( A @ ( B @ ax0_sk4 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ end_point ) )
| ~ ( A @ closed ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closed_defn_31) ).
thf(125,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ end_point ) )
| ~ ( A @ closed ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ meet ) ) )
| ~ ( C @ ( E @ end_point ) )
| ( A
!= ( D @ ( C @ sum ) ) )
| ~ ( D @ ( C @ ( B @ meet ) ) )
| ~ ( A @ closed ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c7_43) ).
thf(54,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ meet ) ) )
| ~ ( C @ ( E @ end_point ) )
| ( A
!= ( D @ ( C @ sum ) ) )
| ~ ( D @ ( C @ ( B @ meet ) ) )
| ~ ( A @ closed ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(55,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ meet ) ) )
| ~ ( C @ ( E @ end_point ) )
| ( A
!= ( D @ ( C @ sum ) ) )
| ~ ( D @ ( C @ ( B @ meet ) ) )
| ~ ( A @ closed ) ),
inference(cnf,[status(esa)],[54]) ).
thf(56,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ meet ) ) )
| ~ ( C @ ( E @ end_point ) )
| ~ ( D @ ( C @ ( B @ meet ) ) )
| ~ ( A @ closed )
| ( A
!= ( D @ ( C @ sum ) ) ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(57,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ meet ) ) )
| ~ ( B @ ( D @ end_point ) )
| ~ ( C @ ( B @ ( A @ meet ) ) )
| ~ ( C @ ( B @ sum ) @ closed ) ),
inference(simp,[status(thm)],[56]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ax0_sk12 ) )
= ( C @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c8_44) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ax0_sk12 ) )
= ( C @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) )
| ~ ( D @ ( A @ incident_c ) )
| ~ ( C @ ( A @ incident_c ) )
| ~ ( B @ ( D @ part_of ) )
| ~ ( B @ ( C @ part_of ) )
| ~ ( B @ ( A @ end_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn_14) ).
thf(106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) )
| ~ ( D @ ( A @ incident_c ) )
| ~ ( C @ ( A @ incident_c ) )
| ~ ( B @ ( D @ part_of ) )
| ~ ( B @ ( C @ part_of ) )
| ~ ( B @ ( A @ end_point ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ incident_c ) )
| ~ ( B @ ( A @ end_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn_13) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ incident_c ) )
| ~ ( B @ ( A @ end_point ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != D )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',between_c_defn_1) ).
thf(147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != D )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( A @ ax0_sk11 ) ) )
| ~ ( B @ ( A @ end_point ) ) ),
inference(cnf,[status(esa)],[114]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ end_point ) )
| ( ( B @ ( A @ ax0_sk11 ) )
!= A ) ),
inference(lifteq,[status(thm)],[115]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( A @ open )
| ( A = B )
| ~ ( B @ ( A @ part_of ) ) ),
inference(cnf,[status(esa)],[97]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( A @ open )
| ~ ( B @ ( A @ part_of ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ part_of ) )
!= ( D @ ( C @ part_of ) ) )
| ( C @ open )
| ~ $true
| ( C = D )
| ( A @ ( B @ ( A @ ax0_sk1 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[88,99]) ).
thf(264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ part_of ) )
!= ( D @ ( C @ part_of ) ) )
| ( C @ open )
| ( C = D )
| ( A @ ( B @ ( A @ ax0_sk1 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[263]) ).
thf(265,plain,
! [B: $i,A: $i] :
( ( A @ open )
| ( A = B )
| ( A @ ( B @ ( A @ ax0_sk1 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[264:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ incident_c ) )
| ~ ( C @ ( D @ incident_c ) )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_defn_6) ).
thf(74,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ incident_c ) )
| ~ ( C @ ( D @ incident_c ) )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(18,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ part_of ) )
| ( D @ ( A @ part_of ) )
| ( A @ ( C @ part_of ) )
| ( C @ ( A @ part_of ) )
| ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) )
| ~ ( D @ ( E @ end_point ) )
| ~ ( C @ ( E @ end_point ) )
| ~ ( A @ ( E @ end_point ) )
| ~ ( B @ ( D @ part_of ) )
| ~ ( B @ ( C @ part_of ) )
| ~ ( B @ ( A @ part_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_36) ).
thf(89,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ part_of ) )
| ( D @ ( A @ part_of ) )
| ( A @ ( C @ part_of ) )
| ( C @ ( A @ part_of ) )
| ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) )
| ~ ( D @ ( E @ end_point ) )
| ~ ( C @ ( E @ end_point ) )
| ~ ( A @ ( E @ end_point ) )
| ~ ( B @ ( D @ part_of ) )
| ~ ( B @ ( C @ part_of ) )
| ~ ( B @ ( A @ part_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,negated_conjecture,
sk18 @ ( sk17 @ ( sk16 @ ( sk15 @ between_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_3_8_2_77) ).
thf(47,plain,
sk18 @ ( sk17 @ ( sk16 @ ( sk15 @ between_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
~ ( sk16 @ ( sk17 @ ( sk18 @ ( sk15 @ between_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_3_8_2_78) ).
thf(48,plain,
~ ( sk16 @ ( sk17 @ ( sk18 @ ( sk15 @ between_c ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,plain,
~ ( sk16 @ ( sk17 @ ( sk18 @ ( sk15 @ between_c ) ) ) ),
inference(polarity_switch,[status(thm)],[48]) ).
thf(153,plain,
( ( ( sk16 @ ( sk17 @ ( sk18 @ ( sk15 @ between_c ) ) ) )
!= ( sk18 @ ( sk17 @ ( sk16 @ ( sk15 @ between_c ) ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,49]) ).
thf(154,plain,
( ( sk16 @ ( sk17 @ ( sk18 @ ( sk15 @ between_c ) ) ) )
!= ( sk18 @ ( sk17 @ ( sk16 @ ( sk15 @ between_c ) ) ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(155,plain,
( ( sk18 != sk16 )
| ( sk17 != sk17 )
| ( sk18 != sk16 )
| ( sk15 != sk15 ) ),
inference(simp,[status(thm)],[154]) ).
thf(156,plain,
sk18 != sk16,
inference(simp,[status(thm)],[155]) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( A != sk18 )
| ( B != sk16 )
| ( A @ open )
| ~ ( B @ ( A @ part_of ) ) ),
inference(paramod_ordered,[status(thm)],[99,156]) ).
thf(315,plain,
! [A: $i] :
( ( A != sk16 )
| ( sk18 @ open )
| ~ ( A @ ( sk18 @ part_of ) ) ),
inference(pattern_uni,[status(thm)],[314:[bind(A,$thf( sk18 ))]]) ).
thf(381,plain,
( ( sk18 @ open )
| ~ ( sk16 @ ( sk18 @ part_of ) ) ),
inference(simp,[status(thm)],[315]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ meet ) ) )
| ~ ( C @ ( A @ ( B @ ( C @ ax0_sk5 ) ) @ end_point ) )
| ~ ( B @ ( A @ ( B @ ( C @ ax0_sk5 ) ) @ end_point ) )
| ~ ( C @ ( A @ incident_c ) )
| ~ ( B @ ( A @ incident_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_defn_30) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ meet ) ) )
| ~ ( C @ ( A @ ( B @ ( C @ ax0_sk5 ) ) @ end_point ) )
| ~ ( B @ ( A @ ( B @ ( C @ ax0_sk5 ) ) @ end_point ) )
| ~ ( C @ ( A @ incident_c ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( B @ open )
| ~ ( B @ ( A @ end_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',open_defn_34) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( B @ open )
| ~ ( B @ ( A @ end_point ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ( A @ ( B @ ax0_sk3 ) @ ( A @ incident_c ) )
| ~ ( B @ ( A @ incident_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn_17) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ( A @ ( B @ ax0_sk3 ) @ ( A @ incident_c ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(194,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk7 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ~ $true
| ~ ( C @ ( B @ inner_point ) )
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[134,103]) ).
thf(195,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk7 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ~ ( C @ ( B @ inner_point ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[194]) ).
thf(196,plain,
! [A: $i] :
( ~ ( A @ ( A @ ax0_sk7 @ inner_point ) )
| ~ ( A @ open ) ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( D )),bind(B,$thf( D @ ax0_sk7 )),bind(C,$thf( D ))]]) ).
thf(201,plain,
! [A: $i] :
( ~ ( A @ ( A @ ax0_sk7 @ inner_point ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[196]) ).
thf(53,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ end_point ) )
| ~ ( C @ ( D @ incident_c ) )
| ~ ( B @ ( D @ incident_c ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ( B @ open )
| ~ ( B @ ( A @ end_point ) ) ),
inference(cnf,[status(esa)],[117]) ).
thf(164,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk6 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ( C @ open )
| ~ $true
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[136,118]) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk6 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ( C @ open )
| ( A @ closed ) ),
inference(simp,[status(thm)],[164]) ).
thf(166,plain,
! [A: $i] :
( ( A @ open )
| ( A @ closed ) ),
inference(pattern_uni,[status(thm)],[165:[bind(A,$thf( D )),bind(B,$thf( D @ ax0_sk6 )),bind(C,$thf( D ))]]) ).
thf(167,plain,
! [A: $i] :
( ( A @ open )
| ( A @ closed ) ),
inference(simp,[status(thm)],[166]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( ( A @ open )
!= ( B @ open ) )
| ( B @ ( B @ ax0_sk7 @ end_point ) )
| ~ $true
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[167,134]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( ( A @ open )
!= ( B @ open ) )
| ( B @ ( B @ ax0_sk7 @ end_point ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[171]) ).
thf(173,plain,
! [A: $i] :
( ( A @ ( A @ ax0_sk7 @ end_point ) )
| ( A @ closed ) ),
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ incident_c ) )
| ~ ( B @ ( A @ inner_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_point_defn_21) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ incident_c ) )
| ~ ( B @ ( A @ inner_point ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ incident_c ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_defn_24) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ incident_c ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ incident_c ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(44,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( A @ ( D @ between_c ) ) ) )
| ~ ( C @ ( E @ inner_point ) )
| ~ ( C @ ( B @ end_point ) )
| ~ ( C @ ( A @ end_point ) )
| ~ ( D @ ( C @ part_of ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',between_c_defn_6) ).
thf(144,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( A @ ( D @ between_c ) ) ) )
| ~ ( C @ ( E @ inner_point ) )
| ~ ( C @ ( B @ end_point ) )
| ~ ( C @ ( A @ end_point ) )
| ~ ( D @ ( C @ part_of ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(316,plain,
! [B: $i,A: $i] :
( ( B != sk18 )
| ( A != sk16 )
| ( A @ open )
| ~ ( B @ ( A @ part_of ) ) ),
inference(paramod_ordered,[status(thm)],[99,156]) ).
thf(317,plain,
! [A: $i] :
( ( A != sk16 )
| ( A @ open )
| ~ ( sk18 @ ( A @ part_of ) ) ),
inference(pattern_uni,[status(thm)],[316:[bind(A,$thf( A )),bind(B,$thf( sk18 ))]]) ).
thf(382,plain,
( ( sk16 @ open )
| ~ ( sk18 @ ( sk16 @ part_of ) ) ),
inference(simp,[status(thm)],[317]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ ( D @ ax1_sk1 ) ) ) @ part_of ) )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',between_c_defn_2) ).
thf(140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ ( D @ ax1_sk1 ) ) ) @ part_of ) )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(188,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk8 @ inner_point ) )
!= ( C @ ( B @ inner_point ) ) )
| ~ ( C @ ( B @ end_point ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[137,103]) ).
thf(189,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk8 @ inner_point ) )
!= ( C @ ( B @ inner_point ) ) )
| ~ ( C @ ( B @ end_point ) ) ),
inference(simp,[status(thm)],[188]) ).
thf(190,plain,
! [A: $i] :
~ ( A @ ( A @ ax0_sk8 @ end_point ) ),
inference(pattern_uni,[status(thm)],[189:[bind(A,$thf( D )),bind(B,$thf( D @ ax0_sk8 )),bind(C,$thf( D ))]]) ).
thf(203,plain,
! [A: $i] :
~ ( A @ ( A @ ax0_sk8 @ end_point ) ),
inference(simp,[status(thm)],[190]) ).
thf(204,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk7 @ end_point ) )
!= ( B @ ( B @ ax0_sk8 @ end_point ) ) )
| ~ $true
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[173,203]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk7 @ end_point ) )
!= ( B @ ( B @ ax0_sk8 @ end_point ) ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[204]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( A @ ax0_sk7 )
!= ( B @ ax0_sk8 ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[205]) ).
thf(213,plain,
! [A: $i] :
( ( ( A @ ax0_sk8 )
!= ( A @ ax0_sk7 ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[210]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ ax0_sk10 ) @ ( B @ ( A @ ax0_sk9 ) @ sum ) ) )
| ~ ( B @ ( A @ inner_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c4_39) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ ax0_sk10 ) @ ( B @ ( A @ ax0_sk9 ) @ sum ) ) )
| ~ ( B @ ( A @ inner_point ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ meet ) ) )
| ( B @ ( A @ ( B @ ( C @ ax0_sk5 ) ) @ incident_c ) )
| ~ ( C @ ( A @ incident_c ) )
| ~ ( B @ ( A @ incident_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_defn_28) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ meet ) ) )
| ( B @ ( A @ ( B @ ( C @ ax0_sk5 ) ) @ incident_c ) )
| ~ ( C @ ( A @ incident_c ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ( B @ ( A @ ( B @ ax0_sk3 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn_15) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ( B @ ( A @ ( B @ ax0_sk3 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(397,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ part_of ) )
!= ( sk18 @ ( sk16 @ part_of ) ) )
| ( sk16 @ open )
| ~ $true
| ( A @ ( B @ ( A @ ax0_sk1 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[88,382]) ).
thf(398,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ part_of ) )
!= ( sk18 @ ( sk16 @ part_of ) ) )
| ( sk16 @ open )
| ( A @ ( B @ ( A @ ax0_sk1 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[397]) ).
thf(399,plain,
( ( sk16 @ open )
| ( sk16 @ ( sk18 @ ( sk16 @ ax0_sk1 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[398:[bind(A,$thf( sk16 )),bind(B,$thf( sk18 ))]]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ end_point ) )
| ~ ( A @ closed ) ),
inference(cnf,[status(esa)],[125]) ).
thf(239,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ end_point ) )
!= ( E @ ( F @ end_point ) ) )
| ~ $true
| ~ ( E @ closed )
| ~ ( C @ ( D @ incident_c ) )
| ~ ( B @ ( D @ incident_c ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,126]) ).
thf(240,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ end_point ) )
!= ( E @ ( F @ end_point ) ) )
| ~ ( E @ closed )
| ~ ( C @ ( D @ incident_c ) )
| ~ ( B @ ( D @ incident_c ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
inference(simp,[status(thm)],[239]) ).
thf(241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ closed )
| ~ ( C @ ( D @ incident_c ) )
| ~ ( B @ ( D @ incident_c ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( C )),bind(F,$thf( D ))]]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ax0_sk10 ) @ ( B @ ( A @ ax0_sk9 ) @ ( A @ meet ) ) )
| ~ ( B @ ( A @ inner_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c4_38) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ax0_sk10 ) @ ( B @ ( A @ ax0_sk9 ) @ ( A @ meet ) ) )
| ~ ( B @ ( A @ inner_point ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ~ ( A @ ( B @ ax0_sk4 ) @ ( A @ ( B @ ax0_sk3 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn_19) ).
thf(123,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ~ ( A @ ( B @ ax0_sk4 ) @ ( A @ ( B @ ax0_sk3 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != D )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) ),
inference(cnf,[status(esa)],[147]) ).
thf(149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) )
| ( B != D ) ),
inference(lifteq,[status(thm)],[148]) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ ( C @ ( A @ between_c ) ) ) ),
inference(simp,[status(thm)],[149]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ incident_c ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_defn_25) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ incident_c ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(174,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk7 @ end_point ) )
!= ( B @ ( C @ end_point ) ) )
| ~ $true
| ~ ( B @ closed )
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[134,126]) ).
thf(175,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk7 @ end_point ) )
!= ( B @ ( C @ end_point ) ) )
| ~ ( B @ closed )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[174]) ).
thf(176,plain,
! [A: $i] :
( ~ ( A @ closed )
| ~ ( A @ open ) ),
inference(pattern_uni,[status(thm)],[175:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ ax0_sk7 ))]]) ).
thf(177,plain,
! [A: $i] :
( ~ ( A @ closed )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[176]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ~ ( A @ ( B @ ax0_sk3 ) @ ( A @ ( B @ ax0_sk4 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn_20) ).
thf(127,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ~ ( A @ ( B @ ax0_sk3 ) @ ( A @ ( B @ ax0_sk4 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ meet ) ) )
| ( C @ ( A @ ( B @ ( C @ ax0_sk5 ) ) @ incident_c ) )
| ~ ( C @ ( A @ incident_c ) )
| ~ ( B @ ( A @ incident_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_defn_29) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ meet ) ) )
| ( C @ ( A @ ( B @ ( C @ ax0_sk5 ) ) @ incident_c ) )
| ~ ( C @ ( A @ incident_c ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(384,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ part_of ) )
!= ( sk16 @ ( sk18 @ part_of ) ) )
| ( sk18 @ open )
| ~ $true
| ( A @ ( B @ ( A @ ax0_sk1 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[88,381]) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ part_of ) )
!= ( sk16 @ ( sk18 @ part_of ) ) )
| ( sk18 @ open )
| ( A @ ( B @ ( A @ ax0_sk1 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[384]) ).
thf(386,plain,
( ( sk18 @ open )
| ( sk18 @ ( sk16 @ ( sk18 @ ax0_sk1 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[385:[bind(A,$thf( sk18 )),bind(B,$thf( sk16 ))]]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ inner_point ) )
| ( B @ ( A @ end_point ) )
| ~ ( B @ ( A @ incident_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_point_defn_23) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ inner_point ) )
| ( B @ ( A @ end_point ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk7 @ end_point ) )
!= ( B @ ( B @ ax0_sk8 @ end_point ) ) )
| ~ $true
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[134,203]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk7 @ end_point ) )
!= ( B @ ( B @ ax0_sk8 @ end_point ) ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[206]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( A @ ax0_sk7 )
!= ( B @ ax0_sk8 ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[207]) ).
thf(214,plain,
! [A: $i] :
( ( ( A @ ax0_sk8 )
!= ( A @ ax0_sk7 ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[211]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ ax0_sk11 ) @ end_point ) )
| ~ ( B @ ( A @ end_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c6_41) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ ax0_sk11 ) @ end_point ) )
| ~ ( B @ ( A @ end_point ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ax1_sk1 ) ) ) @ ( B @ end_point ) )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',between_c_defn_3) ).
thf(151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ax1_sk1 ) ) ) @ ( B @ end_point ) )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(251,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk7 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ~ $true
| ( ( C @ ( B @ ax0_sk11 ) )
!= B )
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[134,116]) ).
thf(252,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk7 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ( ( C @ ( B @ ax0_sk11 ) )
!= B )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[251]) ).
thf(253,plain,
! [A: $i] :
( ( ( A @ ( A @ ax0_sk7 @ ax0_sk11 ) )
!= ( A @ ax0_sk7 ) )
| ~ ( A @ open ) ),
inference(pattern_uni,[status(thm)],[252:[bind(A,$thf( D )),bind(B,$thf( D @ ax0_sk7 )),bind(C,$thf( D ))]]) ).
thf(262,plain,
! [A: $i] :
( ( ( A @ ( A @ ax0_sk7 @ ax0_sk11 ) )
!= ( A @ ax0_sk7 ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[253]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ incident_c ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( A = D )
| ( A = C )
| ~ ( B @ ( D @ end_point ) )
| ~ ( B @ ( C @ end_point ) )
| ~ ( B @ ( A @ end_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c5_40) ).
thf(94,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( A = D )
| ( A = C )
| ~ ( B @ ( D @ end_point ) )
| ~ ( B @ ( C @ end_point ) )
| ~ ( B @ ( A @ end_point ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(387,plain,
! [B: $i,A: $i] :
( ( A != sk18 )
| ( sk18 @ open )
| ~ ( sk16 @ ( B @ part_of ) )
| ( A @ open )
| ~ ( B @ ( A @ part_of ) ) ),
inference(paramod_ordered,[status(thm)],[99,381]) ).
thf(388,plain,
! [A: $i] :
( ( sk18 @ open )
| ~ ( sk16 @ ( A @ part_of ) )
| ( sk18 @ open )
| ~ ( A @ ( sk18 @ part_of ) ) ),
inference(pattern_uni,[status(thm)],[387:[bind(A,$thf( sk18 ))]]) ).
thf(395,plain,
! [A: $i] :
( ~ ( sk16 @ ( A @ part_of ) )
| ( sk18 @ open )
| ~ ( A @ ( sk18 @ part_of ) ) ),
inference(simp,[status(thm)],[388]) ).
thf(191,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk7 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ~ $true
| ~ ( C @ ( B @ inner_point ) )
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[173,103]) ).
thf(192,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk7 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ~ ( C @ ( B @ inner_point ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[191]) ).
thf(193,plain,
! [A: $i] :
( ~ ( A @ ( A @ ax0_sk7 @ inner_point ) )
| ( A @ closed ) ),
inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( D )),bind(B,$thf( D @ ax0_sk7 )),bind(C,$thf( D ))]]) ).
thf(200,plain,
! [A: $i] :
( ~ ( A @ ( A @ ax0_sk7 @ inner_point ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[193]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) )
| ~ ( A @ ( D @ incident_c ) )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_defn_4) ).
thf(68,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) )
| ~ ( A @ ( D @ incident_c ) )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ incident_c ) )
| ~ ( B @ ( D @ incident_c ) )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_defn_5) ).
thf(62,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ incident_c ) )
| ~ ( B @ ( D @ incident_c ) )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ part_of ) )
| ~ ( B @ ( B @ ( A @ ax0_sk1 ) @ incident_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn_3) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ part_of ) )
| ~ ( B @ ( B @ ( A @ ax0_sk1 ) @ incident_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ end_point ) )
| ~ ( C @ ( D @ incident_c ) )
| ~ ( B @ ( D @ incident_c ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_defn_26) ).
thf(83,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ end_point ) )
| ~ ( C @ ( D @ incident_c ) )
| ~ ( B @ ( D @ incident_c ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk6 @ end_point ) )
!= ( B @ ( B @ ax0_sk8 @ end_point ) ) )
| ~ $true
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[136,203]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ax0_sk6 @ end_point ) )
!= ( B @ ( B @ ax0_sk8 @ end_point ) ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[208]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( A @ ax0_sk6 )
!= ( B @ ax0_sk8 ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[209]) ).
thf(215,plain,
! [A: $i] :
( ( ( A @ ax0_sk8 )
!= ( A @ ax0_sk6 ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[212]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ incident_c ) )
| ~ ( A @ ( C @ incident_c ) )
| ~ ( B @ ( A @ part_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn_1) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ incident_c ) )
| ~ ( A @ ( C @ incident_c ) )
| ~ ( B @ ( A @ part_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3157,plain,
$false,
inference(e,[status(thm)],[202,142,137,97,134,81,114,138,88,52,110,125,57,78,106,121,147,116,265,74,89,133,381,102,60,117,85,201,156,53,173,129,59,118,144,49,382,54,103,140,213,91,66,108,399,135,241,167,112,123,48,150,50,177,127,72,386,99,87,203,104,214,119,58,151,262,51,94,126,136,395,200,68,62,131,47,83,215,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO112-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/0.50 % Computer : n009.cluster.edu
% 0.23/0.50 % Model : x86_64 x86_64
% 0.23/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.50 % Memory : 8046.5625MB
% 0.23/0.50 % OS : Linux 6.8.0-71-generic
% 0.23/0.50 % CPULimit : 300
% 0.23/0.50 % WCLimit : 300
% 0.23/0.50 % DateTime : Fri Sep 25 12:47:59 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.96/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.76/1.20 % [INFO] Parsing done (212ms).
% 1.76/1.21 % [INFO] Running in sequential loop mode.
% 2.54/1.54 % [INFO] eprover registered as external prover.
% 2.54/1.54 % [INFO] Scanning for conjecture ...
% 2.82/1.63 % [INFO] Found a conjecture (or negated_conjecture) and 54 axioms. Running axiom selection ...
% 2.82/1.70 % [INFO] Axiom selection finished. Selected 44 axioms (removed 10 axioms).
% 3.04/1.76 % [INFO] Problem is propositional (TPTP CNF).
% 3.04/1.77 % [INFO] Type checking passed.
% 3.04/1.77 % [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 ...
% 36.57/8.54 % External prover 'e' found a proof!
% 36.57/8.54 % [INFO] Killing All external provers ...
% 36.57/8.54 % Time passed: 7896ms (effective reasoning time: 7327ms)
% 36.57/8.55 % Axioms used in derivation (44): c6_41, part_of_defn_3, c7_43, meet_defn_30, sum_defn_6, end_point_defn_16, inner_point_defn_22, between_c_defn_4, c5_40, meet_defn_25, closed_defn_32, end_point_defn_19, end_point_defn_15, between_c_defn_2, c4_39, c1_35, sum_defn_5, c2_36, c8_44, end_point_defn_18, between_c_defn_5, inner_point_defn_21, sum_defn_4, c3_37, end_point_defn_14, closed_defn_31, meet_defn_28, end_point_defn_20, meet_defn_24, end_point_defn_17, between_c_defn_1, meet_defn_29, part_of_defn_2, between_c_defn_6, end_point_defn_13, open_defn_33, meet_defn_27, meet_defn_26, part_of_defn_1, open_defn_34, between_c_defn_3, inner_point_defn_23, c4_38, c6_42
% 36.57/8.55 % No. of inferences in proof: 181
% 36.57/8.55 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7896 ms resp. 7327 ms w/o parsing
% 31.52/8.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 31.52/8.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------