TSTP Solution File: GEO118-1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO118-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 11:09:24 EDT 2023
% Result : Unsatisfiable 36.58s 7.81s
% Output : Refutation 36.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 124
% Syntax : Number of formulae : 212 ( 19 unt; 37 typ; 0 def)
% Number of atoms : 523 ( 58 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 2038 ( 270 ~; 348 |; 0 &;1420 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 5 con; 0-5 aty)
% Number of variables : 476 ( 0 ^; 476 !; 0 ?; 476 :)
% Comments :
%------------------------------------------------------------------------------
thf(ordered_by_type,type,
ordered_by: $i > $i > $i > $o ).
thf(sk25_type,type,
sk25: $i ).
thf(sk26_type,type,
sk26: $i ).
thf(sk27_type,type,
sk27: $i ).
thf(between_c_type,type,
between_c: $i > $i > $i > $i > $o ).
thf(end_point_type,type,
end_point: $i > $i > $o ).
thf(ax1_sk1_type,type,
ax1_sk1: $i > $i > $i > $i > $i ).
thf(incident_c_type,type,
incident_c: $i > $i > $o ).
thf(part_of_type,type,
part_of: $i > $i > $o ).
thf(ax0_sk3_type,type,
ax0_sk3: $i > $i > $i ).
thf(ax0_sk4_type,type,
ax0_sk4: $i > $i > $i ).
thf(closed_type,type,
closed: $i > $o ).
thf(ax0_sk5_type,type,
ax0_sk5: $i > $i > $i > $i ).
thf(meet_type,type,
meet: $i > $i > $i > $o ).
thf(inner_point_type,type,
inner_point: $i > $i > $o ).
thf(ax0_sk12_type,type,
ax0_sk12: $i > $i > $i ).
thf(sum_type,type,
sum: $i > $i > $i ).
thf(ax0_sk8_type,type,
ax0_sk8: $i > $i ).
thf(incident_o_type,type,
incident_o: $i > $i > $o ).
thf(ax2_sk10_type,type,
ax2_sk10: $i > $i > $i ).
thf(underlying_curve_type,type,
underlying_curve: $i > $i ).
thf(ax0_sk13_type,type,
ax0_sk13: $i > $i > $i ).
thf(open_type,type,
open: $i > $o ).
thf(ax2_sk7_type,type,
ax2_sk7: $i > $i > $i > $i ).
thf(finish_point_type,type,
finish_point: $i > $i > $o ).
thf(ax0_sk1_type,type,
ax0_sk1: $i > $i > $i ).
thf(ax2_sk2_type,type,
ax2_sk2: $i > $i > $i ).
thf(ax2_sk5_type,type,
ax2_sk5: $i > $i > $i > $i > $i > $i ).
thf(between_o_type,type,
between_o: $i > $i > $i > $i > $o ).
thf(ax2_sk1_type,type,
ax2_sk1: $i > $i > $i ).
thf(start_point_type,type,
start_point: $i > $i > $o ).
thf(ax2_sk6_type,type,
ax2_sk6: $i > $i ).
thf(ax2_sk3_type,type,
ax2_sk3: $i > $i ).
thf(ax2_sk4_type,type,
ax2_sk4: $i > $i > $i > $i > $i ).
thf(ax0_sk7_type,type,
ax0_sk7: $i > $i ).
thf(ax2_sk8_type,type,
ax2_sk8: $i > $i > $i ).
thf(ax2_sk9_type,type,
ax2_sk9: $i > $i > $i ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( open @ A )
| ( B = C )
| ~ ( incident_c @ B @ A )
| ~ ( incident_c @ C @ A )
| ~ ( incident_c @ D @ A )
| ( incident_o @ D @ ( ax2_sk7 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o5_31) ).
thf(156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( open @ A )
| ( B = C )
| ~ ( incident_c @ B @ A )
| ~ ( incident_c @ C @ A )
| ~ ( incident_c @ D @ A )
| ( incident_o @ D @ ( ax2_sk7 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(54,axiom,
! [A: $i] :
( ~ ( open @ A )
| ( end_point @ ( ax0_sk7 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_defn_33) ).
thf(209,plain,
! [A: $i] :
( ~ ( open @ A )
| ( end_point @ ( ax0_sk7 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ~ ( ordered_by @ A @ ( ax2_sk8 @ A @ B ) @ ( ax2_sk9 @ A @ B ) )
| ~ ( ordered_by @ B @ ( ax2_sk8 @ A @ B ) @ ( ax2_sk9 @ A @ B ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o6_36) ).
thf(263,plain,
! [B: $i,A: $i] :
( ~ ( ordered_by @ A @ ( ax2_sk8 @ A @ B ) @ ( ax2_sk9 @ A @ B ) )
| ~ ( ordered_by @ B @ ( ax2_sk8 @ A @ B ) @ ( ax2_sk9 @ A @ B ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ~ ( incident_o @ A @ B )
| ( incident_c @ A @ ( ax2_sk3 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o2_20) ).
thf(199,plain,
! [B: $i,A: $i] :
( ~ ( incident_o @ A @ B )
| ( incident_c @ A @ ( ax2_sk3 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( open @ A )
| ( B = C )
| ~ ( incident_c @ B @ A )
| ~ ( incident_c @ C @ A )
| ~ ( incident_o @ D @ ( ax2_sk7 @ A @ C @ B ) )
| ( incident_c @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o5_30) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( open @ A )
| ( B = C )
| ~ ( incident_c @ B @ A )
| ~ ( incident_c @ C @ A )
| ~ ( incident_o @ D @ ( ax2_sk7 @ A @ C @ B ) )
| ( incident_c @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ B @ C ) )
| ~ ( incident_c @ D @ A )
| ( incident_c @ D @ B )
| ( incident_c @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_4) ).
thf(168,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)],[37]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( start_point @ A @ B )
| ( A = C )
| ~ ( incident_o @ C @ B )
| ( ordered_by @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',start_point_defn_8) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( start_point @ A @ B )
| ( A = C )
| ~ ( incident_o @ C @ B )
| ( ordered_by @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( incident_c @ A @ C )
| ( incident_c @ ( ax0_sk5 @ C @ B @ A ) @ C )
| ( meet @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_29) ).
thf(234,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)],[67]) ).
thf(1,negated_conjecture,
ordered_by @ sk25 @ sk26 @ sk27,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_5_133) ).
thf(88,plain,
ordered_by @ sk25 @ sk26 @ sk27,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( part_of @ ( ax0_sk4 @ B @ A ) @ B )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_16) ).
thf(120,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)],[17]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( incident_c @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_24) ).
thf(217,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( incident_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_o @ A @ B @ C @ D )
| ( ordered_by @ A @ C @ D )
| ( ordered_by @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_o_defn_3) ).
thf(276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_o @ A @ B @ C @ D )
| ( ordered_by @ A @ C @ D )
| ( ordered_by @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c9_47) ).
thf(174,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ B @ C ) )
| ~ ( incident_c @ D @ C )
| ( incident_c @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_6) ).
thf(185,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)],[43]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ~ ( incident_o @ A @ B )
| ( A
!= ( ax2_sk1 @ B @ A ) )
| ( start_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',start_point_defn_9) ).
thf(189,plain,
! [B: $i,A: $i] :
( ~ ( incident_o @ A @ B )
| ( A
!= ( ax2_sk1 @ B @ A ) )
| ( start_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c9_48) ).
thf(152,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)],[30]) ).
thf(63,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_o @ ( ax2_sk5 @ A @ B @ C @ D @ E ) @ B )
| ~ ( incident_o @ ( ax2_sk5 @ A @ B @ C @ D @ E ) @ B )
| ~ ( between_c @ A @ E @ D @ C )
| ( between_o @ B @ E @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o3_26) ).
thf(228,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( incident_c @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_25) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( incident_c @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(11,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( part_of @ C @ D )
| ~ ( end_point @ A @ C )
| ~ ( end_point @ B @ C )
| ~ ( inner_point @ E @ C )
| ( between_c @ D @ A @ E @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn_6) ).
thf(106,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( part_of @ C @ D )
| ~ ( end_point @ A @ C )
| ~ ( end_point @ B @ C )
| ~ ( inner_point @ E @ C )
| ( between_c @ D @ A @ E @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ~ ( incident_o @ A @ B )
| ( incident_o @ ( ax2_sk1 @ B @ A ) @ B )
| ( start_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',start_point_defn_10) ).
thf(238,plain,
! [B: $i,A: $i] :
( ~ ( incident_o @ A @ B )
| ( incident_o @ ( ax2_sk1 @ B @ A ) @ B )
| ( start_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( incident_o @ ( ax2_sk10 @ A @ B ) @ A )
| ~ ( incident_o @ ( ax2_sk10 @ A @ B ) @ A )
| ( B
= ( underlying_curve @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',underlying_curve_defn_40) ).
thf(147,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( incident_c @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_13) ).
thf(221,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( incident_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ~ ( end_point @ C @ B )
| ~ ( end_point @ D @ B )
| ( A = C )
| ( A = D )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c5_40) ).
thf(132,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)],[22]) ).
thf(2,negated_conjecture,
ordered_by @ sk25 @ sk27 @ sk26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_5_134) ).
thf(89,plain,
ordered_by @ sk25 @ sk27 @ sk26,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ~ ( part_of @ C @ B )
| ~ ( part_of @ D @ B )
| ~ ( incident_c @ A @ C )
| ~ ( incident_c @ A @ D )
| ( part_of @ C @ D )
| ( part_of @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_14) ).
thf(116,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)],[15]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( ordered_by @ A @ ( ax2_sk8 @ B @ A ) @ ( ax2_sk9 @ B @ A ) )
| ( ordered_by @ B @ ( ax2_sk8 @ B @ A ) @ ( ax2_sk9 @ B @ A ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o6_33) ).
thf(243,plain,
! [B: $i,A: $i] :
( ( ordered_by @ A @ ( ax2_sk8 @ B @ A ) @ ( ax2_sk9 @ B @ A ) )
| ( ordered_by @ B @ ( ax2_sk8 @ B @ A ) @ ( ax2_sk9 @ B @ A ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(66,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax2_sk5 @ A @ B @ C @ D @ E ) @ A )
| ( incident_c @ ( ax2_sk5 @ A @ B @ C @ D @ E ) @ A )
| ~ ( between_c @ A @ E @ D @ C )
| ( between_o @ B @ E @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o3_27) ).
thf(233,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ( ordered_by @ A @ ( ax2_sk8 @ B @ A ) @ ( ax2_sk9 @ B @ A ) )
| ~ ( ordered_by @ A @ ( ax2_sk8 @ B @ A ) @ ( ax2_sk9 @ B @ A ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o6_34) ).
thf(248,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(83,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ordered_by @ A @ B @ C )
| ( incident_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o1_17) ).
thf(270,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ordered_by @ A @ B @ C )
| ( incident_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk1 @ A @ B ) @ B )
| ( part_of @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn_3) ).
thf(201,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk1 @ A @ B ) @ B )
| ( part_of @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( incident_c @ A @ ( ax0_sk3 @ B @ A ) )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_17) ).
thf(102,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)],[9]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( open @ A )
| ( B = C )
| ~ ( incident_c @ B @ A )
| ~ ( incident_c @ C @ A )
| ( ordered_by @ ( ax2_sk7 @ A @ C @ B ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o5_32) ).
thf(260,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( open @ A )
| ( B = C )
| ~ ( incident_c @ B @ A )
| ~ ( incident_c @ C @ A )
| ( ordered_by @ ( ax2_sk7 @ A @ C @ B ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(45,axiom,
! [A: $i] : ( start_point @ ( ax2_sk6 @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o4_29) ).
thf(192,plain,
! [A: $i] : ( start_point @ ( ax2_sk6 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ~ ( incident_c @ D @ B )
| ~ ( incident_c @ D @ C )
| ( end_point @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_27) ).
thf(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(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ~ ( incident_o @ A @ B )
| ( A
!= ( ax2_sk2 @ B @ A ) )
| ( finish_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finish_point_defn_14) ).
thf(165,plain,
! [B: $i,A: $i] :
( ~ ( incident_o @ A @ B )
| ( A
!= ( ax2_sk2 @ B @ A ) )
| ( finish_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( part_of @ ( ax0_sk3 @ B @ A ) @ ( ax0_sk4 @ B @ A ) )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_19) ).
thf(92,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)],[4]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_o @ A @ B @ C @ D )
| ( between_c @ ( ax2_sk4 @ A @ D @ C @ B ) @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o3_24) ).
thf(229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_o @ A @ B @ C @ D )
| ( between_c @ ( ax2_sk4 @ A @ D @ C @ B ) @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ordered_by @ A @ B @ C )
| ( incident_o @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o1_18) ).
thf(252,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ordered_by @ A @ B @ C )
| ( incident_o @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sum @ B @ C ) )
| ~ ( incident_c @ D @ B )
| ( incident_c @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_5) ).
thf(224,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)],[62]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_c @ A @ B @ C @ D )
| ( inner_point @ C @ ( ax1_sk1 @ D @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn_5) ).
thf(124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_c @ A @ B @ C @ D )
| ( inner_point @ C @ ( ax1_sk1 @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( incident_c @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn_21) ).
thf(193,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( incident_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( part_of @ ( ax0_sk4 @ B @ A ) @ ( ax0_sk3 @ B @ A ) )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_20) ).
thf(96,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)],[6]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ~ ( end_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn_22) ).
thf(109,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ~ ( end_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( finish_point @ A @ B )
| ( A = C )
| ~ ( incident_o @ C @ B )
| ( ordered_by @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finish_point_defn_13) ).
thf(256,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( finish_point @ A @ B )
| ( A = C )
| ~ ( incident_o @ C @ B )
| ( ordered_by @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_o @ A @ B @ C @ D )
| ( ordered_by @ A @ B @ C )
| ( ordered_by @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_o_defn_2) ).
thf(266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_o @ A @ B @ C @ D )
| ( ordered_by @ A @ B @ C )
| ( ordered_by @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ~ ( incident_o @ A @ B )
| ( incident_o @ ( ax2_sk2 @ B @ A ) @ B )
| ( finish_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finish_point_defn_15) ).
thf(205,plain,
! [B: $i,A: $i] :
( ~ ( incident_o @ A @ B )
| ( incident_o @ ( ax2_sk2 @ B @ A ) @ B )
| ( finish_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( underlying_curve @ B ) )
| ~ ( incident_o @ C @ B )
| ( incident_c @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',underlying_curve_defn_37) ).
thf(148,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( underlying_curve @ B ) )
| ~ ( incident_o @ C @ B )
| ( incident_c @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( incident_c @ A @ C )
| ( incident_c @ ( ax0_sk5 @ C @ B @ A ) @ B )
| ( meet @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_28) ).
thf(161,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)],[34]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( part_of @ ( ax0_sk3 @ B @ A ) @ B )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_15) ).
thf(118,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)],[16]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ~ ( ordered_by @ A @ ( ax2_sk8 @ A @ B ) @ ( ax2_sk9 @ A @ B ) )
| ( ordered_by @ A @ ( ax2_sk8 @ A @ B ) @ ( ax2_sk9 @ A @ B ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o6_35) ).
thf(259,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( incident_o @ ( ax2_sk10 @ A @ B ) @ A )
| ( incident_c @ ( ax2_sk10 @ A @ B ) @ B )
| ( B
= ( underlying_curve @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',underlying_curve_defn_39) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( incident_o @ ( ax2_sk10 @ A @ B ) @ A )
| ( incident_c @ ( ax2_sk10 @ A @ B ) @ B )
| ( B
= ( underlying_curve @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ~ ( incident_c @ C @ A )
| ( incident_c @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn_1) ).
thf(236,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)],[68]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( underlying_curve @ B ) )
| ~ ( incident_c @ C @ A )
| ( incident_o @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',underlying_curve_defn_38) ).
thf(181,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( underlying_curve @ B ) )
| ~ ( incident_c @ C @ A )
| ( incident_o @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ~ ( finish_point @ A @ B )
| ( incident_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finish_point_defn_12) ).
thf(159,plain,
! [B: $i,A: $i] :
( ~ ( finish_point @ A @ B )
| ( incident_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(38,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_o @ ( ax2_sk5 @ A @ B @ C @ D @ E ) @ B )
| ( incident_c @ ( ax2_sk5 @ A @ B @ C @ D @ E ) @ A )
| ~ ( between_c @ A @ E @ D @ C )
| ( between_o @ B @ E @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o3_25) ).
thf(172,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( incident_o @ ( ax2_sk5 @ A @ B @ C @ D @ E ) @ B )
| ( incident_c @ ( ax2_sk5 @ A @ B @ C @ D @ E ) @ A )
| ~ ( between_c @ A @ E @ D @ C )
| ( between_o @ B @ E @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( open @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_defn_34) ).
thf(219,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( open @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ~ ( incident_o @ A @ B )
| ~ ( ordered_by @ B @ A @ ( ax2_sk1 @ B @ A ) )
| ( start_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',start_point_defn_11) ).
thf(274,plain,
! [B: $i,A: $i] :
( ~ ( incident_o @ A @ B )
| ~ ( ordered_by @ B @ A @ ( ax2_sk1 @ B @ A ) )
| ( start_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_c @ A @ B @ C @ D )
| ( end_point @ B @ ( ax1_sk1 @ D @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn_3) ).
thf(98,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_c @ A @ B @ C @ D )
| ( end_point @ B @ ( ax1_sk1 @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( closed @ A )
| ~ ( meet @ B @ C @ D )
| ( A
!= ( sum @ C @ D ) )
| ~ ( end_point @ E @ C )
| ( meet @ E @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c7_43) ).
thf(140,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)],[26]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ ( ax2_sk3 @ B ) )
| ( incident_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o2_21) ).
thf(213,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ ( ax2_sk3 @ B ) )
| ( incident_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( incident_c @ ( ax0_sk13 @ A @ B ) @ A )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c9_45) ).
thf(240,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)],[70]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax2_sk10 @ A @ B ) @ B )
| ( incident_c @ ( ax2_sk10 @ A @ B ) @ B )
| ( B
= ( underlying_curve @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',underlying_curve_defn_41) ).
thf(155,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(48,axiom,
! [A: $i] : ( open @ ( ax2_sk3 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o2_19) ).
thf(198,plain,
! [A: $i] : ( open @ ( ax2_sk3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(21,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ~ ( part_of @ C @ B )
| ~ ( part_of @ D @ B )
| ~ ( end_point @ E @ A )
| ~ ( end_point @ E @ C )
| ~ ( end_point @ E @ D )
| ( part_of @ C @ D )
| ( part_of @ D @ C )
| ( part_of @ A @ C )
| ( part_of @ C @ A )
| ( part_of @ A @ D )
| ( part_of @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2_36) ).
thf(130,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)],[21]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ~ ( incident_o @ A @ B )
| ~ ( ordered_by @ B @ ( ax2_sk2 @ B @ A ) @ A )
| ( finish_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finish_point_defn_16) ).
thf(278,plain,
! [B: $i,A: $i] :
( ~ ( incident_o @ A @ B )
| ~ ( ordered_by @ B @ ( ax2_sk2 @ B @ A ) @ A )
| ( finish_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ~ ( incident_c @ ( ax0_sk13 @ A @ B ) @ B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c9_46) ).
thf(223,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ~ ( incident_c @ D @ B )
| ~ ( incident_c @ D @ C )
| ( end_point @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_26) ).
thf(135,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)],[23]) ).
thf(65,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax2_sk5 @ A @ B @ C @ D @ E ) @ A )
| ~ ( incident_o @ ( ax2_sk5 @ A @ B @ C @ D @ E ) @ B )
| ~ ( between_c @ A @ E @ D @ C )
| ( between_o @ B @ E @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o3_28) ).
thf(231,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax2_sk5 @ A @ B @ C @ D @ E ) @ A )
| ~ ( incident_o @ ( ax2_sk5 @ A @ B @ C @ D @ E ) @ B )
| ~ ( between_c @ A @ E @ D @ C )
| ( between_o @ B @ E @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( start_point @ A @ B )
| ( incident_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',start_point_defn_7) ).
thf(203,plain,
! [B: $i,A: $i] :
( ~ ( start_point @ A @ B )
| ( incident_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( incident_c @ A @ C )
| ~ ( end_point @ ( ax0_sk5 @ C @ B @ A ) @ B )
| ~ ( end_point @ ( ax0_sk5 @ C @ B @ A ) @ C )
| ( meet @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_30) ).
thf(104,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)],[10]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( end_point @ A @ B )
| ( inner_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn_23) ).
thf(114,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( end_point @ A @ B )
| ( inner_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(25,axiom,
! [A: $i] : ( inner_point @ ( ax0_sk8 @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c3_37) ).
thf(139,plain,
! [A: $i] : ( inner_point @ ( ax0_sk8 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( ordered_by @ A @ B @ C )
| ~ ( ordered_by @ A @ C @ D )
| ( between_o @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_o_defn_5) ).
thf(246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( ordered_by @ A @ B @ C )
| ~ ( ordered_by @ A @ C @ D )
| ( between_o @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(53,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_o @ A @ B @ C @ D )
| ~ ( incident_c @ E @ ( ax2_sk4 @ A @ D @ C @ B ) )
| ( incident_o @ E @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o3_23) ).
thf(207,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_o @ A @ B @ C @ D )
| ~ ( incident_c @ E @ ( ax2_sk4 @ A @ D @ C @ B ) )
| ( incident_o @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_o @ A @ B @ C @ D )
| ( ordered_by @ A @ C @ D )
| ( ordered_by @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_o_defn_4) ).
thf(272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_o @ A @ B @ C @ D )
| ( ordered_by @ A @ C @ D )
| ( ordered_by @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_c @ A @ B @ C @ D )
| ( B != D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn_1) ).
thf(126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_c @ A @ B @ C @ D )
| ( B != D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( ordered_by @ A @ B @ C )
| ~ ( ordered_by @ A @ C @ D )
| ( between_o @ A @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_o_defn_6) ).
thf(268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( ordered_by @ A @ B @ C )
| ~ ( ordered_by @ A @ C @ D )
| ( between_o @ A @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax2_sk10 @ A @ B ) @ B )
| ~ ( incident_o @ ( ax2_sk10 @ A @ B ) @ A )
| ( B
= ( underlying_curve @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',underlying_curve_defn_42) ).
thf(195,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax2_sk10 @ A @ B ) @ B )
| ~ ( incident_o @ ( ax2_sk10 @ A @ B ) @ A )
| ( B
= ( underlying_curve @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( closed @ A )
| ~ ( end_point @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_defn_31) ).
thf(94,plain,
! [B: $i,A: $i] :
( ~ ( closed @ A )
| ~ ( end_point @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk1 @ A @ B ) @ A )
| ( part_of @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn_2) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk1 @ A @ B ) @ A )
| ( part_of @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ( A = B )
| ( open @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c1_35) ).
thf(178,plain,
! [B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ( A = B )
| ( open @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_o @ A @ B @ C @ D )
| ( ordered_by @ A @ B @ C )
| ( ordered_by @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_o_defn_1) ).
thf(254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_o @ A @ B @ C @ D )
| ( ordered_by @ A @ B @ C )
| ( ordered_by @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_c @ A @ B @ C @ D )
| ( part_of @ ( ax1_sk1 @ D @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn_2) ).
thf(122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_c @ A @ B @ C @ D )
| ( part_of @ ( ax1_sk1 @ D @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(57,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_o @ A @ B @ C @ D )
| ~ ( incident_o @ E @ A )
| ( incident_c @ E @ ( ax2_sk4 @ A @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o3_22) ).
thf(215,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_o @ A @ B @ C @ D )
| ~ ( incident_o @ E @ A )
| ( incident_c @ E @ ( ax2_sk4 @ A @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ( incident_c @ A @ ( ax0_sk4 @ B @ A ) )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_18) ).
thf(100,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)],[8]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_c @ A @ B @ C @ D )
| ( end_point @ D @ ( ax1_sk1 @ D @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn_4) ).
thf(90,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between_c @ A @ B @ C @ D )
| ( end_point @ D @ ( ax1_sk1 @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( ( ax0_sk12 @ C @ B )
= ( sum @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c8_44) ).
thf(111,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)],[13]) ).
thf(15318,plain,
$false,
inference(cvc4,[status(thm)],[156,209,263,199,175,168,249,234,88,120,217,276,174,185,189,152,228,211,106,238,147,221,132,89,116,243,233,248,270,201,102,260,192,137,165,92,229,252,224,124,193,96,109,256,266,205,148,161,118,259,144,236,181,159,172,219,274,98,140,213,240,155,198,130,278,223,135,231,203,104,114,139,246,207,272,126,268,195,94,163,178,254,122,215,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO118-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 04:29:13 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.93/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.05 % [INFO] Parsing done (172ms).
% 1.27/1.06 % [INFO] Running in sequential loop mode.
% 1.85/1.25 % [INFO] eprover registered as external prover.
% 1.85/1.25 % [INFO] cvc4 registered as external prover.
% 1.85/1.26 % [INFO] Scanning for conjecture ...
% 2.00/1.32 % [INFO] Found a conjecture and 96 axioms. Running axiom selection ...
% 2.32/1.37 % [INFO] Axiom selection finished. Selected 85 axioms (removed 11 axioms).
% 2.52/1.44 % [INFO] Problem is propositional (TPTP CNF).
% 2.58/1.45 % [INFO] Type checking passed.
% 2.58/1.46 % [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 ...
% 36.58/7.80 % External prover 'cvc4' found a proof!
% 36.58/7.80 % [INFO] Killing All external provers ...
% 36.58/7.81 % Time passed: 7285ms (effective reasoning time: 6744ms)
% 36.58/7.81 % 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)>
% 36.58/7.81 % Axioms used in derivation (85): o5_32, c7_43, c9_48, o5_30, finish_point_defn_14, start_point_defn_9, between_o_defn_1, between_o_defn_6, o3_25, o3_24, finish_point_defn_13, o1_17, part_of_defn_3, inner_point_defn_22, between_c_defn_4, c5_40, underlying_curve_defn_37, meet_defn_25, start_point_defn_8, between_o_defn_5, end_point_defn_19, end_point_defn_15, between_c_defn_2, c9_46, c1_35, between_o_defn_2, sum_defn_5, c2_36, c9_47, c8_44, end_point_defn_18, o6_33, o2_21, finish_point_defn_16, o1_18, meet_defn_30, between_c_defn_5, inner_point_defn_21, sum_defn_4, c3_37, finish_point_defn_12, start_point_defn_10, o3_23, o6_36, end_point_defn_14, closed_defn_31, meet_defn_28, end_point_defn_20, o2_20, sum_defn_6, meet_defn_24, underlying_curve_defn_38, finish_point_defn_15, o2_19, between_o_defn_3, end_point_defn_17, between_c_defn_1, meet_defn_29, o3_22, o3_27, start_point_defn_11, o3_28, part_of_defn_2, between_c_defn_6, end_point_defn_13, open_defn_33, meet_defn_27, o6_35, underlying_curve_defn_42, underlying_curve_defn_40, o3_26, underlying_curve_defn_39, o5_31, meet_defn_26, part_of_defn_1, between_o_defn_4, start_point_defn_7, end_point_defn_16, c9_45, open_defn_34, o6_34, between_c_defn_3, inner_point_defn_23, o4_29, underlying_curve_defn_41
% 36.58/7.81 % No. of inferences in proof: 175
% 36.58/7.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7285 ms resp. 6744 ms w/o parsing
% 36.58/7.85 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 36.58/7.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------