TSTP Solution File: GEO083-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO083-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 11:09:16 EDT 2023
% Result : Unsatisfiable 4.22s 2.17s
% Output : Refutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 77
% Syntax : Number of formulae : 130 ( 15 unt; 25 typ; 0 def)
% Number of atoms : 308 ( 38 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1150 ( 154 ~; 203 |; 0 &; 793 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 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 : 242 ( 0 ^; 242 !; 0 ?; 242 :)
% Comments :
%------------------------------------------------------------------------------
thf(part_of_type,type,
part_of: $i > $i > $o ).
thf(sk15_type,type,
sk15: $i ).
thf(sk16_type,type,
sk16: $i ).
thf(meet_type,type,
meet: $i > $i > $i > $o ).
thf(sk17_type,type,
sk17: $i ).
thf(sk14_type,type,
sk14: $i ).
thf(sum_type,type,
sum: $i > $i > $i ).
thf(end_point_type,type,
end_point: $i > $i > $o ).
thf(ax0_sk11_type,type,
ax0_sk11: $i > $i > $i ).
thf(incident_c_type,type,
incident_c: $i > $i > $o ).
thf(ax0_sk13_type,type,
ax0_sk13: $i > $i > $i ).
thf(inner_point_type,type,
inner_point: $i > $i > $o ).
thf(ax0_sk3_type,type,
ax0_sk3: $i > $i > $i ).
thf(ax0_sk8_type,type,
ax0_sk8: $i > $i ).
thf(open_type,type,
open: $i > $o ).
thf(closed_type,type,
closed: $i > $o ).
thf(ax0_sk4_type,type,
ax0_sk4: $i > $i > $i ).
thf(ax0_sk7_type,type,
ax0_sk7: $i > $i ).
thf(ax0_sk6_type,type,
ax0_sk6: $i > $i ).
thf(ax0_sk5_type,type,
ax0_sk5: $i > $i > $i > $i ).
thf(ax0_sk2_type,type,
ax0_sk2: $i > $i > $i > $i ).
thf(ax0_sk1_type,type,
ax0_sk1: $i > $i > $i ).
thf(ax0_sk9_type,type,
ax0_sk9: $i > $i > $i ).
thf(ax0_sk10_type,type,
ax0_sk10: $i > $i > $i ).
thf(ax0_sk12_type,type,
ax0_sk12: $i > $i > $i ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ B )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ B )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A )
| ( C
= ( sum @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_9) ).
thf(115,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(4,negated_conjecture,
~ ( part_of @ ( sum @ sk14 @ sk15 ) @ ( sum @ sk14 @ sk16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_6_1_70) ).
thf(56,plain,
~ ( part_of @ ( sum @ sk14 @ sk15 ) @ ( sum @ sk14 @ sk16 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(24,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(97,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)],[24]) ).
thf(38,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(129,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(12,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(73,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)],[12]) ).
thf(33,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(118,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)],[33]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( open @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_defn_34) ).
thf(76,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( open @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,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(80,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( incident_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(23,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(95,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)],[23]) ).
thf(11,axiom,
! [A: $i] : ( inner_point @ ( ax0_sk8 @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c3_37) ).
thf(72,plain,
! [A: $i] : ( inner_point @ ( ax0_sk8 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(36,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(125,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)],[36]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( incident_c @ A @ C )
| ( incident_c @ ( ax0_sk5 @ C @ B @ A ) @ C )
| ( meet @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn_29) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( incident_c @ A @ C )
| ( incident_c @ ( ax0_sk5 @ C @ B @ A ) @ C )
| ( meet @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(22,axiom,
! [A: $i] :
( ( end_point @ ( ax0_sk6 @ A ) @ A )
| ( closed @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_defn_32) ).
thf(93,plain,
! [A: $i] :
( ( end_point @ ( ax0_sk6 @ A ) @ A )
| ( closed @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ( A = B )
| ( open @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c1_35) ).
thf(152,plain,
! [B: $i,A: $i] :
( ~ ( part_of @ A @ B )
| ( A = B )
| ( open @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( end_point @ ( ax0_sk11 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c6_41) ).
thf(78,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( end_point @ ( ax0_sk11 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(28,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(106,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)],[28]) ).
thf(34,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(121,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)],[34]) ).
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/sandbox/benchmark/theBenchmark.p',c9_48) ).
thf(61,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(32,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(116,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)],[32]) ).
thf(20,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(89,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)],[20]) ).
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/sandbox/benchmark/theBenchmark.p',c7_43) ).
thf(133,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(18,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(85,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ~ ( end_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,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(102,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)],[26]) ).
thf(10,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(70,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)],[10]) ).
thf(41,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(137,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(1,negated_conjecture,
part_of @ sk15 @ sk16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_6_1_67) ).
thf(53,plain,
part_of @ sk15 @ sk16,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ B )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A )
| ( C
= ( sum @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_10) ).
thf(141,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)],[43]) ).
thf(52,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(166,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)],[52]) ).
thf(7,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(64,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)],[7]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ B )
| ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C )
| ( C
= ( sum @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_11) ).
thf(149,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)],[46]) ).
thf(2,negated_conjecture,
meet @ sk17 @ sk14 @ sk15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_6_1_68) ).
thf(54,plain,
meet @ sk17 @ sk14 @ sk15,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C )
| ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C )
| ( C
= ( sum @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_8) ).
thf(144,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(50,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(159,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)],[50]) ).
thf(21,axiom,
! [A: $i] :
( ~ ( open @ A )
| ( end_point @ ( ax0_sk7 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_defn_33) ).
thf(91,plain,
! [A: $i] :
( ~ ( open @ A )
| ( end_point @ ( ax0_sk7 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( part_of @ ( ax0_sk4 @ B @ A ) @ ( ax0_sk3 @ B @ A ) )
| ( end_point @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_20) ).
thf(155,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ A @ B )
| ~ ( part_of @ ( ax0_sk4 @ B @ A ) @ ( ax0_sk3 @ B @ A ) )
| ( end_point @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( B
= ( sum @ ( ax0_sk9 @ A @ B ) @ ( ax0_sk10 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c4_39) ).
thf(108,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)],[29]) ).
thf(35,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(123,plain,
! [B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk1 @ A @ B ) @ B )
| ( part_of @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(45,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(145,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)],[45]) ).
thf(8,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(67,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(37,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(127,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)],[37]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ B )
| ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A )
| ( C
= ( sum @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_7) ).
thf(99,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)],[25]) ).
thf(19,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(87,plain,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( incident_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(27,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(104,plain,
! [B: $i,A: $i] :
( ( incident_c @ ( ax0_sk1 @ A @ B ) @ A )
| ( part_of @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(3,negated_conjecture,
meet @ sk17 @ sk14 @ sk16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_6_1_69) ).
thf(55,plain,
meet @ sk17 @ sk14 @ sk16,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ~ ( inner_point @ A @ B )
| ( meet @ A @ ( ax0_sk9 @ A @ B ) @ ( ax0_sk10 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c4_38) ).
thf(139,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(5,axiom,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( A
!= ( ax0_sk11 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c6_42) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ ( end_point @ A @ B )
| ( A
!= ( ax0_sk11 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,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(82,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
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/sandbox/benchmark/theBenchmark.p',meet_defn_27) ).
thf(131,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(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ A )
| ~ ( incident_c @ ( ax0_sk2 @ A @ B @ C ) @ C )
| ( C
= ( sum @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn_12) ).
thf(163,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)],[51]) ).
thf(9,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(68,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)],[9]) ).
thf(30,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(111,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)],[30]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( closed @ A )
| ~ ( end_point @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_defn_31) ).
thf(83,plain,
! [B: $i,A: $i] :
( ~ ( closed @ A )
| ~ ( end_point @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(170,plain,
$false,
inference(cvc4,[status(thm)],[115,56,97,129,73,118,76,80,95,72,125,157,93,152,78,106,121,61,116,89,133,85,102,70,137,53,141,166,64,149,54,144,159,91,155,108,123,145,67,127,99,87,104,55,139,58,82,131,163,68,111,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO083-1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.13 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri May 19 04:37:52 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.90/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.05 % [INFO] Parsing done (158ms).
% 1.26/1.06 % [INFO] Running in sequential loop mode.
% 1.75/1.31 % [INFO] eprover registered as external prover.
% 1.75/1.31 % [INFO] cvc4 registered as external prover.
% 1.75/1.32 % [INFO] Scanning for conjecture ...
% 1.91/1.39 % [INFO] Found a conjecture and 48 axioms. Running axiom selection ...
% 2.10/1.44 % [INFO] Axiom selection finished. Selected 48 axioms (removed 0 axioms).
% 2.31/1.50 % [INFO] Problem is propositional (TPTP CNF).
% 2.31/1.50 % [INFO] Type checking passed.
% 2.31/1.51 % [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 ...
% 4.22/2.17 % External prover 'cvc4' found a proof!
% 4.22/2.17 % [INFO] Killing All external provers ...
% 4.22/2.17 % Time passed: 1627ms (effective reasoning time: 1104ms)
% 4.22/2.17 % 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)>
% 4.22/2.17 % 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
% 4.22/2.17 % No. of inferences in proof: 105
% 4.22/2.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1627 ms resp. 1104 ms w/o parsing
% 4.37/2.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.37/2.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------