TSTP Solution File: PRO009+2 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : PRO009+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 : Tue May 7 08:03:20 EDT 2024
% Result : Theorem 4.67s 2.15s
% Output : Refutation 4.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 68
% Syntax : Number of formulae : 116 ( 25 unt; 22 typ; 0 def)
% Number of atoms : 307 ( 20 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 810 ( 38 ~; 12 |; 123 &; 559 @)
% ( 7 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 6 con; 0-3 aty)
% Number of variables : 213 ( 0 ^ 163 !; 50 ?; 213 :)
% Comments :
%------------------------------------------------------------------------------
thf(occurrence_of_type,type,
occurrence_of: $i > $i > $o ).
thf(tptp0_type,type,
tptp0: $i ).
thf(tptp3_type,type,
tptp3: $i ).
thf(root_occ_type,type,
root_occ: $i > $i > $o ).
thf(tptp2_type,type,
tptp2: $i ).
thf(tptp1_type,type,
tptp1: $i ).
thf(min_precedes_type,type,
min_precedes: $i > $i > $i > $o ).
thf(leaf_occ_type,type,
leaf_occ: $i > $i > $o ).
thf(earlier_type,type,
earlier: $i > $i > $o ).
thf(root_type,type,
root: $i > $i > $o ).
thf(legal_type,type,
legal: $i > $o ).
thf(precedes_type,type,
precedes: $i > $i > $o ).
thf(activity_type,type,
activity: $i > $o ).
thf(subactivity_type,type,
subactivity: $i > $i > $o ).
thf(atocc_type,type,
atocc: $i > $i > $o ).
thf(atomic_type,type,
atomic: $i > $o ).
thf(tptp4_type,type,
tptp4: $i ).
thf(arboreal_type,type,
arboreal: $i > $o ).
thf(subactivity_occurrence_type,type,
subactivity_occurrence: $i > $i > $o ).
thf(activity_occurrence_type,type,
activity_occurrence: $i > $o ).
thf(next_subocc_type,type,
next_subocc: $i > $i > $i > $o ).
thf(leaf_type,type,
leaf: $i > $i > $o ).
thf(39,axiom,
tptp4 != tptp3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_39) ).
thf(174,plain,
tptp4 != tptp3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( root @ A @ B )
=> ( legal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( root @ A @ B )
=> ( legal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
atomic @ tptp4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_35) ).
thf(70,plain,
atomic @ tptp4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( occurrence_of @ A @ C )
& ( leaf_occ @ B @ A ) )
=> ~ ? [D: $i] : ( min_precedes @ B @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_21) ).
thf(97,plain,
! [A: $i,B: $i,C: $i] :
( ( ( occurrence_of @ A @ C )
& ( leaf_occ @ B @ A ) )
=> ~ ? [D: $i] : ( min_precedes @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( atocc @ A @ B )
<=> ? [C: $i] :
( ( subactivity @ B @ C )
& ( atomic @ C )
& ( occurrence_of @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_15) ).
thf(193,plain,
! [A: $i,B: $i] :
( ( ( atocc @ A @ B )
=> ? [C: $i] :
( ( subactivity @ B @ C )
& ( atomic @ C )
& ( occurrence_of @ A @ C ) ) )
& ( ? [C: $i] :
( ( subactivity @ B @ C )
& ( atomic @ C )
& ( occurrence_of @ A @ C ) )
=> ( atocc @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( occurrence_of @ A @ B )
=> ( ( arboreal @ A )
<=> ( atomic @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_13) ).
thf(129,plain,
! [A: $i,B: $i] :
( ( occurrence_of @ A @ B )
=> ( ( ( arboreal @ A )
=> ( atomic @ B ) )
& ( ( atomic @ B )
=> ( arboreal @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( leaf @ A @ B )
<=> ( ( ( root @ A @ B )
| ? [C: $i] : ( min_precedes @ C @ A @ B ) )
& ~ ? [C: $i] : ( min_precedes @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_14) ).
thf(134,plain,
! [A: $i,B: $i] :
( ( ( leaf @ A @ B )
=> ( ( ( root @ A @ B )
| ? [C: $i] : ( min_precedes @ C @ A @ B ) )
& ~ ? [C: $i] : ( min_precedes @ A @ C @ B ) ) )
& ( ( ( ( root @ A @ B )
| ? [C: $i] : ( min_precedes @ C @ A @ B ) )
& ~ ? [C: $i] : ( min_precedes @ A @ C @ B ) )
=> ( leaf @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(37,axiom,
tptp4 != tptp2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_40) ).
thf(167,plain,
tptp4 != tptp2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( min_precedes @ B @ C @ A )
=> ? [D: $i] :
( ( occurrence_of @ D @ A )
& ( subactivity_occurrence @ B @ D )
& ( subactivity_occurrence @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_24) ).
thf(123,plain,
! [A: $i,B: $i,C: $i] :
( ( min_precedes @ B @ C @ A )
=> ? [D: $i] :
( ( occurrence_of @ D @ A )
& ( subactivity_occurrence @ B @ D )
& ( subactivity_occurrence @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1,conjecture,
! [A: $i] :
( ( occurrence_of @ A @ tptp0 )
=> ? [B: $i,C: $i] :
( ( occurrence_of @ B @ tptp3 )
& ( root_occ @ B @ A )
& ( ( occurrence_of @ C @ tptp2 )
| ( occurrence_of @ C @ tptp1 ) )
& ( min_precedes @ B @ C @ tptp0 )
& ( leaf_occ @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( occurrence_of @ A @ tptp0 )
=> ? [B: $i,C: $i] :
( ( occurrence_of @ B @ tptp3 )
& ( root_occ @ B @ A )
& ( ( occurrence_of @ C @ tptp2 )
| ( occurrence_of @ C @ tptp1 ) )
& ( min_precedes @ B @ C @ tptp0 )
& ( leaf_occ @ C @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(48,plain,
~ ! [A: $i] :
( ( occurrence_of @ A @ tptp0 )
=> ? [B: $i,C: $i] :
( ( occurrence_of @ B @ tptp3 )
& ( root_occ @ B @ A )
& ( ( occurrence_of @ C @ tptp2 )
| ( occurrence_of @ C @ tptp1 ) )
& ( min_precedes @ B @ C @ tptp0 )
& ( leaf_occ @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( occurrence_of @ B @ A )
& ( arboreal @ C )
& ( arboreal @ D )
& ( subactivity_occurrence @ C @ B )
& ( subactivity_occurrence @ D @ B ) )
=> ( ( min_precedes @ C @ D @ A )
| ( min_precedes @ D @ C @ A )
| ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_28) ).
thf(143,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( occurrence_of @ B @ A )
& ( arboreal @ C )
& ( arboreal @ D )
& ( subactivity_occurrence @ C @ B )
& ( subactivity_occurrence @ D @ B ) )
=> ( ( min_precedes @ C @ D @ A )
| ( min_precedes @ D @ C @ A )
| ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(18,axiom,
! [A: $i] :
( ( occurrence_of @ A @ tptp0 )
=> ? [B: $i,C: $i,D: $i] :
( ( occurrence_of @ B @ tptp3 )
& ( root_occ @ B @ A )
& ( occurrence_of @ C @ tptp4 )
& ( next_subocc @ B @ C @ tptp0 )
& ( ( occurrence_of @ D @ tptp2 )
| ( occurrence_of @ D @ tptp1 ) )
& ( next_subocc @ C @ D @ tptp0 )
& ( leaf_occ @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_32) ).
thf(99,plain,
! [A: $i] :
( ( occurrence_of @ A @ tptp0 )
=> ? [B: $i,C: $i,D: $i] :
( ( occurrence_of @ B @ tptp3 )
& ( root_occ @ B @ A )
& ( occurrence_of @ C @ tptp4 )
& ( next_subocc @ B @ C @ tptp0 )
& ( ( occurrence_of @ D @ tptp2 )
| ( occurrence_of @ D @ tptp1 ) )
& ( next_subocc @ C @ D @ tptp0 )
& ( leaf_occ @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( earlier @ A @ B )
& ( earlier @ B @ C ) )
=> ( earlier @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
thf(55,plain,
! [A: $i,B: $i,C: $i] :
( ( ( earlier @ A @ B )
& ( earlier @ B @ C ) )
=> ( earlier @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( next_subocc @ A @ B @ C )
=> ( ( arboreal @ A )
& ( arboreal @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
thf(79,plain,
! [A: $i,B: $i,C: $i] :
( ( next_subocc @ A @ B @ C )
=> ( ( arboreal @ A )
& ( arboreal @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( leaf @ A @ B )
& ~ ( atomic @ B ) )
=> ? [C: $i] :
( ( occurrence_of @ C @ B )
& ( leaf_occ @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_23) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( ( leaf @ A @ B )
& ~ ( atomic @ B ) )
=> ? [C: $i] :
( ( occurrence_of @ C @ B )
& ( leaf_occ @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( occurrence_of @ C @ D )
& ( root_occ @ A @ C )
& ( root_occ @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
thf(170,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( occurrence_of @ C @ D )
& ( root_occ @ A @ C )
& ( root_occ @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( occurrence_of @ B @ A )
& ~ ( atomic @ A ) )
=> ? [C: $i] :
( ( root @ C @ A )
& ( subactivity_occurrence @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_30) ).
thf(120,plain,
! [A: $i,B: $i] :
( ( ( occurrence_of @ B @ A )
& ~ ( atomic @ A ) )
=> ? [C: $i] :
( ( root @ C @ A )
& ( subactivity_occurrence @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(30,axiom,
atomic @ tptp1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_37) ).
thf(142,plain,
atomic @ tptp1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(33,axiom,
tptp4 != tptp1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_41) ).
thf(153,plain,
tptp4 != tptp1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(43,axiom,
tptp3 != tptp1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_43) ).
thf(184,plain,
tptp3 != tptp1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(20,axiom,
tptp3 != tptp2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_42) ).
thf(110,plain,
tptp3 != tptp2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( root_occ @ A @ B )
<=> ? [C: $i] :
( ( occurrence_of @ B @ C )
& ( subactivity_occurrence @ A @ B )
& ( root @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).
thf(157,plain,
! [A: $i,B: $i] :
( ( ( root_occ @ A @ B )
=> ? [C: $i] :
( ( occurrence_of @ B @ C )
& ( subactivity_occurrence @ A @ B )
& ( root @ A @ C ) ) )
& ( ? [C: $i] :
( ( occurrence_of @ B @ C )
& ( subactivity_occurrence @ A @ B )
& ( root @ A @ C ) )
=> ( root_occ @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( occurrence_of @ B @ A )
=> ( ( activity @ A )
& ( activity_occurrence @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_29) ).
thf(164,plain,
! [A: $i,B: $i] :
( ( occurrence_of @ B @ A )
=> ( ( activity @ A )
& ( activity_occurrence @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( occurrence_of @ A @ C )
& ( root_occ @ B @ A ) )
=> ~ ? [D: $i] : ( min_precedes @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_20) ).
thf(179,plain,
! [A: $i,B: $i,C: $i] :
( ( ( occurrence_of @ A @ C )
& ( root_occ @ B @ A ) )
=> ~ ? [D: $i] : ( min_precedes @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(27,axiom,
activity @ tptp0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_33) ).
thf(132,plain,
activity @ tptp0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(11,axiom,
! [A: $i] :
( ( legal @ A )
=> ( arboreal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_17) ).
thf(74,plain,
! [A: $i] :
( ( legal @ A )
=> ( arboreal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( next_subocc @ A @ B @ C )
<=> ( ( min_precedes @ A @ B @ C )
& ~ ? [D: $i] :
( ( min_precedes @ A @ D @ C )
& ( min_precedes @ D @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
thf(89,plain,
! [A: $i,B: $i,C: $i] :
( ( ( next_subocc @ A @ B @ C )
=> ( ( min_precedes @ A @ B @ C )
& ~ ? [D: $i] :
( ( min_precedes @ A @ D @ C )
& ( min_precedes @ D @ B @ C ) ) ) )
& ( ( ( min_precedes @ A @ B @ C )
& ~ ? [D: $i] :
( ( min_precedes @ A @ D @ C )
& ( min_precedes @ D @ B @ C ) ) )
=> ( next_subocc @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(28,axiom,
atomic @ tptp2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_36) ).
thf(133,plain,
atomic @ tptp2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( precedes @ A @ B )
<=> ( ( earlier @ A @ B )
& ( legal @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( ( precedes @ A @ B )
=> ( ( earlier @ A @ B )
& ( legal @ B ) ) )
& ( ( ( earlier @ A @ B )
& ( legal @ B ) )
=> ( precedes @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,axiom,
tptp2 != tptp1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_44) ).
thf(117,plain,
tptp2 != tptp1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(34,axiom,
atomic @ tptp3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_38) ).
thf(156,plain,
atomic @ tptp3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( earlier @ A @ B )
=> ~ ( earlier @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( earlier @ A @ B )
=> ~ ( earlier @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( root @ B @ A )
=> ? [C: $i] :
( ( subactivity @ C @ A )
& ( atocc @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_27) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( root @ B @ A )
=> ? [C: $i] :
( ( subactivity @ C @ A )
& ( atocc @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( occurrence_of @ A @ B )
& ( occurrence_of @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_22) ).
thf(181,plain,
! [A: $i,B: $i,C: $i] :
( ( ( occurrence_of @ A @ B )
& ( occurrence_of @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( leaf @ A @ B )
& ~ ( atomic @ B ) )
=> ? [C: $i] :
( ( occurrence_of @ C @ B )
& ( leaf_occ @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_25) ).
thf(86,plain,
! [A: $i,B: $i] :
( ( ( leaf @ A @ B )
& ~ ( atomic @ B ) )
=> ? [C: $i] :
( ( occurrence_of @ C @ B )
& ( leaf_occ @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(44,axiom,
! [A: $i] :
( ( activity_occurrence @ A )
=> ? [B: $i] :
( ( activity @ B )
& ( occurrence_of @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_18) ).
thf(187,plain,
! [A: $i] :
( ( activity_occurrence @ A )
=> ? [B: $i] :
( ( activity @ B )
& ( occurrence_of @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( occurrence_of @ C @ D )
& ~ ( atomic @ D )
& ( leaf_occ @ A @ C )
& ( leaf_occ @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
thf(113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( occurrence_of @ C @ D )
& ~ ( atomic @ D )
& ( leaf_occ @ A @ C )
& ( leaf_occ @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( subactivity_occurrence @ A @ B )
=> ( ( activity_occurrence @ A )
& ( activity_occurrence @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_19) ).
thf(76,plain,
! [A: $i,B: $i] :
( ( subactivity_occurrence @ A @ B )
=> ( ( activity_occurrence @ A )
& ( activity_occurrence @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
! [A: $i] :
( ( activity @ A )
=> ( subactivity @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_31) ).
thf(66,plain,
! [A: $i] :
( ( activity @ A )
=> ( subactivity @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( min_precedes @ A @ B @ D )
& ( min_precedes @ B @ C @ D ) )
=> ( min_precedes @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos) ).
thf(108,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( min_precedes @ A @ B @ D )
& ( min_precedes @ B @ C @ D ) )
=> ( min_precedes @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(40,axiom,
~ ( atomic @ tptp0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_34) ).
thf(177,plain,
~ ( atomic @ tptp0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( min_precedes @ A @ B @ C )
=> ~ ( root @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
thf(127,plain,
! [A: $i,B: $i,C: $i] :
( ( min_precedes @ A @ B @ C )
=> ~ ( root @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( leaf_occ @ A @ B )
<=> ? [C: $i] :
( ( occurrence_of @ B @ C )
& ( subactivity_occurrence @ A @ B )
& ( leaf @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_11) ).
thf(146,plain,
! [A: $i,B: $i] :
( ( ( leaf_occ @ A @ B )
=> ? [C: $i] :
( ( occurrence_of @ B @ C )
& ( subactivity_occurrence @ A @ B )
& ( leaf @ A @ C ) ) )
& ( ? [C: $i] :
( ( occurrence_of @ B @ C )
& ( subactivity_occurrence @ A @ B )
& ( leaf @ A @ C ) )
=> ( leaf_occ @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( min_precedes @ A @ B @ C )
=> ( precedes @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
thf(190,plain,
! [A: $i,B: $i,C: $i] :
( ( min_precedes @ A @ B @ C )
=> ( precedes @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( min_precedes @ B @ C @ A )
=> ? [D: $i,E: $i] :
( ( subactivity @ D @ A )
& ( subactivity @ E @ A )
& ( atocc @ B @ D )
& ( atocc @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_26) ).
thf(200,plain,
! [A: $i,B: $i,C: $i] :
( ( min_precedes @ B @ C @ A )
=> ? [D: $i,E: $i] :
( ( subactivity @ D @ A )
& ( subactivity @ E @ A )
& ( atocc @ B @ D )
& ( atocc @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( atocc @ A @ B )
& ( legal @ A ) )
=> ( root @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_16) ).
thf(68,plain,
! [A: $i,B: $i] :
( ( ( atocc @ A @ B )
& ( legal @ A ) )
=> ( root @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(206,plain,
$false,
inference(e,[status(thm)],[174,57,70,97,193,129,134,167,123,48,143,99,55,79,83,170,120,142,153,184,110,157,164,179,132,74,89,133,60,117,156,53,71,181,86,187,113,76,66,108,177,127,146,190,200,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : PRO009+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n007.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 15:57:24 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.86/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.99 % [INFO] Parsing done (139ms).
% 1.20/1.00 % [INFO] Running in sequential loop mode.
% 1.87/1.22 % [INFO] eprover registered as external prover.
% 1.87/1.22 % [INFO] cvc4 registered as external prover.
% 1.87/1.22 % [INFO] Scanning for conjecture ...
% 1.97/1.29 % [INFO] Found a conjecture and 45 axioms. Running axiom selection ...
% 2.29/1.35 % [INFO] Axiom selection finished. Selected 45 axioms (removed 0 axioms).
% 2.51/1.40 % [INFO] Problem is first-order (TPTP FOF).
% 2.51/1.41 % [INFO] Type checking passed.
% 2.51/1.42 % [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 ...
% 4.67/2.14 % External prover 'e' found a proof!
% 4.67/2.15 % [INFO] Killing All external provers ...
% 4.67/2.15 % Time passed: 1607ms (effective reasoning time: 1139ms)
% 4.67/2.15 % 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)>
% 4.67/2.15 % Axioms used in derivation (45): sos_42, sos_16, sos_05, sos_40, sos_02, sos_38, sos_28, sos_44, sos_13, sos_36, sos_32, sos_01, sos_30, sos_34, sos_20, sos_37, sos_27, sos_41, sos_17, sos_23, sos_12, sos_06, sos_11, sos_25, sos_22, sos_09, sos_35, sos_03, sos_33, sos_24, sos_07, sos_39, sos_29, sos_18, sos, sos_31, sos_26, sos_15, sos_04, sos_10, sos_43, sos_21, sos_19, sos_08, sos_14
% 4.67/2.15 % No. of inferences in proof: 94
% 4.67/2.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1607 ms resp. 1139 ms w/o parsing
% 4.96/2.22 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.96/2.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------