%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PRO009+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n008.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 08:20:34 AM UTC 2026
% Result : Theorem 9.35s 4.51s
% Output : Refutation 9.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 46
% Syntax : Number of formulae : 94 ( 25 unt; 0 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 : 0 ( 0 >; 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_decl,type,
occurrence_of: $i > $i > $o ).
thf(tptp0_decl,type,
tptp0: $i ).
thf(tptp3_decl,type,
tptp3: $i ).
thf(root_occ_decl,type,
root_occ: $i > $i > $o ).
thf(tptp2_decl,type,
tptp2: $i ).
thf(tptp1_decl,type,
tptp1: $i ).
thf(min_precedes_decl,type,
min_precedes: $i > $i > $i > $o ).
thf(leaf_occ_decl,type,
leaf_occ: $i > $i > $o ).
thf(earlier_decl,type,
earlier: $i > $i > $o ).
thf(root_decl,type,
root: $i > $i > $o ).
thf(legal_decl,type,
legal: $i > $o ).
thf(precedes_decl,type,
precedes: $i > $i > $o ).
thf(activity_decl,type,
activity: $i > $o ).
thf(subactivity_decl,type,
subactivity: $i > $i > $o ).
thf(atocc_decl,type,
atocc: $i > $i > $o ).
thf(atomic_decl,type,
atomic: $i > $o ).
thf(tptp4_decl,type,
tptp4: $i ).
thf(arboreal_decl,type,
arboreal: $i > $o ).
thf(subactivity_occurrence_decl,type,
subactivity_occurrence: $i > $i > $o ).
thf(activity_occurrence_decl,type,
activity_occurrence: $i > $o ).
thf(next_subocc_decl,type,
next_subocc: $i > $i > $i > $o ).
thf(leaf_decl,type,
leaf: $i > $i > $o ).
thf(34,axiom,
tptp3 @ atomic,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_38) ).
thf(170,plain,
tptp3 @ atomic,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ earlier ) )
& ( B @ ( A @ earlier ) ) )
=> ( C @ ( A @ earlier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
thf(56,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ earlier ) )
& ( B @ ( A @ earlier ) ) )
=> ( C @ ( A @ earlier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ occurrence_of ) )
=> ( ( B @ activity_occurrence )
& ( A @ activity ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_29) ).
thf(179,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ occurrence_of ) )
=> ( ( B @ activity_occurrence )
& ( A @ activity ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( B @ min_precedes ) ) )
& ( D @ ( B @ ( A @ min_precedes ) ) ) )
=> ( D @ ( C @ ( A @ min_precedes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos) ).
thf(117,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( B @ min_precedes ) ) )
& ( D @ ( B @ ( A @ min_precedes ) ) ) )
=> ( D @ ( C @ ( A @ min_precedes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( A @ legal )
& ( B @ ( A @ atocc ) ) )
=> ( B @ ( A @ root ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_16) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( ( A @ legal )
& ( B @ ( A @ atocc ) ) )
=> ( B @ ( A @ root ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ subactivity_occurrence ) )
& ( B @ ( C @ subactivity_occurrence ) )
& ( D @ arboreal )
& ( C @ arboreal )
& ( A @ ( B @ occurrence_of ) ) )
=> ( ( C = D )
| ( A @ ( C @ ( D @ min_precedes ) ) )
| ( A @ ( D @ ( C @ min_precedes ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_28) ).
thf(156,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ subactivity_occurrence ) )
& ( B @ ( C @ subactivity_occurrence ) )
& ( D @ arboreal )
& ( C @ arboreal )
& ( A @ ( B @ occurrence_of ) ) )
=> ( ( C = D )
| ( A @ ( C @ ( D @ min_precedes ) ) )
| ( A @ ( D @ ( C @ min_precedes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ atomic )
& ( A @ ( B @ occurrence_of ) ) )
=> ? [C: $i] :
( ( B @ ( C @ subactivity_occurrence ) )
& ( A @ ( C @ root ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_30) ).
thf(129,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ atomic )
& ( A @ ( B @ occurrence_of ) ) )
=> ? [C: $i] :
( ( B @ ( C @ subactivity_occurrence ) )
& ( A @ ( C @ root ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(33,axiom,
tptp4 != tptp1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_41) ).
thf(167,plain,
tptp4 != tptp1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(28,axiom,
tptp2 @ atomic,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_36) ).
thf(145,plain,
tptp2 @ atomic,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1,conjecture,
! [A: $i] :
( ( tptp0 @ ( A @ occurrence_of ) )
=> ? [B: $i,C: $i] :
( ( A @ ( C @ leaf_occ ) )
& ( tptp0 @ ( C @ ( B @ min_precedes ) ) )
& ( ( tptp1 @ ( C @ occurrence_of ) )
| ( tptp2 @ ( C @ occurrence_of ) ) )
& ( A @ ( B @ root_occ ) )
& ( tptp3 @ ( B @ occurrence_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( tptp0 @ ( A @ occurrence_of ) )
=> ? [B: $i,C: $i] :
( ( A @ ( C @ leaf_occ ) )
& ( tptp0 @ ( C @ ( B @ min_precedes ) ) )
& ( ( tptp1 @ ( C @ occurrence_of ) )
| ( tptp2 @ ( C @ occurrence_of ) ) )
& ( A @ ( B @ root_occ ) )
& ( tptp3 @ ( B @ occurrence_of ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(48,plain,
~ ! [A: $i] :
( ( tptp0 @ ( A @ occurrence_of ) )
=> ? [B: $i,C: $i] :
( ( A @ ( C @ leaf_occ ) )
& ( tptp0 @ ( C @ ( B @ min_precedes ) ) )
& ( ( tptp1 @ ( C @ occurrence_of ) )
| ( tptp2 @ ( C @ occurrence_of ) ) )
& ( A @ ( B @ root_occ ) )
& ( tptp3 @ ( B @ occurrence_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
tptp4 @ atomic,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_35) ).
thf(72,plain,
tptp4 @ atomic,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ min_precedes ) ) )
=> ~ ( C @ ( B @ root ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
thf(138,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ min_precedes ) ) )
=> ~ ( C @ ( B @ root ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ atomic )
& ( B @ ( A @ leaf ) ) )
=> ? [C: $i] :
( ( C @ ( A @ leaf_occ ) )
& ( B @ ( C @ occurrence_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_23) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ atomic )
& ( B @ ( A @ leaf ) ) )
=> ? [C: $i] :
( ( C @ ( A @ leaf_occ ) )
& ( B @ ( C @ occurrence_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ precedes ) )
<=> ( ( B @ legal )
& ( B @ ( A @ earlier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
thf(61,plain,
! [A: $i,B: $i] :
( ( ( ( B @ legal )
& ( B @ ( A @ earlier ) ) )
=> ( B @ ( A @ precedes ) ) )
& ( ( B @ ( A @ precedes ) )
=> ( ( B @ legal )
& ( B @ ( A @ earlier ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ min_precedes ) ) )
=> ? [D: $i] :
( ( D @ ( C @ subactivity_occurrence ) )
& ( D @ ( B @ subactivity_occurrence ) )
& ( A @ ( D @ occurrence_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_24) ).
thf(133,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ min_precedes ) ) )
=> ? [D: $i] :
( ( D @ ( C @ subactivity_occurrence ) )
& ( D @ ( B @ subactivity_occurrence ) )
& ( A @ ( D @ occurrence_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ atomic )
& ( B @ ( A @ leaf ) ) )
=> ? [C: $i] :
( ( C @ ( A @ leaf_occ ) )
& ( B @ ( C @ occurrence_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_25) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ atomic )
& ( B @ ( A @ leaf ) ) )
=> ? [C: $i] :
( ( C @ ( A @ leaf_occ ) )
& ( B @ ( C @ occurrence_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ occurrence_of ) )
& ( B @ ( A @ occurrence_of ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_22) ).
thf(197,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ occurrence_of ) )
& ( B @ ( A @ occurrence_of ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ legal )
=> ( A @ arboreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_17) ).
thf(77,plain,
! [A: $i] :
( ( A @ legal )
=> ( A @ arboreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(40,axiom,
~ ( tptp0 @ atomic ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_34) ).
thf(193,plain,
~ ( tptp0 @ atomic ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ next_subocc ) ) )
<=> ( ~ ? [D: $i] :
( ( C @ ( B @ ( D @ min_precedes ) ) )
& ( C @ ( D @ ( A @ min_precedes ) ) ) )
& ( C @ ( B @ ( A @ min_precedes ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
thf(96,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ? [D: $i] :
( ( C @ ( B @ ( D @ min_precedes ) ) )
& ( C @ ( D @ ( A @ min_precedes ) ) ) )
& ( C @ ( B @ ( A @ min_precedes ) ) ) )
=> ( C @ ( B @ ( A @ next_subocc ) ) ) )
& ( ( C @ ( B @ ( A @ next_subocc ) ) )
=> ( ~ ? [D: $i] :
( ( C @ ( B @ ( D @ min_precedes ) ) )
& ( C @ ( D @ ( A @ min_precedes ) ) ) )
& ( C @ ( B @ ( A @ min_precedes ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ root ) )
=> ? [C: $i] :
( ( C @ ( B @ atocc ) )
& ( A @ ( C @ subactivity ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_27) ).
thf(73,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ root ) )
=> ? [C: $i] :
( ( C @ ( B @ atocc ) )
& ( A @ ( C @ subactivity ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ leaf_occ ) )
& ( C @ ( A @ occurrence_of ) ) )
=> ~ ? [D: $i] : ( C @ ( D @ ( B @ min_precedes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_21) ).
thf(105,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ leaf_occ ) )
& ( C @ ( A @ occurrence_of ) ) )
=> ~ ? [D: $i] : ( C @ ( D @ ( B @ min_precedes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ earlier ) )
=> ~ ( A @ ( B @ earlier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ earlier ) )
=> ~ ( A @ ( B @ earlier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,axiom,
tptp0 @ activity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_33) ).
thf(144,plain,
tptp0 @ activity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leaf_occ ) )
<=> ? [C: $i] :
( ( C @ ( A @ leaf ) )
& ( B @ ( A @ subactivity_occurrence ) )
& ( C @ ( B @ occurrence_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_11) ).
thf(159,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ ( A @ leaf ) )
& ( B @ ( A @ subactivity_occurrence ) )
& ( C @ ( B @ occurrence_of ) ) )
=> ( B @ ( A @ leaf_occ ) ) )
& ( ( B @ ( A @ leaf_occ ) )
=> ? [C: $i] :
( ( C @ ( A @ leaf ) )
& ( B @ ( A @ subactivity_occurrence ) )
& ( C @ ( B @ occurrence_of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ occurrence_of ) )
=> ( ( A @ arboreal )
<=> ( B @ atomic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_13) ).
thf(140,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ occurrence_of ) )
=> ( ( ( B @ atomic )
=> ( A @ arboreal ) )
& ( ( A @ arboreal )
=> ( B @ atomic ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(30,axiom,
tptp1 @ atomic,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_37) ).
thf(155,plain,
tptp1 @ atomic,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ activity_occurrence )
=> ? [B: $i] :
( ( B @ ( A @ occurrence_of ) )
& ( B @ activity ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_18) ).
thf(203,plain,
! [A: $i] :
( ( A @ activity_occurrence )
=> ? [B: $i] :
( ( B @ ( A @ occurrence_of ) )
& ( B @ activity ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ min_precedes ) ) )
=> ? [D: $i,E: $i] :
( ( E @ ( C @ atocc ) )
& ( D @ ( B @ atocc ) )
& ( A @ ( E @ subactivity ) )
& ( A @ ( D @ subactivity ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_26) ).
thf(218,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ min_precedes ) ) )
=> ? [D: $i,E: $i] :
( ( E @ ( C @ atocc ) )
& ( D @ ( B @ atocc ) )
& ( A @ ( E @ subactivity ) )
& ( A @ ( D @ subactivity ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ root_occ ) )
& ( C @ ( A @ root_occ ) )
& ( D @ ( C @ occurrence_of ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
thf(186,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ root_occ ) )
& ( C @ ( A @ root_occ ) )
& ( D @ ( C @ occurrence_of ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ root_occ ) )
<=> ? [C: $i] :
( ( C @ ( A @ root ) )
& ( B @ ( A @ subactivity_occurrence ) )
& ( C @ ( B @ occurrence_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).
thf(171,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ ( A @ root ) )
& ( B @ ( A @ subactivity_occurrence ) )
& ( C @ ( B @ occurrence_of ) ) )
=> ( B @ ( A @ root_occ ) ) )
& ( ( B @ ( A @ root_occ ) )
=> ? [C: $i] :
( ( C @ ( A @ root ) )
& ( B @ ( A @ subactivity_occurrence ) )
& ( C @ ( B @ occurrence_of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ min_precedes ) ) )
=> ( B @ ( A @ precedes ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
thf(207,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ min_precedes ) ) )
=> ( B @ ( A @ precedes ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(20,axiom,
tptp3 != tptp2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_42) ).
thf(119,plain,
tptp3 != tptp2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ root ) )
=> ( A @ legal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ root ) )
=> ( A @ legal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leaf ) )
<=> ( ~ ? [C: $i] : ( B @ ( C @ ( A @ min_precedes ) ) )
& ( ? [C: $i] : ( B @ ( A @ ( C @ min_precedes ) ) )
| ( B @ ( A @ root ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_14) ).
thf(146,plain,
! [A: $i,B: $i] :
( ( ( ~ ? [C: $i] : ( B @ ( C @ ( A @ min_precedes ) ) )
& ( ? [C: $i] : ( B @ ( A @ ( C @ min_precedes ) ) )
| ( B @ ( A @ root ) ) ) )
=> ( B @ ( A @ leaf ) ) )
& ( ( B @ ( A @ leaf ) )
=> ( ~ ? [C: $i] : ( B @ ( C @ ( A @ min_precedes ) ) )
& ( ? [C: $i] : ( B @ ( A @ ( C @ min_precedes ) ) )
| ( B @ ( A @ root ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(39,axiom,
tptp4 != tptp3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_39) ).
thf(190,plain,
tptp4 != tptp3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(37,axiom,
tptp4 != tptp2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_40) ).
thf(183,plain,
tptp4 != tptp2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ atocc ) )
<=> ? [C: $i] :
( ( C @ ( A @ occurrence_of ) )
& ( C @ atomic )
& ( C @ ( B @ subactivity ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_15) ).
thf(210,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ ( A @ occurrence_of ) )
& ( C @ atomic )
& ( C @ ( B @ subactivity ) ) )
=> ( B @ ( A @ atocc ) ) )
& ( ( B @ ( A @ atocc ) )
=> ? [C: $i] :
( ( C @ ( A @ occurrence_of ) )
& ( C @ atomic )
& ( C @ ( B @ subactivity ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(18,axiom,
! [A: $i] :
( ( tptp0 @ ( A @ occurrence_of ) )
=> ? [B: $i,C: $i,D: $i] :
( ( A @ ( D @ leaf_occ ) )
& ( tptp0 @ ( D @ ( C @ next_subocc ) ) )
& ( ( tptp1 @ ( D @ occurrence_of ) )
| ( tptp2 @ ( D @ occurrence_of ) ) )
& ( tptp0 @ ( C @ ( B @ next_subocc ) ) )
& ( tptp4 @ ( C @ occurrence_of ) )
& ( A @ ( B @ root_occ ) )
& ( tptp3 @ ( B @ occurrence_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_32) ).
thf(107,plain,
! [A: $i] :
( ( tptp0 @ ( A @ occurrence_of ) )
=> ? [B: $i,C: $i,D: $i] :
( ( A @ ( D @ leaf_occ ) )
& ( tptp0 @ ( D @ ( C @ next_subocc ) ) )
& ( ( tptp1 @ ( D @ occurrence_of ) )
| ( tptp2 @ ( D @ occurrence_of ) ) )
& ( tptp0 @ ( C @ ( B @ next_subocc ) ) )
& ( tptp4 @ ( C @ occurrence_of ) )
& ( A @ ( B @ root_occ ) )
& ( tptp3 @ ( B @ occurrence_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(22,axiom,
tptp2 != tptp1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_44) ).
thf(126,plain,
tptp2 != tptp1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subactivity_occurrence ) )
=> ( ( B @ activity_occurrence )
& ( A @ activity_occurrence ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_19) ).
thf(79,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subactivity_occurrence ) )
=> ( ( B @ activity_occurrence )
& ( A @ activity_occurrence ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ root_occ ) )
& ( C @ ( A @ occurrence_of ) ) )
=> ~ ? [D: $i] : ( C @ ( B @ ( D @ min_precedes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_20) ).
thf(195,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ root_occ ) )
& ( C @ ( A @ occurrence_of ) ) )
=> ~ ? [D: $i] : ( C @ ( B @ ( D @ min_precedes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(43,axiom,
tptp3 != tptp1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_43) ).
thf(200,plain,
tptp3 != tptp1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ activity )
=> ( A @ ( A @ subactivity ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_31) ).
thf(68,plain,
! [A: $i] :
( ( A @ activity )
=> ( A @ ( A @ subactivity ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ leaf_occ ) )
& ( C @ ( A @ leaf_occ ) )
& ~ ( D @ atomic )
& ( D @ ( C @ occurrence_of ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
thf(122,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ leaf_occ ) )
& ( C @ ( A @ leaf_occ ) )
& ~ ( D @ atomic )
& ( D @ ( C @ occurrence_of ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ next_subocc ) ) )
=> ( ( B @ arboreal )
& ( A @ arboreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
thf(83,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ next_subocc ) ) )
=> ( ( B @ arboreal )
& ( A @ arboreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(241,plain,
$false,
inference(e,[status(thm)],[170,56,179,117,70,156,129,167,145,48,72,138,88,61,133,92,197,77,193,96,73,105,54,144,159,140,155,203,218,186,171,207,119,58,146,190,183,210,107,126,79,195,200,68,122,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : PRO009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.24/0.49 % Computer : n008.cluster.edu
% 0.24/0.49 % Model : x86_64 x86_64
% 0.24/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.49 % Memory : 8046.5625MB
% 0.24/0.49 % OS : Linux 6.8.0-71-generic
% 0.24/0.49 % CPULimit : 300
% 0.24/0.49 % WCLimit : 300
% 0.24/0.49 % DateTime : Sat Sep 26 04:58:54 UTC 2026
% 0.24/0.49 % CPUTime :
% 0.24/0.49 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.43/1.37 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.27/1.70 % [INFO] Parsing done (325ms).
% 2.27/1.72 % [INFO] Running in sequential loop mode.
% 3.31/2.35 % [INFO] eprover registered as external prover.
% 3.31/2.37 % [INFO] Scanning for conjecture ...
% 3.74/2.54 % [INFO] Found a conjecture (or negated_conjecture) and 45 axioms. Running axiom selection ...
% 3.91/2.68 % [INFO] Axiom selection finished. Selected 45 axioms (removed 0 axioms).
% 4.12/2.78 % [INFO] Problem is first-order (TPTP FOF).
% 4.36/2.80 % [INFO] Type checking passed.
% 4.36/2.81 % [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 ...
% 9.35/4.50 % External prover 'e' found a proof!
% 9.35/4.50 % [INFO] Killing All external provers ...
% 9.35/4.51 % Time passed: 3805ms (effective reasoning time: 2772ms)
% 9.35/4.51 % 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)>
% 9.35/4.51 % 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
% 9.35/4.51 % No. of inferences in proof: 94
% 9.35/4.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3805 ms resp. 2772 ms w/o parsing
% 9.73/4.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.73/4.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------