%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV396+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.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 08:59:16 AM UTC 2026
% Result : Theorem 15.97s 5.74s
% Output : Refutation 15.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 49
% Syntax : Number of formulae : 172 ( 86 unt; 0 typ; 7 def)
% Number of atoms : 434 ( 121 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1886 ( 143 ~; 63 |; 68 &;1536 @)
% ( 7 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 34 usr; 12 con; 0-3 aty)
% Number of variables : 430 ( 0 ^; 418 !; 5 ?; 430 :)
% ( 0 !>; 0 ?*; 0 @-; 7 @+)
% Comments :
%------------------------------------------------------------------------------
thf(pair_in_list_decl,type,
pair_in_list: $i > $i > $i > $o ).
thf(strictly_less_than_decl,type,
strictly_less_than: $i > $i > $o ).
thf(ok_decl,type,
ok: $i > $o ).
thf(remove_cpq_decl,type,
remove_cpq: $i > $i > $i ).
thf(triple_decl,type,
triple: $i > $i > $i > $i ).
thf(remove_slb_decl,type,
remove_slb: $i > $i > $i ).
thf(insert_slb_decl,type,
insert_slb: $i > $i > $i ).
thf(pair_decl,type,
pair: $i > $i > $i ).
thf(contains_slb_decl,type,
contains_slb: $i > $i > $o ).
thf(create_slb_decl,type,
create_slb: $i ).
thf(less_than_decl,type,
less_than: $i > $i > $o ).
thf(succ_cpq_decl,type,
succ_cpq: $i > $i > $o ).
thf(insert_cpq_decl,type,
insert_cpq: $i > $i > $i ).
thf(isnonempty_slb_decl,type,
isnonempty_slb: $i > $o ).
thf(removemin_cpq_eff_decl,type,
removemin_cpq_eff: $i > $i ).
thf(findmin_cpq_eff_decl,type,
findmin_cpq_eff: $i > $i ).
thf(bottom_decl,type,
bottom: $i ).
thf(update_slb_decl,type,
update_slb: $i > $i > $i ).
thf(removemin_cpq_res_decl,type,
removemin_cpq_res: $i > $i ).
thf(findmin_cpq_res_decl,type,
findmin_cpq_res: $i > $i ).
thf(bad_decl,type,
bad: $i ).
thf(lookup_slb_decl,type,
lookup_slb: $i > $i > $i ).
thf(remove_pqp_decl,type,
remove_pqp: $i > $i > $i ).
thf(findmin_pqp_res_decl,type,
findmin_pqp_res: $i > $i ).
thf(check_cpq_decl,type,
check_cpq: $i > $o ).
thf(insert_pqp_decl,type,
insert_pqp: $i > $i > $i ).
thf(contains_cpq_decl,type,
contains_cpq: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( A @ ( B @ triple ) ) @ remove_cpq ) @ ok )
& ( E @ ( D @ strictly_less_than ) )
& ( E @ ( D @ ( A @ pair_in_list ) ) ) )
=> ( E @ ( D @ ( D @ ( A @ remove_slb ) @ pair_in_list ) ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ ( C @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ ( B @ triple ) ) @ remove_cpq ) @ ok )
& ( E @ ( D @ strictly_less_than ) )
& ( E @ ( D @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ pair_in_list ) ) ) )
=> ( E @ ( D @ ( D @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ remove_slb ) @ pair_in_list ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( F @ ( E @ pair ) @ ( sk1 @ insert_slb ) @ ( A @ triple ) ) @ remove_cpq ) @ ok )
& ( D @ ( C @ strictly_less_than ) )
& ( D @ ( C @ ( F @ ( E @ pair ) @ ( sk1 @ insert_slb ) @ pair_in_list ) ) ) )
=> ( D @ ( C @ ( C @ ( F @ ( E @ pair ) @ ( sk1 @ insert_slb ) @ remove_slb ) @ pair_in_list ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ ( D @ pair ) @ ( sk1 @ insert_slb ) @ ( sk2 @ triple ) ) @ remove_cpq ) @ ok )
& ( C @ ( B @ strictly_less_than ) )
& ( C @ ( B @ ( E @ ( D @ pair ) @ ( sk1 @ insert_slb ) @ pair_in_list ) ) ) )
=> ( C @ ( B @ ( B @ ( E @ ( D @ pair ) @ ( sk1 @ insert_slb ) @ remove_slb ) @ pair_in_list ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( sk3 @ ( D @ ( C @ pair ) @ ( sk1 @ insert_slb ) @ ( sk2 @ triple ) ) @ remove_cpq ) @ ok )
& ( B @ ( A @ strictly_less_than ) )
& ( B @ ( A @ ( D @ ( C @ pair ) @ ( sk1 @ insert_slb ) @ pair_in_list ) ) ) )
=> ( B @ ( A @ ( A @ ( D @ ( C @ pair ) @ ( sk1 @ insert_slb ) @ remove_slb ) @ pair_in_list ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk4 @ ( sk3 @ ( C @ ( B @ pair ) @ ( sk1 @ insert_slb ) @ ( sk2 @ triple ) ) @ remove_cpq ) @ ok )
& ( A @ ( sk4 @ strictly_less_than ) )
& ( A @ ( sk4 @ ( C @ ( B @ pair ) @ ( sk1 @ insert_slb ) @ pair_in_list ) ) ) )
=> ( A @ ( sk4 @ ( sk4 @ ( C @ ( B @ pair ) @ ( sk1 @ insert_slb ) @ remove_slb ) @ pair_in_list ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk4 @ ( sk3 @ ( B @ ( A @ pair ) @ ( sk1 @ insert_slb ) @ ( sk2 @ triple ) ) @ remove_cpq ) @ ok )
& ( sk5 @ ( sk4 @ strictly_less_than ) )
& ( sk5 @ ( sk4 @ ( B @ ( A @ pair ) @ ( sk1 @ insert_slb ) @ pair_in_list ) ) ) )
=> ( sk5 @ ( sk4 @ ( sk4 @ ( B @ ( A @ pair ) @ ( sk1 @ insert_slb ) @ remove_slb ) @ pair_in_list ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( ( sk4 @ ( sk3 @ ( A @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ ( sk2 @ triple ) ) @ remove_cpq ) @ ok )
& ( sk5 @ ( sk4 @ strictly_less_than ) )
& ( sk5 @ ( sk4 @ ( A @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ pair_in_list ) ) ) )
=> ( sk5 @ ( sk4 @ ( sk4 @ ( A @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ remove_slb ) @ pair_in_list ) ) ) ) ) ) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_res )
= bottom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).
thf(142,plain,
! [A: $i,B: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_res )
= bottom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_res )
= bottom ),
inference(cnf,[status(esa)],[142]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_res )
= bottom ),
inference(lifteq,[status(thm)],[143]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ removemin_cpq_res )
= ( A @ findmin_cpq_res ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
thf(76,plain,
! [A: $i] :
( ( A @ removemin_cpq_res )
= ( A @ findmin_cpq_res ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(77,plain,
! [A: $i] :
( ( A @ removemin_cpq_res )
= ( A @ findmin_cpq_res ) ),
inference(cnf,[status(esa)],[76]) ).
thf(78,plain,
! [A: $i] :
( ( A @ findmin_cpq_res )
= ( A @ removemin_cpq_res ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ removemin_cpq_res )
= bottom ),
inference(rewrite,[status(thm)],[144,78]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( A @ findmin_pqp_res @ ( B @ contains_slb ) )
& ( B != create_slb ) )
=> ( ( C @ ( B @ ( A @ triple ) ) @ findmin_cpq_eff )
= ( bad @ ( A @ findmin_pqp_res @ ( B @ update_slb ) @ ( A @ triple ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).
thf(121,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( A @ findmin_pqp_res @ ( B @ contains_slb ) )
& ( B != create_slb ) )
=> ( ( C @ ( B @ ( A @ triple ) ) @ findmin_cpq_eff )
= ( bad @ ( A @ findmin_pqp_res @ ( B @ update_slb ) @ ( A @ triple ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(3,axiom,
! [A: $i] :
~ ( A @ ( create_slb @ contains_slb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
thf(51,plain,
! [A: $i] :
~ ( A @ ( create_slb @ contains_slb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(52,plain,
~ ? [A: $i] : ( A @ ( create_slb @ contains_slb ) ),
inference(miniscope,[status(thm)],[51]) ).
thf(53,plain,
! [A: $i] :
~ ( A @ ( create_slb @ contains_slb ) ),
inference(cnf,[status(esa)],[52]) ).
thf(1,conjecture,
! [A: $i] :
( ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( A @ ( B @ triple ) ) @ remove_cpq ) @ ok )
& ( E @ ( D @ strictly_less_than ) )
& ( E @ ( D @ ( A @ pair_in_list ) ) ) )
=> ( E @ ( D @ ( D @ ( A @ remove_slb ) @ pair_in_list ) ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ ( C @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ ( B @ triple ) ) @ remove_cpq ) @ ok )
& ( E @ ( D @ strictly_less_than ) )
& ( E @ ( D @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ pair_in_list ) ) ) )
=> ( E @ ( D @ ( D @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ remove_slb ) @ pair_in_list ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_co) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( A @ ( B @ triple ) ) @ remove_cpq ) @ ok )
& ( E @ ( D @ strictly_less_than ) )
& ( E @ ( D @ ( A @ pair_in_list ) ) ) )
=> ( E @ ( D @ ( D @ ( A @ remove_slb ) @ pair_in_list ) ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ ( C @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ ( B @ triple ) ) @ remove_cpq ) @ ok )
& ( E @ ( D @ strictly_less_than ) )
& ( E @ ( D @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ pair_in_list ) ) ) )
=> ( E @ ( D @ ( D @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ remove_slb ) @ pair_in_list ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(44,plain,
~ ! [A: $i] :
( ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( A @ ( B @ triple ) ) @ remove_cpq ) @ ok )
& ( E @ ( D @ strictly_less_than ) )
& ( E @ ( D @ ( A @ pair_in_list ) ) ) )
=> ( E @ ( D @ ( D @ ( A @ remove_slb ) @ pair_in_list ) ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ ( C @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ ( B @ triple ) ) @ remove_cpq ) @ ok )
& ( E @ ( D @ strictly_less_than ) )
& ( E @ ( D @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ pair_in_list ) ) ) )
=> ( E @ ( D @ ( D @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ remove_slb ) @ pair_in_list ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sk5 @ ( sk4 @ ( sk4 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ remove_slb ) @ pair_in_list ) ) )
& ( sk4 @ ( sk3 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ ( sk2 @ triple ) ) @ remove_cpq ) @ ok )
& ( sk5 @ ( sk4 @ strictly_less_than ) )
& ( sk5 @ ( sk4 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ pair_in_list ) ) )
& ( ( D @ ( C @ ( C @ ( sk1 @ remove_slb ) @ pair_in_list ) ) )
| ~ ( C @ ( B @ ( sk1 @ ( A @ triple ) ) @ remove_cpq ) @ ok )
| ~ ( D @ ( C @ strictly_less_than ) )
| ~ ( D @ ( C @ ( sk1 @ pair_in_list ) ) ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(49,plain,
sk4 @ ( sk3 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ ( sk2 @ triple ) ) @ remove_cpq ) @ ok,
inference(cnfConj,[status(thm)],[45]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( bad @ ( B @ ( A @ triple ) ) @ ok )
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).
thf(111,plain,
! [A: $i,B: $i] :
~ ( bad @ ( B @ ( A @ triple ) ) @ ok ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(112,plain,
~ ? [A: $i,B: $i] : ( bad @ ( B @ ( A @ triple ) ) @ ok ),
inference(miniscope,[status(thm)],[111]) ).
thf(113,plain,
! [B: $i,A: $i] :
~ ( bad @ ( B @ ( A @ triple ) ) @ ok ),
inference(cnf,[status(esa)],[112]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ ( sk2 @ triple ) ) @ remove_cpq ) @ ok )
!= ( bad @ ( B @ ( A @ triple ) ) @ ok ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,113]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( sk4 @ ( sk3 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ ( sk2 @ triple ) ) @ remove_cpq ) @ ok )
!= ( bad @ ( B @ ( A @ triple ) ) @ ok ) ),
inference(simp,[status(thm)],[223]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( sk4 @ ( sk3 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ ( sk2 @ triple ) ) @ remove_cpq ) )
!= ( bad @ ( B @ ( A @ triple ) ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
thf(73,plain,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
thf(79,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb ),
inference(cnf,[status(esa)],[79]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
=> ( C = bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
thf(145,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
=> ( C = bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(11,axiom,
! [A: $i] : ( A @ ( bottom @ less_than ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom_smallest) ).
thf(69,plain,
! [A: $i] : ( A @ ( bottom @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(28,axiom,
! [A: $i,B: $i] : ( B @ ( create_slb @ ( A @ triple ) ) @ check_cpq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
thf(137,plain,
! [A: $i,B: $i] : ( B @ ( create_slb @ ( A @ triple ) ) @ check_cpq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(138,plain,
! [B: $i,A: $i] : ( B @ ( create_slb @ ( A @ triple ) ) @ check_cpq ),
inference(cnf,[status(esa)],[137]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ strictly_less_than ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ update_slb ) )
= ( C @ ( B @ pair ) @ ( C @ ( A @ update_slb ) @ insert_slb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).
thf(101,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ strictly_less_than ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ update_slb ) )
= ( C @ ( B @ pair ) @ ( C @ ( A @ update_slb ) @ insert_slb ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( C @ ( B @ insert_cpq ) @ ( A @ succ_cpq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).
thf(56,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( C @ ( B @ insert_cpq ) @ ( A @ succ_cpq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ findmin_pqp_res @ ( B @ lookup_slb ) @ ( A @ findmin_pqp_res @ strictly_less_than ) )
& ( A @ findmin_pqp_res @ ( B @ contains_slb ) )
& ( B != create_slb ) )
=> ( ( C @ ( B @ ( A @ triple ) ) @ findmin_cpq_eff )
= ( bad @ ( A @ findmin_pqp_res @ ( B @ update_slb ) @ ( A @ triple ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).
thf(174,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ findmin_pqp_res @ ( B @ lookup_slb ) @ ( A @ findmin_pqp_res @ strictly_less_than ) )
& ( A @ findmin_pqp_res @ ( B @ contains_slb ) )
& ( B != create_slb ) )
=> ( ( C @ ( B @ ( A @ triple ) ) @ findmin_cpq_eff )
= ( bad @ ( A @ findmin_pqp_res @ ( B @ update_slb ) @ ( A @ triple ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(46,plain,
sk5 @ ( sk4 @ strictly_less_than ),
inference(cnfConj,[status(thm)],[45]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ strictly_less_than ) )
<=> ( ~ ( A @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(154,plain,
! [A: $i,B: $i] :
( ( ( ~ ( A @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) )
=> ( B @ ( A @ strictly_less_than ) ) )
& ( ( B @ ( A @ strictly_less_than ) )
=> ( ~ ( A @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(155,plain,
( ! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) )
=> ( B @ ( A @ strictly_less_than ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ strictly_less_than ) )
=> ( ~ ( A @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) ) ) ),
inference(miniscope,[status(thm)],[154]) ).
thf(156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ strictly_less_than ) )
| ( C @ ( D @ less_than ) )
| ~ ( D @ ( C @ less_than ) ) )
& ( ~ ( A @ ( B @ less_than ) )
| ~ ( B @ ( A @ strictly_less_than ) ) )
& ( ( B @ ( A @ less_than ) )
| ~ ( B @ ( A @ strictly_less_than ) ) ) ),
inference(cnf,[status(esa)],[155]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_than ) )
| ~ ( B @ ( A @ strictly_less_than ) ) ),
inference(cnfConj,[status(thm)],[156]) ).
thf(299,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk4 @ strictly_less_than ) )
!= ( B @ ( A @ strictly_less_than ) ) )
| ~ ( A @ ( B @ less_than ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,158]) ).
thf(300,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk4 @ strictly_less_than ) )
!= ( B @ ( A @ strictly_less_than ) ) )
| ~ ( A @ ( B @ less_than ) ) ),
inference(simp,[status(thm)],[299]) ).
thf(301,plain,
~ ( sk4 @ ( sk5 @ less_than ) ),
inference(pattern_uni,[status(thm)],[300:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ less_than ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ update_slb ) )
= ( D @ ( B @ pair ) @ ( C @ ( A @ update_slb ) @ insert_slb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).
thf(184,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ less_than ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ update_slb ) )
= ( D @ ( B @ pair ) @ ( C @ ( A @ update_slb ) @ insert_slb ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff )
= ( bad @ ( create_slb @ ( A @ triple ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
thf(108,plain,
! [A: $i,B: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff )
= ( bad @ ( create_slb @ ( A @ triple ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff )
= ( bad @ ( create_slb @ ( A @ triple ) ) ) ),
inference(cnf,[status(esa)],[108]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff )
= ( bad @ ( create_slb @ ( A @ triple ) ) ) ),
inference(lifteq,[status(thm)],[109]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ pair_in_list ) ) )
<=> ( ( ( D = E )
& ( B = C ) )
| ( E @ ( C @ ( A @ pair_in_list ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
thf(125,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( D = E )
& ( B = C ) )
| ( E @ ( C @ ( A @ pair_in_list ) ) ) )
=> ( E @ ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ pair_in_list ) ) ) )
& ( ( E @ ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ pair_in_list ) ) )
=> ( ( ( D = E )
& ( B = C ) )
| ( E @ ( C @ ( A @ pair_in_list ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ strictly_less_than ) )
=> ( ( C @ ( E @ ( D @ pair ) @ ( B @ insert_slb ) @ ( A @ triple ) ) @ check_cpq )
<=> $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
thf(152,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ strictly_less_than ) )
=> ~ ( C @ ( E @ ( D @ pair ) @ ( B @ insert_slb ) @ ( A @ triple ) ) @ check_cpq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(9,axiom,
! [A: $i] : ( A @ ( A @ less_than ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(65,plain,
! [A: $i] : ( A @ ( A @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(66,plain,
! [A: $i] : ( A @ ( A @ less_than ) ),
inference(cnf,[status(esa)],[65]) ).
thf(307,plain,
! [A: $i] :
( ( ( A @ ( A @ less_than ) )
!= ( sk4 @ ( sk5 @ less_than ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[66,301]) ).
thf(308,plain,
! [A: $i] :
( ( A @ ( A @ less_than ) )
!= ( sk4 @ ( sk5 @ less_than ) ) ),
inference(simp,[status(thm)],[307]) ).
thf(313,plain,
! [A: $i] :
( ( A != sk4 )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[308]) ).
thf(316,plain,
sk5 != sk4,
inference(simp,[status(thm)],[313]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ removemin_cpq_eff )
= ( A @ findmin_cpq_res @ ( A @ findmin_cpq_eff @ remove_cpq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
thf(139,plain,
! [A: $i] :
( ( A @ removemin_cpq_eff )
= ( A @ findmin_cpq_res @ ( A @ findmin_cpq_eff @ remove_cpq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(140,plain,
! [A: $i] :
( ( A @ removemin_cpq_eff )
= ( A @ findmin_cpq_res @ ( A @ findmin_cpq_eff @ remove_cpq ) ) ),
inference(cnf,[status(esa)],[139]) ).
thf(141,plain,
! [A: $i] :
( ( A @ findmin_cpq_res @ ( A @ findmin_cpq_eff @ remove_cpq ) )
= ( A @ removemin_cpq_eff ) ),
inference(lifteq,[status(thm)],[140]) ).
thf(280,plain,
! [A: $i] :
( ( A @ removemin_cpq_res @ ( A @ findmin_cpq_eff @ remove_cpq ) )
= ( A @ removemin_cpq_eff ) ),
inference(rewrite,[status(thm)],[141,78]) ).
thf(7,axiom,
! [A: $i] : ( A @ ( A @ succ_cpq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
thf(61,plain,
! [A: $i] : ( A @ ( A @ succ_cpq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
thf(114,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(115,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
inference(miniscope,[status(thm)],[114]) ).
thf(116,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
inference(cnf,[status(esa)],[115]) ).
thf(6,axiom,
~ ( create_slb @ isnonempty_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
thf(59,plain,
~ ( create_slb @ isnonempty_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(60,plain,
~ ( create_slb @ isnonempty_slb ),
inference(polarity_switch,[status(thm)],[59]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ less_than ) )
=> ( ( C @ ( E @ ( D @ pair ) @ ( B @ insert_slb ) @ ( A @ triple ) ) @ check_cpq )
<=> ( C @ ( B @ ( A @ triple ) ) @ check_cpq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
thf(117,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ less_than ) )
=> ( ( ( C @ ( B @ ( A @ triple ) ) @ check_cpq )
=> ( C @ ( E @ ( D @ pair ) @ ( B @ insert_slb ) @ ( A @ triple ) ) @ check_cpq ) )
& ( ( C @ ( E @ ( D @ pair ) @ ( B @ insert_slb ) @ ( A @ triple ) ) @ check_cpq )
=> ( C @ ( B @ ( A @ triple ) ) @ check_cpq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(70,plain,
! [A: $i] : ( A @ ( bottom @ less_than ) ),
inference(cnf,[status(esa)],[69]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ triple ) ) @ insert_cpq ) )
= ( C @ ( bottom @ ( D @ pair ) @ ( B @ insert_slb ) @ ( D @ ( A @ insert_pqp ) @ triple ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
thf(165,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ triple ) ) @ insert_cpq ) )
= ( C @ ( bottom @ ( D @ pair ) @ ( B @ insert_slb ) @ ( D @ ( A @ insert_pqp ) @ triple ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B != create_slb )
=> ( ( C @ ( B @ ( A @ triple ) ) @ findmin_cpq_res )
= ( A @ findmin_pqp_res ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
thf(97,plain,
! [A: $i,B: $i,C: $i] :
( ( B != create_slb )
=> ( ( C @ ( B @ ( A @ triple ) ) @ findmin_cpq_res )
= ( A @ findmin_pqp_res ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(296,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ less_than ) )
!= ( B @ ( C @ less_than ) ) )
| ~ $true
| ~ ( C @ ( B @ strictly_less_than ) ) ),
inference(paramod_ordered,[status(thm)],[66,158]) ).
thf(297,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ less_than ) )
!= ( B @ ( C @ less_than ) ) )
| ~ ( C @ ( B @ strictly_less_than ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(298,plain,
! [A: $i] :
~ ( A @ ( A @ strictly_less_than ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ contains_slb ) )
& ( B != C ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ lookup_slb ) )
= ( C @ ( A @ lookup_slb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).
thf(148,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ contains_slb ) )
& ( B != C ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ lookup_slb ) )
= ( C @ ( A @ lookup_slb ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ findmin_pqp_res @ ( A @ findmin_pqp_res @ ( B @ lookup_slb ) @ less_than ) )
& ( A @ findmin_pqp_res @ ( B @ contains_slb ) )
& ( B != create_slb ) )
=> ( ( C @ ( B @ ( A @ triple ) ) @ findmin_cpq_eff )
= ( C @ ( A @ findmin_pqp_res @ ( B @ update_slb ) @ ( A @ triple ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
thf(161,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ findmin_pqp_res @ ( A @ findmin_pqp_res @ ( B @ lookup_slb ) @ less_than ) )
& ( A @ findmin_pqp_res @ ( B @ contains_slb ) )
& ( B != create_slb ) )
=> ( ( C @ ( B @ ( A @ triple ) ) @ findmin_cpq_eff )
= ( C @ ( A @ findmin_pqp_res @ ( B @ update_slb ) @ ( A @ triple ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(277,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb )
!= ( create_slb @ isnonempty_slb ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,60]) ).
thf(278,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb )
!= ( create_slb @ isnonempty_slb ) ),
inference(simp,[status(thm)],[277]) ).
thf(279,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ pair ) @ ( A @ insert_slb ) )
!= create_slb ),
inference(simp,[status(thm)],[278]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) )
=> ( C @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(54,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) )
=> ( C @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( C @ ( B @ remove_cpq ) @ ( A @ succ_cpq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).
thf(187,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( C @ ( B @ remove_cpq ) @ ( A @ succ_cpq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) )
<=> ( ( B = C )
| ( C @ ( A @ contains_slb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
thf(81,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B = C )
| ( C @ ( A @ contains_slb ) ) )
=> ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) ) )
& ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) )
=> ( ( B = C )
| ( C @ ( A @ contains_slb ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( bad @ ( create_slb @ ( A @ triple ) ) )
!= ( D @ ( create_slb @ ( C @ triple ) ) ) )
| ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff @ check_cpq ) ),
inference(paramod_ordered,[status(thm)],[110,138]) ).
thf(318,plain,
! [B: $i,A: $i] : ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff @ check_cpq ),
inference(pattern_uni,[status(thm)],[317:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ less_than ) )
| ~ ( C @ ( B @ less_than ) )
| ~ ( B @ ( A @ less_than ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(309,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ less_than ) )
!= ( sk4 @ ( sk5 @ less_than ) ) )
| ~ $true
| ~ ( C @ ( B @ less_than ) )
| ~ ( B @ ( A @ less_than ) ) ),
inference(paramod_ordered,[status(thm)],[55,301]) ).
thf(310,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ less_than ) )
!= ( sk4 @ ( sk5 @ less_than ) ) )
| ~ ( C @ ( B @ less_than ) )
| ~ ( B @ ( A @ less_than ) ) ),
inference(simp,[status(thm)],[309]) ).
thf(311,plain,
! [A: $i] :
( ~ ( sk4 @ ( A @ less_than ) )
| ~ ( A @ ( sk5 @ less_than ) ) ),
inference(pattern_uni,[status(thm)],[310:[bind(A,$thf( sk5 )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(314,plain,
! [A: $i] :
( ~ ( sk4 @ ( A @ less_than ) )
| ~ ( A @ ( sk5 @ less_than ) ) ),
inference(simp,[status(thm)],[311]) ).
thf(365,plain,
! [B: $i,A: $i] :
( ( ( A @ ( bottom @ less_than ) )
!= ( sk4 @ ( B @ less_than ) ) )
| ~ $true
| ~ ( B @ ( sk5 @ less_than ) ) ),
inference(paramod_ordered,[status(thm)],[70,314]) ).
thf(366,plain,
! [B: $i,A: $i] :
( ( ( A @ ( bottom @ less_than ) )
!= ( sk4 @ ( B @ less_than ) ) )
| ~ ( B @ ( sk5 @ less_than ) ) ),
inference(simp,[status(thm)],[365]) ).
thf(367,plain,
~ ( bottom @ ( sk5 @ less_than ) ),
inference(pattern_uni,[status(thm)],[366:[bind(A,$thf( sk4 )),bind(B,$thf( bottom ))]]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( B @ contains_slb ) )
=> ( ( D @ ( C @ ( B @ ( A @ triple ) ) @ remove_cpq ) )
= ( bad @ ( B @ ( A @ triple ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).
thf(91,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( B @ contains_slb ) )
=> ( ( D @ ( C @ ( B @ ( A @ triple ) ) @ remove_cpq ) )
= ( bad @ ( B @ ( A @ triple ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( C @ ( sk1 @ remove_slb ) @ pair_in_list ) ) )
| ~ ( C @ ( B @ ( sk1 @ ( A @ triple ) ) @ remove_cpq ) @ ok )
| ~ ( D @ ( C @ strictly_less_than ) )
| ~ ( D @ ( C @ ( sk1 @ pair_in_list ) ) ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( B @ removemin_cpq_eff @ ( A @ succ_cpq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).
thf(63,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( B @ removemin_cpq_eff @ ( A @ succ_cpq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(293,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( bottom @ less_than ) )
!= ( B @ ( C @ less_than ) ) )
| ~ $true
| ~ ( C @ ( B @ strictly_less_than ) ) ),
inference(paramod_ordered,[status(thm)],[70,158]) ).
thf(294,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( bottom @ less_than ) )
!= ( B @ ( C @ less_than ) ) )
| ~ ( C @ ( B @ strictly_less_than ) ) ),
inference(simp,[status(thm)],[293]) ).
thf(295,plain,
! [A: $i] :
~ ( bottom @ ( A @ strictly_less_than ) ),
inference(pattern_uni,[status(thm)],[294:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( bottom ))]]) ).
thf(50,plain,
~ ( sk5 @ ( sk4 @ ( sk4 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ remove_slb ) @ pair_in_list ) ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( B @ findmin_cpq_eff @ ( A @ succ_cpq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( B @ findmin_cpq_eff @ ( A @ succ_cpq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(47,plain,
sk5 @ ( sk4 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ pair_in_list ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk4 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ pair_in_list ) ) )
!= ( B @ ( A @ ( create_slb @ pair_in_list ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,116]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ( sk5 @ ( sk4 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ pair_in_list ) ) )
!= ( B @ ( A @ ( create_slb @ pair_in_list ) ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( sk5 != B )
| ( sk4 != A )
| ( ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) )
!= create_slb ) ),
inference(simp,[status(thm)],[194]) ).
thf(199,plain,
( ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) )
!= create_slb ),
inference(simp,[status(thm)],[197]) ).
thf(201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( sk4 @ strictly_less_than ) )
!= ( D @ ( C @ strictly_less_than ) ) )
| ( D @ ( C @ ( C @ ( sk1 @ remove_slb ) @ pair_in_list ) ) )
| ~ ( C @ ( B @ ( sk1 @ ( A @ triple ) ) @ remove_cpq ) @ ok )
| ~ $true
| ~ ( D @ ( C @ ( sk1 @ pair_in_list ) ) ) ),
inference(paramod_ordered,[status(thm)],[46,48]) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( sk4 @ strictly_less_than ) )
!= ( D @ ( C @ strictly_less_than ) ) )
| ( D @ ( C @ ( C @ ( sk1 @ remove_slb ) @ pair_in_list ) ) )
| ~ ( C @ ( B @ ( sk1 @ ( A @ triple ) ) @ remove_cpq ) @ ok )
| ~ ( D @ ( C @ ( sk1 @ pair_in_list ) ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( sk5 @ ( sk4 @ ( sk4 @ ( sk1 @ remove_slb ) @ pair_in_list ) ) )
| ~ ( sk4 @ ( B @ ( sk1 @ ( A @ triple ) ) @ remove_cpq ) @ ok )
| ~ ( sk5 @ ( sk4 @ ( sk1 @ pair_in_list ) ) ) ),
inference(pattern_uni,[status(thm)],[202:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( sk5 ))]]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ contains_slb ) )
& ( B != C ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ remove_slb ) )
= ( D @ ( B @ pair ) @ ( C @ ( A @ remove_slb ) @ insert_slb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).
thf(104,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ contains_slb ) )
& ( B != C ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ remove_slb ) )
= ( D @ ( B @ pair ) @ ( C @ ( A @ remove_slb ) @ insert_slb ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ remove_slb ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
thf(171,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ remove_slb ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(74,plain,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
inference(cnf,[status(esa)],[73]) ).
thf(75,plain,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
inference(lifteq,[status(thm)],[74]) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ! [C: $i] : ( C @ ( B @ insert_cpq ) @ ( A @ succ_cpq ) ) ),
inference(miniscope,[status(thm)],[56]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ insert_cpq ) @ ( A @ succ_cpq ) )
| ~ ( B @ ( A @ succ_cpq ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(305,plain,
! [A: $i] :
( ( ( A @ ( bottom @ less_than ) )
!= ( sk4 @ ( sk5 @ less_than ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,301]) ).
thf(306,plain,
! [A: $i] :
( ( A @ ( bottom @ less_than ) )
!= ( sk4 @ ( sk5 @ less_than ) ) ),
inference(simp,[status(thm)],[305]) ).
thf(312,plain,
! [A: $i] :
( ( A != sk4 )
| ( sk5 != bottom ) ),
inference(simp,[status(thm)],[306]) ).
thf(315,plain,
sk5 != bottom,
inference(simp,[status(thm)],[312]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ lookup_slb ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
thf(168,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ lookup_slb ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ lookup_slb ) @ ( D @ strictly_less_than ) )
& ( D @ ( B @ contains_slb ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ triple ) ) @ remove_cpq ) )
= ( bad @ ( D @ ( B @ remove_slb ) @ ( D @ ( A @ remove_pqp ) @ triple ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
thf(190,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ lookup_slb ) @ ( D @ strictly_less_than ) )
& ( D @ ( B @ contains_slb ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ triple ) ) @ remove_cpq ) )
= ( bad @ ( D @ ( B @ remove_slb ) @ ( D @ ( A @ remove_pqp ) @ triple ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( D @ ( B @ lookup_slb ) @ less_than ) )
& ( D @ ( B @ contains_slb ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ triple ) ) @ remove_cpq ) )
= ( C @ ( D @ ( B @ remove_slb ) @ ( D @ ( A @ remove_pqp ) @ triple ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax44) ).
thf(94,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( D @ ( B @ lookup_slb ) @ less_than ) )
& ( D @ ( B @ contains_slb ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ triple ) ) @ remove_cpq ) )
= ( C @ ( D @ ( B @ remove_slb ) @ ( D @ ( A @ remove_pqp ) @ triple ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(195,plain,
( ( ( sk5 @ ( sk4 @ ( sk4 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ remove_slb ) @ pair_in_list ) ) )
!= ( sk5 @ ( sk4 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ pair_in_list ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,50]) ).
thf(196,plain,
( ( sk5 @ ( sk4 @ ( sk4 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ remove_slb ) @ pair_in_list ) ) )
!= ( sk5 @ ( sk4 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ pair_in_list ) ) ) ),
inference(simp,[status(thm)],[195]) ).
thf(198,plain,
( ( sk5 != sk5 )
| ( sk4 != sk4 )
| ( ( sk4 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ remove_slb ) )
!= ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(200,plain,
( ( sk4 @ ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) @ remove_slb ) )
!= ( sk7 @ ( sk6 @ pair ) @ ( sk1 @ insert_slb ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(62,plain,
! [A: $i] : ( A @ ( A @ succ_cpq ) ),
inference(cnf,[status(esa)],[61]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ triple ) ) @ contains_cpq ) )
<=> ( D @ ( B @ contains_slb ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
thf(178,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ contains_slb ) )
=> ( D @ ( C @ ( B @ ( A @ triple ) ) @ contains_cpq ) ) )
& ( ( D @ ( C @ ( B @ ( A @ triple ) ) @ contains_cpq ) )
=> ( D @ ( B @ contains_slb ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(540,plain,
$false,
inference(e,[status(thm)],[276,121,53,225,73,80,145,111,69,138,101,56,142,174,301,184,110,125,46,152,316,78,280,61,116,60,117,70,137,165,65,97,298,148,161,279,44,59,71,54,49,187,113,81,76,318,367,91,66,108,48,63,295,50,67,199,154,314,203,104,158,171,139,55,114,75,58,315,168,51,190,79,94,47,200,62,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV396+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.22/0.47 % Computer : n014.cluster.edu
% 0.22/0.47 % Model : x86_64 x86_64
% 0.22/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.47 % Memory : 8046.5625MB
% 0.22/0.47 % OS : Linux 6.8.0-71-generic
% 0.22/0.47 % CPULimit : 300
% 0.22/0.47 % WCLimit : 300
% 0.22/0.47 % DateTime : Sat Sep 26 13:40:46 UTC 2026
% 0.22/0.47 % CPUTime :
% 0.22/0.47 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.44/1.30 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.06/1.66 % [INFO] Parsing done (353ms).
% 2.06/1.68 % [INFO] Running in sequential loop mode.
% 3.22/2.27 % [INFO] eprover registered as external prover.
% 3.22/2.28 % [INFO] Scanning for conjecture ...
% 3.64/2.47 % [INFO] Found a conjecture (or negated_conjecture) and 41 axioms. Running axiom selection ...
% 4.03/2.61 % [INFO] Axiom selection finished. Selected 41 axioms (removed 0 axioms).
% 4.28/2.72 % [INFO] Problem is first-order (TPTP FOF).
% 4.28/2.74 % [INFO] Type checking passed.
% 4.28/2.75 % [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 ...
% 15.97/5.73 % External prover 'e' found a proof!
% 15.97/5.73 % [INFO] Killing All external provers ...
% 15.97/5.73 % Time passed: 5051ms (effective reasoning time: 4042ms)
% 15.97/5.73 % 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)>
% 15.97/5.74 % Axioms used in derivation (41): ax28, ax39, ax27, ax32, ax22, ax43, ax19, ax49, ax25, ax53, ax20, ax52, ax24, ax47, ax41, stricly_smaller_definition, ax31, ax45, ax40, ax35, ax51, ax48, ax21, ax38, ax44, reflexivity, ax33, ax26, bottom_smallest, ax50, ax37, totality, ax46, ax34, ax23, transitivity, ax30, ax42, ax18, ax36, ax29
% 15.97/5.74 % No. of inferences in proof: 165
% 15.97/5.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5051 ms resp. 4042 ms w/o parsing
% 15.38/5.92 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.38/5.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------