%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV415+2 : 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 : n013.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 08:59:19 AM UTC 2026
% Result : Theorem 29.91s 13.47s
% Output : Refutation 27.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 68
% Syntax : Number of formulae : 214 ( 99 unt; 0 typ; 4 def)
% Number of atoms : 505 ( 155 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1971 ( 129 ~; 68 |; 72 &;1599 @)
% ( 16 <=>; 87 =>; 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 : 52 ( 49 usr; 10 con; 0-3 aty)
% Number of variables : 552 ( 0 ^; 533 !; 15 ?; 552 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(i_decl,type,
i: $i > $i ).
thf(insert_cpq_decl,type,
insert_cpq: $i > $i > $i ).
thf(triple_decl,type,
triple: $i > $i > $i > $i ).
thf(insert_pq_decl,type,
insert_pq: $i > $i > $i ).
thf(contains_pq_decl,type,
contains_pq: $i > $i > $o ).
thf(issmallestelement_pq_decl,type,
issmallestelement_pq: $i > $i > $o ).
thf(removemin_pq_res_decl,type,
removemin_pq_res: $i > $i > $i ).
thf(succ_cpq_decl,type,
succ_cpq: $i > $i > $o ).
thf(removemin_cpq_eff_decl,type,
removemin_cpq_eff: $i > $i ).
thf(strictly_less_than_decl,type,
strictly_less_than: $i > $i > $o ).
thf(less_than_decl,type,
less_than: $i > $i > $o ).
thf(isnonempty_slb_decl,type,
isnonempty_slb: $i > $o ).
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(removemin_pq_eff_decl,type,
removemin_pq_eff: $i > $i > $i ).
thf(remove_pq_decl,type,
remove_pq: $i > $i > $i ).
thf(remove_slb_decl,type,
remove_slb: $i > $i > $i ).
thf(bottom_decl,type,
bottom: $i ).
thf(isnonempty_pq_decl,type,
isnonempty_pq: $i > $o ).
thf(create_pq_decl,type,
create_pq: $i ).
thf(update_slb_decl,type,
update_slb: $i > $i > $i ).
thf(findmin_pq_res_decl,type,
findmin_pq_res: $i > $i > $i ).
thf(findmin_pq_eff_decl,type,
findmin_pq_eff: $i > $i > $i ).
thf(remove_cpq_decl,type,
remove_cpq: $i > $i > $i ).
thf(findmin_cpq_eff_decl,type,
findmin_cpq_eff: $i > $i ).
thf(findmin_cpq_res_decl,type,
findmin_cpq_res: $i > $i ).
thf(pi_sharp_find_min_decl,type,
pi_sharp_find_min: $i > $i > $o ).
thf(phi_decl,type,
phi: $i > $o ).
thf(ok_decl,type,
ok: $i > $o ).
thf(check_cpq_decl,type,
check_cpq: $i > $o ).
thf(pi_sharp_removemin_decl,type,
pi_sharp_removemin: $i > $i > $o ).
thf(lookup_slb_decl,type,
lookup_slb: $i > $i > $i ).
thf(pi_sharp_remove_decl,type,
pi_sharp_remove: $i > $i > $o ).
thf(pair_in_list_decl,type,
pair_in_list: $i > $i > $i > $o ).
thf(removemin_cpq_res_decl,type,
removemin_cpq_res: $i > $i ).
thf(pi_find_min_decl,type,
pi_find_min: $i > $o ).
thf(pi_removemin_decl,type,
pi_removemin: $i > $o ).
thf(bad_decl,type,
bad: $i ).
thf(remove_pqp_decl,type,
remove_pqp: $i > $i > $i ).
thf(findmin_pqp_res_decl,type,
findmin_pqp_res: $i > $i ).
thf(pi_remove_decl,type,
pi_remove: $i > $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(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ triple ) ) @ insert_cpq ) @ i )
= ( D @ ( C @ ( B @ ( A @ triple ) ) @ i @ insert_pq ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( sk1 @ triple ) ) @ insert_cpq ) @ i )
= ( C @ ( B @ ( A @ ( sk1 @ triple ) ) @ i @ insert_pq ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ ( sk2 @ ( sk1 @ triple ) ) @ insert_cpq ) @ i )
= ( B @ ( A @ ( sk2 @ ( sk1 @ triple ) ) @ i @ insert_pq ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
( ( A @ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ insert_cpq ) @ i )
!= ( A @ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ i @ insert_pq ) ) ) ) ) ).
thf(49,axiom,
! [A: $i,B: $i] : ( B @ ( create_slb @ ( A @ triple ) ) @ check_cpq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
thf(259,plain,
! [A: $i,B: $i] : ( B @ ( create_slb @ ( A @ triple ) ) @ check_cpq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(260,plain,
! [B: $i,A: $i] : ( B @ ( create_slb @ ( A @ triple ) ) @ check_cpq ),
inference(cnf,[status(esa)],[259]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ pi_remove ) )
<=> ( B @ ( A @ i @ pi_sharp_remove ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
thf(273,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ i @ pi_sharp_remove ) )
=> ( B @ ( A @ pi_remove ) ) )
& ( ( B @ ( A @ pi_remove ) )
=> ( B @ ( A @ i @ pi_sharp_remove ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ issmallestelement_pq ) )
& ( B @ ( A @ contains_pq ) ) )
=> ( ( B @ ( A @ removemin_pq_res ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ issmallestelement_pq ) )
& ( B @ ( A @ contains_pq ) ) )
=> ( ( B @ ( A @ removemin_pq_res ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ i )
= create_pq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
thf(308,plain,
! [A: $i,B: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ i )
= create_pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ i )
= create_pq ),
inference(cnf,[status(esa)],[308]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ i )
= create_pq ),
inference(lifteq,[status(thm)],[309]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ triple ) ) @ insert_cpq ) @ i )
= ( D @ ( C @ ( B @ ( A @ triple ) ) @ i @ insert_pq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ triple ) ) @ insert_cpq ) @ i )
= ( D @ ( C @ ( B @ ( A @ triple ) ) @ i @ insert_pq ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(66,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ triple ) ) @ insert_cpq ) @ i )
= ( D @ ( C @ ( B @ ( A @ triple ) ) @ i @ insert_pq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(67,plain,
( ( sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ insert_cpq ) @ i )
!= ( sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ i @ insert_pq ) ) ),
inference(cnf,[status(esa)],[66]) ).
thf(68,plain,
( ( sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ i @ insert_pq ) )
!= ( sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ insert_cpq ) @ i ) ),
inference(lifteq,[status(thm)],[67]) ).
thf(340,plain,
! [B: $i,A: $i] :
( ( ( B @ ( create_slb @ ( A @ triple ) ) @ i )
!= ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ i ) )
| ( ( sk4 @ ( create_pq @ insert_pq ) )
!= ( sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ insert_cpq ) @ i ) ) ),
inference(paramod_ordered,[status(thm)],[310,68]) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( ( B @ ( create_slb @ ( A @ triple ) ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) ) )
| ( ( sk4 @ ( create_pq @ insert_pq ) )
!= ( sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ insert_cpq ) @ i ) ) ),
inference(simp,[status(thm)],[340]) ).
thf(342,plain,
! [B: $i,A: $i] :
( ( B != sk3 )
| ( sk2 != create_slb )
| ( A != sk1 )
| ( ( sk4 @ ( create_pq @ insert_pq ) )
!= ( sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ insert_cpq ) @ i ) ) ),
inference(simp,[status(thm)],[341]) ).
thf(347,plain,
( ( sk2 != create_slb )
| ( ( sk4 @ ( create_pq @ insert_pq ) )
!= ( sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ insert_cpq ) @ i ) ) ),
inference(simp,[status(thm)],[342]) ).
thf(45,axiom,
( ( ! [A: $i] :
( ! [B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( A @ ( B @ triple ) ) @ i )
= ( E @ ( A @ ( C @ triple ) ) @ i ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ ( B @ triple ) ) @ i )
= ( E @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ ( C @ triple ) ) @ i ) ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( create_slb @ ( A @ triple ) ) @ i )
= ( D @ ( create_slb @ ( B @ triple ) ) @ i ) ) )
=> ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( A @ triple ) ) @ i )
= ( E @ ( C @ ( B @ triple ) ) @ i ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big2_induction) ).
thf(234,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( A @ ( B @ triple ) ) @ i )
= ( E @ ( A @ ( C @ triple ) ) @ i ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ ( B @ triple ) ) @ i )
= ( E @ ( G @ ( F @ pair ) @ ( A @ insert_slb ) @ ( C @ triple ) ) @ i ) ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( create_slb @ ( A @ triple ) ) @ i )
= ( D @ ( create_slb @ ( B @ triple ) ) @ i ) ) )
=> ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( A @ triple ) ) @ i )
= ( E @ ( C @ ( B @ triple ) ) @ i ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(30,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(170,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)],[30]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
thf(120,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ removemin_cpq_res )
= ( A @ findmin_cpq_res ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
thf(200,plain,
! [A: $i] :
( ( A @ removemin_cpq_res )
= ( A @ findmin_cpq_res ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(201,plain,
! [A: $i] :
( ( A @ removemin_cpq_res )
= ( A @ findmin_cpq_res ) ),
inference(cnf,[status(esa)],[200]) ).
thf(202,plain,
! [A: $i] :
( ( A @ removemin_cpq_res )
= ( A @ findmin_cpq_res ) ),
inference(lifteq,[status(thm)],[201]) ).
thf(25,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(142,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)],[25]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ phi )
<=> ? [B: $i] :
( ( B @ check_cpq )
& ( B @ ok )
& ( B @ ( A @ succ_cpq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
thf(153,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ check_cpq )
& ( B @ ok )
& ( B @ ( A @ succ_cpq ) ) )
=> ( A @ phi ) )
& ( ( A @ phi )
=> ? [B: $i] :
( ( B @ check_cpq )
& ( B @ ok )
& ( B @ ( A @ succ_cpq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(15,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(110,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)],[15]) ).
thf(20,axiom,
! [A: $i] : ( A @ ( A @ succ_cpq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
thf(124,plain,
! [A: $i] : ( A @ ( A @ succ_cpq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(125,plain,
! [A: $i] : ( A @ ( A @ succ_cpq ) ),
inference(cnf,[status(esa)],[124]) ).
thf(8,axiom,
! [A: $i] : ( A @ ( A @ less_than ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(93,plain,
! [A: $i] : ( A @ ( A @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(58,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(289,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)],[58]) ).
thf(5,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(74,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)],[5]) ).
thf(75,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)],[74]) ).
thf(76,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)],[75]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_than ) )
| ~ ( B @ ( A @ strictly_less_than ) ) ),
inference(cnfConj,[status(thm)],[76]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_res )
= bottom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).
thf(261,plain,
! [A: $i,B: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_res )
= bottom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ pi_removemin )
<=> ? [B: $i] : ( B @ ( A @ i @ pi_sharp_find_min ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).
thf(216,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ i @ pi_sharp_find_min ) )
=> ( A @ pi_removemin ) )
& ( ( A @ pi_removemin )
=> ? [B: $i] : ( B @ ( A @ i @ pi_sharp_find_min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(32,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
thf(179,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(13,axiom,
! [A: $i] : ( A @ ( bottom @ less_than ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom_smallest) ).
thf(106,plain,
! [A: $i] : ( A @ ( bottom @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(107,plain,
! [A: $i] : ( A @ ( bottom @ less_than ) ),
inference(cnf,[status(esa)],[106]) ).
thf(319,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)],[107,78]) ).
thf(320,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( bottom @ less_than ) )
!= ( B @ ( C @ less_than ) ) )
| ~ ( C @ ( B @ strictly_less_than ) ) ),
inference(simp,[status(thm)],[319]) ).
thf(321,plain,
! [A: $i] :
~ ( bottom @ ( A @ strictly_less_than ) ),
inference(pattern_uni,[status(thm)],[320:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( bottom ))]]) ).
thf(23,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(132,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)],[23]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( bad @ ( B @ ( A @ triple ) ) @ ok )
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).
thf(292,plain,
! [A: $i,B: $i] :
~ ( bad @ ( B @ ( A @ triple ) ) @ ok ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ issmallestelement_pq ) )
& ( B @ ( A @ contains_pq ) ) )
=> ( ( B @ ( A @ findmin_pq_res ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).
thf(117,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ issmallestelement_pq ) )
& ( B @ ( A @ contains_pq ) ) )
=> ( ( B @ ( A @ findmin_pq_res ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ ( D @ pair ) @ ( B @ insert_slb ) @ ( A @ triple ) ) @ i )
= ( D @ ( C @ ( B @ ( A @ triple ) ) @ i @ insert_pq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
thf(270,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ ( D @ pair ) @ ( B @ insert_slb ) @ ( A @ triple ) ) @ i )
= ( D @ ( C @ ( B @ ( A @ triple ) ) @ i @ insert_pq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(35,axiom,
! [A: $i] :
~ ( A @ ( create_pq @ contains_pq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).
thf(197,plain,
! [A: $i] :
~ ( A @ ( create_pq @ contains_pq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(9,axiom,
! [A: $i] :
~ ( A @ ( create_slb @ contains_slb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
thf(95,plain,
! [A: $i] :
~ ( A @ ( create_slb @ contains_slb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(96,plain,
~ ? [A: $i] : ( A @ ( create_slb @ contains_slb ) ),
inference(miniscope,[status(thm)],[95]) ).
thf(97,plain,
! [A: $i] :
~ ( A @ ( create_slb @ contains_slb ) ),
inference(cnf,[status(esa)],[96]) ).
thf(94,plain,
! [A: $i] : ( A @ ( A @ less_than ) ),
inference(cnf,[status(esa)],[93]) ).
thf(322,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)],[94,78]) ).
thf(323,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ less_than ) )
!= ( B @ ( C @ less_than ) ) )
| ~ ( C @ ( B @ strictly_less_than ) ) ),
inference(simp,[status(thm)],[322]) ).
thf(324,plain,
! [A: $i] :
~ ( A @ ( A @ strictly_less_than ) ),
inference(pattern_uni,[status(thm)],[323:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(42,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(224,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)],[42]) ).
thf(14,axiom,
~ ( create_pq @ isnonempty_pq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(108,plain,
~ ( create_pq @ isnonempty_pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(109,plain,
~ ( create_pq @ isnonempty_pq ),
inference(polarity_switch,[status(thm)],[108]) ).
thf(4,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(72,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( B @ removemin_cpq_eff @ ( A @ succ_cpq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( B @ removemin_cpq_eff @ ( A @ succ_cpq ) )
| ~ ( B @ ( A @ succ_cpq ) ) ),
inference(cnf,[status(esa)],[72]) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ succ_cpq ) )
!= ( C @ ( B @ succ_cpq ) ) )
| ( C @ removemin_cpq_eff @ ( B @ succ_cpq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[125,73]) ).
thf(326,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ succ_cpq ) )
!= ( C @ ( B @ succ_cpq ) ) )
| ( C @ removemin_cpq_eff @ ( B @ succ_cpq ) ) ),
inference(simp,[status(thm)],[325]) ).
thf(327,plain,
! [A: $i] : ( A @ removemin_cpq_eff @ ( A @ succ_cpq ) ),
inference(pattern_uni,[status(thm)],[326:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(332,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ removemin_cpq_eff @ ( A @ succ_cpq ) )
!= ( C @ ( B @ succ_cpq ) ) )
| ( C @ removemin_cpq_eff @ ( B @ succ_cpq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[327,73]) ).
thf(333,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ removemin_cpq_eff @ ( A @ succ_cpq ) )
!= ( C @ ( B @ succ_cpq ) ) )
| ( C @ removemin_cpq_eff @ ( B @ succ_cpq ) ) ),
inference(simp,[status(thm)],[332]) ).
thf(334,plain,
! [A: $i] : ( A @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) ),
inference(pattern_uni,[status(thm)],[333:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ removemin_cpq_eff ))]]) ).
thf(335,plain,
! [A: $i] : ( A @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) ),
inference(simp,[status(thm)],[334]) ).
thf(336,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) )
!= ( C @ ( B @ succ_cpq ) ) )
| ( C @ removemin_cpq_eff @ ( B @ succ_cpq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[335,73]) ).
thf(337,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) )
!= ( C @ ( B @ succ_cpq ) ) )
| ( C @ removemin_cpq_eff @ ( B @ succ_cpq ) ) ),
inference(simp,[status(thm)],[336]) ).
thf(338,plain,
! [A: $i] : ( A @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) ),
inference(pattern_uni,[status(thm)],[337:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ removemin_cpq_eff @ removemin_cpq_eff ))]]) ).
thf(339,plain,
! [A: $i] : ( A @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) ),
inference(simp,[status(thm)],[338]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ less_than ) )
| ~ ( B @ ( A @ strictly_less_than ) ) ),
inference(cnfConj,[status(thm)],[76]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ pi_sharp_remove ) )
<=> ( B @ ( A @ contains_pq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56) ).
thf(173,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ contains_pq ) )
=> ( B @ ( A @ pi_sharp_remove ) ) )
& ( ( B @ ( A @ pi_sharp_remove ) )
=> ( B @ ( A @ contains_pq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
thf(129,plain,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(64,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(311,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)],[64]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
=> ( C = bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
thf(264,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
=> ( C = bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(28,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(161,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( B @ findmin_cpq_eff @ ( A @ succ_cpq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(55,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(279,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)],[55]) ).
thf(57,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(286,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)],[57]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ removemin_pq_res ) )
= B )
| ~ ( B @ ( A @ issmallestelement_pq ) )
| ~ ( B @ ( A @ contains_pq ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ issmallestelement_pq ) )
| ~ ( B @ ( A @ contains_pq ) )
| ( ( B @ ( A @ removemin_pq_res ) )
= B ) ),
inference(lifteq,[status(thm)],[70]) ).
thf(180,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
inference(miniscope,[status(thm)],[179]) ).
thf(181,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
inference(cnf,[status(esa)],[180]) ).
thf(16,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(113,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)],[16]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
thf(81,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb ),
inference(cnf,[status(esa)],[81]) ).
thf(19,axiom,
~ ( create_slb @ isnonempty_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
thf(122,plain,
~ ( create_slb @ isnonempty_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(123,plain,
~ ( create_slb @ isnonempty_slb ),
inference(polarity_switch,[status(thm)],[122]) ).
thf(375,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)],[82,123]) ).
thf(376,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb )
!= ( create_slb @ isnonempty_slb ) ),
inference(simp,[status(thm)],[375]) ).
thf(377,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ pair ) @ ( A @ insert_slb ) )
!= create_slb ),
inference(simp,[status(thm)],[376]) ).
thf(44,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(230,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)],[44]) ).
thf(352,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) )
!= ( C @ ( B @ succ_cpq ) ) )
| ( C @ removemin_cpq_eff @ ( B @ succ_cpq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[339,73]) ).
thf(353,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) )
!= ( C @ ( B @ succ_cpq ) ) )
| ( C @ removemin_cpq_eff @ ( B @ succ_cpq ) ) ),
inference(simp,[status(thm)],[352]) ).
thf(354,plain,
! [A: $i] : ( A @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) ),
inference(pattern_uni,[status(thm)],[353:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff ))]]) ).
thf(355,plain,
! [A: $i] : ( A @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) ),
inference(simp,[status(thm)],[354]) ).
thf(359,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) )
!= ( C @ ( B @ succ_cpq ) ) )
| ( C @ removemin_cpq_eff @ ( B @ succ_cpq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[355,73]) ).
thf(360,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) )
!= ( C @ ( B @ succ_cpq ) ) )
| ( C @ removemin_cpq_eff @ ( B @ succ_cpq ) ) ),
inference(simp,[status(thm)],[359]) ).
thf(361,plain,
! [A: $i] : ( A @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) ),
inference(pattern_uni,[status(thm)],[360:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( G @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff ))]]) ).
thf(362,plain,
! [A: $i] : ( A @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) ),
inference(simp,[status(thm)],[361]) ).
thf(41,axiom,
! [A: $i,B: $i] : ( B @ ( A @ insert_pq ) @ isnonempty_pq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
thf(222,plain,
! [A: $i,B: $i] : ( B @ ( A @ insert_pq ) @ isnonempty_pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(223,plain,
! [B: $i,A: $i] : ( B @ ( A @ insert_pq ) @ isnonempty_pq ),
inference(cnf,[status(esa)],[222]) ).
thf(316,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ insert_pq ) @ isnonempty_pq )
!= ( create_pq @ isnonempty_pq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[223,109]) ).
thf(317,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ insert_pq ) @ isnonempty_pq )
!= ( create_pq @ isnonempty_pq ) ),
inference(simp,[status(thm)],[316]) ).
thf(318,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ insert_pq ) )
!= create_pq ),
inference(simp,[status(thm)],[317]) ).
thf(10,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(98,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)],[10]) ).
thf(12,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(103,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)],[12]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ insert_pq ) @ remove_pq ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11) ).
thf(213,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ insert_pq ) @ remove_pq ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(47,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(251,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)],[47]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ pi_sharp_find_min ) )
<=> ( ( B @ ( A @ issmallestelement_pq ) )
& ( B @ ( A @ contains_pq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ issmallestelement_pq ) )
& ( B @ ( A @ contains_pq ) ) )
=> ( B @ ( A @ pi_sharp_find_min ) ) )
& ( ( B @ ( A @ pi_sharp_find_min ) )
=> ( ( B @ ( A @ issmallestelement_pq ) )
& ( B @ ( A @ contains_pq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(61,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(299,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)],[61]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ insert_pq ) @ insert_pq ) )
= ( B @ ( C @ ( A @ insert_pq ) @ insert_pq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
thf(267,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ insert_pq ) @ insert_pq ) )
= ( B @ ( C @ ( A @ insert_pq ) @ insert_pq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ insert_pq ) @ contains_pq ) )
<=> ( ( B = C )
| ( C @ ( A @ contains_pq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9) ).
thf(241,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B = C )
| ( C @ ( A @ contains_pq ) ) )
=> ( C @ ( B @ ( A @ insert_pq ) @ contains_pq ) ) )
& ( ( C @ ( B @ ( A @ insert_pq ) @ contains_pq ) )
=> ( ( B = C )
| ( C @ ( A @ contains_pq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(371,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) )
!= ( C @ ( B @ succ_cpq ) ) )
| ( C @ removemin_cpq_eff @ ( B @ succ_cpq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[362,73]) ).
thf(372,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) )
!= ( C @ ( B @ succ_cpq ) ) )
| ( C @ removemin_cpq_eff @ ( B @ succ_cpq ) ) ),
inference(simp,[status(thm)],[371]) ).
thf(373,plain,
! [A: $i] : ( A @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) ),
inference(pattern_uni,[status(thm)],[372:[bind(A,$thf( H )),bind(B,$thf( H )),bind(C,$thf( H @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff ))]]) ).
thf(374,plain,
! [A: $i] : ( A @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ removemin_cpq_eff @ ( A @ succ_cpq ) ),
inference(simp,[status(thm)],[373]) ).
thf(48,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(255,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)],[48]) ).
thf(34,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(194,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)],[34]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ issmallestelement_pq ) )
<=> ! [C: $i] :
( ( C @ ( A @ contains_pq ) )
=> ( C @ ( B @ less_than ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).
thf(145,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ ( A @ contains_pq ) )
=> ( C @ ( B @ less_than ) ) )
=> ( B @ ( A @ issmallestelement_pq ) ) )
& ( ( B @ ( A @ issmallestelement_pq ) )
=> ! [C: $i] :
( ( C @ ( A @ contains_pq ) )
=> ( C @ ( B @ less_than ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(60,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(295,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)],[60]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_res )
= bottom ),
inference(cnf,[status(esa)],[261]) ).
thf(263,plain,
! [B: $i,A: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_res )
= bottom ),
inference(lifteq,[status(thm)],[262]) ).
thf(198,plain,
~ ? [A: $i] : ( A @ ( create_pq @ contains_pq ) ),
inference(miniscope,[status(thm)],[197]) ).
thf(199,plain,
! [A: $i] :
~ ( A @ ( create_pq @ contains_pq ) ),
inference(cnf,[status(esa)],[198]) ).
thf(33,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(182,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)],[33]) ).
thf(65,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(314,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)],[65]) ).
thf(242,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( B = C )
| ( C @ ( A @ contains_pq ) ) )
=> ( C @ ( B @ ( A @ insert_pq ) @ contains_pq ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ insert_pq ) @ contains_pq ) )
=> ( ( B = C )
| ( C @ ( A @ contains_pq ) ) ) ) ),
inference(miniscope,[status(thm)],[241]) ).
thf(243,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ insert_pq ) @ contains_pq ) )
| ( E != F ) )
& ( ( F @ ( E @ ( D @ insert_pq ) @ contains_pq ) )
| ~ ( F @ ( D @ contains_pq ) ) )
& ( ( B = C )
| ( C @ ( A @ contains_pq ) )
| ~ ( C @ ( B @ ( A @ insert_pq ) @ contains_pq ) ) ) ),
inference(cnf,[status(esa)],[242]) ).
thf(246,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ insert_pq ) @ contains_pq ) )
| ( B != C ) ),
inference(cnfConj,[status(thm)],[243]) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ insert_pq ) @ contains_pq ) )
| ( B != C ) ),
inference(lifteq,[status(thm)],[246]) ).
thf(250,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ insert_pq ) @ contains_pq ) ),
inference(simp,[status(thm)],[249]) ).
thf(37,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(203,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)],[37]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ pi_find_min )
<=> ? [B: $i] : ( B @ ( A @ i @ pi_sharp_find_min ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
thf(207,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ i @ pi_sharp_find_min ) )
=> ( A @ pi_find_min ) )
& ( ( A @ pi_find_min )
=> ? [B: $i] : ( B @ ( A @ i @ pi_sharp_find_min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B != C )
& ( C @ ( A @ contains_pq ) ) )
=> ( ( C @ ( B @ ( A @ insert_pq ) @ remove_pq ) )
= ( B @ ( C @ ( A @ remove_pq ) @ insert_pq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax12) ).
thf(305,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B != C )
& ( C @ ( A @ contains_pq ) ) )
=> ( ( C @ ( B @ ( A @ insert_pq ) @ remove_pq ) )
= ( B @ ( C @ ( A @ remove_pq ) @ insert_pq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ less_than ) )
!= ( C @ ( D @ less_than ) ) )
| ~ $true
| ~ ( D @ ( C @ strictly_less_than ) )
| ~ ( B @ ( A @ strictly_less_than ) ) ),
inference(paramod_ordered,[status(thm)],[77,78]) ).
thf(357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ less_than ) )
!= ( C @ ( D @ less_than ) ) )
| ~ ( D @ ( C @ strictly_less_than ) )
| ~ ( B @ ( A @ strictly_less_than ) ) ),
inference(simp,[status(thm)],[356]) ).
thf(358,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ strictly_less_than ) )
| ~ ( B @ ( A @ strictly_less_than ) ) ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(56,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(283,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)],[56]) ).
thf(293,plain,
~ ? [A: $i,B: $i] : ( bad @ ( B @ ( A @ triple ) ) @ ok ),
inference(miniscope,[status(thm)],[292]) ).
thf(294,plain,
! [B: $i,A: $i] :
~ ( bad @ ( B @ ( A @ triple ) ) @ ok ),
inference(cnf,[status(esa)],[293]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ issmallestelement_pq ) )
& ( B @ ( A @ contains_pq ) ) )
=> ( ( B @ ( A @ findmin_pq_eff ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).
thf(126,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ issmallestelement_pq ) )
& ( B @ ( A @ contains_pq ) ) )
=> ( ( B @ ( A @ findmin_pq_eff ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(130,plain,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
inference(cnf,[status(esa)],[129]) ).
thf(131,plain,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
inference(lifteq,[status(thm)],[130]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ pi_sharp_removemin ) )
<=> ( ( B @ ( A @ issmallestelement_pq ) )
& ( B @ ( A @ contains_pq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
thf(163,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ issmallestelement_pq ) )
& ( B @ ( A @ contains_pq ) ) )
=> ( B @ ( A @ pi_sharp_removemin ) ) )
& ( ( B @ ( A @ pi_sharp_removemin ) )
=> ( ( B @ ( A @ issmallestelement_pq ) )
& ( B @ ( A @ contains_pq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(43,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(227,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)],[43]) ).
thf(7,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(83,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)],[7]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ issmallestelement_pq ) )
& ( B @ ( A @ contains_pq ) ) )
=> ( ( B @ ( A @ removemin_pq_eff ) )
= ( B @ ( A @ remove_pq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
thf(100,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ issmallestelement_pq ) )
& ( B @ ( A @ contains_pq ) ) )
=> ( ( B @ ( A @ removemin_pq_eff ) )
= ( B @ ( A @ remove_pq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1792,plain,
$false,
inference(e,[status(thm)],[260,273,69,347,234,170,308,120,202,142,153,110,125,93,289,78,261,216,179,321,106,132,74,292,117,270,197,97,324,224,109,124,339,77,173,129,73,311,264,161,279,286,259,71,335,181,113,81,377,230,362,318,98,103,213,66,251,108,223,135,299,267,241,374,255,123,355,194,145,295,95,327,263,310,199,182,72,314,250,203,207,82,305,107,341,358,94,283,294,126,131,68,163,200,227,122,83,222,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV415+2 : 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
% 0.22/5.50 % Computer : n013.cluster.edu
% 0.22/5.50 % Model : x86_64 x86_64
% 0.22/5.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/5.50 % Memory : 8046.5625MB
% 0.22/5.50 % OS : Linux 6.8.0-71-generic
% 0.22/5.50 % CPULimit : 300
% 0.22/5.50 % WCLimit : 300
% 0.22/5.50 % DateTime : Sat Sep 26 13:41:42 UTC 2026
% 0.27/5.50 % CPUTime :
% 0.27/5.50 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
% 1.36/6.38 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.54/6.80 % [INFO] Parsing done (420ms).
% 2.54/6.82 % [INFO] Running in sequential loop mode.
% 3.42/7.42 % [INFO] eprover registered as external prover.
% 3.42/7.44 % [INFO] Scanning for conjecture ...
% 3.76/7.61 % [INFO] Found a conjecture (or negated_conjecture) and 63 axioms. Running axiom selection ...
% 3.94/7.77 % [INFO] Axiom selection finished. Selected 63 axioms (removed 0 axioms).
% 4.38/7.94 % [INFO] Problem is first-order (TPTP FOF).
% 4.38/7.97 % [INFO] Type checking passed.
% 4.38/7.97 % [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 ...
% 29.91/13.46 % External prover 'e' found a proof!
% 29.91/13.46 % [INFO] Killing All external provers ...
% 29.91/13.46 % Time passed: 7752ms (effective reasoning time: 6627ms)
% 29.91/13.46 % 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)>
% 29.91/13.47 % Axioms used in derivation (63): ax13, ax39, ax59, ax7, ax43, ax19, ax12, ax53, ax20, ax52, ax24, ax56, ax47, ax41, stricly_smaller_definition, ax31, ax28, ax9, ax17, ax6, ax45, ax40, ax35, ax58, ax27, ax8, ax51, ax48, ax21, ax62, ax10, ax55, ax32, ax16, ax38, ax44, reflexivity, ax33, ax26, ax61, ax11, bottom_smallest, ax50, ax22, ax15, ax37, totality, ax54, ax49, big2_induction, ax14, ax46, ax34, ax23, ax25, ax60, transitivity, ax57, ax30, ax42, ax18, ax36, ax29
% 29.91/13.47 % No. of inferences in proof: 210
% 29.91/13.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7752 ms resp. 6627 ms w/o parsing
% 27.26/13.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 27.26/13.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------