%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV384+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n026.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 08:59:14 AM UTC 2026
% Result : Theorem 20.22s 6.36s
% Output : Refutation 18.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 56
% Syntax : Number of formulae : 170 ( 83 unt; 0 typ; 12 def)
% Number of atoms : 439 ( 128 equ; 0 cnn)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 2114 ( 198 ~; 103 |; 42 &;1675 @)
% ( 7 <=>; 89 =>; 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 : 44 ( 41 usr; 18 con; 0-3 aty)
% Number of variables : 456 ( 0 ^; 438 !; 6 ?; 456 :)
% ( 0 !>; 0 ?*; 0 @-; 12 @+)
% Comments :
%------------------------------------------------------------------------------
thf(check_cpq_decl,type,
check_cpq: $i > $o ).
thf(triple_decl,type,
triple: $i > $i > $i > $i ).
thf(ok_decl,type,
ok: $i > $o ).
thf(succ_cpq_decl,type,
succ_cpq: $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(less_than_decl,type,
less_than: $i > $i > $o ).
thf(create_slb_decl,type,
create_slb: $i ).
thf(remove_slb_decl,type,
remove_slb: $i > $i > $i ).
thf(bottom_decl,type,
bottom: $i ).
thf(strictly_less_than_decl,type,
strictly_less_than: $i > $i > $o ).
thf(update_slb_decl,type,
update_slb: $i > $i > $i ).
thf(removemin_cpq_eff_decl,type,
removemin_cpq_eff: $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(lookup_slb_decl,type,
lookup_slb: $i > $i > $i ).
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(insert_cpq_decl,type,
insert_cpq: $i > $i > $i ).
thf(insert_pqp_decl,type,
insert_pqp: $i > $i > $i ).
thf(im_succ_cpq_decl,type,
im_succ_cpq: $i > $i ).
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(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: $o ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
| ~ ( C @ ( B @ ( A @ triple ) ) @ check_cpq ) )
=> ! [D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ triple ) ) @ ( C @ ( B @ ( A @ triple ) ) @ succ_cpq ) )
=> ( ~ ( F @ ( E @ ( D @ triple ) ) @ check_cpq )
| ~ ( F @ ( E @ ( D @ triple ) ) @ ok ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ~ ( B @ ( A @ ( sk1 @ triple ) ) @ ok )
| ~ ( B @ ( A @ ( sk1 @ triple ) ) @ check_cpq ) )
=> ! [C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ triple ) ) @ ( B @ ( A @ ( sk1 @ triple ) ) @ succ_cpq ) )
=> ( ~ ( E @ ( D @ ( C @ triple ) ) @ check_cpq )
| ~ ( E @ ( D @ ( C @ triple ) ) @ ok ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ~ ( A @ ( sk2 @ ( sk1 @ triple ) ) @ ok )
| ~ ( A @ ( sk2 @ ( sk1 @ triple ) ) @ check_cpq ) )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ triple ) ) @ ( A @ ( sk2 @ ( sk1 @ triple ) ) @ succ_cpq ) )
=> ( ~ ( D @ ( C @ ( B @ triple ) ) @ check_cpq )
| ~ ( D @ ( C @ ( B @ triple ) ) @ ok ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ triple ) ) @ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ succ_cpq ) )
=> ( ~ ( C @ ( B @ ( A @ triple ) ) @ check_cpq )
| ~ ( C @ ( B @ ( A @ triple ) ) @ ok ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ ( sk4 @ triple ) ) @ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ succ_cpq ) )
=> ( ~ ( B @ ( A @ ( sk4 @ triple ) ) @ check_cpq )
| ~ ( B @ ( A @ ( sk4 @ triple ) ) @ ok ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( A @ ( sk5 @ ( sk4 @ triple ) ) @ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ succ_cpq ) )
=> ( ~ ( A @ ( sk5 @ ( sk4 @ triple ) ) @ check_cpq )
| ~ ( A @ ( sk5 @ ( sk4 @ triple ) ) @ ok ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ triple ) ) @ ( C @ ( B @ ( A @ triple ) ) @ succ_cpq ) )
=> ( ( ~ ( F @ ( E @ ( D @ triple ) ) @ ok )
| ~ ( F @ ( E @ ( D @ triple ) ) @ check_cpq ) )
=> ( ~ ( F @ ( E @ ( D @ triple ) ) @ im_succ_cpq @ ok )
| ~ ( F @ ( E @ ( D @ triple ) ) @ im_succ_cpq @ check_cpq ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ triple ) ) @ ( B @ ( A @ ( sk8 @ triple ) ) @ succ_cpq ) )
=> ( ( ~ ( E @ ( D @ ( C @ triple ) ) @ ok )
| ~ ( E @ ( D @ ( C @ triple ) ) @ check_cpq ) )
=> ( ~ ( E @ ( D @ ( C @ triple ) ) @ im_succ_cpq @ ok )
| ~ ( E @ ( D @ ( C @ triple ) ) @ im_succ_cpq @ check_cpq ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ triple ) ) @ ( A @ ( sk9 @ ( sk8 @ triple ) ) @ succ_cpq ) )
=> ( ( ~ ( D @ ( C @ ( B @ triple ) ) @ ok )
| ~ ( D @ ( C @ ( B @ triple ) ) @ check_cpq ) )
=> ( ~ ( D @ ( C @ ( B @ triple ) ) @ im_succ_cpq @ ok )
| ~ ( D @ ( C @ ( B @ triple ) ) @ im_succ_cpq @ check_cpq ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ triple ) ) @ ( sk10 @ ( sk9 @ ( sk8 @ triple ) ) @ succ_cpq ) )
=> ( ( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
| ~ ( C @ ( B @ ( A @ triple ) ) @ check_cpq ) )
=> ( ~ ( C @ ( B @ ( A @ triple ) ) @ im_succ_cpq @ ok )
| ~ ( C @ ( B @ ( A @ triple ) ) @ im_succ_cpq @ check_cpq ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ ( sk11 @ triple ) ) @ ( sk10 @ ( sk9 @ ( sk8 @ triple ) ) @ succ_cpq ) )
=> ( ( ~ ( B @ ( A @ ( sk11 @ triple ) ) @ ok )
| ~ ( B @ ( A @ ( sk11 @ triple ) ) @ check_cpq ) )
=> ( ~ ( B @ ( A @ ( sk11 @ triple ) ) @ im_succ_cpq @ ok )
| ~ ( B @ ( A @ ( sk11 @ triple ) ) @ im_succ_cpq @ check_cpq ) ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i] :
~ ( ( A @ ( sk12 @ ( sk11 @ triple ) ) @ ( sk10 @ ( sk9 @ ( sk8 @ triple ) ) @ succ_cpq ) )
=> ( ( ~ ( A @ ( sk12 @ ( sk11 @ triple ) ) @ ok )
| ~ ( A @ ( sk12 @ ( sk11 @ triple ) ) @ check_cpq ) )
=> ( ~ ( A @ ( sk12 @ ( sk11 @ triple ) ) @ im_succ_cpq @ ok )
| ~ ( A @ ( sk12 @ ( sk11 @ triple ) ) @ im_succ_cpq @ check_cpq ) ) ) ) ) ) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_res )
= bottom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
thf(170,plain,
! [A: $i,B: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_res )
= bottom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
| ~ ( C @ ( B @ ( A @ triple ) ) @ check_cpq ) )
=> ! [D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ triple ) ) @ ( C @ ( B @ ( A @ triple ) ) @ succ_cpq ) )
=> ( ~ ( F @ ( E @ ( D @ triple ) ) @ check_cpq )
| ~ ( F @ ( E @ ( D @ triple ) ) @ ok ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l20_co) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
| ~ ( C @ ( B @ ( A @ triple ) ) @ check_cpq ) )
=> ! [D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ triple ) ) @ ( C @ ( B @ ( A @ triple ) ) @ succ_cpq ) )
=> ( ~ ( F @ ( E @ ( D @ triple ) ) @ check_cpq )
| ~ ( F @ ( E @ ( D @ triple ) ) @ ok ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(46,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
| ~ ( C @ ( B @ ( A @ triple ) ) @ check_cpq ) )
=> ! [D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ triple ) ) @ ( C @ ( B @ ( A @ triple ) ) @ succ_cpq ) )
=> ( ~ ( F @ ( E @ ( D @ triple ) ) @ check_cpq )
| ~ ( F @ ( E @ ( D @ triple ) ) @ ok ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(47,plain,
( ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) @ check_cpq )
& ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) @ ok )
& ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) @ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ succ_cpq ) )
& ( ~ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ ok )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ check_cpq ) ) ),
inference(cnf,[status(esa)],[46]) ).
thf(50,plain,
sk6 @ ( sk5 @ ( sk4 @ triple ) ) @ ok,
inference(cnfConj,[status(thm)],[47]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( bad @ ( B @ ( A @ triple ) ) @ ok )
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
thf(185,plain,
! [A: $i,B: $i] :
~ ( bad @ ( B @ ( A @ triple ) ) @ ok ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(186,plain,
~ ? [A: $i,B: $i] : ( bad @ ( B @ ( A @ triple ) ) @ ok ),
inference(miniscope,[status(thm)],[185]) ).
thf(187,plain,
! [B: $i,A: $i] :
~ ( bad @ ( B @ ( A @ triple ) ) @ ok ),
inference(cnf,[status(esa)],[186]) ).
thf(523,plain,
! [B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) @ ok )
!= ( bad @ ( B @ ( A @ triple ) ) @ ok ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,187]) ).
thf(524,plain,
! [B: $i,A: $i] :
( ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) @ ok )
!= ( bad @ ( B @ ( A @ triple ) ) @ ok ) ),
inference(simp,[status(thm)],[523]) ).
thf(533,plain,
! [B: $i,A: $i] :
( ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) )
!= ( bad @ ( B @ ( A @ triple ) ) ) ),
inference(simp,[status(thm)],[524]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ removemin_cpq_res )
= ( A @ findmin_cpq_res ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
thf(121,plain,
! [A: $i] :
( ( A @ removemin_cpq_res )
= ( A @ findmin_cpq_res ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
=> ( C = bad ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
thf(173,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
=> ( C = bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( B @ findmin_cpq_eff @ ( A @ succ_cpq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).
thf(128,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( B @ findmin_cpq_eff @ ( A @ succ_cpq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',ax37) ).
thf(154,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)],[30]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',ax47) ).
thf(158,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)],[31]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) )
=> ( C @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(69,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)],[7]) ).
thf(16,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(99,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(100,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
inference(miniscope,[status(thm)],[99]) ).
thf(101,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
inference(cnf,[status(esa)],[100]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ removemin_cpq_eff )
= ( A @ findmin_cpq_res @ ( A @ findmin_cpq_eff @ remove_cpq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(86,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)],[13]) ).
thf(87,plain,
! [A: $i] :
( ( A @ removemin_cpq_eff )
= ( A @ findmin_cpq_res @ ( A @ findmin_cpq_eff @ remove_cpq ) ) ),
inference(cnf,[status(esa)],[86]) ).
thf(88,plain,
! [A: $i] :
( ( A @ findmin_cpq_res @ ( A @ findmin_cpq_eff @ remove_cpq ) )
= ( A @ removemin_cpq_eff ) ),
inference(lifteq,[status(thm)],[87]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
thf(52,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff )
= ( bad @ ( create_slb @ ( A @ triple ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
thf(182,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)],[39]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff )
= ( bad @ ( create_slb @ ( A @ triple ) ) ) ),
inference(cnf,[status(esa)],[182]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff )
= ( bad @ ( create_slb @ ( A @ triple ) ) ) ),
inference(lifteq,[status(thm)],[183]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',ax44) ).
thf(147,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)],[28]) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(54,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)],[4]) ).
thf(55,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( B = C )
| ( C @ ( A @ contains_slb ) ) )
=> ! [D: $i] : ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) ) )
& ! [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) )
=> ( ( B = C )
| ( C @ ( A @ contains_slb ) ) ) ) ),
inference(miniscope,[status(thm)],[54]) ).
thf(56,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( H @ ( F @ pair ) @ ( E @ insert_slb ) @ contains_slb ) )
| ( F != G ) )
& ( ( G @ ( H @ ( F @ pair ) @ ( E @ insert_slb ) @ contains_slb ) )
| ~ ( G @ ( E @ contains_slb ) ) )
& ( ( B = C )
| ( C @ ( A @ contains_slb ) )
| ~ ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(58,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) )
| ~ ( C @ ( A @ contains_slb ) ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(61,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) )
| ~ ( C @ ( A @ contains_slb ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb ),
inference(cnf,[status(esa)],[52]) ).
thf(19,axiom,
~ ( create_slb @ isnonempty_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(116,plain,
~ ( create_slb @ isnonempty_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(117,plain,
~ ( create_slb @ isnonempty_slb ),
inference(polarity_switch,[status(thm)],[116]) ).
thf(219,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)],[53,117]) ).
thf(220,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb )
!= ( create_slb @ isnonempty_slb ) ),
inference(simp,[status(thm)],[219]) ).
thf(221,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ pair ) @ ( A @ insert_slb ) )
!= create_slb ),
inference(simp,[status(thm)],[220]) ).
thf(9,axiom,
! [A: $i] : ( A @ ( bottom @ less_than ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).
thf(74,plain,
! [A: $i] : ( A @ ( bottom @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ strictly_less_than ) )
<=> ( ~ ( A @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(89,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)],[14]) ).
thf(25,axiom,
( ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ triple ) ) @ ( C @ ( B @ ( A @ triple ) ) @ succ_cpq ) )
=> ( ( ~ ( F @ ( E @ ( D @ triple ) ) @ ok )
| ~ ( F @ ( E @ ( D @ triple ) ) @ check_cpq ) )
=> ( ~ ( F @ ( E @ ( D @ triple ) ) @ im_succ_cpq @ ok )
| ~ ( F @ ( E @ ( D @ triple ) ) @ im_succ_cpq @ check_cpq ) ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
| ~ ( C @ ( B @ ( A @ triple ) ) @ check_cpq ) )
=> ! [D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ triple ) ) @ ( C @ ( B @ ( A @ triple ) ) @ succ_cpq ) )
=> ( ~ ( F @ ( E @ ( D @ triple ) ) @ check_cpq )
| ~ ( F @ ( E @ ( D @ triple ) ) @ ok ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l20_induction) ).
thf(133,plain,
( ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ triple ) ) @ ( C @ ( B @ ( A @ triple ) ) @ succ_cpq ) )
=> ( ( ~ ( F @ ( E @ ( D @ triple ) ) @ ok )
| ~ ( F @ ( E @ ( D @ triple ) ) @ check_cpq ) )
=> ( ~ ( F @ ( E @ ( D @ triple ) ) @ im_succ_cpq @ ok )
| ~ ( F @ ( E @ ( D @ triple ) ) @ im_succ_cpq @ check_cpq ) ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
| ~ ( C @ ( B @ ( A @ triple ) ) @ check_cpq ) )
=> ! [D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ triple ) ) @ ( C @ ( B @ ( A @ triple ) ) @ succ_cpq ) )
=> ( ~ ( F @ ( E @ ( D @ triple ) ) @ check_cpq )
| ~ ( F @ ( E @ ( D @ triple ) ) @ ok ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(760,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( bad @ ( create_slb @ ( A @ triple ) ) )
!= ( bad @ ( D @ ( C @ triple ) ) ) )
| ~ ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff @ ok ) ),
inference(paramod_ordered,[status(thm)],[184,187]) ).
thf(761,plain,
! [B: $i,A: $i] :
~ ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff @ ok ),
inference(pattern_uni,[status(thm)],[760:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( create_slb ))]]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(102,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(57,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( C @ ( A @ contains_slb ) )
| ~ ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(60,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ contains_slb ) )
| ~ ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) )
| ( B = C ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(83,plain,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(84,plain,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
inference(cnf,[status(esa)],[83]) ).
thf(85,plain,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
inference(lifteq,[status(thm)],[84]) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',ax45) ).
thf(201,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)],[44]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
| ~ ( C @ ( B @ ( A @ triple ) ) @ check_cpq ) )
=> ( ~ ( C @ ( B @ ( A @ triple ) ) @ im_succ_cpq @ ok )
| ~ ( C @ ( B @ ( A @ triple ) ) @ im_succ_cpq @ check_cpq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_l13) ).
thf(197,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
| ~ ( C @ ( B @ ( A @ triple ) ) @ check_cpq ) )
=> ( ~ ( C @ ( B @ ( A @ triple ) ) @ im_succ_cpq @ ok )
| ~ ( C @ ( B @ ( A @ triple ) ) @ im_succ_cpq @ check_cpq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(5,axiom,
! [A: $i] : ( A @ ( A @ less_than ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(64,plain,
! [A: $i] : ( A @ ( A @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(65,plain,
! [A: $i] : ( A @ ( A @ less_than ) ),
inference(cnf,[status(esa)],[64]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ triple ) ) @ contains_cpq ) )
<=> ( D @ ( B @ contains_slb ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(188,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)],[41]) ).
thf(34,axiom,
! [A: $i,B: $i] : ( B @ ( create_slb @ ( A @ triple ) ) @ check_cpq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
thf(168,plain,
! [A: $i,B: $i] : ( B @ ( create_slb @ ( A @ triple ) ) @ check_cpq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(169,plain,
! [B: $i,A: $i] : ( B @ ( create_slb @ ( A @ triple ) ) @ check_cpq ),
inference(cnf,[status(esa)],[168]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( C @ ( B @ insert_cpq ) @ ( A @ succ_cpq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).
thf(141,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)],[26]) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',ax27) ).
thf(124,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)],[22]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ lookup_slb ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(96,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)],[15]) ).
thf(33,axiom,
! [A: $i] : ( A @ ( A @ succ_cpq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(166,plain,
! [A: $i] : ( A @ ( A @ succ_cpq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( B @ removemin_cpq_eff @ ( A @ succ_cpq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
thf(176,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( B @ removemin_cpq_eff @ ( A @ succ_cpq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',ax30) ).
thf(118,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)],[20]) ).
thf(45,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/sandbox/benchmark/theBenchmark.p',ax38) ).
thf(204,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)],[45]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ remove_slb ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(71,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)],[8]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',ax43) ).
thf(144,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)],[27]) ).
thf(49,plain,
sk6 @ ( sk5 @ ( sk4 @ triple ) ) @ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ succ_cpq ),
inference(cnfConj,[status(thm)],[47]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_res )
= bottom ),
inference(cnf,[status(esa)],[170]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_res )
= bottom ),
inference(lifteq,[status(thm)],[171]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',ax29) ).
thf(76,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)],[10]) ).
thf(134,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( F @ ( E @ ( D @ triple ) ) @ check_cpq )
| ~ ( F @ ( E @ ( D @ triple ) ) @ ok )
| ~ ( F @ ( E @ ( D @ triple ) ) @ ( C @ ( B @ ( A @ triple ) ) @ succ_cpq ) )
| ( C @ ( B @ ( A @ triple ) ) @ ok )
| ~ sk7 )
& ( ~ ( F @ ( E @ ( D @ triple ) ) @ check_cpq )
| ~ ( F @ ( E @ ( D @ triple ) ) @ ok )
| ~ ( F @ ( E @ ( D @ triple ) ) @ ( C @ ( B @ ( A @ triple ) ) @ succ_cpq ) )
| ( C @ ( B @ ( A @ triple ) ) @ check_cpq )
| ~ sk7 )
& ( sk7
| ( sk13 @ ( sk12 @ ( sk11 @ triple ) ) @ im_succ_cpq @ ok ) )
& ( sk7
| ( sk13 @ ( sk12 @ ( sk11 @ triple ) ) @ im_succ_cpq @ check_cpq ) )
& ( sk7
| ~ ( sk13 @ ( sk12 @ ( sk11 @ triple ) ) @ ok )
| ~ ( sk13 @ ( sk12 @ ( sk11 @ triple ) ) @ check_cpq ) )
& ( sk7
| ( sk13 @ ( sk12 @ ( sk11 @ triple ) ) @ ( sk10 @ ( sk9 @ ( sk8 @ triple ) ) @ succ_cpq ) ) ) ),
inference(cnf,[status(esa)],[133]) ).
thf(140,plain,
( sk7
| ( sk13 @ ( sk12 @ ( sk11 @ triple ) ) @ im_succ_cpq @ ok ) ),
inference(cnfConj,[status(thm)],[134]) ).
thf(6,axiom,
! [A: $i] :
~ ( A @ ( create_slb @ contains_slb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
thf(66,plain,
! [A: $i] :
~ ( A @ ( create_slb @ contains_slb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(130,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)],[24]) ).
thf(135,plain,
( sk7
| ( sk13 @ ( sk12 @ ( sk11 @ triple ) ) @ im_succ_cpq @ check_cpq ) ),
inference(cnfConj,[status(thm)],[134]) ).
thf(167,plain,
! [A: $i] : ( A @ ( A @ succ_cpq ) ),
inference(cnf,[status(esa)],[166]) ).
thf(721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( bad @ ( create_slb @ ( A @ triple ) ) )
!= ( bad @ ( D @ ( C @ triple ) ) ) )
| ( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff )
!= ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[184,533]) ).
thf(722,plain,
! [B: $i,A: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff )
!= ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) ) ),
inference(pattern_uni,[status(thm)],[721:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( create_slb ))]]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',ax48) ).
thf(162,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)],[32]) ).
thf(122,plain,
! [A: $i] :
( ( A @ removemin_cpq_res )
= ( A @ findmin_cpq_res ) ),
inference(cnf,[status(esa)],[121]) ).
thf(123,plain,
! [A: $i] :
( ( A @ removemin_cpq_res )
= ( A @ findmin_cpq_res ) ),
inference(lifteq,[status(thm)],[122]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( C @ ( B @ remove_cpq ) @ ( A @ succ_cpq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
thf(194,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(48,plain,
( ~ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ ok )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ check_cpq ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(854,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff )
!= ( D @ ( create_slb @ ( C @ triple ) ) @ findmin_cpq_eff ) )
| ( ( bad @ ( create_slb @ ( A @ triple ) ) )
!= ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[184,722]) ).
thf(855,plain,
! [A: $i] :
( ( bad @ ( create_slb @ ( A @ triple ) ) )
!= ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) ) ),
inference(pattern_uni,[status(thm)],[854:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(59,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) )
| ( B != C ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(62,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) )
| ( B != C ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) ),
inference(simp,[status(thm)],[62]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',ax51) ).
thf(150,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)],[29]) ).
thf(557,plain,
! [B: $i,A: $i] :
( ( sk6 != bad )
| ( sk5 != B )
| ( sk4 != A ) ),
inference(simp,[status(thm)],[533]) ).
thf(585,plain,
sk6 != bad,
inference(simp,[status(thm)],[557]) ).
thf(758,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)],[184,169]) ).
thf(759,plain,
! [B: $i,A: $i] : ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff @ check_cpq ),
inference(pattern_uni,[status(thm)],[758:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(51,plain,
sk6 @ ( sk5 @ ( sk4 @ triple ) ) @ check_cpq,
inference(cnfConj,[status(thm)],[47]) ).
thf(206,plain,
( ( ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) @ ok )
!= ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ ok ) )
| ~ $true
| ~ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ check_cpq ) ),
inference(paramod_ordered,[status(thm)],[50,48]) ).
thf(207,plain,
( ( ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) @ ok )
!= ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ ok ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ check_cpq ) ),
inference(simp,[status(thm)],[206]) ).
thf(210,plain,
( ( ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ check_cpq ) ),
inference(simp,[status(thm)],[207]) ).
thf(213,plain,
( ( ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) @ check_cpq )
!= ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ check_cpq ) )
| ( ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[51,210]) ).
thf(214,plain,
( ( ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) @ check_cpq )
!= ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) @ check_cpq ) )
| ( ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) ) ) ),
inference(simp,[status(thm)],[213]) ).
thf(216,plain,
( ( ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) ) )
| ( ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) ) ) ),
inference(simp,[status(thm)],[214]) ).
thf(218,plain,
( ( sk6 @ ( sk5 @ ( sk4 @ triple ) ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ triple ) ) ) ),
inference(simp,[status(thm)],[216]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',ax23) ).
thf(104,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)],[18]) ).
thf(75,plain,
! [A: $i] : ( A @ ( bottom @ less_than ) ),
inference(cnf,[status(esa)],[74]) ).
thf(762,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 @ findmin_cpq_res )
= bottom ) ),
inference(paramod_ordered,[status(thm)],[184,172]) ).
thf(763,plain,
! [B: $i,A: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_eff @ findmin_cpq_res )
= bottom ),
inference(pattern_uni,[status(thm)],[762:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',ax25) ).
thf(79,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)],[11]) ).
thf(631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != sk6 )
| ( C != bad )
| ( C @ ( A @ contains_slb ) )
| ~ ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) ) ),
inference(paramod_ordered,[status(thm)],[60,585]) ).
thf(632,plain,
! [C: $i,B: $i,A: $i] :
( ( B != bad )
| ( B @ ( A @ contains_slb ) )
| ~ ( B @ ( C @ ( sk6 @ pair ) @ ( A @ insert_slb ) @ contains_slb ) ) ),
inference(pattern_uni,[status(thm)],[631:[bind(A,$thf( A )),bind(B,$thf( sk6 ))]]) ).
thf(635,plain,
! [B: $i,A: $i] :
( ( bad @ ( A @ contains_slb ) )
| ~ ( bad @ ( B @ ( sk6 @ pair ) @ ( A @ insert_slb ) @ contains_slb ) ) ),
inference(simp,[status(thm)],[632]) ).
thf(67,plain,
~ ? [A: $i] : ( A @ ( create_slb @ contains_slb ) ),
inference(miniscope,[status(thm)],[66]) ).
thf(68,plain,
! [A: $i] :
~ ( A @ ( create_slb @ contains_slb ) ),
inference(cnf,[status(esa)],[67]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(178,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)],[38]) ).
thf(222,plain,
( ( sk6 != sk3 )
| ( sk5 != sk2 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[218]) ).
thf(1217,plain,
$false,
inference(e,[status(thm)],[170,533,185,46,121,173,128,154,158,69,101,88,52,184,147,61,221,116,74,89,133,761,102,60,117,85,201,197,65,188,53,169,141,124,96,166,64,176,118,204,71,54,144,49,86,187,172,76,140,66,130,135,167,722,162,123,194,48,855,63,150,50,182,585,99,759,218,104,75,763,168,51,79,635,68,178,83,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV384+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.25/0.60 % Computer : n026.cluster.edu
% 0.25/0.60 % Model : x86_64 x86_64
% 0.25/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.60 % Memory : 8046.5625MB
% 0.25/0.60 % OS : Linux 6.8.0-71-generic
% 0.25/0.60 % CPULimit : 300
% 0.25/0.60 % WCLimit : 300
% 0.25/0.60 % DateTime : Sat Sep 26 13:42:56 UTC 2026
% 0.25/0.60 % CPUTime :
% 0.25/0.60 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.43/1.47 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.30/1.85 % [INFO] Parsing done (370ms).
% 2.30/1.87 % [INFO] Running in sequential loop mode.
% 3.41/2.46 % [INFO] eprover registered as external prover.
% 3.41/2.48 % [INFO] Scanning for conjecture ...
% 3.81/2.66 % [INFO] Found a conjecture (or negated_conjecture) and 43 axioms. Running axiom selection ...
% 4.23/2.80 % [INFO] Axiom selection finished. Selected 43 axioms (removed 0 axioms).
% 4.46/2.90 % [INFO] Problem is first-order (TPTP FOF).
% 4.46/2.91 % [INFO] Type checking passed.
% 4.46/2.92 % [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 ...
% 20.22/6.35 % External prover 'e' found a proof!
% 20.22/6.35 % [INFO] Killing All external provers ...
% 20.22/6.36 % Time passed: 5548ms (effective reasoning time: 4479ms)
% 20.22/6.36 % 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)>
% 20.22/6.36 % Axioms used in derivation (43): l20_induction, ax28, ax39, ax27, ax32, 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, ax22, l12_l13, ax37, totality, ax46, ax34, ax23, transitivity, ax30, ax42, ax18, ax36, ax29
% 20.22/6.36 % No. of inferences in proof: 158
% 20.22/6.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5548 ms resp. 4479 ms w/o parsing
% 18.70/6.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.70/6.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------