%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV408+2 : 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 : n001.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 08:59:18 AM UTC 2026
% Result : Theorem 5.73s 3.67s
% Output : Refutation 6.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 45
% Syntax : Number of formulae : 92 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 208 ( 61 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 944 ( 31 ~; 11 |; 41 &; 797 @)
% ( 7 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 4 con; 0-3 aty)
% Number of variables : 267 ( 0 ^; 262 !; 5 ?; 267 :)
% Comments :
%------------------------------------------------------------------------------
thf(contains_slb_decl,type,
contains_slb: $i > $i > $o ).
thf(strictly_less_than_decl,type,
strictly_less_than: $i > $i > $o ).
thf(findmin_cpq_res_decl,type,
findmin_cpq_res: $i > $i ).
thf(triple_decl,type,
triple: $i > $i > $i > $i ).
thf(pair_in_list_decl,type,
pair_in_list: $i > $i > $i > $o ).
thf(update_slb_decl,type,
update_slb: $i > $i > $i ).
thf(findmin_pqp_res_decl,type,
findmin_pqp_res: $i > $i ).
thf(less_than_decl,type,
less_than: $i > $i > $o ).
thf(succ_cpq_decl,type,
succ_cpq: $i > $i > $o ).
thf(removemin_cpq_eff_decl,type,
removemin_cpq_eff: $i > $i ).
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(findmin_cpq_eff_decl,type,
findmin_cpq_eff: $i > $i ).
thf(insert_cpq_decl,type,
insert_cpq: $i > $i > $i ).
thf(lookup_slb_decl,type,
lookup_slb: $i > $i > $i ).
thf(remove_slb_decl,type,
remove_slb: $i > $i > $i ).
thf(create_slb_decl,type,
create_slb: $i ).
thf(remove_cpq_decl,type,
remove_cpq: $i > $i > $i ).
thf(bottom_decl,type,
bottom: $i ).
thf(bad_decl,type,
bad: $i ).
thf(remove_pqp_decl,type,
remove_pqp: $i > $i > $i ).
thf(ok_decl,type,
ok: $i > $o ).
thf(check_cpq_decl,type,
check_cpq: $i > $o ).
thf(insert_pqp_decl,type,
insert_pqp: $i > $i > $i ).
thf(contains_cpq_decl,type,
contains_cpq: $i > $i > $o ).
thf(removemin_cpq_res_decl,type,
removemin_cpq_res: $i > $i ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ strictly_less_than ) )
& ( C @ ( B @ ( A @ pair_in_list ) ) ) )
=> ( D @ ( B @ ( D @ ( A @ update_slb ) @ pair_in_list ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l48_li3839) ).
thf(142,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ strictly_less_than ) )
& ( C @ ( B @ ( A @ pair_in_list ) ) ) )
=> ( D @ ( B @ ( D @ ( A @ update_slb ) @ pair_in_list ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(43,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(185,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)],[43]) ).
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(157,plain,
! [A: $i,B: $i] :
( ( B @ ( create_slb @ ( A @ triple ) ) @ findmin_cpq_res )
= bottom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(21,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(106,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)],[21]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ less_than ) )
& ( C @ ( B @ ( A @ pair_in_list ) ) ) )
=> ( C @ ( B @ ( D @ ( A @ update_slb ) @ pair_in_list ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l49_li3637) ).
thf(92,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ less_than ) )
& ( C @ ( B @ ( A @ pair_in_list ) ) ) )
=> ( C @ ( B @ ( D @ ( A @ update_slb ) @ pair_in_list ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(30,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(144,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)],[30]) ).
thf(23,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(113,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)],[23]) ).
thf(46,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(198,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)],[46]) ).
thf(9,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(67,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)],[9]) ).
thf(4,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(55,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(44,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(189,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)],[44]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
thf(57,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,axiom,
! [A: $i,B: $i] : ( B @ ( create_slb @ ( A @ triple ) ) @ check_cpq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
thf(147,plain,
! [A: $i,B: $i] : ( B @ ( create_slb @ ( A @ triple ) ) @ check_cpq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(7,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(61,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)],[7]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( bad @ ( B @ ( A @ triple ) ) @ ok )
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
thf(116,plain,
! [A: $i,B: $i] :
~ ( bad @ ( B @ ( A @ triple ) ) @ ok ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(13,axiom,
! [A: $i] : ( A @ ( A @ less_than ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(85,plain,
! [A: $i] : ( A @ ( A @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,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(102,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)],[20]) ).
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(160,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ triple ) ) @ ok )
=> ( C = bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(10,axiom,
~ ( create_slb @ isnonempty_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(70,plain,
~ ( create_slb @ isnonempty_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i] : ( A @ ( A @ succ_cpq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(53,plain,
! [A: $i] : ( A @ ( A @ succ_cpq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(39,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(169,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)],[39]) ).
thf(22,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(109,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)],[22]) ).
thf(18,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(96,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)],[18]) ).
thf(8,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(64,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)],[8]) ).
thf(41,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(180,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)],[41]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ contains_slb ) )
=> ? [C: $i] : ( C @ ( B @ ( A @ pair_in_list ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_li4647) ).
thf(149,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ contains_slb ) )
=> ? [C: $i] : ( C @ ( B @ ( A @ pair_in_list ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(40,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(176,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)],[40]) ).
thf(6,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(59,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ succ_cpq ) )
=> ( B @ findmin_cpq_eff @ ( A @ succ_cpq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,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(130,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)],[28]) ).
thf(38,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(167,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)],[38]) ).
thf(34,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(154,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)],[34]) ).
thf(11,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(72,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)],[11]) ).
thf(19,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(99,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)],[19]) ).
thf(14,axiom,
! [A: $i] :
~ ( A @ ( create_slb @ contains_slb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
thf(87,plain,
! [A: $i] :
~ ( A @ ( create_slb @ contains_slb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,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(75,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)],[12]) ).
thf(25,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(119,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(151,plain,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(183,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(27,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(126,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)],[27]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ removemin_cpq_res )
= ( A @ findmin_cpq_res ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
thf(195,plain,
! [A: $i] :
( ( A @ removemin_cpq_res )
= ( A @ findmin_cpq_res ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(17,axiom,
! [A: $i] : ( A @ ( bottom @ less_than ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).
thf(94,plain,
! [A: $i] : ( A @ ( bottom @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ triple ) ) @ findmin_cpq_res @ ( D @ strictly_less_than ) )
& ( D @ ( B @ contains_slb ) ) )
=> ( ? [E: $i] :
( ( E @ ( A @ findmin_pqp_res @ less_than ) )
& ( E @ ( D @ ( A @ findmin_pqp_res @ ( B @ update_slb ) @ pair_in_list ) ) ) )
| ( A @ findmin_pqp_res @ ( D @ ( A @ findmin_pqp_res @ ( B @ update_slb ) @ pair_in_list ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l44_co) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ triple ) ) @ findmin_cpq_res @ ( D @ strictly_less_than ) )
& ( D @ ( B @ contains_slb ) ) )
=> ( ? [E: $i] :
( ( E @ ( A @ findmin_pqp_res @ less_than ) )
& ( E @ ( D @ ( A @ findmin_pqp_res @ ( B @ update_slb ) @ pair_in_list ) ) ) )
| ( A @ findmin_pqp_res @ ( D @ ( A @ findmin_pqp_res @ ( B @ update_slb ) @ pair_in_list ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(47,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ triple ) ) @ findmin_cpq_res @ ( D @ strictly_less_than ) )
& ( D @ ( B @ contains_slb ) ) )
=> ( ? [E: $i] :
( ( E @ ( A @ findmin_pqp_res @ less_than ) )
& ( E @ ( D @ ( A @ findmin_pqp_res @ ( B @ update_slb ) @ pair_in_list ) ) ) )
| ( A @ findmin_pqp_res @ ( D @ ( A @ findmin_pqp_res @ ( B @ update_slb ) @ pair_in_list ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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/sandbox/benchmark/theBenchmark.p',ax27) ).
thf(163,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(15,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(90,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)],[15]) ).
thf(26,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(122,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)],[26]) ).
thf(205,plain,
$false,
inference(e,[status(thm)],[142,185,157,106,92,144,113,198,67,55,189,57,147,61,116,85,102,160,70,53,169,109,96,64,180,149,176,59,130,167,154,72,99,87,75,119,151,183,126,195,94,47,163,90,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV408+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.12/0.98 % Computer : n001.cluster.edu
% 0.12/0.98 % Model : x86_64 x86_64
% 0.12/0.98 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.98 % Memory : 8046.5625MB
% 0.12/0.98 % OS : Linux 6.8.0-71-generic
% 0.12/0.98 % CPULimit : 300
% 0.12/0.98 % WCLimit : 300
% 0.12/0.98 % DateTime : Sat Sep 26 13:47:45 UTC 2026
% 0.12/0.98 % CPUTime :
% 0.12/0.98 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
% 0.90/1.57 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.50/1.82 % [INFO] Parsing done (249ms).
% 1.50/1.84 % [INFO] Running in sequential loop mode.
% 2.17/2.25 % [INFO] eprover registered as external prover.
% 2.17/2.26 % [INFO] Scanning for conjecture ...
% 2.40/2.38 % [INFO] Found a conjecture (or negated_conjecture) and 44 axioms. Running axiom selection ...
% 2.60/2.48 % [INFO] Axiom selection finished. Selected 44 axioms (removed 0 axioms).
% 2.81/2.57 % [INFO] Problem is first-order (TPTP FOF).
% 2.81/2.58 % [INFO] Type checking passed.
% 2.81/2.59 % [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 ...
% 5.73/3.67 % External prover 'e' found a proof!
% 5.73/3.67 % [INFO] Killing All external provers ...
% 5.73/3.67 % Time passed: 2542ms (effective reasoning time: 1824ms)
% 5.73/3.67 % 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)>
% 5.73/3.67 % Axioms used in derivation (44): ax28, ax39, ax27, l49_li3637, ax32, l45_li4647, ax22, ax43, ax19, ax49, ax25, ax53, ax20, ax52, ax24, ax47, ax41, stricly_smaller_definition, ax31, ax45, ax40, ax35, ax51, ax48, ax21, ax38, ax44, reflexivity, ax33, ax26, bottom_smallest, ax50, ax37, totality, ax46, ax34, ax23, transitivity, ax30, ax42, l48_li3839, ax18, ax36, ax29
% 5.73/3.67 % No. of inferences in proof: 92
% 5.73/3.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2542 ms resp. 1824 ms w/o parsing
% 6.11/3.77 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.11/3.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------