TSTP Solution File: SWV391+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV391+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:15:36 EDT 2023
% Result : Theorem 5.04s 2.43s
% Output : Refutation 5.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 73
% Syntax : Number of formulae : 121 ( 34 unt; 27 typ; 0 def)
% Number of atoms : 215 ( 63 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 972 ( 31 ~; 10 |; 37 &; 820 @)
% ( 8 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 4 con; 0-3 aty)
% Number of variables : 280 ( 0 ^; 280 !; 0 ?; 280 :)
% Comments :
%------------------------------------------------------------------------------
thf(check_cpq_type,type,
check_cpq: $i > $o ).
thf(remove_cpq_type,type,
remove_cpq: $i > $i > $i ).
thf(triple_type,type,
triple: $i > $i > $i > $i ).
thf(ok_type,type,
ok: $i > $o ).
thf(succ_cpq_type,type,
succ_cpq: $i > $i > $o ).
thf(removemin_cpq_eff_type,type,
removemin_cpq_eff: $i > $i ).
thf(strictly_less_than_type,type,
strictly_less_than: $i > $i > $o ).
thf(less_than_type,type,
less_than: $i > $i > $o ).
thf(isnonempty_slb_type,type,
isnonempty_slb: $i > $o ).
thf(insert_slb_type,type,
insert_slb: $i > $i > $i ).
thf(pair_type,type,
pair: $i > $i > $i ).
thf(contains_slb_type,type,
contains_slb: $i > $i > $o ).
thf(create_slb_type,type,
create_slb: $i ).
thf(insert_cpq_type,type,
insert_cpq: $i > $i > $i ).
thf(remove_slb_type,type,
remove_slb: $i > $i > $i ).
thf(bottom_type,type,
bottom: $i ).
thf(update_slb_type,type,
update_slb: $i > $i > $i ).
thf(pair_in_list_type,type,
pair_in_list: $i > $i > $i > $o ).
thf(findmin_cpq_eff_type,type,
findmin_cpq_eff: $i > $i ).
thf(lookup_slb_type,type,
lookup_slb: $i > $i > $i ).
thf(removemin_cpq_res_type,type,
removemin_cpq_res: $i > $i ).
thf(findmin_cpq_res_type,type,
findmin_cpq_res: $i > $i ).
thf(bad_type,type,
bad: $i ).
thf(remove_pqp_type,type,
remove_pqp: $i > $i > $i ).
thf(findmin_pqp_res_type,type,
findmin_pqp_res: $i > $i ).
thf(insert_pqp_type,type,
insert_pqp: $i > $i > $i ).
thf(contains_cpq_type,type,
contains_cpq: $i > $i > $o ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( check_cpq @ ( triple @ A @ B @ C ) )
<=> ! [D: $i,E: $i] :
( ( pair_in_list @ B @ D @ E )
=> ( less_than @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l27_li4142) ).
thf(152,plain,
! [A: $i,B: $i,C: $i] :
( ( ( check_cpq @ ( triple @ A @ B @ C ) )
=> ! [D: $i,E: $i] :
( ( pair_in_list @ B @ D @ E )
=> ( less_than @ E @ D ) ) )
& ( ! [D: $i,E: $i] :
( ( pair_in_list @ B @ D @ E )
=> ( less_than @ E @ D ) )
=> ( check_cpq @ ( triple @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(12,axiom,
! [A: $i] : ( less_than @ bottom @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).
thf(85,plain,
! [A: $i] : ( less_than @ bottom @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(25,axiom,
! [A: $i] :
( ( removemin_cpq_res @ A )
= ( findmin_cpq_res @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
thf(128,plain,
! [A: $i] :
( ( removemin_cpq_res @ A )
= ( findmin_cpq_res @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( contains_cpq @ ( triple @ A @ B @ C ) @ D )
<=> ( contains_slb @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(191,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( contains_cpq @ ( triple @ A @ B @ C ) @ D )
=> ( contains_slb @ B @ D ) )
& ( ( contains_slb @ B @ D )
=> ( contains_cpq @ ( triple @ A @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(33,axiom,
! [A: $i,B: $i] : ( check_cpq @ ( triple @ A @ create_slb @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
thf(159,plain,
! [A: $i,B: $i] : ( check_cpq @ ( triple @ A @ create_slb @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B != create_slb )
& ( contains_slb @ B @ ( findmin_pqp_res @ A ) )
& ( strictly_less_than @ ( findmin_pqp_res @ A ) @ ( lookup_slb @ B @ ( findmin_pqp_res @ A ) ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ A @ B @ C ) )
= ( triple @ A @ ( update_slb @ B @ ( findmin_pqp_res @ A ) ) @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
thf(187,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B != create_slb )
& ( contains_slb @ B @ ( findmin_pqp_res @ A ) )
& ( strictly_less_than @ ( findmin_pqp_res @ A ) @ ( lookup_slb @ B @ ( findmin_pqp_res @ A ) ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ A @ B @ C ) )
= ( triple @ A @ ( update_slb @ B @ ( findmin_pqp_res @ A ) ) @ bad ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(103,plain,
! [A: $i,B: $i,C: $i] :
( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( less_than @ E @ D )
=> ( ( check_cpq @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) )
<=> ( check_cpq @ ( triple @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
thf(145,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( less_than @ E @ D )
=> ( ( ( check_cpq @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) )
=> ( check_cpq @ ( triple @ A @ B @ C ) ) )
& ( ( check_cpq @ ( triple @ A @ B @ C ) )
=> ( check_cpq @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(7,axiom,
! [A: $i] : ( less_than @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(72,plain,
! [A: $i] : ( less_than @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( strictly_less_than @ A @ B )
<=> ( ( less_than @ A @ B )
& ~ ( less_than @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( ( strictly_less_than @ A @ B )
=> ( ( less_than @ A @ B )
& ~ ( less_than @ B @ A ) ) )
& ( ( ( less_than @ A @ B )
& ~ ( less_than @ B @ A ) )
=> ( strictly_less_than @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(82,plain,
! [A: $i,B: $i,C: $i] :
( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B != C )
& ( contains_slb @ A @ C ) )
=> ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( lookup_slb @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
thf(131,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B != C )
& ( contains_slb @ A @ C ) )
=> ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( lookup_slb @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( contains_slb @ B @ D )
& ( less_than @ ( lookup_slb @ B @ D ) @ D ) )
=> ( ( remove_cpq @ ( triple @ A @ B @ C ) @ D )
= ( triple @ ( remove_pqp @ A @ D ) @ ( remove_slb @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax44) ).
thf(138,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( contains_slb @ B @ D )
& ( less_than @ ( lookup_slb @ B @ D ) @ D ) )
=> ( ( remove_cpq @ ( triple @ A @ B @ C ) @ D )
= ( triple @ ( remove_pqp @ A @ D ) @ ( remove_slb @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( succ_cpq @ A @ B )
=> ( succ_cpq @ A @ ( findmin_cpq_eff @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).
thf(101,plain,
! [A: $i,B: $i] :
( ( succ_cpq @ A @ B )
=> ( succ_cpq @ A @ ( findmin_cpq_eff @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B != create_slb )
& ( contains_slb @ B @ ( findmin_pqp_res @ A ) )
& ( less_than @ ( lookup_slb @ B @ ( findmin_pqp_res @ A ) ) @ ( findmin_pqp_res @ A ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ A @ B @ C ) )
= ( triple @ A @ ( update_slb @ B @ ( findmin_pqp_res @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(170,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B != create_slb )
& ( contains_slb @ B @ ( findmin_pqp_res @ A ) )
& ( less_than @ ( lookup_slb @ B @ ( findmin_pqp_res @ A ) ) @ ( findmin_pqp_res @ A ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ A @ B @ C ) )
= ( triple @ A @ ( update_slb @ B @ ( findmin_pqp_res @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( strictly_less_than @ D @ E )
=> ( ( check_cpq @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) )
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
thf(202,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( strictly_less_than @ D @ E )
=> ~ ( check_cpq @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( insert_cpq @ ( triple @ A @ B @ C ) @ D )
= ( triple @ ( insert_pqp @ A @ D ) @ ( insert_slb @ B @ ( pair @ D @ bottom ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(174,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( insert_cpq @ ( triple @ A @ B @ C ) @ D )
= ( triple @ ( insert_pqp @ A @ D ) @ ( insert_slb @ B @ ( pair @ D @ bottom ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( check_cpq @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) )
& ( ok @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) ) )
=> ! [E: $i] :
( ( pair_in_list @ B @ D @ E )
=> ( less_than @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l27_l30) ).
thf(185,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( check_cpq @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) )
& ( ok @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) ) )
=> ! [E: $i] :
( ( pair_in_list @ B @ D @ E )
=> ( less_than @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(24,axiom,
! [A: $i] :
( ( update_slb @ create_slb @ A )
= create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(125,plain,
! [A: $i] :
( ( update_slb @ create_slb @ A )
= create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( succ_cpq @ A @ B )
=> ( succ_cpq @ A @ ( remove_cpq @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
thf(196,plain,
! [A: $i,B: $i,C: $i] :
( ( succ_cpq @ A @ B )
=> ( succ_cpq @ A @ ( remove_cpq @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( findmin_cpq_res @ ( triple @ A @ create_slb @ B ) )
= bottom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
thf(164,plain,
! [A: $i,B: $i] :
( ( findmin_cpq_res @ ( triple @ A @ create_slb @ B ) )
= bottom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
= ( triple @ A @ create_slb @ bad ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
thf(179,plain,
! [A: $i,B: $i] :
( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
= ( triple @ A @ create_slb @ bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( pair_in_list @ create_slb @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(106,plain,
! [A: $i,B: $i] :
~ ( pair_in_list @ create_slb @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] : ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
thf(61,plain,
! [A: $i,B: $i,C: $i] : ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i] :
~ ( contains_slb @ create_slb @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
thf(74,plain,
! [A: $i] :
~ ( contains_slb @ create_slb @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( succ_cpq @ A @ B )
=> ( succ_cpq @ A @ ( removemin_cpq_eff @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( succ_cpq @ A @ B )
=> ( succ_cpq @ A @ ( removemin_cpq_eff @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B != create_slb )
=> ( ( findmin_cpq_res @ ( triple @ A @ B @ C ) )
= ( findmin_pqp_res @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
thf(141,plain,
! [A: $i,B: $i,C: $i] :
( ( B != create_slb )
=> ( ( findmin_cpq_res @ ( triple @ A @ B @ C ) )
= ( findmin_pqp_res @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(109,plain,
! [A: $i,B: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( less_than @ A @ B )
& ( less_than @ B @ C ) )
=> ( less_than @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(77,plain,
! [A: $i,B: $i,C: $i] :
( ( ( less_than @ A @ B )
& ( less_than @ B @ C ) )
=> ( less_than @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( pair_in_list @ A @ B @ C )
=> ! [D: $i] :
( ( contains_slb @ A @ D )
=> ( ( pair_in_list @ ( remove_slb @ A @ D ) @ B @ C )
| ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l27_li2829) ).
thf(96,plain,
! [A: $i,B: $i,C: $i] :
( ( pair_in_list @ A @ B @ C )
=> ! [D: $i] :
( ( contains_slb @ A @ D )
=> ( ( pair_in_list @ ( remove_slb @ A @ D ) @ B @ C )
| ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B != create_slb )
& ~ ( contains_slb @ B @ ( findmin_pqp_res @ A ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ A @ B @ C ) )
= ( triple @ A @ ( update_slb @ B @ ( findmin_pqp_res @ A ) ) @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).
thf(148,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B != create_slb )
& ~ ( contains_slb @ B @ ( findmin_pqp_res @ A ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ A @ B @ C ) )
= ( triple @ A @ ( update_slb @ B @ ( findmin_pqp_res @ A ) ) @ bad ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(34,axiom,
! [A: $i] :
( ( removemin_cpq_eff @ A )
= ( remove_cpq @ ( findmin_cpq_eff @ A ) @ ( findmin_cpq_res @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(161,plain,
! [A: $i] :
( ( removemin_cpq_eff @ A )
= ( remove_cpq @ ( findmin_cpq_eff @ A ) @ ( findmin_cpq_res @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( contains_slb @ B @ D )
=> ( ( remove_cpq @ ( triple @ A @ B @ C ) @ D )
= ( triple @ A @ B @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).
thf(135,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( contains_slb @ B @ D )
=> ( ( remove_cpq @ ( triple @ A @ B @ C ) @ D )
= ( triple @ A @ B @ bad ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ok @ ( triple @ A @ B @ C ) )
=> ( C = bad ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
thf(167,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ok @ ( triple @ A @ B @ C ) )
=> ( C = bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( check_cpq @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) )
& ( ok @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) ) )
=> ( check_cpq @ ( triple @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l27_co) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( check_cpq @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) )
& ( ok @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) ) )
=> ( check_cpq @ ( triple @ A @ B @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(48,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( check_cpq @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) )
& ( ok @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) ) )
=> ( check_cpq @ ( triple @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
<=> ( ( contains_slb @ A @ C )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(63,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
=> ( ( contains_slb @ A @ C )
| ( B = C ) ) )
& ( ( ( contains_slb @ A @ C )
| ( B = C ) )
=> ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( contains_slb @ B @ D )
& ( strictly_less_than @ D @ ( lookup_slb @ B @ D ) ) )
=> ( ( remove_cpq @ ( triple @ A @ B @ C ) @ D )
= ( triple @ ( remove_pqp @ A @ D ) @ ( remove_slb @ B @ D ) @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
thf(199,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( contains_slb @ B @ D )
& ( strictly_less_than @ D @ ( lookup_slb @ B @ D ) ) )
=> ( ( remove_cpq @ ( triple @ A @ B @ C ) @ D )
= ( triple @ ( remove_pqp @ A @ D ) @ ( remove_slb @ B @ D ) @ bad ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ok @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) )
=> ( contains_slb @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l27_l33) ).
thf(177,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ok @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) )
=> ( contains_slb @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ok @ ( triple @ A @ B @ bad ) )
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
thf(182,plain,
! [A: $i,B: $i] :
~ ( ok @ ( triple @ A @ B @ bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(17,axiom,
! [A: $i] : ( succ_cpq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(99,plain,
! [A: $i] : ( succ_cpq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( strictly_less_than @ D @ C )
=> ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
thf(87,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( strictly_less_than @ D @ C )
=> ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( succ_cpq @ A @ B )
=> ( succ_cpq @ A @ ( insert_cpq @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).
thf(79,plain,
! [A: $i,B: $i,C: $i] :
( ( succ_cpq @ A @ B )
=> ( succ_cpq @ A @ ( insert_cpq @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(94,plain,
~ ( isnonempty_slb @ create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( less_than @ C @ D )
=> ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).
thf(122,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( less_than @ C @ D )
=> ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B != C )
& ( contains_slb @ A @ C ) )
=> ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( remove_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
thf(90,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B != C )
& ( contains_slb @ A @ C ) )
=> ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( remove_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
<=> ( ( pair_in_list @ A @ C @ E )
| ( ( B = C )
& ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
thf(111,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
=> ( ( pair_in_list @ A @ C @ E )
| ( ( B = C )
& ( D = E ) ) ) )
& ( ( ( pair_in_list @ A @ C @ E )
| ( ( B = C )
& ( D = E ) ) )
=> ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(211,plain,
$false,
inference(cvc4,[status(thm)],[152,85,128,191,159,187,103,145,72,55,82,131,138,101,170,202,174,185,125,196,164,179,106,61,74,53,141,109,77,96,148,161,135,167,48,63,199,177,182,99,87,79,94,122,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV391+1 : TPTP v8.1.2. Released v3.3.0.
% 0.17/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n026.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Fri May 19 02:54:52 EDT 2023
% 0.24/0.38 % CPUTime :
% 1.05/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.53/1.13 % [INFO] Parsing done (185ms).
% 1.53/1.14 % [INFO] Running in sequential loop mode.
% 1.99/1.40 % [INFO] eprover registered as external prover.
% 1.99/1.40 % [INFO] cvc4 registered as external prover.
% 1.99/1.41 % [INFO] Scanning for conjecture ...
% 2.28/1.49 % [INFO] Found a conjecture and 45 axioms. Running axiom selection ...
% 2.47/1.55 % [INFO] Axiom selection finished. Selected 45 axioms (removed 0 axioms).
% 2.60/1.61 % [INFO] Problem is first-order (TPTP FOF).
% 2.60/1.62 % [INFO] Type checking passed.
% 2.60/1.63 % [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 ...
% 5.04/2.42 % External prover 'cvc4' found a proof!
% 5.04/2.42 % [INFO] Killing All external provers ...
% 5.04/2.43 % Time passed: 1871ms (effective reasoning time: 1277ms)
% 5.04/2.43 % 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)>
% 5.04/2.43 % Axioms used in derivation (45): ax28, ax39, ax32, l27_li4142, l27_li2829, ax22, ax43, ax19, ax49, ax25, ax53, ax20, ax52, ax24, ax47, ax41, stricly_smaller_definition, ax31, ax45, ax40, ax35, ax27, l27_l33, ax51, ax48, ax21, ax38, ax44, reflexivity, ax33, ax26, bottom_smallest, ax50, ax37, totality, ax46, ax34, ax23, l27_l30, transitivity, ax30, ax42, ax18, ax36, ax29
% 5.04/2.43 % No. of inferences in proof: 94
% 5.04/2.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1871 ms resp. 1277 ms w/o parsing
% 5.34/2.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.34/2.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------