TSTP Solution File: SWV416+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV416+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 12:15:41 EDT 2023
% Result : Theorem 109.15s 20.74s
% Output : Refutation 109.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 111
% Syntax : Number of formulae : 179 ( 48 unt; 45 typ; 0 def)
% Number of atoms : 353 ( 103 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 1704 ( 37 ~; 11 |; 75 &;1448 @)
% ( 20 <=>; 113 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 45 usr; 5 con; 0-3 aty)
% Number of variables : 442 ( 0 ^; 433 !; 9 ?; 442 :)
% Comments :
%------------------------------------------------------------------------------
thf(pi_remove_type,type,
pi_remove: $i > $i > $o ).
thf(triple_type,type,
triple: $i > $i > $i > $i ).
thf(phi_type,type,
phi: $i > $o ).
thf(remove_cpq_type,type,
remove_cpq: $i > $i > $i ).
thf(pi_sharp_remove_type,type,
pi_sharp_remove: $i > $i > $o ).
thf(i_type,type,
i: $i > $i ).
thf(remove_pq_type,type,
remove_pq: $i > $i > $i ).
thf(contains_pq_type,type,
contains_pq: $i > $i > $o ).
thf(issmallestelement_pq_type,type,
issmallestelement_pq: $i > $i > $o ).
thf(removemin_pq_res_type,type,
removemin_pq_res: $i > $i > $i ).
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(isnonempty_pq_type,type,
isnonempty_pq: $i > $o ).
thf(create_pq_type,type,
create_pq: $i ).
thf(update_slb_type,type,
update_slb: $i > $i > $i ).
thf(insert_pq_type,type,
insert_pq: $i > $i > $i ).
thf(findmin_pq_res_type,type,
findmin_pq_res: $i > $i > $i ).
thf(findmin_pq_eff_type,type,
findmin_pq_eff: $i > $i > $i ).
thf(findmin_cpq_eff_type,type,
findmin_cpq_eff: $i > $i ).
thf(pi_sharp_removemin_type,type,
pi_sharp_removemin: $i > $i > $o ).
thf(lookup_slb_type,type,
lookup_slb: $i > $i > $i ).
thf(pair_in_list_type,type,
pair_in_list: $i > $i > $i > $o ).
thf(pi_sharp_find_min_type,type,
pi_sharp_find_min: $i > $i > $o ).
thf(removemin_cpq_res_type,type,
removemin_cpq_res: $i > $i ).
thf(findmin_cpq_res_type,type,
findmin_cpq_res: $i > $i ).
thf(insert_pqp_type,type,
insert_pqp: $i > $i > $i ).
thf(pi_find_min_type,type,
pi_find_min: $i > $o ).
thf(contains_cpq_type,type,
contains_cpq: $i > $i > $o ).
thf(pi_removemin_type,type,
pi_removemin: $i > $o ).
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(check_cpq_type,type,
check_cpq: $i > $o ).
thf(ok_type,type,
ok: $i > $o ).
thf(removemin_pq_eff_type,type,
removemin_pq_eff: $i > $i > $i ).
thf(34,axiom,
! [A: $i] :
( ( removemin_cpq_res @ A )
= ( findmin_cpq_res @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
thf(185,plain,
! [A: $i] :
( ( removemin_cpq_res @ A )
= ( findmin_cpq_res @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( succ_cpq @ A @ B )
=> ( succ_cpq @ A @ ( findmin_cpq_eff @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).
thf(149,plain,
! [A: $i,B: $i] :
( ( succ_cpq @ A @ B )
=> ( succ_cpq @ A @ ( findmin_cpq_eff @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(8,axiom,
! [A: $i] : ( less_than @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(95,plain,
! [A: $i] : ( less_than @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(37,axiom,
( ( ! [A: $i,B: $i,C: $i] :
( ( contains_pq @ ( i @ ( triple @ A @ create_slb @ B ) ) @ C )
=> ( ( i @ ( remove_cpq @ ( triple @ A @ create_slb @ B ) @ C ) )
= ( remove_pq @ ( i @ ( triple @ A @ create_slb @ B ) ) @ C ) ) )
& ! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( contains_pq @ ( i @ ( triple @ B @ A @ C ) ) @ D )
=> ( ( i @ ( remove_cpq @ ( triple @ B @ A @ C ) @ D ) )
= ( remove_pq @ ( i @ ( triple @ B @ A @ C ) ) @ D ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( contains_pq @ ( i @ ( triple @ B @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ C ) ) @ D )
=> ( ( i @ ( remove_cpq @ ( triple @ B @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ C ) @ D ) )
= ( remove_pq @ ( i @ ( triple @ B @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ C ) ) @ D ) ) ) ) )
=> ! [A: $i,B: $i,C: $i,D: $i] :
( ( contains_pq @ ( i @ ( triple @ A @ B @ C ) ) @ D )
=> ( ( i @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) )
= ( remove_pq @ ( i @ ( triple @ A @ B @ C ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big3_induction2) ).
thf(199,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( contains_pq @ ( i @ ( triple @ A @ create_slb @ B ) ) @ C )
=> ( ( i @ ( remove_cpq @ ( triple @ A @ create_slb @ B ) @ C ) )
= ( remove_pq @ ( i @ ( triple @ A @ create_slb @ B ) ) @ C ) ) )
& ! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( contains_pq @ ( i @ ( triple @ B @ A @ C ) ) @ D )
=> ( ( i @ ( remove_cpq @ ( triple @ B @ A @ C ) @ D ) )
= ( remove_pq @ ( i @ ( triple @ B @ A @ C ) ) @ D ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( contains_pq @ ( i @ ( triple @ B @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ C ) ) @ D )
=> ( ( i @ ( remove_cpq @ ( triple @ B @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ C ) @ D ) )
= ( remove_pq @ ( i @ ( triple @ B @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ C ) ) @ D ) ) ) ) )
=> ! [A: $i,B: $i,C: $i,D: $i] :
( ( contains_pq @ ( i @ ( triple @ A @ B @ C ) ) @ D )
=> ( ( i @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) )
= ( remove_pq @ ( i @ ( triple @ A @ B @ C ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',ax25) ).
thf(115,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)],[16]) ).
thf(39,axiom,
! [A: $i] :
( ( pi_find_min @ A )
<=> ? [B: $i] : ( pi_sharp_find_min @ ( i @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
thf(217,plain,
! [A: $i] :
( ( ( pi_find_min @ A )
=> ? [B: $i] : ( pi_sharp_find_min @ ( i @ A ) @ B ) )
& ( ? [B: $i] : ( pi_sharp_find_min @ ( i @ A ) @ B )
=> ( pi_find_min @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( ( contains_pq @ A @ B )
& ( issmallestelement_pq @ A @ B ) )
=> ( ( removemin_pq_eff @ A @ B )
= ( remove_pq @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
thf(308,plain,
! [A: $i,B: $i] :
( ( ( contains_pq @ A @ B )
& ( issmallestelement_pq @ A @ B ) )
=> ( ( removemin_pq_eff @ A @ B )
= ( remove_pq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( pi_sharp_remove @ A @ B )
<=> ( contains_pq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56) ).
thf(247,plain,
! [A: $i,B: $i] :
( ( ( pi_sharp_remove @ A @ B )
=> ( contains_pq @ A @ B ) )
& ( ( contains_pq @ A @ B )
=> ( pi_sharp_remove @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(49,axiom,
! [A: $i,B: $i] : ( check_cpq @ ( triple @ A @ create_slb @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
thf(269,plain,
! [A: $i,B: $i] : ( check_cpq @ ( triple @ A @ create_slb @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(14,axiom,
~ ( isnonempty_pq @ create_pq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(110,plain,
~ ( isnonempty_pq @ create_pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
thf(157,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)],[28]) ).
thf(55,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/sandbox2/benchmark/theBenchmark.p',ax45) ).
thf(289,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)],[55]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( strictly_less_than @ A @ B )
<=> ( ( less_than @ A @ B )
& ~ ( less_than @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(78,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)],[5]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( pi_sharp_find_min @ A @ B )
<=> ( ( contains_pq @ A @ B )
& ( issmallestelement_pq @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
thf(179,plain,
! [A: $i,B: $i] :
( ( ( pi_sharp_find_min @ A @ B )
=> ( ( contains_pq @ A @ B )
& ( issmallestelement_pq @ A @ B ) ) )
& ( ( ( contains_pq @ A @ B )
& ( issmallestelement_pq @ A @ B ) )
=> ( pi_sharp_find_min @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( contains_cpq @ ( triple @ A @ B @ C ) @ D )
<=> ( contains_slb @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
thf(321,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)],[63]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] : ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
thf(84,plain,
! [A: $i,B: $i,C: $i] : ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(53,axiom,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( i @ ( triple @ A @ create_slb @ C ) )
= ( i @ ( triple @ B @ create_slb @ D ) ) )
& ! [A: $i] :
( ! [B: $i,C: $i,D: $i,E: $i] :
( ( i @ ( triple @ B @ A @ D ) )
= ( i @ ( triple @ C @ A @ E ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( i @ ( triple @ B @ ( insert_slb @ A @ ( pair @ F @ G ) ) @ D ) )
= ( i @ ( triple @ C @ ( insert_slb @ A @ ( pair @ F @ G ) ) @ E ) ) ) ) )
=> ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( i @ ( triple @ A @ C @ D ) )
= ( i @ ( triple @ B @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big3_induction1) ).
thf(280,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( i @ ( triple @ A @ create_slb @ C ) )
= ( i @ ( triple @ B @ create_slb @ D ) ) )
& ! [A: $i] :
( ! [B: $i,C: $i,D: $i,E: $i] :
( ( i @ ( triple @ B @ A @ D ) )
= ( i @ ( triple @ C @ A @ E ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( i @ ( triple @ B @ ( insert_slb @ A @ ( pair @ F @ G ) ) @ D ) )
= ( i @ ( triple @ C @ ( insert_slb @ A @ ( pair @ F @ G ) ) @ E ) ) ) ) )
=> ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( i @ ( triple @ A @ C @ D ) )
= ( i @ ( triple @ B @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(20,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
thf(133,plain,
~ ( isnonempty_slb @ create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',ax47) ).
thf(265,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)],[48]) ).
thf(56,axiom,
! [A: $i] :
( ( phi @ A )
<=> ? [B: $i] :
( ( succ_cpq @ A @ B )
& ( ok @ B )
& ( check_cpq @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
thf(292,plain,
! [A: $i] :
( ( ( phi @ A )
=> ? [B: $i] :
( ( succ_cpq @ A @ B )
& ( ok @ B )
& ( check_cpq @ B ) ) )
& ( ? [B: $i] :
( ( succ_cpq @ A @ B )
& ( ok @ B )
& ( check_cpq @ B ) )
=> ( phi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( succ_cpq @ A @ B )
=> ( succ_cpq @ A @ ( insert_cpq @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).
thf(102,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)],[11]) ).
thf(29,axiom,
! [A: $i,B: $i] : ( isnonempty_pq @ ( insert_pq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
thf(160,plain,
! [A: $i,B: $i] : ( isnonempty_pq @ ( insert_pq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( contains_pq @ A @ B )
& ( issmallestelement_pq @ A @ B ) )
=> ( ( findmin_pq_eff @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).
thf(137,plain,
! [A: $i,B: $i] :
( ( ( contains_pq @ A @ B )
& ( issmallestelement_pq @ A @ B ) )
=> ( ( findmin_pq_eff @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(31,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/sandbox2/benchmark/theBenchmark.p',ax23) ).
thf(165,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)],[31]) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',ax43) ).
thf(252,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)],[44]) ).
thf(9,axiom,
! [A: $i] :
~ ( contains_slb @ create_slb @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
thf(97,plain,
! [A: $i] :
~ ( contains_slb @ create_slb @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( i @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) )
= ( insert_pq @ ( i @ ( triple @ A @ B @ C ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
thf(329,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( i @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) )
= ( insert_pq @ ( i @ ( triple @ A @ B @ C ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(62,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/sandbox2/benchmark/theBenchmark.p',ax48) ).
thf(317,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)],[62]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( issmallestelement_pq @ A @ B )
<=> ! [C: $i] :
( ( contains_pq @ A @ C )
=> ( less_than @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).
thf(188,plain,
! [A: $i,B: $i] :
( ( ( issmallestelement_pq @ A @ B )
=> ! [C: $i] :
( ( contains_pq @ A @ C )
=> ( less_than @ B @ C ) ) )
& ( ! [C: $i] :
( ( contains_pq @ A @ C )
=> ( less_than @ B @ C ) )
=> ( issmallestelement_pq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( contains_pq @ A @ B )
& ( issmallestelement_pq @ A @ B ) )
=> ( ( removemin_pq_res @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
thf(73,plain,
! [A: $i,B: $i] :
( ( ( contains_pq @ A @ B )
& ( issmallestelement_pq @ A @ B ) )
=> ( ( removemin_pq_res @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( contains_pq @ A @ B )
& ( issmallestelement_pq @ A @ B ) )
=> ( ( findmin_pq_res @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).
thf(128,plain,
! [A: $i,B: $i] :
( ( ( contains_pq @ A @ B )
& ( issmallestelement_pq @ A @ B ) )
=> ( ( findmin_pq_res @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
thf(105,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)],[12]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
= ( triple @ A @ create_slb @ bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
thf(311,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)],[60]) ).
thf(32,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/sandbox2/benchmark/theBenchmark.p',ax30) ).
thf(176,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)],[32]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( contains_pq @ A @ C )
& ( B != C ) )
=> ( ( remove_pq @ ( insert_pq @ A @ B ) @ C )
= ( insert_pq @ ( remove_pq @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax12) ).
thf(286,plain,
! [A: $i,B: $i,C: $i] :
( ( ( contains_pq @ A @ C )
& ( B != C ) )
=> ( ( remove_pq @ ( insert_pq @ A @ B ) @ C )
= ( insert_pq @ ( remove_pq @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',ax38) ).
thf(335,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)],[67]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',ax21) ).
thf(86,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)],[7]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( findmin_cpq_res @ ( triple @ A @ create_slb @ B ) )
= bottom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).
thf(274,plain,
! [A: $i,B: $i] :
( ( findmin_cpq_res @ ( triple @ A @ create_slb @ B ) )
= bottom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( succ_cpq @ A @ B )
=> ( succ_cpq @ A @ ( removemin_cpq_eff @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).
thf(76,plain,
! [A: $i,B: $i] :
( ( succ_cpq @ A @ B )
=> ( succ_cpq @ A @ ( removemin_cpq_eff @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(50,axiom,
! [A: $i] :
( ( removemin_cpq_eff @ A )
= ( remove_cpq @ ( findmin_cpq_eff @ A ) @ ( findmin_cpq_res @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
thf(271,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)],[50]) ).
thf(23,axiom,
! [A: $i] :
( ( update_slb @ create_slb @ A )
= create_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
thf(140,plain,
! [A: $i] :
( ( update_slb @ create_slb @ A )
= create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(13,axiom,
! [A: $i] : ( less_than @ bottom @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom_smallest) ).
thf(108,plain,
! [A: $i] : ( less_than @ bottom @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
! [A: $i] : ( succ_cpq @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
thf(135,plain,
! [A: $i] : ( succ_cpq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( pi_remove @ A @ B )
<=> ( pi_sharp_remove @ ( i @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
thf(299,plain,
! [A: $i,B: $i] :
( ( ( pi_remove @ A @ B )
=> ( pi_sharp_remove @ ( i @ A ) @ B ) )
& ( ( pi_sharp_remove @ ( i @ A ) @ B )
=> ( pi_remove @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(30,axiom,
! [A: $i,B: $i] :
~ ( pair_in_list @ create_slb @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
thf(162,plain,
! [A: $i,B: $i] :
~ ( pair_in_list @ create_slb @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(45,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/sandbox2/benchmark/theBenchmark.p',ax44) ).
thf(255,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)],[45]) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',ax29) ).
thf(112,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)],[15]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( ok @ ( triple @ A @ B @ bad ) )
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).
thf(314,plain,
! [A: $i,B: $i] :
~ ( ok @ ( triple @ A @ B @ bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( insert_pq @ ( insert_pq @ A @ B ) @ C )
= ( insert_pq @ ( insert_pq @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
thf(143,plain,
! [A: $i,B: $i,C: $i] :
( ( insert_pq @ ( insert_pq @ A @ B ) @ C )
= ( insert_pq @ ( insert_pq @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',ax49) ).
thf(304,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)],[58]) ).
thf(46,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/sandbox2/benchmark/theBenchmark.p',ax51) ).
thf(258,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)],[46]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( contains_pq @ ( insert_pq @ A @ B ) @ C )
<=> ( ( contains_pq @ A @ C )
| ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9) ).
thf(119,plain,
! [A: $i,B: $i,C: $i] :
( ( ( contains_pq @ ( insert_pq @ A @ B ) @ C )
=> ( ( contains_pq @ A @ C )
| ( B = C ) ) )
& ( ( ( contains_pq @ A @ C )
| ( B = C ) )
=> ( contains_pq @ ( insert_pq @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
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/sandbox2/benchmark/theBenchmark.p',ax42) ).
thf(214,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(27,axiom,
! [A: $i,B: $i] :
( ( pi_sharp_removemin @ A @ B )
<=> ( ( contains_pq @ A @ B )
& ( issmallestelement_pq @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
thf(151,plain,
! [A: $i,B: $i] :
( ( ( pi_sharp_removemin @ A @ B )
=> ( ( contains_pq @ A @ B )
& ( issmallestelement_pq @ A @ B ) ) )
& ( ( ( contains_pq @ A @ B )
& ( issmallestelement_pq @ A @ B ) )
=> ( pi_sharp_removemin @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(47,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/sandbox2/benchmark/theBenchmark.p',ax37) ).
thf(262,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)],[47]) ).
thf(25,axiom,
! [A: $i] :
~ ( contains_pq @ create_pq @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).
thf(146,plain,
! [A: $i] :
~ ( contains_pq @ create_pq @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( succ_cpq @ A @ B )
=> ( succ_cpq @ A @ ( remove_cpq @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).
thf(326,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)],[64]) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',ax27) ).
thf(195,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)],[36]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( remove_pq @ ( insert_pq @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11) ).
thf(239,plain,
! [A: $i,B: $i] :
( ( remove_pq @ ( insert_pq @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(42,axiom,
! [A: $i] :
( ( pi_removemin @ A )
<=> ? [B: $i] : ( pi_sharp_find_min @ ( i @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).
thf(242,plain,
! [A: $i] :
( ( ( pi_removemin @ A )
=> ? [B: $i] : ( pi_sharp_find_min @ ( i @ A ) @ B ) )
& ( ? [B: $i] : ( pi_sharp_find_min @ ( i @ A ) @ B )
=> ( pi_removemin @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( i @ ( triple @ A @ create_slb @ B ) )
= create_pq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
thf(332,plain,
! [A: $i,B: $i] :
( ( i @ ( triple @ A @ create_slb @ B ) )
= create_pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
thf(131,plain,
! [A: $i,B: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( pi_remove @ ( triple @ A @ B @ C ) @ D )
=> ( ( phi @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) )
=> ( ( pi_sharp_remove @ ( i @ ( triple @ A @ B @ C ) ) @ D )
& ( ( i @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) )
= ( remove_pq @ ( i @ ( triple @ A @ B @ C ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co3) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( pi_remove @ ( triple @ A @ B @ C ) @ D )
=> ( ( phi @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) )
=> ( ( pi_sharp_remove @ ( i @ ( triple @ A @ B @ C ) ) @ D )
& ( ( i @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) )
= ( remove_pq @ ( i @ ( triple @ A @ B @ C ) ) @ D ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(68,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( pi_remove @ ( triple @ A @ B @ C ) @ D )
=> ( ( phi @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) )
=> ( ( pi_sharp_remove @ ( i @ ( triple @ A @ B @ C ) ) @ D )
& ( ( i @ ( remove_cpq @ ( triple @ A @ B @ C ) @ D ) )
= ( remove_pq @ ( i @ ( triple @ A @ B @ C ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ok @ ( triple @ A @ B @ C ) )
=> ( C = bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
thf(277,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ok @ ( triple @ A @ B @ C ) )
=> ( C = bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(40,axiom,
( ( ! [A: $i,B: $i,C: $i] :
( ( contains_cpq @ ( triple @ A @ create_slb @ B ) @ C )
<=> ( contains_pq @ ( i @ ( triple @ A @ create_slb @ B ) ) @ C ) )
& ! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( contains_cpq @ ( triple @ B @ A @ C ) @ D )
<=> ( contains_pq @ ( i @ ( triple @ B @ A @ C ) ) @ D ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( contains_cpq @ ( triple @ B @ ( insert_slb @ A @ ( pair @ D @ E ) ) @ C ) @ F )
<=> ( contains_pq @ ( i @ ( triple @ B @ ( insert_slb @ A @ ( pair @ D @ E ) ) @ C ) ) @ F ) ) ) )
=> ! [A: $i,B: $i,C: $i,D: $i] :
( ( contains_cpq @ ( triple @ A @ B @ C ) @ D )
<=> ( contains_pq @ ( i @ ( triple @ A @ B @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big3_induction3) ).
thf(222,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( contains_cpq @ ( triple @ A @ create_slb @ B ) @ C )
=> ( contains_pq @ ( i @ ( triple @ A @ create_slb @ B ) ) @ C ) )
& ( ( contains_pq @ ( i @ ( triple @ A @ create_slb @ B ) ) @ C )
=> ( contains_cpq @ ( triple @ A @ create_slb @ B ) @ C ) ) )
& ! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( contains_cpq @ ( triple @ B @ A @ C ) @ D )
=> ( contains_pq @ ( i @ ( triple @ B @ A @ C ) ) @ D ) )
& ( ( contains_pq @ ( i @ ( triple @ B @ A @ C ) ) @ D )
=> ( contains_cpq @ ( triple @ B @ A @ C ) @ D ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( contains_cpq @ ( triple @ B @ ( insert_slb @ A @ ( pair @ D @ E ) ) @ C ) @ F )
=> ( contains_pq @ ( i @ ( triple @ B @ ( insert_slb @ A @ ( pair @ D @ E ) ) @ C ) ) @ F ) )
& ( ( contains_pq @ ( i @ ( triple @ B @ ( insert_slb @ A @ ( pair @ D @ E ) ) @ C ) ) @ F )
=> ( contains_cpq @ ( triple @ B @ ( insert_slb @ A @ ( pair @ D @ E ) ) @ C ) @ F ) ) ) ) )
=> ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( contains_cpq @ ( triple @ A @ B @ C ) @ D )
=> ( contains_pq @ ( i @ ( triple @ A @ B @ C ) ) @ D ) )
& ( ( contains_pq @ ( i @ ( triple @ A @ B @ C ) ) @ D )
=> ( contains_cpq @ ( triple @ A @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( less_than @ A @ B )
& ( less_than @ B @ C ) )
=> ( less_than @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(100,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)],[10]) ).
thf(38253,plain,
$false,
inference(cvc4,[status(thm)],[185,149,95,199,115,217,308,247,269,110,157,289,78,179,321,84,280,133,265,292,102,160,137,165,252,97,329,317,188,73,128,105,311,176,286,335,86,274,76,271,140,108,135,299,162,255,112,314,143,304,258,119,214,151,262,146,326,195,239,242,332,131,68,277,222,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV416+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 19 02:30:59 EDT 2023
% 0.14/0.35 % CPUTime :
% 1.06/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.46/1.12 % [INFO] Parsing done (170ms).
% 1.46/1.13 % [INFO] Running in sequential loop mode.
% 2.11/1.36 % [INFO] eprover registered as external prover.
% 2.11/1.37 % [INFO] cvc4 registered as external prover.
% 2.11/1.37 % [INFO] Scanning for conjecture ...
% 2.38/1.44 % [INFO] Found a conjecture and 65 axioms. Running axiom selection ...
% 2.45/1.51 % [INFO] Axiom selection finished. Selected 65 axioms (removed 0 axioms).
% 2.81/1.59 % [INFO] Problem is first-order (TPTP FOF).
% 2.81/1.60 % [INFO] Type checking passed.
% 2.81/1.60 % [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 ...
% 109.15/20.74 % External prover 'cvc4' found a proof!
% 109.15/20.74 % [INFO] Killing All external provers ...
% 109.15/20.74 % Time passed: 20169ms (effective reasoning time: 19603ms)
% 109.15/20.74 % 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)>
% 109.15/20.74 % Axioms used in derivation (65): ax13, ax39, ax59, ax43, ax19, ax14, ax12, ax53, ax20, ax52, ax24, ax56, ax47, ax41, stricly_smaller_definition, ax31, ax28, ax9, ax17, ax6, ax45, ax40, ax35, ax58, ax27, ax8, ax51, ax48, ax21, ax62, ax10, ax55, ax32, ax16, big3_induction3, ax7, ax38, ax44, reflexivity, ax33, ax26, ax61, ax11, bottom_smallest, ax50, ax22, ax15, ax37, totality, big3_induction2, ax54, ax49, ax46, ax34, ax23, ax25, ax60, big3_induction1, transitivity, ax57, ax30, ax42, ax18, ax36, ax29
% 109.15/20.74 % No. of inferences in proof: 134
% 109.15/20.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 20169 ms resp. 19603 ms w/o parsing
% 109.15/20.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 109.15/20.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------