TSTP Solution File: SWV398+1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SWV398+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 : Tue May 21 05:45:22 EDT 2024
% Result : Theorem 126.03s 22.22s
% Output : Refutation 126.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 76
% Syntax : Number of formulae : 439 ( 211 unt; 32 typ; 0 def)
% Number of atoms : 818 ( 259 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 3865 ( 255 ~; 172 |; 45 &;3317 @)
% ( 8 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 7 con; 0-3 aty)
% Number of variables : 1072 ( 0 ^1058 !; 14 ?;1072 :)
% Comments :
%------------------------------------------------------------------------------
thf(check_cpq_type,type,
check_cpq: $i > $o ).
thf(triple_type,type,
triple: $i > $i > $i > $i ).
thf(findmin_cpq_eff_type,type,
findmin_cpq_eff: $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(update_slb_type,type,
update_slb: $i > $i > $i ).
thf(pair_in_list_type,type,
pair_in_list: $i > $i > $i > $o ).
thf(lookup_slb_type,type,
lookup_slb: $i > $i > $i ).
thf(remove_cpq_type,type,
remove_cpq: $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(insert_pqp_type,type,
insert_pqp: $i > $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(ok_type,type,
ok: $i > $o ).
thf(contains_cpq_type,type,
contains_cpq: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i > $i > $i ).
thf(sk5_type,type,
sk5: $i > $i > $i ).
thf(7,axiom,
! [A: $i] : ( less_than @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(68,plain,
! [A: $i] : ( less_than @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(69,plain,
! [A: $i] : ( less_than @ A @ A ),
inference(cnf,[status(esa)],[68]) ).
thf(39,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(169,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)],[39]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
= ( triple @ A @ create_slb @ bad ) ),
inference(cnf,[status(esa)],[169]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
= ( triple @ A @ create_slb @ bad ) ),
inference(lifteq,[status(thm)],[170]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ok @ ( triple @ A @ B @ bad ) )
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
thf(172,plain,
! [A: $i,B: $i] :
~ ( ok @ ( triple @ A @ B @ bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(173,plain,
~ ? [A: $i,B: $i] : ( ok @ ( triple @ A @ B @ bad ) ),
inference(miniscope,[status(thm)],[172]) ).
thf(174,plain,
! [B: $i,A: $i] :
~ ( ok @ ( triple @ A @ B @ bad ) ),
inference(cnf,[status(esa)],[173]) ).
thf(291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( ok @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ D @ bad ) ) ),
inference(paramod_ordered,[status(thm)],[171,174]) ).
thf(292,plain,
! [B: $i,A: $i] :
~ ( ok @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ),
inference(pattern_uni,[status(thm)],[291:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( create_slb ))]]) ).
thf(350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,292]) ).
thf(351,plain,
! [B: $i,A: $i] :
~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[350:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,351]) ).
thf(400,plain,
! [B: $i,A: $i] :
~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[399:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(1334,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,400]) ).
thf(1335,plain,
! [B: $i,A: $i] :
~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1334:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(1660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,1335]) ).
thf(1661,plain,
! [B: $i,A: $i] :
~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1660:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(2184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,1661]) ).
thf(2185,plain,
! [B: $i,A: $i] :
~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2184:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(2411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,2185]) ).
thf(2412,plain,
! [B: $i,A: $i] :
~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2411:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(16,axiom,
! [A: $i] : ( succ_cpq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(92,plain,
! [A: $i] : ( succ_cpq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(93,plain,
! [A: $i] : ( succ_cpq @ A @ A ),
inference(cnf,[status(esa)],[92]) ).
thf(27,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(132,plain,
! [A: $i,B: $i] :
( ( succ_cpq @ A @ B )
=> ( succ_cpq @ A @ ( findmin_cpq_eff @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ~ ( succ_cpq @ A @ B )
| ( succ_cpq @ A @ ( findmin_cpq_eff @ B ) ) ),
inference(cnf,[status(esa)],[132]) ).
thf(11005,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( findmin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ A )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[93,133]) ).
thf(11006,plain,
! [A: $i] : ( succ_cpq @ A @ ( findmin_cpq_eff @ A ) ),
inference(pattern_uni,[status(thm)],[11005:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
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(49,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(50,plain,
! [B: $i,A: $i] :
( ~ ( succ_cpq @ A @ B )
| ( succ_cpq @ A @ ( removemin_cpq_eff @ B ) ) ),
inference(cnf,[status(esa)],[49]) ).
thf(11144,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( findmin_cpq_eff @ A ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11006,50]) ).
thf(11145,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( findmin_cpq_eff @ A ) ) ),
inference(pattern_uni,[status(thm)],[11144:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( findmin_cpq_eff @ D ))]]) ).
thf(11164,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( findmin_cpq_eff @ A ) ) ),
inference(simp,[status(thm)],[11145]) ).
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(57,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(58,plain,
! [C: $i,B: $i,A: $i] : ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(15,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(90,plain,
~ ( isnonempty_slb @ create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(91,plain,
~ ( isnonempty_slb @ create_slb ),
inference(polarity_switch,[status(thm)],[90]) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) )
!= ( isnonempty_slb @ create_slb ) ),
inference(paramod_ordered,[status(thm)],[58,91]) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( insert_slb @ A @ ( pair @ B @ C ) )
!= create_slb ),
inference(simp,[status(thm)],[233]) ).
thf(34,axiom,
! [A: $i,B: $i] : ( check_cpq @ ( triple @ A @ create_slb @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
thf(154,plain,
! [A: $i,B: $i] : ( check_cpq @ ( triple @ A @ create_slb @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(155,plain,
! [B: $i,A: $i] : ( check_cpq @ ( triple @ A @ create_slb @ B ) ),
inference(cnf,[status(esa)],[154]) ).
thf(312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( check_cpq @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,155]) ).
thf(313,plain,
! [B: $i,A: $i] : ( check_cpq @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ),
inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,313]) ).
thf(358,plain,
! [B: $i,A: $i] : ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,358]) ).
thf(408,plain,
! [B: $i,A: $i] : ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[407:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(21,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(105,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)],[21]) ).
thf(106,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 ) ) ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( pair_in_list @ A @ C @ E )
| ( ( B = C )
& ( D = E ) ) )
=> ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ) ),
inference(miniscope,[status(thm)],[105]) ).
thf(110,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
| ( pair_in_list @ A @ C @ E )
| ( B = C ) ),
inference(cnf,[status(esa)],[106]) ).
thf(115,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
| ( pair_in_list @ A @ C @ E ) ),
inference(lifteq,[status(thm)],[110]) ).
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(75,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(76,plain,
! [A: $i,B: $i] :
( ( succ_cpq @ A @ B )
=> ! [C: $i] : ( succ_cpq @ A @ ( insert_cpq @ B @ C ) ) ),
inference(miniscope,[status(thm)],[75]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( succ_cpq @ A @ B )
| ( succ_cpq @ A @ ( insert_cpq @ B @ C ) ) ),
inference(cnf,[status(esa)],[76]) ).
thf(1761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( insert_cpq @ C @ D ) )
| ( ( succ_cpq @ A @ A )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[93,77]) ).
thf(1762,plain,
! [B: $i,A: $i] : ( succ_cpq @ A @ ( insert_cpq @ A @ B ) ),
inference(pattern_uni,[status(thm)],[1761:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(1786,plain,
! [B: $i,A: $i] : ( succ_cpq @ A @ ( insert_cpq @ A @ B ) ),
inference(simp,[status(thm)],[1762]) ).
thf(1800,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ C @ ( insert_cpq @ D @ E ) )
| ( ( succ_cpq @ A @ ( insert_cpq @ A @ B ) )
!= ( succ_cpq @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1786,77]) ).
thf(1801,plain,
! [C: $i,B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( insert_cpq @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[1800:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( insert_cpq @ F @ G ))]]) ).
thf(1808,plain,
! [C: $i,B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( insert_cpq @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[1801]) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ A )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[93,50]) ).
thf(202,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ A ) ),
inference(pattern_uni,[status(thm)],[201:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(203,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ A ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[202,50]) ).
thf(204,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ),
inference(pattern_uni,[status(thm)],[203:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( removemin_cpq_eff @ D ))]]) ).
thf(205,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ),
inference(simp,[status(thm)],[204]) ).
thf(216,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[205,50]) ).
thf(217,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[216:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ E ) ))]]) ).
thf(218,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ),
inference(simp,[status(thm)],[217]) ).
thf(220,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[218,50]) ).
thf(221,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[220:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ F ) ) ))]]) ).
thf(222,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[222,50]) ).
thf(231,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[230:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ G ) ) ) ))]]) ).
thf(232,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(245,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[232,50]) ).
thf(246,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[245:[bind(A,$thf( H )),bind(B,$thf( H )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ H ) ) ) ) ))]]) ).
thf(247,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(1765,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( insert_cpq @ C @ D ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[205,77]) ).
thf(1766,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[1765:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ F ) )),bind(D,$thf( D ))]]) ).
thf(1788,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) ),
inference(simp,[status(thm)],[1766]) ).
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(51,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(52,plain,
( ! [A: $i,B: $i] :
( ( strictly_less_than @ A @ B )
=> ( ( less_than @ A @ B )
& ~ ( less_than @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ( ( less_than @ A @ B )
& ~ ( less_than @ B @ A ) )
=> ( strictly_less_than @ A @ B ) ) ),
inference(miniscope,[status(thm)],[51]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( less_than @ A @ B )
| ( less_than @ B @ A )
| ( strictly_less_than @ A @ B ) ),
inference(cnf,[status(esa)],[52]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ~ ( less_than @ A @ B )
| ( less_than @ B @ A )
| ( strictly_less_than @ A @ B ) ),
inference(simp,[status(thm)],[53]) ).
thf(11305,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( findmin_cpq_eff @ A ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11164,50]) ).
thf(11306,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( findmin_cpq_eff @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[11305:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( removemin_cpq_eff @ ( findmin_cpq_eff @ E ) ))]]) ).
thf(11335,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( findmin_cpq_eff @ A ) ) ) ),
inference(simp,[status(thm)],[11306]) ).
thf(2868,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ) ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,2412]) ).
thf(2869,plain,
! [B: $i,A: $i] :
~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2868:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(43,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',l26_li4142) ).
thf(184,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)],[43]) ).
thf(35,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(156,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)],[35]) ).
thf(157,plain,
! [A: $i] :
( ( removemin_cpq_eff @ A )
= ( remove_cpq @ ( findmin_cpq_eff @ A ) @ ( findmin_cpq_res @ A ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(158,plain,
! [A: $i] :
( ( remove_cpq @ ( findmin_cpq_eff @ A ) @ ( findmin_cpq_res @ A ) )
= ( removemin_cpq_eff @ A ) ),
inference(lifteq,[status(thm)],[157]) ).
thf(25,axiom,
! [A: $i] :
( ( removemin_cpq_res @ A )
= ( findmin_cpq_res @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
thf(125,plain,
! [A: $i] :
( ( removemin_cpq_res @ A )
= ( findmin_cpq_res @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(126,plain,
! [A: $i] :
( ( removemin_cpq_res @ A )
= ( findmin_cpq_res @ A ) ),
inference(cnf,[status(esa)],[125]) ).
thf(127,plain,
! [A: $i] :
( ( findmin_cpq_res @ A )
= ( removemin_cpq_res @ A ) ),
inference(lifteq,[status(thm)],[126]) ).
thf(251,plain,
! [A: $i] :
( ( remove_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_res @ A ) )
= ( removemin_cpq_eff @ A ) ),
inference(rewrite,[status(thm)],[158,127]) ).
thf(24,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(122,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)],[24]) ).
thf(123,plain,
! [A: $i,B: $i] :
( ( succ_cpq @ A @ B )
=> ! [C: $i] : ( succ_cpq @ A @ ( remove_cpq @ B @ C ) ) ),
inference(miniscope,[status(thm)],[122]) ).
thf(124,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( succ_cpq @ A @ B )
| ( succ_cpq @ A @ ( remove_cpq @ B @ C ) ) ),
inference(cnf,[status(esa)],[123]) ).
thf(10362,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( remove_cpq @ C @ D ) )
| ( ( succ_cpq @ A @ A )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[93,124]) ).
thf(10363,plain,
! [B: $i,A: $i] : ( succ_cpq @ A @ ( remove_cpq @ A @ B ) ),
inference(pattern_uni,[status(thm)],[10362:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(10459,plain,
! [B: $i,A: $i] : ( succ_cpq @ A @ ( remove_cpq @ A @ B ) ),
inference(simp,[status(thm)],[10363]) ).
thf(10470,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ A ) )
| ( ( remove_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_res @ A ) )
!= ( remove_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[251,10459]) ).
thf(10471,plain,
! [A: $i] : ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_eff @ A ) ),
inference(pattern_uni,[status(thm)],[10470:[bind(A,$thf( E )),bind(B,$thf( findmin_cpq_eff @ E )),bind(C,$thf( removemin_cpq_res @ E ))]]) ).
thf(10486,plain,
! [A: $i] : ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_eff @ A ) ),
inference(simp,[status(thm)],[10471]) ).
thf(314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
= ( triple @ C @ create_slb @ bad ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,171]) ).
thf(315,plain,
! [B: $i,A: $i] :
( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
= ( triple @ A @ create_slb @ bad ) ),
inference(pattern_uni,[status(thm)],[314:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(3874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) )
= ( triple @ C @ create_slb @ bad ) )
| ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
!= ( findmin_cpq_eff @ ( triple @ C @ create_slb @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[171,315]) ).
thf(3875,plain,
! [A: $i] :
( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) )
= ( triple @ A @ create_slb @ bad ) ),
inference(pattern_uni,[status(thm)],[3874:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1374,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,408]) ).
thf(1375,plain,
! [B: $i,A: $i] : ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1374:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(1708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,1375]) ).
thf(1709,plain,
! [B: $i,A: $i] : ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1708:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ~ ( check_cpq @ ( triple @ A @ B @ C ) )
=> ~ ( check_cpq @ ( findmin_cpq_eff @ ( triple @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l24_co) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ~ ( check_cpq @ ( triple @ A @ B @ C ) )
=> ~ ( check_cpq @ ( findmin_cpq_eff @ ( triple @ A @ B @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(46,plain,
~ ! [A: $i,B: $i,C: $i] :
( ~ ( check_cpq @ ( triple @ A @ B @ C ) )
=> ~ ( check_cpq @ ( findmin_cpq_eff @ ( triple @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,plain,
~ ( check_cpq @ ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(cnf,[status(esa)],[46]) ).
thf(2205,plain,
! [B: $i,A: $i] :
( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) )
!= ( check_cpq @ ( triple @ sk1 @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1709,48]) ).
thf(2246,plain,
! [B: $i,A: $i] :
( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(simp,[status(thm)],[2205]) ).
thf(6945,plain,
! [C: $i,B: $i,A: $i] :
( ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) ) ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) )
| ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) )
!= ( findmin_cpq_eff @ ( triple @ B @ create_slb @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[3875,2246]) ).
thf(6946,plain,
! [A: $i] :
( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) ) ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[6945:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( bad ))]]) ).
thf(10121,plain,
! [A: $i] :
( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(rewrite,[status(thm)],[6946,3875]) ).
thf(1349,plain,
! [B: $i,A: $i] :
( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) )
!= ( check_cpq @ ( triple @ sk1 @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[408,48]) ).
thf(1379,plain,
! [B: $i,A: $i] :
( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(simp,[status(thm)],[1349]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( findmin_cpq_res @ ( triple @ A @ create_slb @ B ) )
= bottom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
thf(159,plain,
! [A: $i,B: $i] :
( ( findmin_cpq_res @ ( triple @ A @ create_slb @ B ) )
= bottom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( findmin_cpq_res @ ( triple @ A @ create_slb @ B ) )
= bottom ),
inference(cnf,[status(esa)],[159]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( findmin_cpq_res @ ( triple @ A @ create_slb @ B ) )
= bottom ),
inference(lifteq,[status(thm)],[160]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( removemin_cpq_res @ ( triple @ A @ create_slb @ B ) )
= bottom ),
inference(rewrite,[status(thm)],[161,127]) ).
thf(293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
= bottom )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,219]) ).
thf(294,plain,
! [B: $i,A: $i] :
( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
= bottom ),
inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(391,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) )
= bottom )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,294]) ).
thf(392,plain,
! [B: $i,A: $i] :
( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) )
= bottom ),
inference(pattern_uni,[status(thm)],[391:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(1292,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) )
= bottom )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,392]) ).
thf(1293,plain,
! [B: $i,A: $i] :
( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) )
= bottom ),
inference(pattern_uni,[status(thm)],[1292:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(1610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) )
= bottom )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,1293]) ).
thf(1611,plain,
! [B: $i,A: $i] :
( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) )
= bottom ),
inference(pattern_uni,[status(thm)],[1610:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(1889,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) )
= bottom )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,1611]) ).
thf(1890,plain,
! [B: $i,A: $i] :
( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) )
= bottom ),
inference(pattern_uni,[status(thm)],[1889:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(47,plain,
check_cpq @ ( findmin_cpq_eff @ ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(cnf,[status(esa)],[46]) ).
thf(45,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(194,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)],[45]) ).
thf(195,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( strictly_less_than @ D @ E )
| ~ ( check_cpq @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) ) ),
inference(cnf,[status(esa)],[194]) ).
thf(226,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( strictly_less_than @ D @ E )
| ( ( check_cpq @ ( findmin_cpq_eff @ ( triple @ sk1 @ sk2 @ sk3 ) ) )
!= ( check_cpq @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[47,195]) ).
thf(228,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( strictly_less_than @ D @ E )
| ( ( findmin_cpq_eff @ ( triple @ sk1 @ sk2 @ sk3 ) )
!= ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) ) ),
inference(simp,[status(thm)],[226]) ).
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(78,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(1678,plain,
! [B: $i,A: $i] :
( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) )
!= ( check_cpq @ ( triple @ sk1 @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1375,48]) ).
thf(1714,plain,
! [B: $i,A: $i] :
( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(simp,[status(thm)],[1678]) ).
thf(42,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(179,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)],[42]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( check_cpq @ ( triple @ A @ create_slb @ B ) )
!= ( check_cpq @ ( triple @ sk1 @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[155,48]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( triple @ A @ create_slb @ B )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(simp,[status(thm)],[210]) ).
thf(2104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
| ( ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) )
!= ( succ_cpq @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1788,50]) ).
thf(2105,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[2104:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( H )),bind(D,$thf( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ H ) ) @ F ))]]) ).
thf(2122,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) ) ),
inference(simp,[status(thm)],[2105]) ).
thf(23,axiom,
! [A: $i] :
( ( update_slb @ create_slb @ A )
= create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(119,plain,
! [A: $i] :
( ( update_slb @ create_slb @ A )
= create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(120,plain,
! [A: $i] :
( ( update_slb @ create_slb @ A )
= create_slb ),
inference(cnf,[status(esa)],[119]) ).
thf(121,plain,
! [A: $i] :
( ( update_slb @ create_slb @ A )
= create_slb ),
inference(lifteq,[status(thm)],[120]) ).
thf(32,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(147,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)],[32]) ).
thf(1781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( insert_cpq @ C @ D ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[222,77]) ).
thf(1782,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[1781:[bind(A,$thf( H )),bind(B,$thf( H )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ H ) ) ) )),bind(D,$thf( D ))]]) ).
thf(1796,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) ) ) @ A ) ),
inference(simp,[status(thm)],[1782]) ).
thf(2240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,1709]) ).
thf(2241,plain,
! [B: $i,A: $i] : ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2240:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(2798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,2241]) ).
thf(2799,plain,
! [B: $i,A: $i] : ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2798:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(22,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(116,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)],[22]) ).
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(73,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(74,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_than @ A @ B )
| ~ ( less_than @ B @ C )
| ( less_than @ A @ C ) ),
inference(cnf,[status(esa)],[73]) ).
thf(2344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
| ( ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) ) )
!= ( succ_cpq @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[2122,50]) ).
thf(2345,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2344:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( I )),bind(D,$thf( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ I ) ) @ G ) ))]]) ).
thf(2367,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) ) ) ),
inference(simp,[status(thm)],[2345]) ).
thf(10999,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( findmin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ A ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[202,133]) ).
thf(11000,plain,
! [A: $i] : ( succ_cpq @ A @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ),
inference(pattern_uni,[status(thm)],[10999:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( removemin_cpq_eff @ D ))]]) ).
thf(11131,plain,
! [A: $i] : ( succ_cpq @ A @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ),
inference(simp,[status(thm)],[11000]) ).
thf(11181,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( findmin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ A ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11131,133]) ).
thf(11182,plain,
! [A: $i] : ( succ_cpq @ A @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[11181:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( findmin_cpq_eff @ ( removemin_cpq_eff @ E ) ))]]) ).
thf(11218,plain,
! [A: $i] : ( succ_cpq @ A @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ),
inference(simp,[status(thm)],[11182]) ).
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(86,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(87,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B != C )
& ( contains_slb @ A @ C ) )
=> ! [D: $i] :
( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( remove_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[86]) ).
thf(88,plain,
! [D: $i,C: $i,B: $i,A: $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(cnf,[status(esa)],[87]) ).
thf(89,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( remove_slb @ A @ C ) @ ( pair @ B @ D ) ) )
| ~ ( contains_slb @ A @ C ) ),
inference(lifteq,[status(thm)],[88]) ).
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(83,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(84,plain,
! [D: $i,C: $i,B: $i,A: $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(cnf,[status(esa)],[83]) ).
thf(85,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) )
| ~ ( strictly_less_than @ D @ C ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(19,axiom,
! [A: $i,B: $i] :
~ ( pair_in_list @ create_slb @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(100,plain,
! [A: $i,B: $i] :
~ ( pair_in_list @ create_slb @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(101,plain,
~ ? [A: $i,B: $i] : ( pair_in_list @ create_slb @ A @ B ),
inference(miniscope,[status(thm)],[100]) ).
thf(102,plain,
! [B: $i,A: $i] :
~ ( pair_in_list @ create_slb @ A @ B ),
inference(cnf,[status(esa)],[101]) ).
thf(8,axiom,
! [A: $i] :
~ ( contains_slb @ create_slb @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
thf(70,plain,
! [A: $i] :
~ ( contains_slb @ create_slb @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(29,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(137,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)],[29]) ).
thf(38,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(165,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)],[38]) ).
thf(227,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( strictly_less_than @ F @ G )
| ( ( check_cpq @ ( triple @ A @ create_slb @ B ) )
!= ( check_cpq @ ( triple @ C @ ( insert_slb @ D @ ( pair @ F @ G ) ) @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,195]) ).
thf(229,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( strictly_less_than @ F @ G )
| ( ( triple @ A @ create_slb @ B )
!= ( triple @ C @ ( insert_slb @ D @ ( pair @ F @ G ) ) @ E ) ) ),
inference(simp,[status(thm)],[227]) ).
thf(196,plain,
( ( check_cpq @ ( findmin_cpq_eff @ ( triple @ sk1 @ sk2 @ sk3 ) ) )
!= ( check_cpq @ ( triple @ sk1 @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[47,48]) ).
thf(197,plain,
( ( findmin_cpq_eff @ ( triple @ sk1 @ sk2 @ sk3 ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(simp,[status(thm)],[196]) ).
thf(18,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(97,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)],[18]) ).
thf(10504,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_eff @ A ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10486,50]) ).
thf(10505,plain,
! [A: $i] : ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ),
inference(pattern_uni,[status(thm)],[10504:[bind(A,$thf( E )),bind(B,$thf( findmin_cpq_eff @ E )),bind(C,$thf( removemin_cpq_eff @ E ))]]) ).
thf(10532,plain,
! [A: $i] : ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ),
inference(simp,[status(thm)],[10505]) ).
thf(11035,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( findmin_cpq_eff @ C ) )
| ( ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10532,133]) ).
thf(11036,plain,
! [A: $i] : ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[11035:[bind(A,$thf( F )),bind(B,$thf( findmin_cpq_eff @ F )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ F ) ))]]) ).
thf(11101,plain,
! [A: $i] : ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ),
inference(simp,[status(thm)],[11036]) ).
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(59,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(60,plain,
( ! [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
=> ( ( contains_slb @ A @ C )
| ( B = C ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( contains_slb @ A @ C )
| ( B = C ) )
=> ! [D: $i] : ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) ) ),
inference(miniscope,[status(thm)],[59]) ).
thf(63,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
| ( contains_slb @ A @ C )
| ( B = C ) ),
inference(cnf,[status(esa)],[60]) ).
thf(67,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
| ( contains_slb @ A @ C ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( sk2 != create_slb )
| ( B != sk3 ) ),
inference(simp,[status(thm)],[211]) ).
thf(213,plain,
sk2 != create_slb,
inference(simp,[status(thm)],[212]) ).
thf(726,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
| ( contains_slb @ A @ C )
| ( B != create_slb )
| ( C != sk2 ) ),
inference(paramod_ordered,[status(thm)],[67,213]) ).
thf(727,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ sk2 )
| ( contains_slb @ A @ sk2 )
| ( B != create_slb ) ),
inference(pattern_uni,[status(thm)],[726:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(1089,plain,
! [B: $i,A: $i] :
( ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ create_slb @ B ) ) @ sk2 )
| ( contains_slb @ A @ sk2 ) ),
inference(simp,[status(thm)],[727]) ).
thf(11003,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( findmin_cpq_eff @ C ) )
| ( ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_eff @ A ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10486,133]) ).
thf(11004,plain,
! [A: $i] : ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ),
inference(pattern_uni,[status(thm)],[11003:[bind(A,$thf( E )),bind(B,$thf( findmin_cpq_eff @ E )),bind(C,$thf( removemin_cpq_eff @ E ))]]) ).
thf(11133,plain,
! [A: $i] : ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ),
inference(simp,[status(thm)],[11004]) ).
thf(1777,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( insert_cpq @ C @ D ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[218,77]) ).
thf(1778,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[1777:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ G ) ) )),bind(D,$thf( D ))]]) ).
thf(1794,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) ) @ A ) ),
inference(simp,[status(thm)],[1778]) ).
thf(11187,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ A ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11131,50]) ).
thf(11188,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[11187:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( findmin_cpq_eff @ ( removemin_cpq_eff @ E ) ))]]) ).
thf(11221,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ),
inference(simp,[status(thm)],[11188]) ).
thf(11138,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( findmin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( findmin_cpq_eff @ A ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11006,133]) ).
thf(11139,plain,
! [A: $i] : ( succ_cpq @ A @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ A ) ) ),
inference(pattern_uni,[status(thm)],[11138:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( findmin_cpq_eff @ D ))]]) ).
thf(11161,plain,
! [A: $i] : ( succ_cpq @ A @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ A ) ) ),
inference(simp,[status(thm)],[11139]) ).
thf(11241,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ A ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11161,50]) ).
thf(11242,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[11241:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( findmin_cpq_eff @ ( findmin_cpq_eff @ E ) ))]]) ).
thf(11278,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ A ) ) ) ),
inference(simp,[status(thm)],[11242]) ).
thf(28,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(134,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)],[28]) ).
thf(135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( insert_cpq @ ( triple @ A @ B @ C ) @ D )
= ( triple @ ( insert_pqp @ A @ D ) @ ( insert_slb @ B @ ( pair @ D @ bottom ) ) @ C ) ),
inference(cnf,[status(esa)],[134]) ).
thf(136,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( triple @ ( insert_pqp @ A @ D ) @ ( insert_slb @ B @ ( pair @ D @ bottom ) ) @ C )
= ( insert_cpq @ ( triple @ A @ B @ C ) @ D ) ),
inference(lifteq,[status(thm)],[135]) ).
thf(11444,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( ok @ ( insert_cpq @ ( triple @ A @ B @ C ) @ D ) )
| ( ( triple @ ( insert_pqp @ A @ D ) @ ( insert_slb @ B @ ( pair @ D @ bottom ) ) @ C )
!= ( triple @ E @ F @ bad ) ) ),
inference(paramod_ordered,[status(thm)],[136,174]) ).
thf(11445,plain,
! [C: $i,B: $i,A: $i] :
~ ( ok @ ( insert_cpq @ ( triple @ A @ B @ bad ) @ C ) ),
inference(pattern_uni,[status(thm)],[11444:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( bad )),bind(D,$thf( K )),bind(E,$thf( insert_pqp @ G @ K )),bind(F,$thf( insert_slb @ I @ ( pair @ K @ bottom ) ))]]) ).
thf(11642,plain,
! [C: $i,B: $i,A: $i] :
~ ( ok @ ( insert_cpq @ ( triple @ A @ B @ bad ) @ C ) ),
inference(simp,[status(thm)],[11445]) ).
thf(10472,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
| ( ( succ_cpq @ A @ ( remove_cpq @ A @ B ) )
!= ( succ_cpq @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[10459,50]) ).
thf(10473,plain,
! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( remove_cpq @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[10472:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( remove_cpq @ E @ F ))]]) ).
thf(10487,plain,
! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( remove_cpq @ A @ B ) ) ),
inference(simp,[status(thm)],[10473]) ).
thf(17,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( ( pair_in_list @ A @ B @ C )
& ( strictly_less_than @ B @ C ) )
=> ! [B: $i] :
? [C: $i,D: $i] :
( ( pair_in_list @ ( update_slb @ A @ B ) @ C @ D )
& ( strictly_less_than @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_l35) ).
thf(94,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( ( pair_in_list @ A @ B @ C )
& ( strictly_less_than @ B @ C ) )
=> ! [B: $i] :
? [C: $i,D: $i] :
( ( pair_in_list @ ( update_slb @ A @ B ) @ C @ D )
& ( strictly_less_than @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(96,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( pair_in_list @ A @ B @ C )
| ~ ( strictly_less_than @ B @ C )
| ( strictly_less_than @ ( sk4 @ D @ A ) @ ( sk5 @ D @ A ) ) ),
inference(cnf,[status(esa)],[94]) ).
thf(1759,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( insert_cpq @ C @ D ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ A ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[202,77]) ).
thf(1760,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[1759:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( removemin_cpq_eff @ E ))]]) ).
thf(1785,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ),
inference(simp,[status(thm)],[1760]) ).
thf(1814,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
| ( ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) )
!= ( succ_cpq @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1785,50]) ).
thf(1815,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[1814:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( insert_cpq @ ( removemin_cpq_eff @ G ) @ F ))]]) ).
thf(1825,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) ),
inference(simp,[status(thm)],[1815]) ).
thf(11235,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( findmin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ A ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11161,133]) ).
thf(11236,plain,
! [A: $i] : ( succ_cpq @ A @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[11235:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( findmin_cpq_eff @ ( findmin_cpq_eff @ E ) ))]]) ).
thf(11274,plain,
! [A: $i] : ( succ_cpq @ A @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ A ) ) ) ),
inference(simp,[status(thm)],[11236]) ).
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(128,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(2314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
| ( ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) ) @ A ) )
!= ( succ_cpq @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1794,50]) ).
thf(2315,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[2314:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( I )),bind(D,$thf( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ I ) ) ) @ F ))]]) ).
thf(2338,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) ) @ A ) ) ),
inference(simp,[status(thm)],[2315]) ).
thf(12,axiom,
! [A: $i] : ( less_than @ bottom @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).
thf(81,plain,
! [A: $i] : ( less_than @ bottom @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(82,plain,
! [A: $i] : ( less_than @ bottom @ A ),
inference(cnf,[status(esa)],[81]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ( less_than @ C @ B )
| ( strictly_less_than @ B @ C )
| ( ( less_than @ bottom @ A )
!= ( less_than @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[82,56]) ).
thf(244,plain,
! [A: $i] :
( ( less_than @ A @ bottom )
| ( strictly_less_than @ bottom @ A ) ),
inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( A )),bind(B,$thf( bottom )),bind(C,$thf( A ))]]) ).
thf(11299,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( findmin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( findmin_cpq_eff @ A ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11164,133]) ).
thf(11300,plain,
! [A: $i] : ( succ_cpq @ A @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ ( findmin_cpq_eff @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[11299:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( removemin_cpq_eff @ ( findmin_cpq_eff @ E ) ))]]) ).
thf(11332,plain,
! [A: $i] : ( succ_cpq @ A @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ ( findmin_cpq_eff @ A ) ) ) ),
inference(simp,[status(thm)],[11300]) ).
thf(61,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( contains_slb @ A @ C )
| ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) ),
inference(cnf,[status(esa)],[60]) ).
thf(64,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( contains_slb @ A @ C )
| ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) ),
inference(simp,[status(thm)],[61]) ).
thf(44,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(191,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)],[44]) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( less_than @ C @ D )
| ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
inference(cnf,[status(esa)],[116]) ).
thf(118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) )
| ~ ( less_than @ C @ D ) ),
inference(lifteq,[status(thm)],[117]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( strictly_less_than @ A @ B )
| ( less_than @ A @ B ) ),
inference(cnf,[status(esa)],[52]) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
( ( less_than @ C @ B )
| ( strictly_less_than @ B @ C )
| ( ( less_than @ A @ A )
!= ( less_than @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[69,56]) ).
thf(236,plain,
! [A: $i] :
( ( less_than @ A @ A )
| ( strictly_less_than @ A @ A ) ),
inference(pattern_uni,[status(thm)],[235:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(108,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B != C )
| ( D != E )
| ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ),
inference(cnf,[status(esa)],[106]) ).
thf(112,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B != C )
| ( D != E )
| ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] : ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B @ C ),
inference(simp,[status(thm)],[112]) ).
thf(302,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,211]) ).
thf(303,plain,
! [B: $i,A: $i] :
( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[302:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(361,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( triple @ A @ create_slb @ bad )
!= ( triple @ sk1 @ sk2 @ sk3 ) )
| ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
!= ( findmin_cpq_eff @ ( triple @ C @ create_slb @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[171,303]) ).
thf(362,plain,
! [A: $i] :
( ( triple @ A @ create_slb @ bad )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[361:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(103,plain,
! [A: $i,B: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(30,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(140,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)],[30]) ).
thf(62,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != C )
| ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) ),
inference(cnf,[status(esa)],[60]) ).
thf(65,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != C )
| ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] : ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B ),
inference(simp,[status(thm)],[65]) ).
thf(2128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
| ( ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) )
!= ( succ_cpq @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1825,50]) ).
thf(2129,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2128:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( H )),bind(D,$thf( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ H ) @ G ) ))]]) ).
thf(2142,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) ) ),
inference(simp,[status(thm)],[2129]) ).
thf(2700,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
| ( ( succ_cpq @ B @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) ) )
!= ( succ_cpq @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[2142,50]) ).
thf(2701,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2700:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( I )),bind(D,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ I ) @ H ) ) ))]]) ).
thf(2725,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) ) ) ),
inference(simp,[status(thm)],[2701]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= A ),
inference(cnf,[status(esa)],[78]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= A ),
inference(lifteq,[status(thm)],[79]) ).
thf(1802,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
| ( ( succ_cpq @ A @ ( insert_cpq @ A @ B ) )
!= ( succ_cpq @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1786,50]) ).
thf(1803,plain,
! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[1802:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( insert_cpq @ E @ F ))]]) ).
thf(1809,plain,
! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ),
inference(simp,[status(thm)],[1803]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ok @ ( triple @ A @ B @ C ) )
=> ( C = bad ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
thf(162,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ok @ ( triple @ A @ B @ C ) )
=> ( C = bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( strictly_less_than @ A @ B )
| ~ ( less_than @ B @ A ) ),
inference(cnf,[status(esa)],[52]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( strictly_less_than @ B @ C )
| ( ( less_than @ bottom @ A )
!= ( less_than @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[82,55]) ).
thf(209,plain,
! [A: $i] :
~ ( strictly_less_than @ A @ bottom ),
inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( bottom ))]]) ).
thf(2550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) )
| ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
!= ( findmin_cpq_eff @ ( triple @ C @ create_slb @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[171,1714]) ).
thf(2551,plain,
! [A: $i] :
( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[2550:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(6869,plain,
! [A: $i] :
( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(rewrite,[status(thm)],[2551,3875]) ).
thf(9656,plain,
! [A: $i] :
( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(rewrite,[status(thm)],[6869,3875]) ).
thf(10358,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( remove_cpq @ C @ D ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ A ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[202,124]) ).
thf(10359,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( remove_cpq @ ( removemin_cpq_eff @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[10358:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( removemin_cpq_eff @ E ))]]) ).
thf(10456,plain,
! [B: $i,A: $i] : ( succ_cpq @ B @ ( remove_cpq @ ( removemin_cpq_eff @ B ) @ A ) ),
inference(simp,[status(thm)],[10359]) ).
thf(10562,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10532,50]) ).
thf(10563,plain,
! [A: $i] : ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[10562:[bind(A,$thf( F )),bind(B,$thf( findmin_cpq_eff @ F )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ F ) ))]]) ).
thf(10595,plain,
! [A: $i] : ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ),
inference(simp,[status(thm)],[10563]) ).
thf(10638,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10595,50]) ).
thf(10639,plain,
! [A: $i] : ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[10638:[bind(A,$thf( G )),bind(B,$thf( findmin_cpq_eff @ G )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ G ) ) ))]]) ).
thf(10685,plain,
! [A: $i] : ( succ_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ),
inference(simp,[status(thm)],[10639]) ).
thf(11029,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( findmin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[205,133]) ).
thf(11030,plain,
! [A: $i] : ( succ_cpq @ A @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[11029:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ E ) ))]]) ).
thf(11098,plain,
! [A: $i] : ( succ_cpq @ A @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ),
inference(simp,[status(thm)],[11030]) ).
thf(33,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(150,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)],[33]) ).
thf(95,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( pair_in_list @ A @ B @ C )
| ~ ( strictly_less_than @ B @ C )
| ( pair_in_list @ ( update_slb @ A @ D ) @ ( sk4 @ D @ A ) @ ( sk5 @ D @ A ) ) ),
inference(cnf,[status(esa)],[94]) ).
thf(71,plain,
~ ? [A: $i] : ( contains_slb @ create_slb @ A ),
inference(miniscope,[status(thm)],[70]) ).
thf(72,plain,
! [A: $i] :
~ ( contains_slb @ create_slb @ A ),
inference(cnf,[status(esa)],[71]) ).
thf(41,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(175,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)],[41]) ).
thf(31,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(143,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)],[31]) ).
thf(248,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[247,50]) ).
thf(249,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( I )),bind(B,$thf( I )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ I ) ) ) ) ) ))]]) ).
thf(250,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[249]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= C ),
inference(cnf,[status(esa)],[97]) ).
thf(99,plain,
! [C: $i,B: $i,A: $i] :
( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= C ),
inference(lifteq,[status(thm)],[98]) ).
thf(1832,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) )
!= ( succ_cpq @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1809,50]) ).
thf(1833,plain,
! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1832:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( removemin_cpq_eff @ ( insert_cpq @ F @ G ) ))]]) ).
thf(1844,plain,
! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) ),
inference(simp,[status(thm)],[1833]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A ) ),
inference(cnf,[status(esa)],[103]) ).
thf(2290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) )
!= ( succ_cpq @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1844,50]) ).
thf(2291,plain,
! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2290:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ G @ H ) ) ))]]) ).
thf(2305,plain,
! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) ) ),
inference(simp,[status(thm)],[2291]) ).
thf(138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( contains_slb @ B @ D )
| ( ( remove_cpq @ ( triple @ A @ B @ C ) @ D )
= ( triple @ A @ B @ bad ) ) ),
inference(cnf,[status(esa)],[137]) ).
thf(139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( remove_cpq @ ( triple @ A @ B @ C ) @ D )
= ( triple @ A @ B @ bad ) )
| ( contains_slb @ B @ D ) ),
inference(lifteq,[status(thm)],[138]) ).
thf(109,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
| ( pair_in_list @ A @ C @ E )
| ( D = E ) ),
inference(cnf,[status(esa)],[106]) ).
thf(114,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
| ( pair_in_list @ A @ C @ E ) ),
inference(lifteq,[status(thm)],[109]) ).
thf(3141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) ) ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) )
| ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
!= ( findmin_cpq_eff @ ( triple @ C @ create_slb @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[171,2246]) ).
thf(3142,plain,
! [A: $i] :
( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) ) ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[3141:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(6870,plain,
! [A: $i] :
( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(rewrite,[status(thm)],[3142,3875]) ).
thf(9919,plain,
! [A: $i] :
( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(rewrite,[status(thm)],[6870,3875]) ).
thf(206,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( strictly_less_than @ B @ C )
| ( ( less_than @ A @ A )
!= ( less_than @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[69,55]) ).
thf(207,plain,
! [A: $i] :
~ ( strictly_less_than @ A @ A ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
!= ( contains_slb @ create_slb @ D ) ),
inference(paramod_ordered,[status(thm)],[66,72]) ).
thf(381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( insert_slb @ A @ ( pair @ B @ C ) )
!= create_slb )
| ( B != D ) ),
inference(simp,[status(thm)],[380]) ).
thf(383,plain,
! [C: $i,B: $i,A: $i] :
( ( insert_slb @ A @ ( pair @ C @ B ) )
!= create_slb ),
inference(simp,[status(thm)],[381]) ).
thf(285,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[250,50]) ).
thf(286,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[285:[bind(A,$thf( J )),bind(B,$thf( J )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ J ) ) ) ) ) ) ))]]) ).
thf(287,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[286]) ).
thf(288,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[287,50]) ).
thf(289,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( K )),bind(B,$thf( K )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ K ) ) ) ) ) ) ) ))]]) ).
thf(290,plain,
! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[289]) ).
thf(11061,plain,
! [C: $i,B: $i,A: $i] :
( ( succ_cpq @ B @ ( findmin_cpq_eff @ C ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) )
!= ( succ_cpq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[218,133]) ).
thf(11062,plain,
! [A: $i] : ( succ_cpq @ A @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[11061:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ F ) ) ))]]) ).
thf(11114,plain,
! [A: $i] : ( succ_cpq @ A @ ( findmin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ),
inference(simp,[status(thm)],[11062]) ).
thf(2483,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) )
= bottom )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,1890]) ).
thf(2484,plain,
! [B: $i,A: $i] :
( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) )
= bottom ),
inference(pattern_uni,[status(thm)],[2483:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(129,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B != C )
& ( contains_slb @ A @ C ) )
=> ! [D: $i] :
( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( lookup_slb @ A @ C ) ) ),
inference(miniscope,[status(thm)],[128]) ).
thf(130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( contains_slb @ A @ C )
| ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( lookup_slb @ A @ C ) ) ),
inference(cnf,[status(esa)],[129]) ).
thf(131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( lookup_slb @ A @ C ) )
| ~ ( contains_slb @ A @ C ) ),
inference(lifteq,[status(thm)],[130]) ).
thf(2730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
| ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) ) )
!= ( succ_cpq @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[2305,50]) ).
thf(2731,plain,
! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2730:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( H )),bind(D,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ H @ I ) ) ) ))]]) ).
thf(2754,plain,
! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[2731]) ).
thf(214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( strictly_less_than @ A @ B )
| ~ ( strictly_less_than @ C @ D )
| ( ( less_than @ A @ B )
!= ( less_than @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[54,55]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ~ ( strictly_less_than @ A @ B )
| ~ ( strictly_less_than @ B @ A ) ),
inference(pattern_uni,[status(thm)],[214:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
| ( contains_slb @ A @ C )
| ( C != create_slb )
| ( B != sk2 ) ),
inference(paramod_ordered,[status(thm)],[67,213]) ).
thf(725,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ sk2 @ C ) ) @ B )
| ( contains_slb @ A @ B )
| ( B != create_slb ) ),
inference(pattern_uni,[status(thm)],[724:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(1088,plain,
! [B: $i,A: $i] :
( ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ sk2 @ B ) ) @ create_slb )
| ( contains_slb @ A @ create_slb ) ),
inference(simp,[status(thm)],[725]) ).
thf(363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) )
| ( ( triple @ A @ create_slb @ bad )
!= ( triple @ C @ create_slb @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,303]) ).
thf(364,plain,
! [B: $i,A: $i] :
( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
!= ( triple @ sk1 @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[363:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).
thf(107,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( pair_in_list @ A @ C @ E )
| ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ),
inference(cnf,[status(esa)],[106]) ).
thf(111,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( pair_in_list @ A @ C @ E )
| ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ),
inference(simp,[status(thm)],[107]) ).
thf(24738,plain,
$false,
inference(cvc4,[status(thm)],[69,2412,11164,234,408,115,1808,247,202,1788,56,174,11335,2869,184,10486,125,2185,10121,1709,1379,1890,46,93,228,57,78,1714,179,211,2122,121,147,1796,132,2799,116,10459,74,2367,11218,89,133,292,85,102,392,70,137,165,92,229,197,97,11101,1089,11133,1794,156,1375,11221,169,11278,124,77,11642,10487,96,1825,11274,134,73,128,205,2338,105,244,11332,64,11006,191,59,118,1786,54,313,49,236,86,159,113,219,81,2246,362,303,172,10532,103,140,213,91,66,251,1293,155,2725,80,1809,162,209,9656,194,10456,11161,48,10685,11098,1611,150,95,50,67,1785,127,154,72,175,143,250,99,10595,1844,218,104,2305,351,171,139,55,114,9919,75,207,383,1661,82,287,290,119,58,2142,11131,315,51,358,1335,400,94,11114,294,136,3875,195,2241,68,2484,131,47,2754,122,83,215,1088,222,364,232,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV398+1 : TPTP v8.2.0. Released v3.3.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n021.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 : Sun May 19 08:23:39 EDT 2024
% 0.14/0.35 % CPUTime :
% 1.17/1.15 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.89/1.39 % [INFO] Parsing done (238ms).
% 1.89/1.41 % [INFO] Running in sequential loop mode.
% 2.65/1.87 % [INFO] eprover registered as external prover.
% 2.65/1.87 % [INFO] cvc4 registered as external prover.
% 2.65/1.88 % [INFO] Scanning for conjecture ...
% 2.92/2.01 % [INFO] Found a conjecture (or negated_conjecture) and 43 axioms. Running axiom selection ...
% 3.18/2.11 % [INFO] Axiom selection finished. Selected 43 axioms (removed 0 axioms).
% 3.38/2.21 % [INFO] Problem is first-order (TPTP FOF).
% 3.57/2.23 % [INFO] Type checking passed.
% 3.57/2.23 % [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 ...
% 126.03/22.20 % External prover 'cvc4' found a proof!
% 126.03/22.20 % [INFO] Killing All external provers ...
% 126.03/22.20 % Time passed: 21668ms (effective reasoning time: 20787ms)
% 126.03/22.20 % 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)>
% 126.03/22.21 % Axioms used in derivation (43): ax28, ax39, ax27, l34_l35, ax32, 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, l26_li4142, totality, ax46, ax34, ax23, transitivity, ax30, ax42, ax18, ax36, ax29
% 126.03/22.21 % No. of inferences in proof: 407
% 126.03/22.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21668 ms resp. 20787 ms w/o parsing
% 126.75/22.38 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 126.75/22.39 % [INFO] Killing All external provers ...
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