%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV417+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:57:38 AM UTC 2026
% Result : Theorem 1.17s 0.46s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 21
% Syntax : Number of formulae : 270 ( 161 unt; 0 typ; 0 def)
% Number of atoms : 1387 ( 464 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 2936 ( 605 ~; 325 |; 21 &;1934 @)
% ( 21 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 51 usr; 9 con; 0-3 aty)
% Number of variables : 624 ( 0 ^; 606 !; 18 ?; 624 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bad,type,
bad: $i ).
thf(tp_bottom,type,
bottom: $i ).
thf(tp_check_cpq,type,
check_cpq: $i > $o ).
thf(tp_contains_cpq,type,
contains_cpq: $i > $i > $o ).
thf(tp_contains_pq,type,
contains_pq: $i > $i > $o ).
thf(tp_contains_slb,type,
contains_slb: $i > $i > $o ).
thf(tp_create_pq,type,
create_pq: $i ).
thf(tp_create_slb,type,
create_slb: $i ).
thf(tp_findmin_cpq_eff,type,
findmin_cpq_eff: $i > $i ).
thf(tp_findmin_cpq_res,type,
findmin_cpq_res: $i > $i ).
thf(tp_findmin_pq_eff,type,
findmin_pq_eff: $i > $i > $i ).
thf(tp_findmin_pq_res,type,
findmin_pq_res: $i > $i > $i ).
thf(tp_findmin_pqp_res,type,
findmin_pqp_res: $i > $i ).
thf(tp_i,type,
i: $i > $i ).
thf(tp_insert_cpq,type,
insert_cpq: $i > $i > $i ).
thf(tp_insert_pq,type,
insert_pq: $i > $i > $i ).
thf(tp_insert_pqp,type,
insert_pqp: $i > $i > $i ).
thf(tp_insert_slb,type,
insert_slb: $i > $i > $i ).
thf(tp_isnonempty_pq,type,
isnonempty_pq: $i > $o ).
thf(tp_isnonempty_slb,type,
isnonempty_slb: $i > $o ).
thf(tp_issmallestelement_pq,type,
issmallestelement_pq: $i > $i > $o ).
thf(tp_less_than,type,
less_than: $i > $i > $o ).
thf(tp_lookup_slb,type,
lookup_slb: $i > $i > $i ).
thf(tp_ok,type,
ok: $i > $o ).
thf(tp_pair,type,
pair: $i > $i > $i ).
thf(tp_pair_in_list,type,
pair_in_list: $i > $i > $i > $o ).
thf(tp_phi,type,
phi: $i > $o ).
thf(tp_pi_find_min,type,
pi_find_min: $i > $o ).
thf(tp_pi_remove,type,
pi_remove: $i > $i > $o ).
thf(tp_pi_removemin,type,
pi_removemin: $i > $o ).
thf(tp_pi_sharp_find_min,type,
pi_sharp_find_min: $i > $i > $o ).
thf(tp_pi_sharp_remove,type,
pi_sharp_remove: $i > $i > $o ).
thf(tp_pi_sharp_removemin,type,
pi_sharp_removemin: $i > $i > $o ).
thf(tp_remove_cpq,type,
remove_cpq: $i > $i > $i ).
thf(tp_remove_pq,type,
remove_pq: $i > $i > $i ).
thf(tp_remove_pqp,type,
remove_pqp: $i > $i > $i ).
thf(tp_remove_slb,type,
remove_slb: $i > $i > $i ).
thf(tp_removemin_cpq_eff,type,
removemin_cpq_eff: $i > $i ).
thf(tp_removemin_cpq_res,type,
removemin_cpq_res: $i > $i ).
thf(tp_removemin_pq_eff,type,
removemin_pq_eff: $i > $i > $i ).
thf(tp_removemin_pq_res,type,
removemin_pq_res: $i > $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SY53,type,
sK2_SY53: $i ).
thf(tp_sK3_SY56,type,
sK3_SY56: $i ).
thf(tp_sK4_SY69,type,
sK4_SY69: $i > $i ).
thf(tp_sK5_SY71,type,
sK5_SY71: $i > $i ).
thf(tp_sK6_SY86,type,
sK6_SY86: $i > $i ).
thf(tp_strictly_less_than,type,
strictly_less_than: $i > $i > $o ).
thf(tp_succ_cpq,type,
succ_cpq: $i > $i > $o ).
thf(tp_triple,type,
triple: $i > $i > $i > $i ).
thf(tp_update_slb,type,
update_slb: $i > $i > $i ).
thf(1,axiom,
! [U: $i] :
( ( phi @ U )
<=> ? [V: $i] :
( ( succ_cpq @ U @ V )
& ( ok @ V )
& ( check_cpq @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
thf(2,axiom,
! [U: $i] :
( ( pi_removemin @ U )
<=> ? [V: $i] : ( pi_sharp_find_min @ ( i @ U ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).
thf(4,axiom,
! [U: $i] :
( ( pi_find_min @ U )
<=> ? [V: $i] : ( pi_sharp_find_min @ ( i @ U ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
thf(5,axiom,
! [U: $i,V: $i] :
( ( pi_sharp_find_min @ U @ V )
<=> ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
thf(6,axiom,
! [U: $i,V: $i] :
( ( pi_remove @ U @ V )
<=> ( pi_sharp_remove @ ( i @ U ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
thf(8,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
= ( insert_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
thf(9,axiom,
! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
thf(10,axiom,
! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
thf(11,axiom,
! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
thf(12,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( V != create_slb )
=> ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
thf(13,axiom,
! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).
thf(17,axiom,
! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
thf(20,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).
thf(22,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
thf(23,axiom,
! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).
thf(24,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
<=> ( contains_slb @ V @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
thf(27,axiom,
! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
thf(29,axiom,
! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).
thf(49,axiom,
! [U: $i,V: $i] :
( ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) )
=> ( ( findmin_pq_res @ U @ V )
= V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).
thf(63,axiom,
! [U: $i,V: $i,W: $i] :
( ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ( pi_sharp_find_min @ ( i @ ( triple @ U @ V @ W ) ) @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main4_l7) ).
thf(64,conjecture,
! [U: $i,V: $i,W: $i] :
( ( pi_find_min @ ( triple @ U @ V @ W ) )
=> ( ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ? [X: $i] :
( ( pi_sharp_find_min @ ( i @ ( triple @ U @ V @ W ) ) @ X )
& ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pq_res @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co4) ).
thf(65,negated_conjecture,
( ( ! [U: $i,V: $i,W: $i] :
( ( pi_find_min @ ( triple @ U @ V @ W ) )
=> ( ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ? [X: $i] :
( ( pi_sharp_find_min @ ( i @ ( triple @ U @ V @ W ) ) @ X )
& ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pq_res @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[64]) ).
thf(66,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( pi_find_min @ ( triple @ U @ V @ W ) )
=> ( ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ? [X: $i] :
( ( pi_sharp_find_min @ ( i @ ( triple @ U @ V @ W ) ) @ X )
& ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pq_res @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[65]) ).
thf(67,plain,
( ( ! [U: $i] :
( ( phi @ U )
<=> ? [V: $i] :
( ( succ_cpq @ U @ V )
& ( ok @ V )
& ( check_cpq @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(68,plain,
( ( ! [U: $i] :
( ( pi_removemin @ U )
<=> ? [V: $i] : ( pi_sharp_find_min @ ( i @ U ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(69,plain,
( ( ! [U: $i] :
( ( pi_find_min @ U )
<=> ? [V: $i] : ( pi_sharp_find_min @ ( i @ U ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(70,plain,
( ( ! [U: $i,V: $i] :
( ( pi_sharp_find_min @ U @ V )
<=> ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(71,plain,
( ( ! [U: $i,V: $i] :
( ( pi_remove @ U @ V )
<=> ( pi_sharp_remove @ ( i @ U ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(72,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
= ( insert_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(73,plain,
( ( ! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(74,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(75,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(76,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( V != create_slb )
=> ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(77,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(78,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(79,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(80,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(81,plain,
( ( ! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(82,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
<=> ( contains_slb @ V @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(83,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(84,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(85,plain,
( ( ! [U: $i,V: $i] :
( ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) )
=> ( ( findmin_pq_res @ U @ V )
= V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(86,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ( pi_sharp_find_min @ ( i @ ( triple @ U @ V @ W ) ) @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(87,plain,
( ( ! [SY53: $i,SY54: $i] :
( ( pi_find_min @ ( triple @ sK1_U @ SY53 @ SY54 ) )
=> ( ( phi @ ( findmin_cpq_eff @ ( triple @ sK1_U @ SY53 @ SY54 ) ) )
=> ? [SY55: $i] :
( ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ SY53 @ SY54 ) ) @ SY55 )
& ( ( findmin_cpq_res @ ( triple @ sK1_U @ SY53 @ SY54 ) )
= ( findmin_pq_res @ ( i @ ( triple @ sK1_U @ SY53 @ SY54 ) ) @ SY55 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(88,plain,
( ( ! [SY56: $i] :
( ( pi_find_min @ ( triple @ sK1_U @ sK2_SY53 @ SY56 ) )
=> ( ( phi @ ( findmin_cpq_eff @ ( triple @ sK1_U @ sK2_SY53 @ SY56 ) ) )
=> ? [SY57: $i] :
( ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ SY56 ) ) @ SY57 )
& ( ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY53 @ SY56 ) )
= ( findmin_pq_res @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ SY56 ) ) @ SY57 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[87]) ).
thf(89,plain,
( ( ( pi_find_min @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
=> ( ( phi @ ( findmin_cpq_eff @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) )
=> ? [SY58: $i] :
( ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SY58 )
& ( ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
= ( findmin_pq_res @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SY58 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[88]) ).
thf(90,plain,
( ( pi_find_min @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
= $true ),
inference(standard_cnf,[status(thm)],[89]) ).
thf(91,plain,
( ( phi @ ( findmin_cpq_eff @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[89]) ).
thf(92,plain,
( ( ? [SY58: $i] :
( ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SY58 )
& ( ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
= ( findmin_pq_res @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SY58 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[89]) ).
thf(93,plain,
( ( ~ ? [SY58: $i] :
( ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SY58 )
& ( ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
= ( findmin_pq_res @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SY58 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[92]) ).
thf(94,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ( pi_sharp_find_min @ ( i @ ( triple @ U @ V @ W ) ) @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(95,plain,
( ( ! [U: $i,V: $i] :
( ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) )
=> ( ( findmin_pq_res @ U @ V )
= V ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(96,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(97,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(98,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
<=> ( contains_slb @ V @ X ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(99,plain,
( ( ! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(100,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(101,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(102,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(103,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(104,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( V != create_slb )
=> ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(105,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(106,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(107,plain,
( ( ! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(108,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
= ( insert_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(109,plain,
( ( ! [U: $i,V: $i] :
( ( pi_remove @ U @ V )
<=> ( pi_sharp_remove @ ( i @ U ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(110,plain,
( ( ! [U: $i,V: $i] :
( ( pi_sharp_find_min @ U @ V )
<=> ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(111,plain,
( ( ! [U: $i] :
( ( pi_find_min @ U )
<=> ? [V: $i] : ( pi_sharp_find_min @ ( i @ U ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(112,plain,
( ( ! [U: $i] :
( ( pi_removemin @ U )
<=> ? [V: $i] : ( pi_sharp_find_min @ ( i @ U ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(113,plain,
( ( ! [U: $i] :
( ( phi @ U )
<=> ? [V: $i] :
( ( succ_cpq @ U @ V )
& ( ok @ V )
& ( check_cpq @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(114,plain,
( ( phi @ ( findmin_cpq_eff @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(115,plain,
( ( pi_find_min @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(116,plain,
( ( ~ ? [SY58: $i] :
( ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SY58 )
& ( ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
= ( findmin_pq_res @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SY58 ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(117,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( contains_pq @ SX0 @ SX1 )
| ~ ( issmallestelement_pq @ SX0 @ SX1 ) )
| ( ( findmin_pq_res @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(118,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ok @ ( triple @ SX0 @ SX1 @ bad ) )
| $false )
| ~ ( ~ $false
| ( ok @ ( triple @ SX0 @ SX1 @ bad ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(119,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( pi_removemin @ SX0 )
| ~ ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(120,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( phi @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( ok @ SX1 ) )
| ~ ( check_cpq @ SX1 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( ok @ SX1 ) )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(121,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SX0 )
| ( ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
!= ( findmin_pq_res @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ~ ( ~ ( contains_pq @ SX0 @ SX1 )
| ~ ( issmallestelement_pq @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( contains_pq @ SX0 @ SX1 )
| ~ ( issmallestelement_pq @ SX0 @ SX1 ) )
| ( pi_sharp_find_min @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(123,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 )
| ( contains_slb @ SX1 @ SX3 ) )
| ~ ( ~ ( contains_slb @ SX1 @ SX3 )
| ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ( SX2 = bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(125,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) )
| ~ ( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(126,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ SX0 @ SX1 @ SX2 ) ) )
| ( pi_sharp_find_min @ ( i @ ( triple @ SX0 @ SX1 @ SX2 ) ) @ ( findmin_cpq_res @ ( triple @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(127,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( succ_cpq @ SX0 @ SX1 )
| ( succ_cpq @ SX0 @ ( findmin_cpq_eff @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(128,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( contains_slb @ SX1 @ SX3 )
| ( ( remove_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( triple @ SX0 @ SX1 @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(129,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( pi_find_min @ SX0 )
| ~ ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_find_min @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(130,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ( SX1 != create_slb ) )
| ( ( findmin_cpq_res @ ( triple @ SX0 @ SX1 @ SX2 ) )
= ( findmin_pqp_res @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(131,plain,
! [SV1: $i] :
( ( ! [SY59: $i] : ( check_cpq @ ( triple @ SV1 @ create_slb @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(132,plain,
! [SV2: $i] :
( ( ! [SY60: $i] :
( ( findmin_cpq_eff @ ( triple @ SV2 @ create_slb @ SY60 ) )
= ( triple @ SV2 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(133,plain,
! [SV3: $i] :
( ( ! [SY61: $i] :
( ( findmin_cpq_res @ ( triple @ SV3 @ create_slb @ SY61 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(134,plain,
! [SV4: $i] :
( ( ( removemin_cpq_eff @ SV4 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV4 ) @ ( findmin_cpq_res @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(135,plain,
! [SV5: $i] :
( ( ( removemin_cpq_res @ SV5 )
= ( findmin_cpq_res @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(136,plain,
! [SV6: $i] :
( ( ! [SY62: $i] :
( ( i @ ( triple @ SV6 @ create_slb @ SY62 ) )
= create_pq ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(137,plain,
! [SV7: $i] :
( ( ! [SY63: $i,SY64: $i,SY65: $i,SY66: $i] :
( ( i @ ( triple @ SV7 @ ( insert_slb @ SY63 @ ( pair @ SY65 @ SY66 ) ) @ SY64 ) )
= ( insert_pq @ ( i @ ( triple @ SV7 @ SY63 @ SY64 ) ) @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(138,plain,
! [SV8: $i] :
( ( ! [SY67: $i] :
( ~ ~ ( ~ ( contains_pq @ SV8 @ SY67 )
| ~ ( issmallestelement_pq @ SV8 @ SY67 ) )
| ( ( findmin_pq_res @ SV8 @ SY67 )
= SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(139,plain,
! [SV9: $i] :
( ( ! [SY68: $i] :
~ ( ~ ( ~ ( ok @ ( triple @ SV9 @ SY68 @ bad ) )
| $false )
| ~ ( ~ $false
| ( ok @ ( triple @ SV9 @ SY68 @ bad ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(140,plain,
! [SV10: $i] :
( ( ~ ( ~ ( ~ ( pi_removemin @ SV10 )
| ~ ! [SY69: $i] :
~ ( pi_sharp_find_min @ ( i @ SV10 ) @ SY69 ) )
| ~ ( ~ ~ ! [SY70: $i] :
~ ( pi_sharp_find_min @ ( i @ SV10 ) @ SY70 )
| ( pi_removemin @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(141,plain,
! [SV11: $i] :
( ( ~ ( ~ ( ~ ( phi @ SV11 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SY71 )
| ~ ( ok @ SY71 ) )
| ~ ( check_cpq @ SY71 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SY72 )
| ~ ( ok @ SY72 ) )
| ~ ( check_cpq @ SY72 ) )
| ( phi @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(142,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SX0 )
| ( ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
!= ( findmin_pq_res @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(143,plain,
! [SV12: $i] :
( ( ! [SY73: $i] :
~ ( ~ ( ~ ( pi_sharp_find_min @ SV12 @ SY73 )
| ~ ( ~ ( contains_pq @ SV12 @ SY73 )
| ~ ( issmallestelement_pq @ SV12 @ SY73 ) ) )
| ~ ( ~ ~ ( ~ ( contains_pq @ SV12 @ SY73 )
| ~ ( issmallestelement_pq @ SV12 @ SY73 ) )
| ( pi_sharp_find_min @ SV12 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(144,plain,
! [SV13: $i] :
( ( ! [SY74: $i,SY75: $i,SY76: $i] :
~ ( ~ ( ~ ( contains_cpq @ ( triple @ SV13 @ SY74 @ SY75 ) @ SY76 )
| ( contains_slb @ SY74 @ SY76 ) )
| ~ ( ~ ( contains_slb @ SY74 @ SY76 )
| ( contains_cpq @ ( triple @ SV13 @ SY74 @ SY75 ) @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(145,plain,
! [SV14: $i] :
( ( ! [SY77: $i,SY78: $i] :
( ~ ~ ( ok @ ( triple @ SV14 @ SY77 @ SY78 ) )
| ( SY78 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(146,plain,
! [SV15: $i] :
( ( ! [SY79: $i] :
~ ( ~ ( ~ ( pi_remove @ SV15 @ SY79 )
| ( pi_sharp_remove @ ( i @ SV15 ) @ SY79 ) )
| ~ ( ~ ( pi_sharp_remove @ ( i @ SV15 ) @ SY79 )
| ( pi_remove @ SV15 @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(147,plain,
! [SV16: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ SV16 @ SY80 @ SY81 ) ) )
| ( pi_sharp_find_min @ ( i @ ( triple @ SV16 @ SY80 @ SY81 ) ) @ ( findmin_cpq_res @ ( triple @ SV16 @ SY80 @ SY81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(148,plain,
! [SV17: $i] :
( ( ! [SY82: $i] :
( ~ ( succ_cpq @ SV17 @ SY82 )
| ( succ_cpq @ SV17 @ ( findmin_cpq_eff @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(149,plain,
! [SV18: $i] :
( ( ! [SY83: $i,SY84: $i,SY85: $i] :
( ~ ~ ( contains_slb @ SY83 @ SY85 )
| ( ( remove_cpq @ ( triple @ SV18 @ SY83 @ SY84 ) @ SY85 )
= ( triple @ SV18 @ SY83 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(150,plain,
! [SV19: $i] :
( ( ~ ( ~ ( ~ ( pi_find_min @ SV19 )
| ~ ! [SY86: $i] :
~ ( pi_sharp_find_min @ ( i @ SV19 ) @ SY86 ) )
| ~ ( ~ ~ ! [SY87: $i] :
~ ( pi_sharp_find_min @ ( i @ SV19 ) @ SY87 )
| ( pi_find_min @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(151,plain,
! [SV20: $i] :
( ( ! [SY88: $i,SY89: $i,SY90: $i] :
( ~ ( ( SY88 != create_slb ) )
| ( ( findmin_cpq_res @ ( triple @ SV20 @ SY88 @ SY89 ) )
= ( findmin_pqp_res @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(152,plain,
! [SV21: $i,SV1: $i] :
( ( check_cpq @ ( triple @ SV1 @ create_slb @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(153,plain,
! [SV22: $i,SV2: $i] :
( ( ( findmin_cpq_eff @ ( triple @ SV2 @ create_slb @ SV22 ) )
= ( triple @ SV2 @ create_slb @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(154,plain,
! [SV23: $i,SV3: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV3 @ create_slb @ SV23 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(155,plain,
! [SV24: $i,SV6: $i] :
( ( ( i @ ( triple @ SV6 @ create_slb @ SV24 ) )
= create_pq )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(156,plain,
! [SV25: $i,SV7: $i] :
( ( ! [SY91: $i,SY92: $i,SY93: $i] :
( ( i @ ( triple @ SV7 @ ( insert_slb @ SV25 @ ( pair @ SY92 @ SY93 ) ) @ SY91 ) )
= ( insert_pq @ ( i @ ( triple @ SV7 @ SV25 @ SY91 ) ) @ SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(157,plain,
! [SV26: $i,SV8: $i] :
( ( ~ ~ ( ~ ( contains_pq @ SV8 @ SV26 )
| ~ ( issmallestelement_pq @ SV8 @ SV26 ) )
| ( ( findmin_pq_res @ SV8 @ SV26 )
= SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(158,plain,
! [SV27: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( ok @ ( triple @ SV9 @ SV27 @ bad ) )
| $false )
| ~ ( ~ $false
| ( ok @ ( triple @ SV9 @ SV27 @ bad ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(159,plain,
! [SV10: $i] :
( ( ~ ( ~ ( pi_removemin @ SV10 )
| ~ ! [SY69: $i] :
~ ( pi_sharp_find_min @ ( i @ SV10 ) @ SY69 ) )
| ~ ( ~ ~ ! [SY70: $i] :
~ ( pi_sharp_find_min @ ( i @ SV10 ) @ SY70 )
| ( pi_removemin @ SV10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(160,plain,
! [SV11: $i] :
( ( ~ ( ~ ( phi @ SV11 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SY71 )
| ~ ( ok @ SY71 ) )
| ~ ( check_cpq @ SY71 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SY72 )
| ~ ( ok @ SY72 ) )
| ~ ( check_cpq @ SY72 ) )
| ( phi @ SV11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(161,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SX0 )
| ( ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
!= ( findmin_pq_res @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(162,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( pi_sharp_find_min @ SV12 @ SV28 )
| ~ ( ~ ( contains_pq @ SV12 @ SV28 )
| ~ ( issmallestelement_pq @ SV12 @ SV28 ) ) )
| ~ ( ~ ~ ( ~ ( contains_pq @ SV12 @ SV28 )
| ~ ( issmallestelement_pq @ SV12 @ SV28 ) )
| ( pi_sharp_find_min @ SV12 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(163,plain,
! [SV29: $i,SV13: $i] :
( ( ! [SY94: $i,SY95: $i] :
~ ( ~ ( ~ ( contains_cpq @ ( triple @ SV13 @ SV29 @ SY94 ) @ SY95 )
| ( contains_slb @ SV29 @ SY95 ) )
| ~ ( ~ ( contains_slb @ SV29 @ SY95 )
| ( contains_cpq @ ( triple @ SV13 @ SV29 @ SY94 ) @ SY95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(164,plain,
! [SV30: $i,SV14: $i] :
( ( ! [SY96: $i] :
( ~ ~ ( ok @ ( triple @ SV14 @ SV30 @ SY96 ) )
| ( SY96 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(165,plain,
! [SV31: $i,SV15: $i] :
( ( ~ ( ~ ( ~ ( pi_remove @ SV15 @ SV31 )
| ( pi_sharp_remove @ ( i @ SV15 ) @ SV31 ) )
| ~ ( ~ ( pi_sharp_remove @ ( i @ SV15 ) @ SV31 )
| ( pi_remove @ SV15 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(166,plain,
! [SV32: $i,SV16: $i] :
( ( ! [SY97: $i] :
( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ SV16 @ SV32 @ SY97 ) ) )
| ( pi_sharp_find_min @ ( i @ ( triple @ SV16 @ SV32 @ SY97 ) ) @ ( findmin_cpq_res @ ( triple @ SV16 @ SV32 @ SY97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(167,plain,
! [SV33: $i,SV17: $i] :
( ( ~ ( succ_cpq @ SV17 @ SV33 )
| ( succ_cpq @ SV17 @ ( findmin_cpq_eff @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(168,plain,
! [SV18: $i,SV34: $i] :
( ( ! [SY98: $i,SY99: $i] :
( ~ ~ ( contains_slb @ SV34 @ SY99 )
| ( ( remove_cpq @ ( triple @ SV18 @ SV34 @ SY98 ) @ SY99 )
= ( triple @ SV18 @ SV34 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(169,plain,
! [SV19: $i] :
( ( ~ ( ~ ( pi_find_min @ SV19 )
| ~ ! [SY86: $i] :
~ ( pi_sharp_find_min @ ( i @ SV19 ) @ SY86 ) )
| ~ ( ~ ~ ! [SY87: $i] :
~ ( pi_sharp_find_min @ ( i @ SV19 ) @ SY87 )
| ( pi_find_min @ SV19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(170,plain,
! [SV20: $i,SV35: $i] :
( ( ! [SY100: $i,SY101: $i] :
( ~ ( ( SV35 != create_slb ) )
| ( ( findmin_cpq_res @ ( triple @ SV20 @ SV35 @ SY100 ) )
= ( findmin_pqp_res @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(171,plain,
! [SV36: $i,SV25: $i,SV7: $i] :
( ( ! [SY102: $i,SY103: $i] :
( ( i @ ( triple @ SV7 @ ( insert_slb @ SV25 @ ( pair @ SY102 @ SY103 ) ) @ SV36 ) )
= ( insert_pq @ ( i @ ( triple @ SV7 @ SV25 @ SV36 ) ) @ SY102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(172,plain,
! [SV26: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( contains_pq @ SV8 @ SV26 )
| ~ ( issmallestelement_pq @ SV8 @ SV26 ) ) )
= $true )
| ( ( ( findmin_pq_res @ SV8 @ SV26 )
= SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(173,plain,
! [SV27: $i,SV9: $i] :
( ( ~ ( ~ ( ok @ ( triple @ SV9 @ SV27 @ bad ) )
| $false )
| ~ ( ~ $false
| ( ok @ ( triple @ SV9 @ SV27 @ bad ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(174,plain,
! [SV10: $i] :
( ( ~ ( ~ ( pi_removemin @ SV10 )
| ~ ! [SY69: $i] :
~ ( pi_sharp_find_min @ ( i @ SV10 ) @ SY69 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(175,plain,
! [SV10: $i] :
( ( ~ ( ~ ~ ! [SY70: $i] :
~ ( pi_sharp_find_min @ ( i @ SV10 ) @ SY70 )
| ( pi_removemin @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(176,plain,
! [SV11: $i] :
( ( ~ ( ~ ( phi @ SV11 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SY71 )
| ~ ( ok @ SY71 ) )
| ~ ( check_cpq @ SY71 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(177,plain,
! [SV11: $i] :
( ( ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SY72 )
| ~ ( ok @ SY72 ) )
| ~ ( check_cpq @ SY72 ) )
| ( phi @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(178,plain,
! [SV37: $i] :
( ( ~ ~ ( ~ ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SV37 )
| ( ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
!= ( findmin_pq_res @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(179,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( ~ ( pi_sharp_find_min @ SV12 @ SV28 )
| ~ ( ~ ( contains_pq @ SV12 @ SV28 )
| ~ ( issmallestelement_pq @ SV12 @ SV28 ) ) )
| ~ ( ~ ~ ( ~ ( contains_pq @ SV12 @ SV28 )
| ~ ( issmallestelement_pq @ SV12 @ SV28 ) )
| ( pi_sharp_find_min @ SV12 @ SV28 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(180,plain,
! [SV38: $i,SV29: $i,SV13: $i] :
( ( ! [SY104: $i] :
~ ( ~ ( ~ ( contains_cpq @ ( triple @ SV13 @ SV29 @ SV38 ) @ SY104 )
| ( contains_slb @ SV29 @ SY104 ) )
| ~ ( ~ ( contains_slb @ SV29 @ SY104 )
| ( contains_cpq @ ( triple @ SV13 @ SV29 @ SV38 ) @ SY104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(181,plain,
! [SV39: $i,SV30: $i,SV14: $i] :
( ( ~ ~ ( ok @ ( triple @ SV14 @ SV30 @ SV39 ) )
| ( SV39 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(182,plain,
! [SV31: $i,SV15: $i] :
( ( ~ ( ~ ( pi_remove @ SV15 @ SV31 )
| ( pi_sharp_remove @ ( i @ SV15 ) @ SV31 ) )
| ~ ( ~ ( pi_sharp_remove @ ( i @ SV15 ) @ SV31 )
| ( pi_remove @ SV15 @ SV31 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(183,plain,
! [SV40: $i,SV32: $i,SV16: $i] :
( ( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ SV16 @ SV32 @ SV40 ) ) )
| ( pi_sharp_find_min @ ( i @ ( triple @ SV16 @ SV32 @ SV40 ) ) @ ( findmin_cpq_res @ ( triple @ SV16 @ SV32 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(184,plain,
! [SV33: $i,SV17: $i] :
( ( ( ~ ( succ_cpq @ SV17 @ SV33 ) )
= $true )
| ( ( succ_cpq @ SV17 @ ( findmin_cpq_eff @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(185,plain,
! [SV41: $i,SV18: $i,SV34: $i] :
( ( ! [SY105: $i] :
( ~ ~ ( contains_slb @ SV34 @ SY105 )
| ( ( remove_cpq @ ( triple @ SV18 @ SV34 @ SV41 ) @ SY105 )
= ( triple @ SV18 @ SV34 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(186,plain,
! [SV19: $i] :
( ( ~ ( ~ ( pi_find_min @ SV19 )
| ~ ! [SY86: $i] :
~ ( pi_sharp_find_min @ ( i @ SV19 ) @ SY86 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(187,plain,
! [SV19: $i] :
( ( ~ ( ~ ~ ! [SY87: $i] :
~ ( pi_sharp_find_min @ ( i @ SV19 ) @ SY87 )
| ( pi_find_min @ SV19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(188,plain,
! [SV42: $i,SV20: $i,SV35: $i] :
( ( ! [SY106: $i] :
( ~ ( ( SV35 != create_slb ) )
| ( ( findmin_cpq_res @ ( triple @ SV20 @ SV35 @ SV42 ) )
= ( findmin_pqp_res @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(189,plain,
! [SV36: $i,SV43: $i,SV25: $i,SV7: $i] :
( ( ! [SY107: $i] :
( ( i @ ( triple @ SV7 @ ( insert_slb @ SV25 @ ( pair @ SV43 @ SY107 ) ) @ SV36 ) )
= ( insert_pq @ ( i @ ( triple @ SV7 @ SV25 @ SV36 ) ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(190,plain,
! [SV26: $i,SV8: $i] :
( ( ( ~ ( ~ ( contains_pq @ SV8 @ SV26 )
| ~ ( issmallestelement_pq @ SV8 @ SV26 ) ) )
= $false )
| ( ( ( findmin_pq_res @ SV8 @ SV26 )
= SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(191,plain,
! [SV27: $i,SV9: $i] :
( ( ~ ( ~ ( ok @ ( triple @ SV9 @ SV27 @ bad ) )
| $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(192,plain,
! [SV27: $i,SV9: $i] :
( ( ~ ( ~ $false
| ( ok @ ( triple @ SV9 @ SV27 @ bad ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(193,plain,
! [SV10: $i] :
( ( ~ ( pi_removemin @ SV10 )
| ~ ! [SY69: $i] :
~ ( pi_sharp_find_min @ ( i @ SV10 ) @ SY69 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(194,plain,
! [SV10: $i] :
( ( ~ ~ ! [SY70: $i] :
~ ( pi_sharp_find_min @ ( i @ SV10 ) @ SY70 )
| ( pi_removemin @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(195,plain,
! [SV11: $i] :
( ( ~ ( phi @ SV11 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SY71 )
| ~ ( ok @ SY71 ) )
| ~ ( check_cpq @ SY71 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(196,plain,
! [SV11: $i] :
( ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SY72 )
| ~ ( ok @ SY72 ) )
| ~ ( check_cpq @ SY72 ) )
| ( phi @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(197,plain,
! [SV37: $i] :
( ( ~ ( ~ ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SV37 )
| ( ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
!= ( findmin_pq_res @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SV37 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(198,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( ~ ( pi_sharp_find_min @ SV12 @ SV28 )
| ~ ( ~ ( contains_pq @ SV12 @ SV28 )
| ~ ( issmallestelement_pq @ SV12 @ SV28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(199,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( ~ ~ ( ~ ( contains_pq @ SV12 @ SV28 )
| ~ ( issmallestelement_pq @ SV12 @ SV28 ) )
| ( pi_sharp_find_min @ SV12 @ SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(200,plain,
! [SV44: $i,SV38: $i,SV29: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( contains_cpq @ ( triple @ SV13 @ SV29 @ SV38 ) @ SV44 )
| ( contains_slb @ SV29 @ SV44 ) )
| ~ ( ~ ( contains_slb @ SV29 @ SV44 )
| ( contains_cpq @ ( triple @ SV13 @ SV29 @ SV38 ) @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(201,plain,
! [SV39: $i,SV30: $i,SV14: $i] :
( ( ( ~ ~ ( ok @ ( triple @ SV14 @ SV30 @ SV39 ) ) )
= $true )
| ( ( SV39 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(202,plain,
! [SV31: $i,SV15: $i] :
( ( ~ ( ~ ( pi_remove @ SV15 @ SV31 )
| ( pi_sharp_remove @ ( i @ SV15 ) @ SV31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(203,plain,
! [SV31: $i,SV15: $i] :
( ( ~ ( ~ ( pi_sharp_remove @ ( i @ SV15 ) @ SV31 )
| ( pi_remove @ SV15 @ SV31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(204,plain,
! [SV40: $i,SV32: $i,SV16: $i] :
( ( ( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ SV16 @ SV32 @ SV40 ) ) ) )
= $true )
| ( ( pi_sharp_find_min @ ( i @ ( triple @ SV16 @ SV32 @ SV40 ) ) @ ( findmin_cpq_res @ ( triple @ SV16 @ SV32 @ SV40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(205,plain,
! [SV33: $i,SV17: $i] :
( ( ( succ_cpq @ SV17 @ SV33 )
= $false )
| ( ( succ_cpq @ SV17 @ ( findmin_cpq_eff @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(206,plain,
! [SV41: $i,SV18: $i,SV45: $i,SV34: $i] :
( ( ~ ~ ( contains_slb @ SV34 @ SV45 )
| ( ( remove_cpq @ ( triple @ SV18 @ SV34 @ SV41 ) @ SV45 )
= ( triple @ SV18 @ SV34 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(207,plain,
! [SV19: $i] :
( ( ~ ( pi_find_min @ SV19 )
| ~ ! [SY86: $i] :
~ ( pi_sharp_find_min @ ( i @ SV19 ) @ SY86 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(208,plain,
! [SV19: $i] :
( ( ~ ~ ! [SY87: $i] :
~ ( pi_sharp_find_min @ ( i @ SV19 ) @ SY87 )
| ( pi_find_min @ SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(209,plain,
! [SV42: $i,SV20: $i,SV35: $i] :
( ( ~ ( ( SV35 != create_slb ) )
| ( ( findmin_cpq_res @ ( triple @ SV20 @ SV35 @ SV42 ) )
= ( findmin_pqp_res @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(210,plain,
! [SV36: $i,SV47: $i,SV43: $i,SV25: $i,SV7: $i] :
( ( ( i @ ( triple @ SV7 @ ( insert_slb @ SV25 @ ( pair @ SV43 @ SV47 ) ) @ SV36 ) )
= ( insert_pq @ ( i @ ( triple @ SV7 @ SV25 @ SV36 ) ) @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(211,plain,
! [SV26: $i,SV8: $i] :
( ( ( ~ ( contains_pq @ SV8 @ SV26 )
| ~ ( issmallestelement_pq @ SV8 @ SV26 ) )
= $true )
| ( ( ( findmin_pq_res @ SV8 @ SV26 )
= SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(212,plain,
! [SV27: $i,SV9: $i] :
( ( ~ ( ok @ ( triple @ SV9 @ SV27 @ bad ) )
| $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(213,plain,
! [SV27: $i,SV9: $i] :
( ( ~ $false
| ( ok @ ( triple @ SV9 @ SV27 @ bad ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(214,plain,
! [SV10: $i] :
( ( ( ~ ( pi_removemin @ SV10 ) )
= $true )
| ( ( ~ ! [SY69: $i] :
~ ( pi_sharp_find_min @ ( i @ SV10 ) @ SY69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(215,plain,
! [SV10: $i] :
( ( ( ~ ~ ! [SY70: $i] :
~ ( pi_sharp_find_min @ ( i @ SV10 ) @ SY70 ) )
= $true )
| ( ( pi_removemin @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(216,plain,
! [SV11: $i] :
( ( ( ~ ( phi @ SV11 ) )
= $true )
| ( ( ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SY71 )
| ~ ( ok @ SY71 ) )
| ~ ( check_cpq @ SY71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(217,plain,
! [SV11: $i] :
( ( ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SY72 )
| ~ ( ok @ SY72 ) )
| ~ ( check_cpq @ SY72 ) ) )
= $true )
| ( ( phi @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(218,plain,
! [SV37: $i] :
( ( ~ ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SV37 )
| ( ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
!= ( findmin_pq_res @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SV37 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(219,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( pi_sharp_find_min @ SV12 @ SV28 )
| ~ ( ~ ( contains_pq @ SV12 @ SV28 )
| ~ ( issmallestelement_pq @ SV12 @ SV28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(220,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ~ ( ~ ( contains_pq @ SV12 @ SV28 )
| ~ ( issmallestelement_pq @ SV12 @ SV28 ) )
| ( pi_sharp_find_min @ SV12 @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(221,plain,
! [SV44: $i,SV38: $i,SV29: $i,SV13: $i] :
( ( ~ ( ~ ( contains_cpq @ ( triple @ SV13 @ SV29 @ SV38 ) @ SV44 )
| ( contains_slb @ SV29 @ SV44 ) )
| ~ ( ~ ( contains_slb @ SV29 @ SV44 )
| ( contains_cpq @ ( triple @ SV13 @ SV29 @ SV38 ) @ SV44 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(222,plain,
! [SV39: $i,SV30: $i,SV14: $i] :
( ( ( ~ ( ok @ ( triple @ SV14 @ SV30 @ SV39 ) ) )
= $false )
| ( ( SV39 = bad )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(223,plain,
! [SV31: $i,SV15: $i] :
( ( ~ ( pi_remove @ SV15 @ SV31 )
| ( pi_sharp_remove @ ( i @ SV15 ) @ SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(224,plain,
! [SV31: $i,SV15: $i] :
( ( ~ ( pi_sharp_remove @ ( i @ SV15 ) @ SV31 )
| ( pi_remove @ SV15 @ SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(225,plain,
! [SV40: $i,SV32: $i,SV16: $i] :
( ( ( phi @ ( findmin_cpq_eff @ ( triple @ SV16 @ SV32 @ SV40 ) ) )
= $false )
| ( ( pi_sharp_find_min @ ( i @ ( triple @ SV16 @ SV32 @ SV40 ) ) @ ( findmin_cpq_res @ ( triple @ SV16 @ SV32 @ SV40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(226,plain,
! [SV41: $i,SV18: $i,SV45: $i,SV34: $i] :
( ( ( ~ ~ ( contains_slb @ SV34 @ SV45 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV18 @ SV34 @ SV41 ) @ SV45 )
= ( triple @ SV18 @ SV34 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(227,plain,
! [SV19: $i] :
( ( ( ~ ( pi_find_min @ SV19 ) )
= $true )
| ( ( ~ ! [SY86: $i] :
~ ( pi_sharp_find_min @ ( i @ SV19 ) @ SY86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(228,plain,
! [SV19: $i] :
( ( ( ~ ~ ! [SY87: $i] :
~ ( pi_sharp_find_min @ ( i @ SV19 ) @ SY87 ) )
= $true )
| ( ( pi_find_min @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(229,plain,
! [SV42: $i,SV20: $i,SV35: $i] :
( ( ( ~ ( ( SV35 != create_slb ) ) )
= $true )
| ( ( ( findmin_cpq_res @ ( triple @ SV20 @ SV35 @ SV42 ) )
= ( findmin_pqp_res @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(230,plain,
! [SV26: $i,SV8: $i] :
( ( ( ~ ( contains_pq @ SV8 @ SV26 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV8 @ SV26 ) )
= $true )
| ( ( ( findmin_pq_res @ SV8 @ SV26 )
= SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(231,plain,
! [SV27: $i,SV9: $i] :
( ( ( ~ ( ok @ ( triple @ SV9 @ SV27 @ bad ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(232,plain,
! [SV27: $i,SV9: $i] :
( ( ( ~ $false ) = $true )
| ( ( ok @ ( triple @ SV9 @ SV27 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(233,plain,
! [SV10: $i] :
( ( ( pi_removemin @ SV10 )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ( pi_sharp_find_min @ ( i @ SV10 ) @ SY69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(234,plain,
! [SV10: $i] :
( ( ( ~ ! [SY70: $i] :
~ ( pi_sharp_find_min @ ( i @ SV10 ) @ SY70 ) )
= $false )
| ( ( pi_removemin @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(235,plain,
! [SV11: $i] :
( ( ( phi @ SV11 )
= $false )
| ( ( ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SY71 )
| ~ ( ok @ SY71 ) )
| ~ ( check_cpq @ SY71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(236,plain,
! [SV11: $i] :
( ( ( ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SY72 )
| ~ ( ok @ SY72 ) )
| ~ ( check_cpq @ SY72 ) ) )
= $false )
| ( ( phi @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(237,plain,
! [SV37: $i] :
( ( ( ~ ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SV37 ) )
= $true )
| ( ( ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
!= ( findmin_pq_res @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(238,plain,
! [SV28: $i,SV12: $i] :
( ( ( ~ ( pi_sharp_find_min @ SV12 @ SV28 ) )
= $true )
| ( ( ~ ( ~ ( contains_pq @ SV12 @ SV28 )
| ~ ( issmallestelement_pq @ SV12 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(239,plain,
! [SV28: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( contains_pq @ SV12 @ SV28 )
| ~ ( issmallestelement_pq @ SV12 @ SV28 ) ) )
= $true )
| ( ( pi_sharp_find_min @ SV12 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(240,plain,
! [SV44: $i,SV38: $i,SV29: $i,SV13: $i] :
( ( ~ ( ~ ( contains_cpq @ ( triple @ SV13 @ SV29 @ SV38 ) @ SV44 )
| ( contains_slb @ SV29 @ SV44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(241,plain,
! [SV38: $i,SV13: $i,SV44: $i,SV29: $i] :
( ( ~ ( ~ ( contains_slb @ SV29 @ SV44 )
| ( contains_cpq @ ( triple @ SV13 @ SV29 @ SV38 ) @ SV44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(242,plain,
! [SV39: $i,SV30: $i,SV14: $i] :
( ( ( ok @ ( triple @ SV14 @ SV30 @ SV39 ) )
= $true )
| ( ( SV39 = bad )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(243,plain,
! [SV31: $i,SV15: $i] :
( ( ( ~ ( pi_remove @ SV15 @ SV31 ) )
= $true )
| ( ( pi_sharp_remove @ ( i @ SV15 ) @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(244,plain,
! [SV31: $i,SV15: $i] :
( ( ( ~ ( pi_sharp_remove @ ( i @ SV15 ) @ SV31 ) )
= $true )
| ( ( pi_remove @ SV15 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(245,plain,
! [SV41: $i,SV18: $i,SV45: $i,SV34: $i] :
( ( ( ~ ( contains_slb @ SV34 @ SV45 ) )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV18 @ SV34 @ SV41 ) @ SV45 )
= ( triple @ SV18 @ SV34 @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(246,plain,
! [SV19: $i] :
( ( ( pi_find_min @ SV19 )
= $false )
| ( ( ~ ! [SY86: $i] :
~ ( pi_sharp_find_min @ ( i @ SV19 ) @ SY86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(247,plain,
! [SV19: $i] :
( ( ( ~ ! [SY87: $i] :
~ ( pi_sharp_find_min @ ( i @ SV19 ) @ SY87 ) )
= $false )
| ( ( pi_find_min @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(248,plain,
! [SV42: $i,SV20: $i,SV35: $i] :
( ( ( SV35 != create_slb )
= $false )
| ( ( ( findmin_cpq_res @ ( triple @ SV20 @ SV35 @ SV42 ) )
= ( findmin_pqp_res @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(249,plain,
! [SV26: $i,SV8: $i] :
( ( ( contains_pq @ SV8 @ SV26 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV8 @ SV26 ) )
= $true )
| ( ( ( findmin_pq_res @ SV8 @ SV26 )
= SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(250,plain,
! [SV27: $i,SV9: $i] :
( ( ( ok @ ( triple @ SV9 @ SV27 @ bad ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(251,plain,
! [SV27: $i,SV9: $i] :
( ( $false = $false )
| ( ( ok @ ( triple @ SV9 @ SV27 @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(252,plain,
! [SV10: $i] :
( ( ( ! [SY69: $i] :
~ ( pi_sharp_find_min @ ( i @ SV10 ) @ SY69 ) )
= $false )
| ( ( pi_removemin @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(253,plain,
! [SV10: $i] :
( ( ( ! [SY70: $i] :
~ ( pi_sharp_find_min @ ( i @ SV10 ) @ SY70 ) )
= $true )
| ( ( pi_removemin @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(254,plain,
! [SV11: $i] :
( ( ( ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SY71 )
| ~ ( ok @ SY71 ) )
| ~ ( check_cpq @ SY71 ) ) )
= $false )
| ( ( phi @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(255,plain,
! [SV11: $i] :
( ( ( ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SY72 )
| ~ ( ok @ SY72 ) )
| ~ ( check_cpq @ SY72 ) ) )
= $true )
| ( ( phi @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(256,plain,
! [SV37: $i] :
( ( ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SV37 )
= $false )
| ( ( ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
!= ( findmin_pq_res @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(257,plain,
! [SV28: $i,SV12: $i] :
( ( ( pi_sharp_find_min @ SV12 @ SV28 )
= $false )
| ( ( ~ ( ~ ( contains_pq @ SV12 @ SV28 )
| ~ ( issmallestelement_pq @ SV12 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(258,plain,
! [SV28: $i,SV12: $i] :
( ( ( ~ ( ~ ( contains_pq @ SV12 @ SV28 )
| ~ ( issmallestelement_pq @ SV12 @ SV28 ) ) )
= $false )
| ( ( pi_sharp_find_min @ SV12 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(259,plain,
! [SV44: $i,SV38: $i,SV29: $i,SV13: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV13 @ SV29 @ SV38 ) @ SV44 )
| ( contains_slb @ SV29 @ SV44 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(260,plain,
! [SV38: $i,SV13: $i,SV44: $i,SV29: $i] :
( ( ~ ( contains_slb @ SV29 @ SV44 )
| ( contains_cpq @ ( triple @ SV13 @ SV29 @ SV38 ) @ SV44 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(261,plain,
! [SV31: $i,SV15: $i] :
( ( ( pi_remove @ SV15 @ SV31 )
= $false )
| ( ( pi_sharp_remove @ ( i @ SV15 ) @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(262,plain,
! [SV31: $i,SV15: $i] :
( ( ( pi_sharp_remove @ ( i @ SV15 ) @ SV31 )
= $false )
| ( ( pi_remove @ SV15 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(263,plain,
! [SV41: $i,SV18: $i,SV45: $i,SV34: $i] :
( ( ( contains_slb @ SV34 @ SV45 )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV18 @ SV34 @ SV41 ) @ SV45 )
= ( triple @ SV18 @ SV34 @ bad ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(264,plain,
! [SV19: $i] :
( ( ( ! [SY86: $i] :
~ ( pi_sharp_find_min @ ( i @ SV19 ) @ SY86 ) )
= $false )
| ( ( pi_find_min @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(265,plain,
! [SV19: $i] :
( ( ( ! [SY87: $i] :
~ ( pi_sharp_find_min @ ( i @ SV19 ) @ SY87 ) )
= $true )
| ( ( pi_find_min @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(266,plain,
! [SV42: $i,SV20: $i,SV35: $i] :
( ( ( SV35 = create_slb )
= $true )
| ( ( ( findmin_cpq_res @ ( triple @ SV20 @ SV35 @ SV42 ) )
= ( findmin_pqp_res @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(267,plain,
! [SV26: $i,SV8: $i] :
( ( ( issmallestelement_pq @ SV8 @ SV26 )
= $false )
| ( ( contains_pq @ SV8 @ SV26 )
= $false )
| ( ( ( findmin_pq_res @ SV8 @ SV26 )
= SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(268,plain,
! [SV10: $i] :
( ( ( ~ ( pi_sharp_find_min @ ( i @ SV10 ) @ ( sK4_SY69 @ SV10 ) ) )
= $false )
| ( ( pi_removemin @ SV10 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[252]) ).
thf(269,plain,
! [SV48: $i,SV10: $i] :
( ( ( ~ ( pi_sharp_find_min @ ( i @ SV10 ) @ SV48 ) )
= $true )
| ( ( pi_removemin @ SV10 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(270,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ ( sK5_SY71 @ SV11 ) )
| ~ ( ok @ ( sK5_SY71 @ SV11 ) ) )
| ~ ( check_cpq @ ( sK5_SY71 @ SV11 ) ) ) )
= $false )
| ( ( phi @ SV11 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[254]) ).
thf(271,plain,
! [SV49: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SV49 )
| ~ ( ok @ SV49 ) )
| ~ ( check_cpq @ SV49 ) ) )
= $true )
| ( ( phi @ SV11 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(272,plain,
! [SV37: $i] :
( ( ( ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) )
= ( findmin_pq_res @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SV37 ) )
= $false )
| ( ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY53 @ sK3_SY56 ) ) @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(273,plain,
! [SV28: $i,SV12: $i] :
( ( ( ~ ( contains_pq @ SV12 @ SV28 )
| ~ ( issmallestelement_pq @ SV12 @ SV28 ) )
= $false )
| ( ( pi_sharp_find_min @ SV12 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(274,plain,
! [SV28: $i,SV12: $i] :
( ( ( ~ ( contains_pq @ SV12 @ SV28 )
| ~ ( issmallestelement_pq @ SV12 @ SV28 ) )
= $true )
| ( ( pi_sharp_find_min @ SV12 @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(275,plain,
! [SV44: $i,SV38: $i,SV29: $i,SV13: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV13 @ SV29 @ SV38 ) @ SV44 ) )
= $true )
| ( ( contains_slb @ SV29 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(276,plain,
! [SV38: $i,SV13: $i,SV44: $i,SV29: $i] :
( ( ( ~ ( contains_slb @ SV29 @ SV44 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV13 @ SV29 @ SV38 ) @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(277,plain,
! [SV19: $i] :
( ( ( ~ ( pi_sharp_find_min @ ( i @ SV19 ) @ ( sK6_SY86 @ SV19 ) ) )
= $false )
| ( ( pi_find_min @ SV19 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[264]) ).
thf(278,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ( pi_sharp_find_min @ ( i @ SV19 ) @ SV50 ) )
= $true )
| ( ( pi_find_min @ SV19 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(279,plain,
! [SV10: $i] :
( ( ( pi_sharp_find_min @ ( i @ SV10 ) @ ( sK4_SY69 @ SV10 ) )
= $true )
| ( ( pi_removemin @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(280,plain,
! [SV48: $i,SV10: $i] :
( ( ( pi_sharp_find_min @ ( i @ SV10 ) @ SV48 )
= $false )
| ( ( pi_removemin @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(281,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ ( sK5_SY71 @ SV11 ) )
| ~ ( ok @ ( sK5_SY71 @ SV11 ) ) )
| ~ ( check_cpq @ ( sK5_SY71 @ SV11 ) ) ) )
= $true )
| ( ( phi @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(282,plain,
! [SV49: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SV49 )
| ~ ( ok @ SV49 ) )
| ~ ( check_cpq @ SV49 ) ) )
= $false )
| ( ( phi @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(283,plain,
! [SV28: $i,SV12: $i] :
( ( ( ~ ( contains_pq @ SV12 @ SV28 ) )
= $false )
| ( ( pi_sharp_find_min @ SV12 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(284,plain,
! [SV28: $i,SV12: $i] :
( ( ( ~ ( issmallestelement_pq @ SV12 @ SV28 ) )
= $false )
| ( ( pi_sharp_find_min @ SV12 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(285,plain,
! [SV28: $i,SV12: $i] :
( ( ( ~ ( contains_pq @ SV12 @ SV28 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV12 @ SV28 ) )
= $true )
| ( ( pi_sharp_find_min @ SV12 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(286,plain,
! [SV44: $i,SV38: $i,SV29: $i,SV13: $i] :
( ( ( contains_cpq @ ( triple @ SV13 @ SV29 @ SV38 ) @ SV44 )
= $false )
| ( ( contains_slb @ SV29 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(287,plain,
! [SV38: $i,SV13: $i,SV44: $i,SV29: $i] :
( ( ( contains_slb @ SV29 @ SV44 )
= $false )
| ( ( contains_cpq @ ( triple @ SV13 @ SV29 @ SV38 ) @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(288,plain,
! [SV19: $i] :
( ( ( pi_sharp_find_min @ ( i @ SV19 ) @ ( sK6_SY86 @ SV19 ) )
= $true )
| ( ( pi_find_min @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(289,plain,
! [SV50: $i,SV19: $i] :
( ( ( pi_sharp_find_min @ ( i @ SV19 ) @ SV50 )
= $false )
| ( ( pi_find_min @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(290,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( succ_cpq @ SV11 @ ( sK5_SY71 @ SV11 ) )
| ~ ( ok @ ( sK5_SY71 @ SV11 ) ) )
| ~ ( check_cpq @ ( sK5_SY71 @ SV11 ) ) )
= $false )
| ( ( phi @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(291,plain,
! [SV49: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SV49 )
| ~ ( ok @ SV49 ) )
| ~ ( check_cpq @ SV49 ) )
= $true )
| ( ( phi @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(292,plain,
! [SV28: $i,SV12: $i] :
( ( ( contains_pq @ SV12 @ SV28 )
= $true )
| ( ( pi_sharp_find_min @ SV12 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(293,plain,
! [SV28: $i,SV12: $i] :
( ( ( issmallestelement_pq @ SV12 @ SV28 )
= $true )
| ( ( pi_sharp_find_min @ SV12 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(294,plain,
! [SV28: $i,SV12: $i] :
( ( ( contains_pq @ SV12 @ SV28 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV12 @ SV28 ) )
= $true )
| ( ( pi_sharp_find_min @ SV12 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(295,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( succ_cpq @ SV11 @ ( sK5_SY71 @ SV11 ) )
| ~ ( ok @ ( sK5_SY71 @ SV11 ) ) ) )
= $false )
| ( ( phi @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(296,plain,
! [SV11: $i] :
( ( ( ~ ( check_cpq @ ( sK5_SY71 @ SV11 ) ) )
= $false )
| ( ( phi @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(297,plain,
! [SV49: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( succ_cpq @ SV11 @ SV49 )
| ~ ( ok @ SV49 ) ) )
= $true )
| ( ( ~ ( check_cpq @ SV49 ) )
= $true )
| ( ( phi @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(298,plain,
! [SV28: $i,SV12: $i] :
( ( ( issmallestelement_pq @ SV12 @ SV28 )
= $false )
| ( ( contains_pq @ SV12 @ SV28 )
= $false )
| ( ( pi_sharp_find_min @ SV12 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(299,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( succ_cpq @ SV11 @ ( sK5_SY71 @ SV11 ) )
| ~ ( ok @ ( sK5_SY71 @ SV11 ) ) ) )
= $true )
| ( ( phi @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(300,plain,
! [SV11: $i] :
( ( ( check_cpq @ ( sK5_SY71 @ SV11 ) )
= $true )
| ( ( phi @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(301,plain,
! [SV49: $i,SV11: $i] :
( ( ( ~ ( ~ ( succ_cpq @ SV11 @ SV49 )
| ~ ( ok @ SV49 ) ) )
= $false )
| ( ( ~ ( check_cpq @ SV49 ) )
= $true )
| ( ( phi @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(302,plain,
! [SV11: $i] :
( ( ( ~ ( succ_cpq @ SV11 @ ( sK5_SY71 @ SV11 ) )
| ~ ( ok @ ( sK5_SY71 @ SV11 ) ) )
= $false )
| ( ( phi @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(303,plain,
! [SV49: $i,SV11: $i] :
( ( ( ~ ( succ_cpq @ SV11 @ SV49 )
| ~ ( ok @ SV49 ) )
= $true )
| ( ( ~ ( check_cpq @ SV49 ) )
= $true )
| ( ( phi @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(304,plain,
! [SV11: $i] :
( ( ( ~ ( succ_cpq @ SV11 @ ( sK5_SY71 @ SV11 ) ) )
= $false )
| ( ( phi @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(305,plain,
! [SV11: $i] :
( ( ( ~ ( ok @ ( sK5_SY71 @ SV11 ) ) )
= $false )
| ( ( phi @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(306,plain,
! [SV49: $i,SV11: $i] :
( ( ( ~ ( succ_cpq @ SV11 @ SV49 ) )
= $true )
| ( ( ~ ( ok @ SV49 ) )
= $true )
| ( ( ~ ( check_cpq @ SV49 ) )
= $true )
| ( ( phi @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(307,plain,
! [SV11: $i] :
( ( ( succ_cpq @ SV11 @ ( sK5_SY71 @ SV11 ) )
= $true )
| ( ( phi @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(308,plain,
! [SV11: $i] :
( ( ( ok @ ( sK5_SY71 @ SV11 ) )
= $true )
| ( ( phi @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(309,plain,
! [SV49: $i,SV11: $i] :
( ( ( succ_cpq @ SV11 @ SV49 )
= $false )
| ( ( ~ ( ok @ SV49 ) )
= $true )
| ( ( ~ ( check_cpq @ SV49 ) )
= $true )
| ( ( phi @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(310,plain,
! [SV11: $i,SV49: $i] :
( ( ( ok @ SV49 )
= $false )
| ( ( succ_cpq @ SV11 @ SV49 )
= $false )
| ( ( ~ ( check_cpq @ SV49 ) )
= $true )
| ( ( phi @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(311,plain,
! [SV11: $i,SV49: $i] :
( ( ( check_cpq @ SV49 )
= $false )
| ( ( succ_cpq @ SV11 @ SV49 )
= $false )
| ( ( ok @ SV49 )
= $false )
| ( ( phi @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(312,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[114,311,308,307,300,298,293,292,289,288,287,286,280,279,272,267,266,263,262,261,251,250,242,225,210,205,155,154,153,152,135,134,115]) ).
thf(313,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[312]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV417+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n011.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 16:28:21 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.17/0.46
% 1.17/0.46 No.of.Axioms: 20
% 1.17/0.46
% 1.17/0.46 Length.of.Defs: 0
% 1.17/0.46
% 1.17/0.46 Contains.Choice.Funs: false
% 1.17/0.46 ........
% 1.17/0.46
% 1.17/0.46 ********************************
% 1.17/0.46 * All subproblems solved! *
% 1.17/0.46 ********************************
% 1.17/0.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:22,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:312,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.17/0.46
% 1.17/0.46 %**** Beginning of derivation protocol ****
% 1.17/0.46 % SZS output start CNFRefutation
% See solution above
% 1.17/0.46
% 1.17/0.46 %**** End of derivation protocol ****
% 1.17/0.46 %**** no. of clauses in derivation: 270 ****
% 1.17/0.46 %**** clause counter: 312 ****
% 1.17/0.46
% 1.17/0.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:22,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:312,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------