%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV376+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 : n015.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 10:57:31 AM UTC 2026
% Result : Theorem 0.56s 0.39s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 10
% Syntax : Number of formulae : 153 ( 73 unt; 0 typ; 0 def)
% Number of atoms : 942 ( 259 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 2612 ( 331 ~; 240 |; 0 &;1990 @)
% ( 3 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 17 con; 0-3 aty)
% Number of variables : 618 ( 0 ^; 618 !; 0 ?; 618 :)
% 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_slb,type,
contains_slb: $i > $i > $o ).
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_pqp_res,type,
findmin_pqp_res: $i > $i ).
thf(tp_im_succ_cpq,type,
im_succ_cpq: $i > $i ).
thf(tp_insert_cpq,type,
insert_cpq: $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_slb,type,
isnonempty_slb: $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_remove_cpq,type,
remove_cpq: $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_sK10_SY76,type,
sK10_SY76: $i ).
thf(tp_sK11_SY79,type,
sK11_SY79: $i ).
thf(tp_sK12_SY81,type,
sK12_SY81: $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SY37,type,
sK2_SY37: $i ).
thf(tp_sK3_SY42,type,
sK3_SY42: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY61,type,
sK5_SY61: $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i ).
thf(tp_sK7_SY66,type,
sK7_SY66: $i ).
thf(tp_sK8_SY67,type,
sK8_SY67: $i ).
thf(tp_sK9_SY72,type,
sK9_SY72: $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,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ( succ_cpq @ ( triple @ U @ V @ W ) @ ( triple @ X @ Y @ Z ) )
=> ( ~ ( ok @ ( triple @ X @ Y @ Z ) )
=> ~ ( ok @ ( im_succ_cpq @ ( triple @ X @ Y @ Z ) ) ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ok @ ( triple @ X1 @ X2 @ X3 ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ( succ_cpq @ ( triple @ X1 @ X2 @ X3 ) @ ( triple @ X4 @ X5 @ X6 ) )
=> ~ ( ok @ ( triple @ X4 @ X5 @ X6 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12_induction) ).
thf(14,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
thf(15,axiom,
! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).
thf(20,axiom,
! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).
thf(21,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(22,axiom,
! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).
thf(23,axiom,
! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).
thf(24,axiom,
! [U: $i] : ( succ_cpq @ U @ U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
thf(43,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ~ ( ok @ ( im_succ_cpq @ ( triple @ U @ V @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12_l13) ).
thf(44,conjecture,
! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ! [X: $i,Y: $i,Z: $i] :
( ( succ_cpq @ ( triple @ U @ V @ W ) @ ( triple @ X @ Y @ Z ) )
=> ~ ( ok @ ( triple @ X @ Y @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12_co) ).
thf(45,negated_conjecture,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ! [X: $i,Y: $i,Z: $i] :
( ( succ_cpq @ ( triple @ U @ V @ W ) @ ( triple @ X @ Y @ Z ) )
=> ~ ( ok @ ( triple @ X @ Y @ Z ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[44]) ).
thf(46,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ! [X: $i,Y: $i,Z: $i] :
( ( succ_cpq @ ( triple @ U @ V @ W ) @ ( triple @ X @ Y @ Z ) )
=> ~ ( ok @ ( triple @ X @ Y @ Z ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[45]) ).
thf(47,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ( succ_cpq @ ( triple @ U @ V @ W ) @ ( triple @ X @ Y @ Z ) )
=> ( ~ ( ok @ ( triple @ X @ Y @ Z ) )
=> ~ ( ok @ ( im_succ_cpq @ ( triple @ X @ Y @ Z ) ) ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ok @ ( triple @ X1 @ X2 @ X3 ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ( succ_cpq @ ( triple @ X1 @ X2 @ X3 ) @ ( triple @ X4 @ X5 @ X6 ) )
=> ~ ( ok @ ( triple @ X4 @ X5 @ X6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(48,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(49,plain,
( ( ! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(50,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(51,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(52,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(53,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(54,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(55,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ~ ( ok @ ( im_succ_cpq @ ( triple @ U @ V @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(56,plain,
( ( ! [SY37: $i,SY38: $i] :
( ~ ( ok @ ( triple @ sK1_U @ SY37 @ SY38 ) )
=> ! [SY39: $i,SY40: $i,SY41: $i] :
( ( succ_cpq @ ( triple @ sK1_U @ SY37 @ SY38 ) @ ( triple @ SY39 @ SY40 @ SY41 ) )
=> ~ ( ok @ ( triple @ SY39 @ SY40 @ SY41 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(57,plain,
( ( ! [SY42: $i] :
( ~ ( ok @ ( triple @ sK1_U @ sK2_SY37 @ SY42 ) )
=> ! [SY43: $i,SY44: $i,SY45: $i] :
( ( succ_cpq @ ( triple @ sK1_U @ sK2_SY37 @ SY42 ) @ ( triple @ SY43 @ SY44 @ SY45 ) )
=> ~ ( ok @ ( triple @ SY43 @ SY44 @ SY45 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(58,plain,
( ( ~ ( ok @ ( triple @ sK1_U @ sK2_SY37 @ sK3_SY42 ) )
=> ! [SY46: $i,SY47: $i,SY48: $i] :
( ( succ_cpq @ ( triple @ sK1_U @ sK2_SY37 @ sK3_SY42 ) @ ( triple @ SY46 @ SY47 @ SY48 ) )
=> ~ ( ok @ ( triple @ SY46 @ SY47 @ SY48 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(59,plain,
( ( ~ ( ok @ ( triple @ sK1_U @ sK2_SY37 @ sK3_SY42 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[58]) ).
thf(60,plain,
( ( ! [SY46: $i,SY47: $i,SY48: $i] :
( ( succ_cpq @ ( triple @ sK1_U @ sK2_SY37 @ sK3_SY42 ) @ ( triple @ SY46 @ SY47 @ SY48 ) )
=> ~ ( ok @ ( triple @ SY46 @ SY47 @ SY48 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[58]) ).
thf(61,plain,
( ( ~ ! [SY46: $i,SY47: $i,SY48: $i] :
( ( succ_cpq @ ( triple @ sK1_U @ sK2_SY37 @ sK3_SY42 ) @ ( triple @ SY46 @ SY47 @ SY48 ) )
=> ~ ( ok @ ( triple @ SY46 @ SY47 @ SY48 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[60]) ).
thf(62,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ~ ( ok @ ( im_succ_cpq @ ( triple @ U @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(63,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(64,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(65,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(66,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(67,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(68,plain,
( ( ! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(69,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(70,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ( succ_cpq @ ( triple @ U @ V @ W ) @ ( triple @ X @ Y @ Z ) )
=> ( ~ ( ok @ ( triple @ X @ Y @ Z ) )
=> ~ ( ok @ ( im_succ_cpq @ ( triple @ X @ Y @ Z ) ) ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ok @ ( triple @ X1 @ X2 @ X3 ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ( succ_cpq @ ( triple @ X1 @ X2 @ X3 ) @ ( triple @ X4 @ X5 @ X6 ) )
=> ~ ( ok @ ( triple @ X4 @ X5 @ X6 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(71,plain,
( ( ~ ( ok @ ( triple @ sK1_U @ sK2_SY37 @ sK3_SY42 ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(72,plain,
( ( ~ ! [SY46: $i,SY47: $i,SY48: $i] :
( ( succ_cpq @ ( triple @ sK1_U @ sK2_SY37 @ sK3_SY42 ) @ ( triple @ SY46 @ SY47 @ SY48 ) )
=> ~ ( ok @ ( triple @ SY46 @ SY47 @ SY48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( succ_cpq @ SX0 @ SX1 )
| ( succ_cpq @ SX0 @ ( findmin_cpq_eff @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( succ_cpq @ SX0 @ SX1 )
| ( succ_cpq @ SX0 @ ( insert_cpq @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(75,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( succ_cpq @ ( triple @ sK1_U @ sK2_SY37 @ sK3_SY42 ) @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(76,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( succ_cpq @ SX0 @ SX1 )
| ( succ_cpq @ SX0 @ ( remove_cpq @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( succ_cpq @ SX0 @ SX1 )
| ( succ_cpq @ SX0 @ ( removemin_cpq_eff @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(78,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ok @ ( triple @ SX0 @ SX1 @ bad ) )
| $false )
| ~ ( ~ $false
| ( ok @ ( triple @ SX0 @ SX1 @ bad ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(79,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( im_succ_cpq @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) )
| ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(80,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ( SX2 = bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(81,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ~ ( ok @ ( im_succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(82,plain,
! [SV1: $i] :
( ( succ_cpq @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(83,plain,
( ( ok @ ( triple @ sK1_U @ sK2_SY37 @ sK3_SY42 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(84,plain,
! [SV2: $i] :
( ( ! [SY49: $i] :
( ~ ( succ_cpq @ SV2 @ SY49 )
| ( succ_cpq @ SV2 @ ( findmin_cpq_eff @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(85,plain,
! [SV3: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ~ ( succ_cpq @ SV3 @ SY50 )
| ( succ_cpq @ SV3 @ ( insert_cpq @ SY50 @ SY51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( succ_cpq @ ( triple @ sK1_U @ sK2_SY37 @ sK3_SY42 ) @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(87,plain,
! [SV4: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ( succ_cpq @ SV4 @ SY52 )
| ( succ_cpq @ SV4 @ ( remove_cpq @ SY52 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(88,plain,
! [SV5: $i] :
( ( ! [SY54: $i] :
( ~ ( succ_cpq @ SV5 @ SY54 )
| ( succ_cpq @ SV5 @ ( removemin_cpq_eff @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(89,plain,
! [SV6: $i] :
( ( ! [SY55: $i] :
~ ( ~ ( ~ ( ok @ ( triple @ SV6 @ SY55 @ bad ) )
| $false )
| ~ ( ~ $false
| ( ok @ ( triple @ SV6 @ SY55 @ bad ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(90,plain,
( ( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( im_succ_cpq @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(91,plain,
! [SV7: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ~ ~ ( ok @ ( triple @ SV7 @ SY56 @ SY57 ) )
| ( SY57 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(92,plain,
! [SV8: $i] :
( ( ! [SY58: $i,SY59: $i] :
( ~ ~ ( ok @ ( triple @ SV8 @ SY58 @ SY59 ) )
| ~ ( ok @ ( im_succ_cpq @ ( triple @ SV8 @ SY58 @ SY59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(93,plain,
! [SV9: $i,SV2: $i] :
( ( ~ ( succ_cpq @ SV2 @ SV9 )
| ( succ_cpq @ SV2 @ ( findmin_cpq_eff @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(94,plain,
! [SV10: $i,SV3: $i] :
( ( ! [SY60: $i] :
( ~ ( succ_cpq @ SV3 @ SV10 )
| ( succ_cpq @ SV3 @ ( insert_cpq @ SV10 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(95,plain,
( ( ! [SY61: $i,SY62: $i] :
( ~ ( succ_cpq @ ( triple @ sK1_U @ sK2_SY37 @ sK3_SY42 ) @ ( triple @ sK4_SX0 @ SY61 @ SY62 ) )
| ~ ( ok @ ( triple @ sK4_SX0 @ SY61 @ SY62 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(96,plain,
! [SV11: $i,SV4: $i] :
( ( ! [SY63: $i] :
( ~ ( succ_cpq @ SV4 @ SV11 )
| ( succ_cpq @ SV4 @ ( remove_cpq @ SV11 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(97,plain,
! [SV12: $i,SV5: $i] :
( ( ~ ( succ_cpq @ SV5 @ SV12 )
| ( succ_cpq @ SV5 @ ( removemin_cpq_eff @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(98,plain,
! [SV13: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( ok @ ( triple @ SV6 @ SV13 @ bad ) )
| $false )
| ~ ( ~ $false
| ( ok @ ( triple @ SV6 @ SV13 @ bad ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(99,plain,
( ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( im_succ_cpq @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(100,plain,
! [SV14: $i,SV7: $i] :
( ( ! [SY64: $i] :
( ~ ~ ( ok @ ( triple @ SV7 @ SV14 @ SY64 ) )
| ( SY64 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(101,plain,
! [SV15: $i,SV8: $i] :
( ( ! [SY65: $i] :
( ~ ~ ( ok @ ( triple @ SV8 @ SV15 @ SY65 ) )
| ~ ( ok @ ( im_succ_cpq @ ( triple @ SV8 @ SV15 @ SY65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(102,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ( succ_cpq @ SV2 @ SV9 ) )
= $true )
| ( ( succ_cpq @ SV2 @ ( findmin_cpq_eff @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(103,plain,
! [SV16: $i,SV10: $i,SV3: $i] :
( ( ~ ( succ_cpq @ SV3 @ SV10 )
| ( succ_cpq @ SV3 @ ( insert_cpq @ SV10 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(104,plain,
( ( ! [SY66: $i] :
( ~ ( succ_cpq @ ( triple @ sK1_U @ sK2_SY37 @ sK3_SY42 ) @ ( triple @ sK4_SX0 @ sK5_SY61 @ SY66 ) )
| ~ ( ok @ ( triple @ sK4_SX0 @ sK5_SY61 @ SY66 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[95]) ).
thf(105,plain,
! [SV17: $i,SV11: $i,SV4: $i] :
( ( ~ ( succ_cpq @ SV4 @ SV11 )
| ( succ_cpq @ SV4 @ ( remove_cpq @ SV11 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV12: $i,SV5: $i] :
( ( ( ~ ( succ_cpq @ SV5 @ SV12 ) )
= $true )
| ( ( succ_cpq @ SV5 @ ( removemin_cpq_eff @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(107,plain,
! [SV13: $i,SV6: $i] :
( ( ~ ( ~ ( ok @ ( triple @ SV6 @ SV13 @ bad ) )
| $false )
| ~ ( ~ $false
| ( ok @ ( triple @ SV6 @ SV13 @ bad ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(108,plain,
( ( ( ! [SY67: $i,SY68: $i,SY69: $i,SY70: $i,SY71: $i] :
( ~ ( succ_cpq @ ( triple @ sK6_SX0 @ SY67 @ SY68 ) @ ( triple @ SY69 @ SY70 @ SY71 ) )
| ~ ~ ( ok @ ( triple @ SY69 @ SY70 @ SY71 ) )
| ~ ( ok @ ( im_succ_cpq @ ( triple @ SY69 @ SY70 @ SY71 ) ) ) ) )
= $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[99]) ).
thf(109,plain,
! [SV18: $i,SV14: $i,SV7: $i] :
( ( ~ ~ ( ok @ ( triple @ SV7 @ SV14 @ SV18 ) )
| ( SV18 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(110,plain,
! [SV19: $i,SV15: $i,SV8: $i] :
( ( ~ ~ ( ok @ ( triple @ SV8 @ SV15 @ SV19 ) )
| ~ ( ok @ ( im_succ_cpq @ ( triple @ SV8 @ SV15 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(111,plain,
! [SV9: $i,SV2: $i] :
( ( ( succ_cpq @ SV2 @ SV9 )
= $false )
| ( ( succ_cpq @ SV2 @ ( findmin_cpq_eff @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(112,plain,
! [SV16: $i,SV10: $i,SV3: $i] :
( ( ( ~ ( succ_cpq @ SV3 @ SV10 ) )
= $true )
| ( ( succ_cpq @ SV3 @ ( insert_cpq @ SV10 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(113,plain,
( ( ~ ( succ_cpq @ ( triple @ sK1_U @ sK2_SY37 @ sK3_SY42 ) @ ( triple @ sK4_SX0 @ sK5_SY61 @ sK7_SY66 ) )
| ~ ( ok @ ( triple @ sK4_SX0 @ sK5_SY61 @ sK7_SY66 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[104]) ).
thf(114,plain,
! [SV17: $i,SV11: $i,SV4: $i] :
( ( ( ~ ( succ_cpq @ SV4 @ SV11 ) )
= $true )
| ( ( succ_cpq @ SV4 @ ( remove_cpq @ SV11 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(115,plain,
! [SV12: $i,SV5: $i] :
( ( ( succ_cpq @ SV5 @ SV12 )
= $false )
| ( ( succ_cpq @ SV5 @ ( removemin_cpq_eff @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(116,plain,
! [SV13: $i,SV6: $i] :
( ( ~ ( ~ ( ok @ ( triple @ SV6 @ SV13 @ bad ) )
| $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(117,plain,
! [SV13: $i,SV6: $i] :
( ( ~ ( ~ $false
| ( ok @ ( triple @ SV6 @ SV13 @ bad ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(118,plain,
( ( ( ! [SY72: $i,SY73: $i,SY74: $i,SY75: $i] :
( ~ ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ SY72 ) @ ( triple @ SY73 @ SY74 @ SY75 ) )
| ~ ~ ( ok @ ( triple @ SY73 @ SY74 @ SY75 ) )
| ~ ( ok @ ( im_succ_cpq @ ( triple @ SY73 @ SY74 @ SY75 ) ) ) ) )
= $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[108]) ).
thf(119,plain,
! [SV18: $i,SV14: $i,SV7: $i] :
( ( ( ~ ~ ( ok @ ( triple @ SV7 @ SV14 @ SV18 ) ) )
= $true )
| ( ( SV18 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV19: $i,SV15: $i,SV8: $i] :
( ( ( ~ ~ ( ok @ ( triple @ SV8 @ SV15 @ SV19 ) ) )
= $true )
| ( ( ~ ( ok @ ( im_succ_cpq @ ( triple @ SV8 @ SV15 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV16: $i,SV10: $i,SV3: $i] :
( ( ( succ_cpq @ SV3 @ SV10 )
= $false )
| ( ( succ_cpq @ SV3 @ ( insert_cpq @ SV10 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(122,plain,
( ( ~ ( succ_cpq @ ( triple @ sK1_U @ sK2_SY37 @ sK3_SY42 ) @ ( triple @ sK4_SX0 @ sK5_SY61 @ sK7_SY66 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(123,plain,
( ( ~ ( ok @ ( triple @ sK4_SX0 @ sK5_SY61 @ sK7_SY66 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(124,plain,
! [SV17: $i,SV11: $i,SV4: $i] :
( ( ( succ_cpq @ SV4 @ SV11 )
= $false )
| ( ( succ_cpq @ SV4 @ ( remove_cpq @ SV11 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(125,plain,
! [SV13: $i,SV6: $i] :
( ( ~ ( ok @ ( triple @ SV6 @ SV13 @ bad ) )
| $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(126,plain,
! [SV13: $i,SV6: $i] :
( ( ~ $false
| ( ok @ ( triple @ SV6 @ SV13 @ bad ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(127,plain,
( ( ( ! [SY76: $i,SY77: $i,SY78: $i] :
( ~ ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ SY76 @ SY77 @ SY78 ) )
| ~ ~ ( ok @ ( triple @ SY76 @ SY77 @ SY78 ) )
| ~ ( ok @ ( im_succ_cpq @ ( triple @ SY76 @ SY77 @ SY78 ) ) ) ) )
= $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[118]) ).
thf(128,plain,
! [SV18: $i,SV14: $i,SV7: $i] :
( ( ( ~ ( ok @ ( triple @ SV7 @ SV14 @ SV18 ) ) )
= $false )
| ( ( SV18 = bad )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(129,plain,
! [SV19: $i,SV15: $i,SV8: $i] :
( ( ( ~ ( ok @ ( triple @ SV8 @ SV15 @ SV19 ) ) )
= $false )
| ( ( ~ ( ok @ ( im_succ_cpq @ ( triple @ SV8 @ SV15 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(130,plain,
( ( succ_cpq @ ( triple @ sK1_U @ sK2_SY37 @ sK3_SY42 ) @ ( triple @ sK4_SX0 @ sK5_SY61 @ sK7_SY66 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(131,plain,
( ( ok @ ( triple @ sK4_SX0 @ sK5_SY61 @ sK7_SY66 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(132,plain,
! [SV13: $i,SV6: $i] :
( ( ( ~ ( ok @ ( triple @ SV6 @ SV13 @ bad ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(133,plain,
! [SV13: $i,SV6: $i] :
( ( ( ~ $false ) = $true )
| ( ( ok @ ( triple @ SV6 @ SV13 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(134,plain,
( ( ( ! [SY79: $i,SY80: $i] :
( ~ ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ SY79 @ SY80 ) )
| ~ ~ ( ok @ ( triple @ sK10_SY76 @ SY79 @ SY80 ) )
| ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ SY79 @ SY80 ) ) ) ) )
= $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[127]) ).
thf(135,plain,
! [SV18: $i,SV14: $i,SV7: $i] :
( ( ( ok @ ( triple @ SV7 @ SV14 @ SV18 ) )
= $true )
| ( ( SV18 = bad )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(136,plain,
! [SV19: $i,SV15: $i,SV8: $i] :
( ( ( ok @ ( triple @ SV8 @ SV15 @ SV19 ) )
= $true )
| ( ( ~ ( ok @ ( im_succ_cpq @ ( triple @ SV8 @ SV15 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(137,plain,
! [SV13: $i,SV6: $i] :
( ( ( ok @ ( triple @ SV6 @ SV13 @ bad ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(138,plain,
! [SV13: $i,SV6: $i] :
( ( $false = $false )
| ( ( ok @ ( triple @ SV6 @ SV13 @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(139,plain,
( ( ( ! [SY81: $i] :
( ~ ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ SY81 ) )
| ~ ~ ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ SY81 ) )
| ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ SY81 ) ) ) ) )
= $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[134]) ).
thf(140,plain,
! [SV19: $i,SV15: $i,SV8: $i] :
( ( ( ok @ ( im_succ_cpq @ ( triple @ SV8 @ SV15 @ SV19 ) ) )
= $false )
| ( ( ok @ ( triple @ SV8 @ SV15 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(141,plain,
( ( ( ~ ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
| ~ ~ ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
| ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) ) )
= $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[139]) ).
thf(142,plain,
( ( ( ~ ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(143,plain,
( ( ( ~ ~ ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
| ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) ) )
= $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(144,plain,
( ( ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(145,plain,
( ( ( ~ ~ ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(146,plain,
( ( ( ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) ) )
= $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(147,plain,
! [SV20: $i] :
( ( ( ! [SY82: $i,SY83: $i] :
( ~ ~ ( ok @ ( triple @ SV20 @ SY82 @ SY83 ) )
| ! [SY84: $i,SY85: $i,SY86: $i] :
( ~ ( succ_cpq @ ( triple @ SV20 @ SY82 @ SY83 ) @ ( triple @ SY84 @ SY85 @ SY86 ) )
| ~ ( ok @ ( triple @ SY84 @ SY85 @ SY86 ) ) ) ) )
= $true )
| ( ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(148,plain,
( ( ( ~ ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(149,plain,
( ( ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(150,plain,
! [SV21: $i,SV20: $i] :
( ( ( ! [SY87: $i] :
( ~ ~ ( ok @ ( triple @ SV20 @ SV21 @ SY87 ) )
| ! [SY88: $i,SY89: $i,SY90: $i] :
( ~ ( succ_cpq @ ( triple @ SV20 @ SV21 @ SY87 ) @ ( triple @ SY88 @ SY89 @ SY90 ) )
| ~ ( ok @ ( triple @ SY88 @ SY89 @ SY90 ) ) ) ) )
= $true )
| ( ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(151,plain,
( ( ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
| ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(152,plain,
! [SV22: $i] :
( ( ( ! [SY91: $i,SY92: $i] :
( ~ ~ ( ok @ ( triple @ SV22 @ SY91 @ SY92 ) )
| ! [SY93: $i,SY94: $i,SY95: $i] :
( ~ ( succ_cpq @ ( triple @ SV22 @ SY91 @ SY92 ) @ ( triple @ SY93 @ SY94 @ SY95 ) )
| ~ ( ok @ ( triple @ SY93 @ SY94 @ SY95 ) ) ) ) )
= $true )
| ( ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(153,plain,
! [SV23: $i,SV21: $i,SV20: $i] :
( ( ( ~ ~ ( ok @ ( triple @ SV20 @ SV21 @ SV23 ) )
| ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ( succ_cpq @ ( triple @ SV20 @ SV21 @ SV23 ) @ ( triple @ SY96 @ SY97 @ SY98 ) )
| ~ ( ok @ ( triple @ SY96 @ SY97 @ SY98 ) ) ) )
= $true )
| ( ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(154,plain,
! [SV24: $i] :
( ( ( ! [SY99: $i,SY100: $i] :
( ~ ~ ( ok @ ( triple @ SV24 @ SY99 @ SY100 ) )
| ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ( succ_cpq @ ( triple @ SV24 @ SY99 @ SY100 ) @ ( triple @ SY101 @ SY102 @ SY103 ) )
| ~ ( ok @ ( triple @ SY101 @ SY102 @ SY103 ) ) ) ) )
= $true )
| ( ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(155,plain,
! [SV25: $i,SV22: $i] :
( ( ( ! [SY104: $i] :
( ~ ~ ( ok @ ( triple @ SV22 @ SV25 @ SY104 ) )
| ! [SY105: $i,SY106: $i,SY107: $i] :
( ~ ( succ_cpq @ ( triple @ SV22 @ SV25 @ SY104 ) @ ( triple @ SY105 @ SY106 @ SY107 ) )
| ~ ( ok @ ( triple @ SY105 @ SY106 @ SY107 ) ) ) ) )
= $true )
| ( ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(156,plain,
! [SV23: $i,SV21: $i,SV20: $i] :
( ( ( ~ ~ ( ok @ ( triple @ SV20 @ SV21 @ SV23 ) ) )
= $true )
| ( ( ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ( succ_cpq @ ( triple @ SV20 @ SV21 @ SV23 ) @ ( triple @ SY96 @ SY97 @ SY98 ) )
| ~ ( ok @ ( triple @ SY96 @ SY97 @ SY98 ) ) ) )
= $true )
| ( ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(157,plain,
! [SV26: $i,SV24: $i] :
( ( ( ! [SY108: $i] :
( ~ ~ ( ok @ ( triple @ SV24 @ SV26 @ SY108 ) )
| ! [SY109: $i,SY110: $i,SY111: $i] :
( ~ ( succ_cpq @ ( triple @ SV24 @ SV26 @ SY108 ) @ ( triple @ SY109 @ SY110 @ SY111 ) )
| ~ ( ok @ ( triple @ SY109 @ SY110 @ SY111 ) ) ) ) )
= $true )
| ( ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(158,plain,
! [SV27: $i,SV25: $i,SV22: $i] :
( ( ( ~ ~ ( ok @ ( triple @ SV22 @ SV25 @ SV27 ) )
| ! [SY112: $i,SY113: $i,SY114: $i] :
( ~ ( succ_cpq @ ( triple @ SV22 @ SV25 @ SV27 ) @ ( triple @ SY112 @ SY113 @ SY114 ) )
| ~ ( ok @ ( triple @ SY112 @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(159,plain,
! [SV23: $i,SV21: $i,SV20: $i] :
( ( ( ~ ( ok @ ( triple @ SV20 @ SV21 @ SV23 ) ) )
= $false )
| ( ( ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ( succ_cpq @ ( triple @ SV20 @ SV21 @ SV23 ) @ ( triple @ SY96 @ SY97 @ SY98 ) )
| ~ ( ok @ ( triple @ SY96 @ SY97 @ SY98 ) ) ) )
= $true )
| ( ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(160,plain,
! [SV28: $i,SV26: $i,SV24: $i] :
( ( ( ~ ~ ( ok @ ( triple @ SV24 @ SV26 @ SV28 ) )
| ! [SY115: $i,SY116: $i,SY117: $i] :
( ~ ( succ_cpq @ ( triple @ SV24 @ SV26 @ SV28 ) @ ( triple @ SY115 @ SY116 @ SY117 ) )
| ~ ( ok @ ( triple @ SY115 @ SY116 @ SY117 ) ) ) )
= $true )
| ( ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(161,plain,
! [SV27: $i,SV25: $i,SV22: $i] :
( ( ( ~ ~ ( ok @ ( triple @ SV22 @ SV25 @ SV27 ) ) )
= $true )
| ( ( ! [SY112: $i,SY113: $i,SY114: $i] :
( ~ ( succ_cpq @ ( triple @ SV22 @ SV25 @ SV27 ) @ ( triple @ SY112 @ SY113 @ SY114 ) )
| ~ ( ok @ ( triple @ SY112 @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(162,plain,
! [SV23: $i,SV21: $i,SV20: $i] :
( ( ( ok @ ( triple @ SV20 @ SV21 @ SV23 ) )
= $true )
| ( ( ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ( succ_cpq @ ( triple @ SV20 @ SV21 @ SV23 ) @ ( triple @ SY96 @ SY97 @ SY98 ) )
| ~ ( ok @ ( triple @ SY96 @ SY97 @ SY98 ) ) ) )
= $true )
| ( ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(163,plain,
! [SV28: $i,SV26: $i,SV24: $i] :
( ( ( ~ ~ ( ok @ ( triple @ SV24 @ SV26 @ SV28 ) ) )
= $true )
| ( ( ! [SY115: $i,SY116: $i,SY117: $i] :
( ~ ( succ_cpq @ ( triple @ SV24 @ SV26 @ SV28 ) @ ( triple @ SY115 @ SY116 @ SY117 ) )
| ~ ( ok @ ( triple @ SY115 @ SY116 @ SY117 ) ) ) )
= $true )
| ( ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(164,plain,
! [SV27: $i,SV25: $i,SV22: $i] :
( ( ( ~ ( ok @ ( triple @ SV22 @ SV25 @ SV27 ) ) )
= $false )
| ( ( ! [SY112: $i,SY113: $i,SY114: $i] :
( ~ ( succ_cpq @ ( triple @ SV22 @ SV25 @ SV27 ) @ ( triple @ SY112 @ SY113 @ SY114 ) )
| ~ ( ok @ ( triple @ SY112 @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(165,plain,
! [SV29: $i,SV23: $i,SV21: $i,SV20: $i] :
( ( ( ! [SY118: $i,SY119: $i] :
( ~ ( succ_cpq @ ( triple @ SV20 @ SV21 @ SV23 ) @ ( triple @ SV29 @ SY118 @ SY119 ) )
| ~ ( ok @ ( triple @ SV29 @ SY118 @ SY119 ) ) ) )
= $true )
| ( ( ok @ ( triple @ SV20 @ SV21 @ SV23 ) )
= $true )
| ( ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(166,plain,
! [SV28: $i,SV26: $i,SV24: $i] :
( ( ( ~ ( ok @ ( triple @ SV24 @ SV26 @ SV28 ) ) )
= $false )
| ( ( ! [SY115: $i,SY116: $i,SY117: $i] :
( ~ ( succ_cpq @ ( triple @ SV24 @ SV26 @ SV28 ) @ ( triple @ SY115 @ SY116 @ SY117 ) )
| ~ ( ok @ ( triple @ SY115 @ SY116 @ SY117 ) ) ) )
= $true )
| ( ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(167,plain,
! [SV27: $i,SV25: $i,SV22: $i] :
( ( ( ok @ ( triple @ SV22 @ SV25 @ SV27 ) )
= $true )
| ( ( ! [SY112: $i,SY113: $i,SY114: $i] :
( ~ ( succ_cpq @ ( triple @ SV22 @ SV25 @ SV27 ) @ ( triple @ SY112 @ SY113 @ SY114 ) )
| ~ ( ok @ ( triple @ SY112 @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(168,plain,
! [SV30: $i,SV29: $i,SV23: $i,SV21: $i,SV20: $i] :
( ( ( ! [SY120: $i] :
( ~ ( succ_cpq @ ( triple @ SV20 @ SV21 @ SV23 ) @ ( triple @ SV29 @ SV30 @ SY120 ) )
| ~ ( ok @ ( triple @ SV29 @ SV30 @ SY120 ) ) ) )
= $true )
| ( ( ok @ ( triple @ SV20 @ SV21 @ SV23 ) )
= $true )
| ( ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(169,plain,
! [SV28: $i,SV26: $i,SV24: $i] :
( ( ( ok @ ( triple @ SV24 @ SV26 @ SV28 ) )
= $true )
| ( ( ! [SY115: $i,SY116: $i,SY117: $i] :
( ~ ( succ_cpq @ ( triple @ SV24 @ SV26 @ SV28 ) @ ( triple @ SY115 @ SY116 @ SY117 ) )
| ~ ( ok @ ( triple @ SY115 @ SY116 @ SY117 ) ) ) )
= $true )
| ( ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(170,plain,
! [SV31: $i,SV27: $i,SV25: $i,SV22: $i] :
( ( ( ! [SY121: $i,SY122: $i] :
( ~ ( succ_cpq @ ( triple @ SV22 @ SV25 @ SV27 ) @ ( triple @ SV31 @ SY121 @ SY122 ) )
| ~ ( ok @ ( triple @ SV31 @ SY121 @ SY122 ) ) ) )
= $true )
| ( ( ok @ ( triple @ SV22 @ SV25 @ SV27 ) )
= $true )
| ( ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(171,plain,
! [SV32: $i,SV30: $i,SV29: $i,SV23: $i,SV21: $i,SV20: $i] :
( ( ( ~ ( succ_cpq @ ( triple @ SV20 @ SV21 @ SV23 ) @ ( triple @ SV29 @ SV30 @ SV32 ) )
| ~ ( ok @ ( triple @ SV29 @ SV30 @ SV32 ) ) )
= $true )
| ( ( ok @ ( triple @ SV20 @ SV21 @ SV23 ) )
= $true )
| ( ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(172,plain,
! [SV33: $i,SV28: $i,SV26: $i,SV24: $i] :
( ( ( ! [SY123: $i,SY124: $i] :
( ~ ( succ_cpq @ ( triple @ SV24 @ SV26 @ SV28 ) @ ( triple @ SV33 @ SY123 @ SY124 ) )
| ~ ( ok @ ( triple @ SV33 @ SY123 @ SY124 ) ) ) )
= $true )
| ( ( ok @ ( triple @ SV24 @ SV26 @ SV28 ) )
= $true )
| ( ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(173,plain,
! [SV34: $i,SV31: $i,SV27: $i,SV25: $i,SV22: $i] :
( ( ( ! [SY125: $i] :
( ~ ( succ_cpq @ ( triple @ SV22 @ SV25 @ SV27 ) @ ( triple @ SV31 @ SV34 @ SY125 ) )
| ~ ( ok @ ( triple @ SV31 @ SV34 @ SY125 ) ) ) )
= $true )
| ( ( ok @ ( triple @ SV22 @ SV25 @ SV27 ) )
= $true )
| ( ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(174,plain,
! [SV32: $i,SV30: $i,SV29: $i,SV23: $i,SV21: $i,SV20: $i] :
( ( ( ~ ( succ_cpq @ ( triple @ SV20 @ SV21 @ SV23 ) @ ( triple @ SV29 @ SV30 @ SV32 ) ) )
= $true )
| ( ( ~ ( ok @ ( triple @ SV29 @ SV30 @ SV32 ) ) )
= $true )
| ( ( ok @ ( triple @ SV20 @ SV21 @ SV23 ) )
= $true )
| ( ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(175,plain,
! [SV35: $i,SV33: $i,SV28: $i,SV26: $i,SV24: $i] :
( ( ( ! [SY126: $i] :
( ~ ( succ_cpq @ ( triple @ SV24 @ SV26 @ SV28 ) @ ( triple @ SV33 @ SV35 @ SY126 ) )
| ~ ( ok @ ( triple @ SV33 @ SV35 @ SY126 ) ) ) )
= $true )
| ( ( ok @ ( triple @ SV24 @ SV26 @ SV28 ) )
= $true )
| ( ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(176,plain,
! [SV36: $i,SV34: $i,SV31: $i,SV27: $i,SV25: $i,SV22: $i] :
( ( ( ~ ( succ_cpq @ ( triple @ SV22 @ SV25 @ SV27 ) @ ( triple @ SV31 @ SV34 @ SV36 ) )
| ~ ( ok @ ( triple @ SV31 @ SV34 @ SV36 ) ) )
= $true )
| ( ( ok @ ( triple @ SV22 @ SV25 @ SV27 ) )
= $true )
| ( ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(177,plain,
! [SV32: $i,SV30: $i,SV29: $i,SV23: $i,SV21: $i,SV20: $i] :
( ( ( succ_cpq @ ( triple @ SV20 @ SV21 @ SV23 ) @ ( triple @ SV29 @ SV30 @ SV32 ) )
= $false )
| ( ( ~ ( ok @ ( triple @ SV29 @ SV30 @ SV32 ) ) )
= $true )
| ( ( ok @ ( triple @ SV20 @ SV21 @ SV23 ) )
= $true )
| ( ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(178,plain,
! [SV37: $i,SV35: $i,SV33: $i,SV28: $i,SV26: $i,SV24: $i] :
( ( ( ~ ( succ_cpq @ ( triple @ SV24 @ SV26 @ SV28 ) @ ( triple @ SV33 @ SV35 @ SV37 ) )
| ~ ( ok @ ( triple @ SV33 @ SV35 @ SV37 ) ) )
= $true )
| ( ( ok @ ( triple @ SV24 @ SV26 @ SV28 ) )
= $true )
| ( ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(179,plain,
! [SV36: $i,SV34: $i,SV31: $i,SV27: $i,SV25: $i,SV22: $i] :
( ( ( ~ ( succ_cpq @ ( triple @ SV22 @ SV25 @ SV27 ) @ ( triple @ SV31 @ SV34 @ SV36 ) ) )
= $true )
| ( ( ~ ( ok @ ( triple @ SV31 @ SV34 @ SV36 ) ) )
= $true )
| ( ( ok @ ( triple @ SV22 @ SV25 @ SV27 ) )
= $true )
| ( ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(180,plain,
! [SV23: $i,SV21: $i,SV20: $i,SV32: $i,SV30: $i,SV29: $i] :
( ( ( ok @ ( triple @ SV29 @ SV30 @ SV32 ) )
= $false )
| ( ( succ_cpq @ ( triple @ SV20 @ SV21 @ SV23 ) @ ( triple @ SV29 @ SV30 @ SV32 ) )
= $false )
| ( ( ok @ ( triple @ SV20 @ SV21 @ SV23 ) )
= $true )
| ( ( succ_cpq @ ( triple @ sK6_SX0 @ sK8_SY67 @ sK9_SY72 ) @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(181,plain,
! [SV37: $i,SV35: $i,SV33: $i,SV28: $i,SV26: $i,SV24: $i] :
( ( ( ~ ( succ_cpq @ ( triple @ SV24 @ SV26 @ SV28 ) @ ( triple @ SV33 @ SV35 @ SV37 ) ) )
= $true )
| ( ( ~ ( ok @ ( triple @ SV33 @ SV35 @ SV37 ) ) )
= $true )
| ( ( ok @ ( triple @ SV24 @ SV26 @ SV28 ) )
= $true )
| ( ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(182,plain,
! [SV36: $i,SV34: $i,SV31: $i,SV27: $i,SV25: $i,SV22: $i] :
( ( ( succ_cpq @ ( triple @ SV22 @ SV25 @ SV27 ) @ ( triple @ SV31 @ SV34 @ SV36 ) )
= $false )
| ( ( ~ ( ok @ ( triple @ SV31 @ SV34 @ SV36 ) ) )
= $true )
| ( ( ok @ ( triple @ SV22 @ SV25 @ SV27 ) )
= $true )
| ( ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(183,plain,
! [SV37: $i,SV35: $i,SV33: $i,SV28: $i,SV26: $i,SV24: $i] :
( ( ( succ_cpq @ ( triple @ SV24 @ SV26 @ SV28 ) @ ( triple @ SV33 @ SV35 @ SV37 ) )
= $false )
| ( ( ~ ( ok @ ( triple @ SV33 @ SV35 @ SV37 ) ) )
= $true )
| ( ( ok @ ( triple @ SV24 @ SV26 @ SV28 ) )
= $true )
| ( ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(184,plain,
! [SV27: $i,SV25: $i,SV22: $i,SV36: $i,SV34: $i,SV31: $i] :
( ( ( ok @ ( triple @ SV31 @ SV34 @ SV36 ) )
= $false )
| ( ( succ_cpq @ ( triple @ SV22 @ SV25 @ SV27 ) @ ( triple @ SV31 @ SV34 @ SV36 ) )
= $false )
| ( ( ok @ ( triple @ SV22 @ SV25 @ SV27 ) )
= $true )
| ( ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(185,plain,
! [SV28: $i,SV26: $i,SV24: $i,SV37: $i,SV35: $i,SV33: $i] :
( ( ( ok @ ( triple @ SV33 @ SV35 @ SV37 ) )
= $false )
| ( ( succ_cpq @ ( triple @ SV24 @ SV26 @ SV28 ) @ ( triple @ SV33 @ SV35 @ SV37 ) )
= $false )
| ( ( ok @ ( triple @ SV24 @ SV26 @ SV28 ) )
= $true )
| ( ( ok @ ( triple @ sK10_SY76 @ sK11_SY79 @ sK12_SY81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(186,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[82,185,184,180,140,138,137,135,131,130,124,121,115,111,83]) ).
thf(187,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV376+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.20 % Computer : n015.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.21 % CPULimit : 300
% 0.07/0.21 % WCLimit : 300
% 0.07/0.21 % DateTime : Tue Oct 6 16:30:43 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.56/0.39
% 0.56/0.39 No.of.Axioms: 9
% 0.56/0.39
% 0.56/0.39 Length.of.Defs: 0
% 0.56/0.39
% 0.56/0.39 Contains.Choice.Funs: false
% 0.56/0.39 ......
% 0.56/0.39
% 0.56/0.39 ********************************
% 0.56/0.39 * All subproblems solved! *
% 0.56/0.39 ********************************
% 0.56/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,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:186,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.56/0.39
% 0.56/0.39 %**** Beginning of derivation protocol ****
% 0.56/0.39 % SZS output start CNFRefutation
% See solution above
% 0.56/0.39
% 0.56/0.39 %**** End of derivation protocol ****
% 0.56/0.39 %**** no. of clauses in derivation: 153 ****
% 0.56/0.39 %**** clause counter: 186 ****
% 0.56/0.39
% 0.56/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,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:186,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------