TSTP Solution File: SEV384^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEV384^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 17:36:28 EDT 2022
% Result : Theorem 0.44s 0.62s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 7
% Syntax : Number of formulae : 128 ( 28 unt; 6 typ; 0 def)
% Number of atoms : 688 ( 273 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 1389 ( 500 ~; 193 |; 19 &; 653 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 81 ( 81 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 306 ( 87 ^ 215 !; 4 ?; 306 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cP,type,
cP: $i > $o ).
thf(tp_cR,type,
cR: $i > $i > $o ).
thf(tp_s,type,
s: $i > $o ).
thf(tp_sK1_Xx2,type,
sK1_Xx2: $i ).
thf(tp_sK2_Xy,type,
sK2_Xy: ( $i > $o ) > $i ).
thf(tp_sK3_Xy1,type,
sK3_Xy1: $i > $i ).
thf(1,conjecture,
( ( ! [Xx: $i > $o,Xz: $i] :
( ( Xx @ Xz )
=> ? [Xy: $i] :
( ( Xx @ Xy )
& ! [Xw: $i] :
( ( cR @ Xy @ Xw )
=> ~ ( Xx @ Xw ) ) ) )
& ! [Xx1: $i] :
( ! [Xy1: $i] :
( ( ( s @ Xy1 )
& ( cR @ Xx1 @ Xy1 ) )
=> ( cP @ Xy1 ) )
=> ( cP @ Xx1 ) ) )
=> ! [Xx2: $i] :
( ( s @ Xx2 )
=> ( cP @ Xx2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM117B) ).
thf(2,negated_conjecture,
( ( ( ! [Xx: $i > $o,Xz: $i] :
( ( Xx @ Xz )
=> ? [Xy: $i] :
( ( Xx @ Xy )
& ! [Xw: $i] :
( ( cR @ Xy @ Xw )
=> ~ ( Xx @ Xw ) ) ) )
& ! [Xx1: $i] :
( ! [Xy1: $i] :
( ( ( s @ Xy1 )
& ( cR @ Xx1 @ Xy1 ) )
=> ( cP @ Xy1 ) )
=> ( cP @ Xx1 ) ) )
=> ! [Xx2: $i] :
( ( s @ Xx2 )
=> ( cP @ Xx2 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Xx: $i > $o,Xz: $i] :
( ( Xx @ Xz )
=> ? [Xy: $i] :
( ( Xx @ Xy )
& ! [Xw: $i] :
( ( cR @ Xy @ Xw )
=> ~ ( Xx @ Xw ) ) ) )
& ! [Xx1: $i] :
( ! [Xy1: $i] :
( ( ( s @ Xy1 )
& ( cR @ Xx1 @ Xy1 ) )
=> ( cP @ Xy1 ) )
=> ( cP @ Xx1 ) ) )
=> ! [Xx2: $i] :
( ( s @ Xx2 )
=> ( cP @ Xx2 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: $i > $o,Xz: $i] :
( ( Xx @ Xz )
=> ? [Xy: $i] :
( ( Xx @ Xy )
& ! [Xw: $i] :
( ( cR @ Xy @ Xw )
=> ~ ( Xx @ Xw ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx1: $i] :
( ! [Xy1: $i] :
( ( ( s @ Xy1 )
& ( cR @ Xx1 @ Xy1 ) )
=> ( cP @ Xy1 ) )
=> ( cP @ Xx1 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx2: $i] :
( ( s @ Xx2 )
=> ( cP @ Xx2 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [Xx2: $i] :
( ( s @ Xx2 )
=> ( cP @ Xx2 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( s @ sK1_Xx2 )
& ~ ( cP @ sK1_Xx2 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [Xx: $i > $o] :
( ! [Xz: $i] :
~ ( Xx @ Xz )
| ( ! [SY7: $i] :
( ~ ( cR @ ( sK2_Xy @ Xx ) @ SY7 )
| ~ ( Xx @ SY7 ) )
& ( Xx @ ( sK2_Xy @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [Xx1: $i] :
( ( ( cR @ Xx1 @ ( sK3_Xy1 @ Xx1 ) )
& ( s @ ( sK3_Xy1 @ Xx1 ) )
& ~ ( cP @ ( sK3_Xy1 @ Xx1 ) ) )
| ( cP @ Xx1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(11,plain,
( ( ! [Xx1: $i] :
( ( ( cR @ Xx1 @ ( sK3_Xy1 @ Xx1 ) )
& ( s @ ( sK3_Xy1 @ Xx1 ) )
& ~ ( cP @ ( sK3_Xy1 @ Xx1 ) ) )
| ( cP @ Xx1 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [Xx: $i > $o] :
( ! [Xz: $i] :
~ ( Xx @ Xz )
| ( ! [SY7: $i] :
( ~ ( cR @ ( sK2_Xy @ Xx ) @ SY7 )
| ~ ( Xx @ SY7 ) )
& ( Xx @ ( sK2_Xy @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ( s @ sK1_Xx2 )
& ~ ( cP @ sK1_Xx2 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ( ~ ( s @ sK1_Xx2 )
| ~ ~ ( cP @ sK1_Xx2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
~ ( SX0 @ SX1 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( cR @ ( sK2_Xy @ SX0 ) @ SX1 )
| ~ ( SX0 @ SX1 ) )
| ~ ( SX0 @ ( sK2_Xy @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( cR @ SX0 @ ( sK3_Xy1 @ SX0 ) )
| ~ ( s @ ( sK3_Xy1 @ SX0 ) ) )
| ~ ~ ( cP @ ( sK3_Xy1 @ SX0 ) ) )
| ( cP @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(17,plain,
( ( ~ ( s @ sK1_Xx2 )
| ~ ~ ( cP @ sK1_Xx2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: $i > $o] :
( ( ! [SY8: $i] :
~ ( SV1 @ SY8 )
| ~ ( ~ ! [SY9: $i] :
( ~ ( cR @ ( sK2_Xy @ SV1 ) @ SY9 )
| ~ ( SV1 @ SY9 ) )
| ~ ( SV1 @ ( sK2_Xy @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: $i] :
( ( ~ ( ~ ~ ( ~ ( cR @ SV2 @ ( sK3_Xy1 @ SV2 ) )
| ~ ( s @ ( sK3_Xy1 @ SV2 ) ) )
| ~ ~ ( cP @ ( sK3_Xy1 @ SV2 ) ) )
| ( cP @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( s @ sK1_Xx2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ~ ( cP @ sK1_Xx2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV1: $i > $o] :
( ( ( ! [SY8: $i] :
~ ( SV1 @ SY8 ) )
= $true )
| ( ( ~ ( ~ ! [SY9: $i] :
( ~ ( cR @ ( sK2_Xy @ SV1 ) @ SY9 )
| ~ ( SV1 @ SY9 ) )
| ~ ( SV1 @ ( sK2_Xy @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ( cR @ SV2 @ ( sK3_Xy1 @ SV2 ) )
| ~ ( s @ ( sK3_Xy1 @ SV2 ) ) )
| ~ ~ ( cP @ ( sK3_Xy1 @ SV2 ) ) ) )
= $true )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( s @ sK1_Xx2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( cP @ sK1_Xx2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV3 ) )
= $true )
| ( ( ~ ( ~ ! [SY9: $i] :
( ~ ( cR @ ( sK2_Xy @ SV1 ) @ SY9 )
| ~ ( SV1 @ SY9 ) )
| ~ ( SV1 @ ( sK2_Xy @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( cR @ SV2 @ ( sK3_Xy1 @ SV2 ) )
| ~ ( s @ ( sK3_Xy1 @ SV2 ) ) )
| ~ ~ ( cP @ ( sK3_Xy1 @ SV2 ) ) )
= $false )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( cP @ sK1_Xx2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ SV3 )
= $false )
| ( ( ~ ( ~ ! [SY9: $i] :
( ~ ( cR @ ( sK2_Xy @ SV1 ) @ SY9 )
| ~ ( SV1 @ SY9 ) )
| ~ ( SV1 @ ( sK2_Xy @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( cR @ SV2 @ ( sK3_Xy1 @ SV2 ) )
| ~ ( s @ ( sK3_Xy1 @ SV2 ) ) ) )
= $false )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(31,plain,
! [SV2: $i] :
( ( ( ~ ~ ( cP @ ( sK3_Xy1 @ SV2 ) ) )
= $false )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(32,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ! [SY9: $i] :
( ~ ( cR @ ( sK2_Xy @ SV1 ) @ SY9 )
| ~ ( SV1 @ SY9 ) )
| ~ ( SV1 @ ( sK2_Xy @ SV1 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( cR @ SV2 @ ( sK3_Xy1 @ SV2 ) )
| ~ ( s @ ( sK3_Xy1 @ SV2 ) ) ) )
= $true )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(34,plain,
! [SV2: $i] :
( ( ( ~ ( cP @ ( sK3_Xy1 @ SV2 ) ) )
= $true )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(35,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ! [SY9: $i] :
( ~ ( cR @ ( sK2_Xy @ SV1 ) @ SY9 )
| ~ ( SV1 @ SY9 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK2_Xy @ SV1 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV2: $i] :
( ( ( ~ ( cR @ SV2 @ ( sK3_Xy1 @ SV2 ) )
| ~ ( s @ ( sK3_Xy1 @ SV2 ) ) )
= $false )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV2: $i] :
( ( ( cP @ ( sK3_Xy1 @ SV2 ) )
= $false )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ! [SY9: $i] :
( ~ ( cR @ ( sK2_Xy @ SV1 ) @ SY9 )
| ~ ( SV1 @ SY9 ) ) )
= $true )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK2_Xy @ SV1 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV2: $i] :
( ( ( ~ ( cR @ SV2 @ ( sK3_Xy1 @ SV2 ) ) )
= $false )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(42,plain,
! [SV2: $i] :
( ( ( ~ ( s @ ( sK3_Xy1 @ SV2 ) ) )
= $false )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(43,plain,
! [SV3: $i,SV4: $i,SV1: $i > $o] :
( ( ( ~ ( cR @ ( sK2_Xy @ SV1 ) @ SV4 )
| ~ ( SV1 @ SV4 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV2: $i] :
( ( ( cR @ SV2 @ ( sK3_Xy1 @ SV2 ) )
= $true )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV2: $i] :
( ( ( s @ ( sK3_Xy1 @ SV2 ) )
= $true )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV3: $i,SV4: $i,SV1: $i > $o] :
( ( ( ~ ( cR @ ( sK2_Xy @ SV1 ) @ SV4 ) )
= $true )
| ( ( ~ ( SV1 @ SV4 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV3: $i,SV4: $i,SV1: $i > $o] :
( ( ( cR @ ( sK2_Xy @ SV1 ) @ SV4 )
= $false )
| ( ( ~ ( SV1 @ SV4 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(48,plain,
! [SV3: $i,SV4: $i,SV1: $i > $o] :
( ( ( SV1 @ SV4 )
= $false )
| ( ( cR @ ( sK2_Xy @ SV1 ) @ SV4 )
= $false )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV3: $i,SV6: $i > $o] :
( ( ( ~ ( SV6
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV6 @ SV3 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[40:[bind(SV1,$thf( ^ [SV5: $i] : ~ ( SV6 @ SV5 ) ))]]) ).
thf(52,plain,
! [SV3: $i] :
( ( ( ( sK2_Xy
@ ^ [SX0: $i] : ( SX0 = sK1_Xx2 ) )
= sK1_Xx2 )
= $true )
| ( ( SV3 = sK1_Xx2 )
= $false ) ),
inference(prim_subst,[status(thm)],[40:[bind(SV1,$thf( ^ [SV9: $i] : ( SV9 = sK1_Xx2 ) ))]]) ).
thf(53,plain,
! [SV4: $i] :
( ( $true = $false )
| ( ( cR
@ ( sK2_Xy
@ ^ [SX0: $i] : $true )
@ SV4 )
= $false )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[48:[bind(SV1,$thf( ^ [SV8: $i] : $true ))]]) ).
thf(55,plain,
! [SV3: $i,SV4: $i,SV6: $i > $o] :
( ( ( ~ ( SV6 @ SV4 ) )
= $false )
| ( ( cR
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV4 )
= $false )
| ( ( ~ ( SV6 @ SV3 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[48:[bind(SV1,$thf( ^ [SV5: $i] : ~ ( SV6 @ SV5 ) ))]]) ).
thf(56,plain,
! [SV3: $i,SV4: $i] :
( ( ( SV4 = sK1_Xx2 )
= $false )
| ( ( cR
@ ( sK2_Xy
@ ^ [SX0: $i] : ( SX0 = sK1_Xx2 ) )
@ SV4 )
= $false )
| ( ( SV3 = sK1_Xx2 )
= $false ) ),
inference(prim_subst,[status(thm)],[48:[bind(SV1,$thf( ^ [SV9: $i] : ( SV9 = sK1_Xx2 ) ))]]) ).
thf(57,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK2_Xy @ SV1 ) )
= $true )
| ( ( ( SV1 @ ( sK2_Xy @ SV1 ) )
= ( ~ ( SV1 @ SV3 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[40]) ).
thf(58,plain,
! [SV2: $i] :
( ( ( cP @ SV2 )
= $true )
| ( ( ( cR @ SV2 @ ( sK3_Xy1 @ SV2 ) )
= ( cP @ SV2 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[44]) ).
thf(59,plain,
! [SV2: $i] :
( ( ( cP @ SV2 )
= $true )
| ( ( ( s @ ( sK3_Xy1 @ SV2 ) )
= ( cP @ SV2 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[45]) ).
thf(60,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( ( SV1 @ ( sK2_Xy @ SV1 ) )
| ~ ( SV1 @ SV3 ) )
| ~ ( ~ ( SV1 @ ( sK2_Xy @ SV1 ) )
| ~ ~ ( SV1 @ SV3 ) ) )
= $false )
| ( ( SV1 @ ( sK2_Xy @ SV1 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[57]) ).
thf(61,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ( SV1 @ ( sK2_Xy @ SV1 ) )
= ( ~ ( SV1 @ SV3 ) ) )
= $false )
| ( ( SV1 @ ( sK2_Xy @ SV1 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV2: $i] :
( ( ( ~ ( ( cR @ SV2 @ ( sK3_Xy1 @ SV2 ) )
| ( cP @ SV2 ) )
| ~ ( ~ ( cR @ SV2 @ ( sK3_Xy1 @ SV2 ) )
| ~ ( cP @ SV2 ) ) )
= $false )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[58]) ).
thf(64,plain,
! [SV2: $i] :
( ( ( ~ ( ( s @ ( sK3_Xy1 @ SV2 ) )
| ( cP @ SV2 ) )
| ~ ( ~ ( s @ ( sK3_Xy1 @ SV2 ) )
| ~ ( cP @ SV2 ) ) )
= $false )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[59]) ).
thf(66,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( ( SV1 @ ( sK2_Xy @ SV1 ) )
| ~ ( SV1 @ SV3 ) ) )
= $false )
| ( ( SV1 @ ( sK2_Xy @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(68,plain,
! [SV2: $i] :
( ( ( ~ ( ( cR @ SV2 @ ( sK3_Xy1 @ SV2 ) )
| ( cP @ SV2 ) ) )
= $false )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(70,plain,
! [SV2: $i] :
( ( ( ~ ( ( s @ ( sK3_Xy1 @ SV2 ) )
| ( cP @ SV2 ) ) )
= $false )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(72,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ( SV1 @ ( sK2_Xy @ SV1 ) )
| ~ ( SV1 @ SV3 ) )
= $true )
| ( ( SV1 @ ( sK2_Xy @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(74,plain,
! [SV2: $i] :
( ( ( ( cR @ SV2 @ ( sK3_Xy1 @ SV2 ) )
| ( cP @ SV2 ) )
= $true )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(76,plain,
! [SV2: $i] :
( ( ( ( s @ ( sK3_Xy1 @ SV2 ) )
| ( cP @ SV2 ) )
= $true )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(78,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK2_Xy @ SV1 ) )
= $true )
| ( ( ~ ( SV1 @ SV3 ) )
= $true )
| ( ( SV1 @ ( sK2_Xy @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(80,plain,
! [SV2: $i] :
( ( ( cR @ SV2 @ ( sK3_Xy1 @ SV2 ) )
= $true )
| ( ( cP @ SV2 )
= $true )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(82,plain,
! [SV2: $i] :
( ( ( s @ ( sK3_Xy1 @ SV2 ) )
= $true )
| ( ( cP @ SV2 )
= $true )
| ( ( cP @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(84,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK2_Xy @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK2_Xy @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(92,plain,
! [SV3: $i,SV24: $i > $o] :
( ( ( ~ ~ ~ ~ ~ ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV24 @ SV3 ) )
= $true ) ),
inference(extuni,[status(esa)],[61:[bind(SV1,$thf( ^ [SX0: $i] : ~ ( ~ ( ~ ( ~ ( ~ ( SV24 @ SX0 ) ) ) ) ) ))]]) ).
thf(95,plain,
! [SV3: $i,SV21: $i > $o] :
( ( ( ~ ~ ~ ~ ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV21 @ SV3 ) )
= $false ) ),
inference(extuni,[status(esa)],[61:[bind(SV1,$thf( ^ [SX0: $i] : ~ ( ~ ( ~ ( ~ ( SV21 @ SX0 ) ) ) ) ))]]) ).
thf(96,plain,
! [SV3: $i,SV18: $i > $o] :
( ( ( ~ ~ ~ ( SV18
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ( SV18 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV18
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ( SV18 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV18 @ SV3 ) )
= $true ) ),
inference(extuni,[status(esa)],[61:[bind(SV1,$thf( ^ [SX0: $i] : ~ ( ~ ( ~ ( SV18 @ SX0 ) ) ) ))]]) ).
thf(99,plain,
! [SV3: $i,SV15: $i > $o] :
( ( ( ~ ~ ( SV15
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ( SV15 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV15
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ( SV15 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV15 @ SV3 ) )
= $false ) ),
inference(extuni,[status(esa)],[61:[bind(SV1,$thf( ^ [SX0: $i] : ~ ( ~ ( SV15 @ SX0 ) ) ))]]) ).
thf(100,plain,
! [SV3: $i,SV12: $i > $o] :
( ( ( ~ ( SV12
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV12
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV12 @ SV3 ) )
= $true ) ),
inference(extuni,[status(esa)],[61:[bind(SV1,$thf( ^ [SX0: $i] : ~ ( SV12 @ SX0 ) ))]]) ).
thf(103,plain,
! [SV3: $i,SV12: $i > $o] :
( ( ( SV12
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV12
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV12 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(104,plain,
! [SV3: $i,SV15: $i > $o] :
( ( ( ~ ( SV15
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ( SV15 @ SX0 ) ) ) )
= $false )
| ( ( ~ ( SV15
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ( SV15 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV15 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(107,plain,
! [SV3: $i,SV18: $i > $o] :
( ( ( ~ ~ ( SV18
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ( SV18 @ SX0 ) ) ) )
= $false )
| ( ( ~ ( SV18
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ( SV18 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV18 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(108,plain,
! [SV3: $i,SV21: $i > $o] :
( ( ( ~ ~ ~ ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $false )
| ( ( ~ ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV21 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(111,plain,
! [SV3: $i,SV24: $i > $o] :
( ( ( ~ ~ ~ ~ ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $false )
| ( ( ~ ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV24 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(113,plain,
! [SV3: $i,SV12: $i > $o] :
( ( ( SV12
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) ) )
= $false )
| ( ( SV12
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) ) )
= $false )
| ( ( ~ ~ ( SV12 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(114,plain,
! [SV3: $i,SV15: $i > $o] :
( ( ( SV15
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ( SV15 @ SX0 ) ) )
= $true )
| ( ( ~ ( SV15
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ( SV15 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV15 @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(117,plain,
! [SV3: $i,SV18: $i > $o] :
( ( ( ~ ( SV18
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ( SV18 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV18
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ( SV18 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV18 @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(118,plain,
! [SV3: $i,SV21: $i > $o] :
( ( ( ~ ~ ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV21 @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(121,plain,
! [SV3: $i,SV24: $i > $o] :
( ( ( ~ ~ ~ ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV24 @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(123,plain,
! [SV3: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ SV3 ) )
= $false )
| ( ( SV12
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) ) )
= $false )
| ( ( SV12
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV3: $i,SV15: $i > $o] :
( ( ( SV15
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ( SV15 @ SX0 ) ) )
= $true )
| ( ( SV15
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ( SV15 @ SX0 ) ) )
= $true )
| ( ( ~ ~ ( SV15 @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(127,plain,
! [SV3: $i,SV18: $i > $o] :
( ( ( SV18
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV18
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ( SV18 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV18 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(128,plain,
! [SV3: $i,SV21: $i > $o] :
( ( ( ~ ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $false )
| ( ( ~ ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV21 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(131,plain,
! [SV3: $i,SV24: $i > $o] :
( ( ( ~ ~ ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $false )
| ( ( ~ ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV24 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(133,plain,
! [SV3: $i,SV12: $i > $o] :
( ( ( SV12 @ SV3 )
= $true )
| ( ( SV12
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) ) )
= $false )
| ( ( SV12
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(134,plain,
! [SV3: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV3 ) )
= $true )
| ( ( SV15
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ( SV15 @ SX0 ) ) )
= $true )
| ( ( SV15
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ( SV15 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(137,plain,
! [SV3: $i,SV18: $i > $o] :
( ( ( SV18
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false )
| ( ( SV18
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false )
| ( ( ~ ~ ( SV18 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(138,plain,
! [SV3: $i,SV21: $i > $o] :
( ( ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true )
| ( ( ~ ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV21 @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(141,plain,
! [SV3: $i,SV24: $i > $o] :
( ( ( ~ ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV24 @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(142,plain,
! [SV3: $i,SV15: $i > $o] :
( ( ( SV15 @ SV3 )
= $false )
| ( ( SV15
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ( SV15 @ SX0 ) ) )
= $true )
| ( ( SV15
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ( SV15 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(145,plain,
! [SV3: $i,SV18: $i > $o] :
( ( ( ~ ( SV18 @ SV3 ) )
= $false )
| ( ( SV18
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false )
| ( ( SV18
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(146,plain,
! [SV3: $i,SV21: $i > $o] :
( ( ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true )
| ( ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true )
| ( ( ~ ~ ( SV21 @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(149,plain,
! [SV3: $i,SV24: $i > $o] :
( ( ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV24 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(151,plain,
! [SV3: $i,SV18: $i > $o] :
( ( ( SV18 @ SV3 )
= $true )
| ( ( SV18
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false )
| ( ( SV18
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(152,plain,
! [SV3: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ SV3 ) )
= $true )
| ( ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true )
| ( ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(155,plain,
! [SV3: $i,SV24: $i > $o] :
( ( ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false )
| ( ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false )
| ( ( ~ ~ ( SV24 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(156,plain,
! [SV3: $i,SV21: $i > $o] :
( ( ( SV21 @ SV3 )
= $false )
| ( ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true )
| ( ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(159,plain,
! [SV3: $i,SV24: $i > $o] :
( ( ( ~ ( SV24 @ SV3 ) )
= $false )
| ( ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false )
| ( ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(161,plain,
! [SV3: $i,SV24: $i > $o] :
( ( ( SV24 @ SV3 )
= $true )
| ( ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false )
| ( ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(162,plain,
! [SV3: $i,SV6: $i > $o] :
( ( ( SV6
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV6 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(163,plain,
! [SV3: $i,SV4: $i,SV6: $i > $o] :
( ( ( SV6 @ SV4 )
= $true )
| ( ( cR
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV4 )
= $false )
| ( ( ~ ( SV6 @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(164,plain,
! [SV3: $i,SV6: $i > $o] :
( ( ( SV6 @ SV3 )
= $true )
| ( ( SV6
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(165,plain,
! [SV4: $i,SV3: $i,SV6: $i > $o] :
( ( ( SV6 @ SV3 )
= $true )
| ( ( cR
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV4 )
= $false )
| ( ( SV6 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(166,plain,
( ( ( sK2_Xy
@ ^ [SX0: $i] : ( SX0 = sK1_Xx2 ) )
= sK1_Xx2 )
= $true ),
inference(extuni,[status(esa)],[52:[bind(SV3,$thf( sK1_Xx2 ))]]) ).
thf(167,plain,
( ( cR
@ ( sK2_Xy
@ ^ [SX0: $i] : ( SX0 = sK1_Xx2 ) )
@ sK1_Xx2 )
= $false ),
inference(extuni,[status(esa)],[56:[bind(SV3,$thf( sK1_Xx2 )),bind(SV4,$thf( sK1_Xx2 ))]]) ).
thf(168,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK2_Xy @ SV1 ) )
= $true ) ),
inference(sim,[status(thm)],[84]) ).
thf(169,plain,
! [SV3: $i,SV12: $i > $o] :
( ( ( SV12 @ SV3 )
= $true )
| ( ( SV12
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) ) )
= $false ) ),
inference(sim,[status(thm)],[133]) ).
thf(170,plain,
! [SV3: $i,SV15: $i > $o] :
( ( ( SV15 @ SV3 )
= $false )
| ( ( SV15
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ( SV15 @ SX0 ) ) )
= $true ) ),
inference(sim,[status(thm)],[142]) ).
thf(171,plain,
! [SV3: $i,SV18: $i > $o] :
( ( ( SV18 @ SV3 )
= $true )
| ( ( SV18
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false ) ),
inference(sim,[status(thm)],[151]) ).
thf(172,plain,
! [SV3: $i,SV21: $i > $o] :
( ( ( SV21 @ SV3 )
= $false )
| ( ( SV21
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true ) ),
inference(sim,[status(thm)],[156]) ).
thf(173,plain,
! [SV3: $i,SV24: $i > $o] :
( ( ( SV24 @ SV3 )
= $true )
| ( ( SV24
@ ( sK2_Xy
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false ) ),
inference(sim,[status(thm)],[161]) ).
thf(174,plain,
! [SV2: $i] :
( ( ( cR @ SV2 @ ( sK3_Xy1 @ SV2 ) )
= $true )
| ( ( cP @ SV2 )
= $true ) ),
inference(sim,[status(thm)],[80]) ).
thf(175,plain,
! [SV2: $i] :
( ( ( s @ ( sK3_Xy1 @ SV2 ) )
= $true )
| ( ( cP @ SV2 )
= $true ) ),
inference(sim,[status(thm)],[82]) ).
thf(176,plain,
! [SV4: $i] :
( ( cR
@ ( sK2_Xy
@ ^ [SX0: $i] : $true )
@ SV4 )
= $false ),
inference(sim,[status(thm)],[53]) ).
thf(177,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,176,175,174,173,172,171,170,169,168,167,166,165,164,48,45,44,40,38,28]) ).
thf(178,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV384^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 28 16:37:25 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 0
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 0
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.35 (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.44/0.62
% 0.44/0.62 ********************************
% 0.44/0.62 * All subproblems solved! *
% 0.44/0.62 ********************************
% 0.44/0.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:177,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.44/0.63
% 0.44/0.63 %**** Beginning of derivation protocol ****
% 0.44/0.63 % SZS output start CNFRefutation
% See solution above
% 0.44/0.63
% 0.44/0.63 %**** End of derivation protocol ****
% 0.44/0.63 %**** no. of clauses in derivation: 122 ****
% 0.44/0.63 %**** clause counter: 177 ****
% 0.44/0.63
% 0.44/0.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:177,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------