%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU861^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n005.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 10:49:08 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 1
% Syntax : Number of formulae : 94 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 818 ( 280 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 1598 ( 389 ~; 314 |; 35 &; 817 @)
% ( 0 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 202 ( 202 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 274 ( 0 ^; 265 !; 9 ?; 274 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cB,type,
cB: a > $o ).
thf(tp_cC,type,
cC: a > $o ).
thf(tp_sK1_P,type,
sK1_P: ( a > $o ) > $o ).
thf(tp_sK2_Xx_28,type,
sK2_Xx_28: ( a > $o ) > a > ( a > $o ) > a ).
thf(tp_sK3_Xt,type,
sK3_Xt: ( a > $o ) > a ).
thf(tp_sK4_Y,type,
sK4_Y: ( ( a > $o ) > $o ) > a > $o ).
thf(tp_sK5_SY21,type,
sK5_SY21: ( ( a > $o ) > $o ) > a ).
thf(tp_sK6_SY24,type,
sK6_SY24: ( ( a > $o ) > $o ) > a > $o ).
thf(tp_sK7_E,type,
sK7_E: ( ( a > $o ) > $o ) > a > $o ).
thf(1,conjecture,
( ( ! [P: ( a > $o ) > $o] :
( ( ! [E: a > $o] :
( ~ ? [Xt: a] : ( E @ Xt )
=> ( P @ E ) )
& ! [Y: a > $o,Xx: a,Z: a > $o] :
( ( ( P @ Y )
& ! [Xx_27: a] :
( ( Z @ Xx_27 )
=> ( ( Y @ Xx_27 )
| ( Xx_27 = Xx ) ) ) )
=> ( P @ Z ) ) )
=> ( P @ cC ) )
& ! [Xx: a] :
( ( cB @ Xx )
=> ( cC @ Xx ) ) )
=> ! [P: ( a > $o ) > $o] :
( ( ! [E: a > $o] :
( ~ ? [Xt: a] : ( E @ Xt )
=> ( P @ E ) )
& ! [Y: a > $o,Xx: a,Z: a > $o] :
( ( ( P @ Y )
& ! [Xx_28: a] :
( ( Z @ Xx_28 )
=> ( ( Y @ Xx_28 )
| ( Xx_28 = Xx ) ) ) )
=> ( P @ Z ) ) )
=> ( P @ cB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM531E_pme) ).
thf(2,negated_conjecture,
( ( ( ! [P: ( a > $o ) > $o] :
( ( ! [E: a > $o] :
( ~ ? [Xt: a] : ( E @ Xt )
=> ( P @ E ) )
& ! [Y: a > $o,Xx: a,Z: a > $o] :
( ( ( P @ Y )
& ! [Xx_27: a] :
( ( Z @ Xx_27 )
=> ( ( Y @ Xx_27 )
| ( Xx_27 = Xx ) ) ) )
=> ( P @ Z ) ) )
=> ( P @ cC ) )
& ! [Xx: a] :
( ( cB @ Xx )
=> ( cC @ Xx ) ) )
=> ! [P: ( a > $o ) > $o] :
( ( ! [E: a > $o] :
( ~ ? [Xt: a] : ( E @ Xt )
=> ( P @ E ) )
& ! [Y: a > $o,Xx: a,Z: a > $o] :
( ( ( P @ Y )
& ! [Xx_28: a] :
( ( Z @ Xx_28 )
=> ( ( Y @ Xx_28 )
| ( Xx_28 = Xx ) ) ) )
=> ( P @ Z ) ) )
=> ( P @ cB ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [P: ( a > $o ) > $o] :
( ( ! [E: a > $o] :
( ~ ? [Xt: a] : ( E @ Xt )
=> ( P @ E ) )
& ! [Y: a > $o,Xx: a,Z: a > $o] :
( ( ( P @ Y )
& ! [Xx_27: a] :
( ( Z @ Xx_27 )
=> ( ( Y @ Xx_27 )
| ( Xx_27 = Xx ) ) ) )
=> ( P @ Z ) ) )
=> ( P @ cC ) )
& ! [Xx: a] :
( ( cB @ Xx )
=> ( cC @ Xx ) ) )
=> ! [P: ( a > $o ) > $o] :
( ( ! [E: a > $o] :
( ~ ? [Xt: a] : ( E @ Xt )
=> ( P @ E ) )
& ! [Y: a > $o,Xx: a,Z: a > $o] :
( ( ( P @ Y )
& ! [Xx_28: a] :
( ( Z @ Xx_28 )
=> ( ( Y @ Xx_28 )
| ( Xx_28 = Xx ) ) ) )
=> ( P @ Z ) ) )
=> ( P @ cB ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [P: ( a > $o ) > $o] :
( ( ! [E: a > $o] :
( ~ ? [Xt: a] : ( E @ Xt )
=> ( P @ E ) )
& ! [Y: a > $o,Xx: a,Z: a > $o] :
( ( ( P @ Y )
& ! [Xx_27: a] :
( ( Z @ Xx_27 )
=> ( ( Y @ Xx_27 )
| ( Xx_27 = Xx ) ) ) )
=> ( P @ Z ) ) )
=> ( P @ cC ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: a] :
( ( cB @ Xx )
=> ( cC @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [P: ( a > $o ) > $o] :
( ( ! [E: a > $o] :
( ~ ? [Xt: a] : ( E @ Xt )
=> ( P @ E ) )
& ! [Y: a > $o,Xx: a,Z: a > $o] :
( ( ( P @ Y )
& ! [Xx_28: a] :
( ( Z @ Xx_28 )
=> ( ( Y @ Xx_28 )
| ( Xx_28 = Xx ) ) ) )
=> ( P @ Z ) ) )
=> ( P @ cB ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [P: ( a > $o ) > $o] :
( ( ! [E: a > $o] :
( ~ ? [Xt: a] : ( E @ Xt )
=> ( P @ E ) )
& ! [Y: a > $o,Xx: a,Z: a > $o] :
( ( ( P @ Y )
& ! [Xx_28: a] :
( ( Z @ Xx_28 )
=> ( ( Y @ Xx_28 )
| ( Xx_28 = Xx ) ) ) )
=> ( P @ Z ) ) )
=> ( P @ cB ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY15: a > $o] :
( ( SY15 @ ( sK3_Xt @ SY15 ) )
| ( sK1_P @ SY15 ) )
& ! [SY17: a > $o,SY18: a,SY19: a > $o] :
( ( ( SY19 @ ( sK2_Xx_28 @ SY19 @ SY18 @ SY17 ) )
& ( ( sK2_Xx_28 @ SY19 @ SY18 @ SY17 )
!= SY18 )
& ~ ( SY17 @ ( sK2_Xx_28 @ SY19 @ SY18 @ SY17 ) ) )
| ~ ( sK1_P @ SY17 )
| ( sK1_P @ SY19 ) )
& ~ ( sK1_P @ cB ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [P: ( a > $o ) > $o] :
( ( ! [SY27: a] :
~ ( sK7_E @ P @ SY27 )
& ~ ( P @ ( sK7_E @ P ) ) )
| ( ! [SY26: a] :
( ~ ( sK6_SY24 @ P @ SY26 )
| ( SY26
= ( sK5_SY21 @ P ) )
| ( sK4_Y @ P @ SY26 ) )
& ( P @ ( sK4_Y @ P ) )
& ~ ( P @ ( sK6_SY24 @ P ) ) )
| ( P @ cC ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [Xx: a] :
( ~ ( cB @ Xx )
| ( cC @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(11,plain,
( ( ! [Xx: a] :
( ~ ( cB @ Xx )
| ( cC @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [P: ( a > $o ) > $o] :
( ( ! [SY27: a] :
~ ( sK7_E @ P @ SY27 )
& ~ ( P @ ( sK7_E @ P ) ) )
| ( ! [SY26: a] :
( ~ ( sK6_SY24 @ P @ SY26 )
| ( SY26
= ( sK5_SY21 @ P ) )
| ( sK4_Y @ P @ SY26 ) )
& ( P @ ( sK4_Y @ P ) )
& ~ ( P @ ( sK6_SY24 @ P ) ) )
| ( P @ cC ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ! [SY15: a > $o] :
( ( SY15 @ ( sK3_Xt @ SY15 ) )
| ( sK1_P @ SY15 ) )
& ! [SY17: a > $o,SY18: a,SY19: a > $o] :
( ( ( SY19 @ ( sK2_Xx_28 @ SY19 @ SY18 @ SY17 ) )
& ( ( sK2_Xx_28 @ SY19 @ SY18 @ SY17 )
!= SY18 )
& ~ ( SY17 @ ( sK2_Xx_28 @ SY19 @ SY18 @ SY17 ) ) )
| ~ ( sK1_P @ SY17 )
| ( sK1_P @ SY19 ) )
& ~ ( sK1_P @ cB ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: a > $o] :
( ( SX0 @ ( sK3_Xt @ SX0 ) )
| ( sK1_P @ SX0 ) )
| ~ ! [SX0: a > $o,SX1: a,SX2: a > $o] :
( ~ ( ~ ( SX2 @ ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ( ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 )
!= SX1 ) )
| ~ ~ ( SX0 @ ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( sK1_P @ SX0 )
| ( sK1_P @ SX2 ) ) )
| ~ ~ ( sK1_P @ cB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [SX0: ( a > $o ) > $o] :
( ~ ( ~ ! [SX1: a] :
~ ( sK7_E @ SX0 @ SX1 )
| ~ ~ ( SX0 @ ( sK7_E @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ! [SX1: a] :
( ~ ( sK6_SY24 @ SX0 @ SX1 )
| ( SX1
= ( sK5_SY21 @ SX0 ) )
| ( sK4_Y @ SX0 @ SX1 ) )
| ~ ( SX0 @ ( sK4_Y @ SX0 ) ) )
| ~ ~ ( SX0 @ ( sK6_SY24 @ SX0 ) ) )
| ( SX0 @ cC ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(16,plain,
! [SV1: a] :
( ( ~ ( cB @ SV1 )
| ( cC @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(17,plain,
( ( ~ ~ ( ~ ! [SX0: a > $o] :
( ( SX0 @ ( sK3_Xt @ SX0 ) )
| ( sK1_P @ SX0 ) )
| ~ ! [SX0: a > $o,SX1: a,SX2: a > $o] :
( ~ ( ~ ( SX2 @ ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ( ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 )
!= SX1 ) )
| ~ ~ ( SX0 @ ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( sK1_P @ SX0 )
| ( sK1_P @ SX2 ) ) )
| ~ ~ ( sK1_P @ cB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: ( a > $o ) > $o] :
( ( ~ ( ~ ! [SY28: a] :
~ ( sK7_E @ SV2 @ SY28 )
| ~ ~ ( SV2 @ ( sK7_E @ SV2 ) ) )
| ~ ( ~ ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
| ~ ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) )
| ( SV2 @ cC ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV1: a] :
( ( ( ~ ( cB @ SV1 ) )
= $true )
| ( ( cC @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ~ ( ~ ! [SX0: a > $o] :
( ( SX0 @ ( sK3_Xt @ SX0 ) )
| ( sK1_P @ SX0 ) )
| ~ ! [SX0: a > $o,SX1: a,SX2: a > $o] :
( ~ ( ~ ( SX2 @ ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ( ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 )
!= SX1 ) )
| ~ ~ ( SX0 @ ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( sK1_P @ SX0 )
| ( sK1_P @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ~ ( sK1_P @ cB ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ~ ( ~ ! [SY28: a] :
~ ( sK7_E @ SV2 @ SY28 )
| ~ ~ ( SV2 @ ( sK7_E @ SV2 ) ) )
| ~ ( ~ ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
| ~ ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) ) )
= $true )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV1: a] :
( ( ( cB @ SV1 )
= $false )
| ( ( cC @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ ( ~ ! [SX0: a > $o] :
( ( SX0 @ ( sK3_Xt @ SX0 ) )
| ( sK1_P @ SX0 ) )
| ~ ! [SX0: a > $o,SX1: a,SX2: a > $o] :
( ~ ( ~ ( SX2 @ ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ( ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 )
!= SX1 ) )
| ~ ~ ( SX0 @ ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( sK1_P @ SX0 )
| ( sK1_P @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( sK1_P @ cB ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ~ ( ~ ! [SY28: a] :
~ ( sK7_E @ SV2 @ SY28 )
| ~ ~ ( SV2 @ ( sK7_E @ SV2 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
| ~ ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) ) )
= $true )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( ~ ! [SX0: a > $o] :
( ( SX0 @ ( sK3_Xt @ SX0 ) )
| ( sK1_P @ SX0 ) )
| ~ ! [SX0: a > $o,SX1: a,SX2: a > $o] :
( ~ ( ~ ( SX2 @ ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ( ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 )
!= SX1 ) )
| ~ ~ ( SX0 @ ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( sK1_P @ SX0 )
| ( sK1_P @ SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( sK1_P @ cB )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ~ ! [SY28: a] :
~ ( sK7_E @ SV2 @ SY28 )
| ~ ~ ( SV2 @ ( sK7_E @ SV2 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
| ~ ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) ) )
= $true )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ~ ! [SX0: a > $o] :
( ( SX0 @ ( sK3_Xt @ SX0 ) )
| ( sK1_P @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(31,plain,
( ( ~ ! [SX0: a > $o,SX1: a,SX2: a > $o] :
( ~ ( ~ ( SX2 @ ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ( ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 )
!= SX1 ) )
| ~ ~ ( SX0 @ ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( sK1_P @ SX0 )
| ( sK1_P @ SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(32,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ~ ! [SY28: a] :
~ ( sK7_E @ SV2 @ SY28 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
| ~ ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) ) )
= $true )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ~ ~ ( SV2 @ ( sK7_E @ SV2 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
| ~ ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) ) )
= $true )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ! [SX0: a > $o] :
( ( SX0 @ ( sK3_Xt @ SX0 ) )
| ( sK1_P @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
( ( ! [SX0: a > $o,SX1: a,SX2: a > $o] :
( ~ ( ~ ( SX2 @ ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ( ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 )
!= SX1 ) )
| ~ ~ ( SX0 @ ( sK2_Xx_28 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( sK1_P @ SX0 )
| ( sK1_P @ SX2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ! [SY28: a] :
~ ( sK7_E @ SV2 @ SY28 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
| ~ ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) ) )
= $true )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ~ ( SV2 @ ( sK7_E @ SV2 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
| ~ ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) ) )
= $true )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(38,plain,
! [SV3: a > $o] :
( ( ( SV3 @ ( sK3_Xt @ SV3 ) )
| ( sK1_P @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV4: a > $o] :
( ( ! [SY30: a,SY31: a > $o] :
( ~ ( ~ ( SY31 @ ( sK2_Xx_28 @ SY31 @ SY30 @ SV4 ) )
| ~ ~ ( ~ ( ( ( sK2_Xx_28 @ SY31 @ SY30 @ SV4 )
!= SY30 ) )
| ~ ~ ( SV4 @ ( sK2_Xx_28 @ SY31 @ SY30 @ SV4 ) ) ) )
| ~ ( sK1_P @ SV4 )
| ( sK1_P @ SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV5: a,SV2: ( a > $o ) > $o] :
( ( ( ~ ( sK7_E @ SV2 @ SV5 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
| ~ ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) ) )
= $true )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
| ~ ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) ) )
= $true )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV3: a > $o] :
( ( ( SV3 @ ( sK3_Xt @ SV3 ) )
= $true )
| ( ( sK1_P @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV4: a > $o,SV6: a] :
( ( ! [SY32: a > $o] :
( ~ ( ~ ( SY32 @ ( sK2_Xx_28 @ SY32 @ SV6 @ SV4 ) )
| ~ ~ ( ~ ( ( ( sK2_Xx_28 @ SY32 @ SV6 @ SV4 )
!= SV6 ) )
| ~ ~ ( SV4 @ ( sK2_Xx_28 @ SY32 @ SV6 @ SV4 ) ) ) )
| ~ ( sK1_P @ SV4 )
| ( sK1_P @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV5: a,SV2: ( a > $o ) > $o] :
( ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
| ~ ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) ) )
= $true )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ~ ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
| ~ ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV4: a > $o,SV6: a,SV7: a > $o] :
( ( ~ ( ~ ( SV7 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) )
| ~ ~ ( ~ ( ( ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 )
!= SV6 ) )
| ~ ~ ( SV4 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) ) ) )
| ~ ( sK1_P @ SV4 )
| ( sK1_P @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV5: a,SV2: ( a > $o ) > $o] :
( ( ( ~ ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
| ~ ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) )
= $false )
| ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ~ ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) ) )
= $false )
| ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(49,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ~ ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV4: a > $o,SV6: a,SV7: a > $o] :
( ( ( ~ ( ~ ( SV7 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) )
| ~ ~ ( ~ ( ( ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 )
!= SV6 ) )
| ~ ~ ( SV4 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) ) ) )
| ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV5: a,SV2: ( a > $o ) > $o] :
( ( ( ~ ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) ) )
= $false )
| ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(52,plain,
! [SV5: a,SV2: ( a > $o ) > $o] :
( ( ( ~ ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) )
= $false )
| ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(53,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) ) )
= $true )
| ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) )
= $true )
| ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(55,plain,
! [SV4: a > $o,SV6: a,SV7: a > $o] :
( ( ( ~ ( ~ ( SV7 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) )
| ~ ~ ( ~ ( ( ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 )
!= SV6 ) )
| ~ ~ ( SV4 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV5: a,SV2: ( a > $o ) > $o] :
( ( ( ~ ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) ) )
= $true )
| ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(57,plain,
! [SV5: a,SV2: ( a > $o ) > $o] :
( ( ( ~ ( SV2 @ ( sK6_SY24 @ SV2 ) ) )
= $true )
| ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(58,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( SV2 @ ( sK6_SY24 @ SV2 ) )
= $false )
| ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV4: a > $o,SV6: a,SV7: a > $o] :
( ( ( ~ ( SV7 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) )
| ~ ~ ( ~ ( ( ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 )
!= SV6 ) )
| ~ ~ ( SV4 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV5: a,SV2: ( a > $o ) > $o] :
( ( ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) )
| ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
= $false )
| ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV5: a,SV2: ( a > $o ) > $o] :
( ( ( SV2 @ ( sK6_SY24 @ SV2 ) )
= $false )
| ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) ) )
= $false )
| ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(64,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(65,plain,
! [SV4: a > $o,SV6: a,SV7: a > $o] :
( ( ( ~ ( SV7 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(66,plain,
! [SV4: a > $o,SV6: a,SV7: a > $o] :
( ( ( ~ ~ ( ~ ( ( ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 )
!= SV6 ) )
| ~ ~ ( SV4 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(67,plain,
! [SV5: a,SV2: ( a > $o ) > $o] :
( ( ( ~ ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) ) )
= $false )
| ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(68,plain,
! [SV5: a,SV2: ( a > $o ) > $o] :
( ( ( ~ ( SV2 @ ( sK4_Y @ SV2 ) ) )
= $false )
| ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(69,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) ) )
= $true )
| ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(70,plain,
! [SV2: ( a > $o ) > $o] :
( ( ( SV2 @ ( sK4_Y @ SV2 ) )
= $true )
| ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(71,plain,
! [SV4: a > $o,SV6: a,SV7: a > $o] :
( ( ( SV7 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) )
= $true )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(72,plain,
! [SV4: a > $o,SV6: a,SV7: a > $o] :
( ( ( ~ ( ~ ( ( ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 )
!= SV6 ) )
| ~ ~ ( SV4 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(73,plain,
! [SV5: a,SV2: ( a > $o ) > $o] :
( ( ( ! [SY29: a] :
( ~ ( sK6_SY24 @ SV2 @ SY29 )
| ( SY29
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SY29 ) ) )
= $true )
| ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(74,plain,
! [SV5: a,SV2: ( a > $o ) > $o] :
( ( ( SV2 @ ( sK4_Y @ SV2 ) )
= $true )
| ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(75,plain,
! [SV8: a,SV2: ( a > $o ) > $o] :
( ( ( ~ ( sK6_SY24 @ SV2 @ SV8 )
| ( SV8
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SV8 ) )
= $true )
| ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV6: a,SV7: a > $o,SV4: a > $o] :
( ( ( sK1_P @ SV4 )
= $false )
| ( ( SV7 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) )
= $true )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV4: a > $o,SV6: a,SV7: a > $o] :
( ( ( ~ ( ( ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 )
!= SV6 ) )
| ~ ~ ( SV4 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV5: a,SV9: a,SV2: ( a > $o ) > $o] :
( ( ( ~ ( sK6_SY24 @ SV2 @ SV9 )
| ( SV9
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SV9 ) )
= $true )
| ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(79,plain,
! [SV8: a,SV2: ( a > $o ) > $o] :
( ( ( ~ ( sK6_SY24 @ SV2 @ SV8 ) )
= $true )
| ( ( ( SV8
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SV8 ) )
= $true )
| ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV4: a > $o,SV6: a,SV7: a > $o] :
( ( ( ~ ( ( ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 )
!= SV6 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(81,plain,
! [SV6: a,SV7: a > $o,SV4: a > $o] :
( ( ( ~ ~ ( SV4 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(82,plain,
! [SV5: a,SV9: a,SV2: ( a > $o ) > $o] :
( ( ( ~ ( sK6_SY24 @ SV2 @ SV9 ) )
= $true )
| ( ( ( SV9
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SV9 ) )
= $true )
| ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV8: a,SV2: ( a > $o ) > $o] :
( ( ( sK6_SY24 @ SV2 @ SV8 )
= $false )
| ( ( ( SV8
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SV8 ) )
= $true )
| ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV4: a > $o,SV6: a,SV7: a > $o] :
( ( ( ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 )
!= SV6 )
= $true )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(85,plain,
! [SV6: a,SV7: a > $o,SV4: a > $o] :
( ( ( ~ ( SV4 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(86,plain,
! [SV5: a,SV9: a,SV2: ( a > $o ) > $o] :
( ( ( sK6_SY24 @ SV2 @ SV9 )
= $false )
| ( ( ( SV9
= ( sK5_SY21 @ SV2 ) )
| ( sK4_Y @ SV2 @ SV9 ) )
= $true )
| ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV2: ( a > $o ) > $o,SV8: a] :
( ( ( SV8
= ( sK5_SY21 @ SV2 ) )
= $true )
| ( ( sK4_Y @ SV2 @ SV8 )
= $true )
| ( ( sK6_SY24 @ SV2 @ SV8 )
= $false )
| ( ( SV2 @ ( sK7_E @ SV2 ) )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV4: a > $o,SV6: a,SV7: a > $o] :
( ( ( ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 )
= SV6 )
= $false )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(89,plain,
! [SV6: a,SV7: a > $o,SV4: a > $o] :
( ( ( SV4 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) )
= $false )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(90,plain,
! [SV5: a,SV2: ( a > $o ) > $o,SV9: a] :
( ( ( SV9
= ( sK5_SY21 @ SV2 ) )
= $true )
| ( ( sK4_Y @ SV2 @ SV9 )
= $true )
| ( ( sK6_SY24 @ SV2 @ SV9 )
= $false )
| ( ( sK7_E @ SV2 @ SV5 )
= $false )
| ( ( SV2 @ cC )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV6: a,SV7: a > $o,SV4: a > $o] :
( ( ( sK1_P @ SV4 )
= $false )
| ( ( ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 )
= SV6 )
= $false )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(92,plain,
! [SV6: a,SV7: a > $o,SV4: a > $o] :
( ( ( sK1_P @ SV4 )
= $false )
| ( ( SV4 @ ( sK2_Xx_28 @ SV7 @ SV6 @ SV4 ) )
= $false )
| ( ( sK1_P @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(93,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,92,91,90,87,76,74,70,62,59,42,28]) ).
thf(94,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU861^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.10/0.21 % Computer : n005.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Oct 6 15:37:00 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.26
% 0.10/0.26 No.of.Axioms: 0
% 0.10/0.26
% 0.10/0.26 Length.of.Defs: 0
% 0.10/0.26
% 0.10/0.26 Contains.Choice.Funs: false
% 0.10/0.26 ..
% 0.10/0.26
% 0.10/0.26 ********************************
% 0.10/0.26 * All subproblems solved! *
% 0.10/0.26 ********************************
% 0.10/0.26 % 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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:93,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.26
% 0.10/0.26 %**** Beginning of derivation protocol ****
% 0.10/0.26 % SZS output start CNFRefutation
% See solution above
% 0.10/0.26
% 0.10/0.26 %**** End of derivation protocol ****
% 0.10/0.26 %**** no. of clauses in derivation: 94 ****
% 0.10/0.26 %**** clause counter: 93 ****
% 0.10/0.26
% 0.10/0.26 % 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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:93,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------