TSTP Solution File: SEU550^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU550^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n025.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 12:12:48 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 113 ( 67 unt; 7 typ; 1 def)
% Number of atoms : 647 ( 269 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 804 ( 254 ~; 180 |; 32 &; 294 @)
% ( 12 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 206 ( 5 ^ 184 !; 17 ?; 206 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $o ).
thf(tp_sK2_SY18,type,
sK2_SY18: $i > $o ).
thf(tp_sK3_SY30,type,
sK3_SY30: $i > $i ).
thf(tp_sK4_SY21,type,
sK4_SY21: $i ).
thf(tp_sK5_SY22,type,
sK5_SY22: $i > $i ).
thf(tp_sK6_SY29,type,
sK6_SY29: $i ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(1,conjecture,
! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
<=> ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(2,negated_conjecture,
( ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
<=> ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $o,SY1: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY0 @ Xx )
<=> ( SY1 @ Xy ) ) )
=> ( ? [SY5: $i] :
( ( SY0 @ SY5 )
& ! [SY6: $i] :
( ( SY0 @ SY6 )
=> ( SY5 = SY6 ) ) )
<=> ? [SY8: $i] :
( ( SY1 @ SY8 )
& ! [SY9: $i] :
( ( SY1 @ SY9 )
=> ( SY8 = SY9 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,exu]) ).
thf(4,plain,
( ( ! [SY18: $i > $o] :
( ! [SY19: $i,SY20: $i] :
( ( SY19 = SY20 )
=> ( ( sK1_SY0 @ SY19 )
<=> ( SY18 @ SY20 ) ) )
=> ( ? [SY21: $i] :
( ( sK1_SY0 @ SY21 )
& ! [SY22: $i] :
( ( sK1_SY0 @ SY22 )
=> ( SY21 = SY22 ) ) )
<=> ? [SY8: $i] :
( ( SY18 @ SY8 )
& ! [SY9: $i] :
( ( SY18 @ SY9 )
=> ( SY8 = SY9 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY25: $i,SY26: $i] :
( ( SY25 = SY26 )
=> ( ( sK1_SY0 @ SY25 )
<=> ( sK2_SY18 @ SY26 ) ) )
=> ( ? [SY21: $i] :
( ( sK1_SY0 @ SY21 )
& ! [SY22: $i] :
( ( sK1_SY0 @ SY22 )
=> ( SY21 = SY22 ) ) )
<=> ? [SY29: $i] :
( ( sK2_SY18 @ SY29 )
& ! [SY30: $i] :
( ( sK2_SY18 @ SY30 )
=> ( SY29 = SY30 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY25: $i,SY26: $i] :
( ( SY25 = SY26 )
=> ( ( sK1_SY0 @ SY25 )
<=> ( sK2_SY18 @ SY26 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ? [SY21: $i] :
( ( sK1_SY0 @ SY21 )
& ! [SY22: $i] :
( ( sK1_SY0 @ SY22 )
=> ( SY21 = SY22 ) ) )
<=> ? [SY29: $i] :
( ( sK2_SY18 @ SY29 )
& ! [SY30: $i] :
( ( sK2_SY18 @ SY30 )
=> ( SY29 = SY30 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ? [SY21: $i] :
( ( sK1_SY0 @ SY21 )
& ! [SY22: $i] :
( ( sK1_SY0 @ SY22 )
=> ( SY21 = SY22 ) ) )
=> ? [SY29: $i] :
( ( sK2_SY18 @ SY29 )
& ! [SY30: $i] :
( ( sK2_SY18 @ SY30 )
=> ( SY29 = SY30 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(9,plain,
( ( ? [SY29: $i] :
( ( sK2_SY18 @ SY29 )
& ! [SY30: $i] :
( ( sK2_SY18 @ SY30 )
=> ( SY29 = SY30 ) ) )
=> ? [SY21: $i] :
( ( sK1_SY0 @ SY21 )
& ! [SY22: $i] :
( ( sK1_SY0 @ SY22 )
=> ( SY21 = SY22 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(10,plain,
( ( ~ ( ? [SY21: $i] :
( ( sK1_SY0 @ SY21 )
& ! [SY22: $i] :
( ( sK1_SY0 @ SY22 )
=> ( SY21 = SY22 ) ) )
=> ? [SY29: $i] :
( ( sK2_SY18 @ SY29 )
& ! [SY30: $i] :
( ( sK2_SY18 @ SY30 )
=> ( SY29 = SY30 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ? [SY29: $i] :
( ( sK2_SY18 @ SY29 )
& ! [SY30: $i] :
( ( sK2_SY18 @ SY30 )
=> ( SY29 = SY30 ) ) )
=> ? [SY21: $i] :
( ( sK1_SY0 @ SY21 )
& ! [SY22: $i] :
( ( sK1_SY0 @ SY22 )
=> ( SY21 = SY22 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [SY31: $i] :
( ~ ( sK1_SY0 @ SY31 )
| ( sK4_SY21 = SY31 ) )
& ( sK1_SY0 @ sK4_SY21 )
& ! [SY29: $i] :
( ( ( sK2_SY18 @ ( sK3_SY30 @ SY29 ) )
& ( SY29
!= ( sK3_SY30 @ SY29 ) ) )
| ~ ( sK2_SY18 @ SY29 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(13,plain,
( ( ! [SY32: $i] :
( ~ ( sK2_SY18 @ SY32 )
| ( sK6_SY29 = SY32 ) )
& ( sK2_SY18 @ sK6_SY29 )
& ! [SY21: $i] :
( ( ( sK1_SY0 @ ( sK5_SY22 @ SY21 ) )
& ( SY21
!= ( sK5_SY22 @ SY21 ) ) )
| ~ ( sK1_SY0 @ SY21 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(14,plain,
( ( ! [SY25: $i,SY26: $i] :
( ( SY25 != SY26 )
| ~ ( sK1_SY0 @ SY25 )
| ( sK2_SY18 @ SY26 ) )
& ! [SY25: $i,SY26: $i] :
( ( SY25 != SY26 )
| ~ ( sK2_SY18 @ SY26 )
| ( sK1_SY0 @ SY25 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(15,plain,
( ( ! [SY25: $i,SY26: $i] :
( ( SY25 != SY26 )
| ~ ( sK1_SY0 @ SY25 )
| ( sK2_SY18 @ SY26 ) )
& ! [SY25: $i,SY26: $i] :
( ( SY25 != SY26 )
| ~ ( sK2_SY18 @ SY26 )
| ( sK1_SY0 @ SY25 ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [SY31: $i] :
( ~ ( sK1_SY0 @ SY31 )
| ( sK4_SY21 = SY31 ) )
& ( sK1_SY0 @ sK4_SY21 )
& ! [SY29: $i] :
( ( ( sK2_SY18 @ ( sK3_SY30 @ SY29 ) )
& ( SY29
!= ( sK3_SY30 @ SY29 ) ) )
| ~ ( sK2_SY18 @ SY29 ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ SX0 )
| ( sK4_SY21 = SX0 ) )
| ~ ( sK1_SY0 @ sK4_SY21 ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SX0 ) )
| ~ ( ( SX0
!= ( sK3_SY30 @ SX0 ) ) ) )
| ~ ( sK2_SY18 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,exu]) ).
thf(18,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK1_SY0 @ SX0 )
| ( sK2_SY18 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK2_SY18 @ SX1 )
| ( sK1_SY0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,exu]) ).
thf(19,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ SX0 )
| ( sK4_SY21 = SX0 ) )
| ~ ( sK1_SY0 @ sK4_SY21 ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SX0 ) )
| ~ ( ( SX0
!= ( sK3_SY30 @ SX0 ) ) ) )
| ~ ( sK2_SY18 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK1_SY0 @ SX0 )
| ( sK2_SY18 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK2_SY18 @ SX1 )
| ( sK1_SY0 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ SX0 )
| ( sK4_SY21 = SX0 ) )
| ~ ( sK1_SY0 @ sK4_SY21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(22,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SX0 ) )
| ~ ( ( SX0
!= ( sK3_SY30 @ SX0 ) ) ) )
| ~ ( sK2_SY18 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK1_SY0 @ SX0 )
| ( sK2_SY18 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK2_SY18 @ SX1 )
| ( sK1_SY0 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ SX0 )
| ( sK4_SY21 = SX0 ) )
| ~ ( sK1_SY0 @ sK4_SY21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SX0 ) )
| ~ ( ( SX0
!= ( sK3_SY30 @ SX0 ) ) ) )
| ~ ( sK2_SY18 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK1_SY0 @ SX0 )
| ( sK2_SY18 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(28,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK2_SY18 @ SX1 )
| ( sK1_SY0 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ SX0 )
| ( sK4_SY21 = SX0 ) )
| ~ ( sK1_SY0 @ sK4_SY21 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV1: $i] :
( ( ~ ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SV1 ) )
| ~ ( ( SV1
!= ( sK3_SY30 @ SV1 ) ) ) )
| ~ ( sK2_SY18 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV2: $i] :
( ( ! [SY33: $i] :
( ( SV2 != SY33 )
| ~ ( sK1_SY0 @ SV2 )
| ( sK2_SY18 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV3: $i] :
( ( ! [SY34: $i] :
( ( SV3 != SY34 )
| ~ ( sK2_SY18 @ SY34 )
| ( sK1_SY0 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ SX0 )
| ( sK4_SY21 = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ( sK1_SY0 @ sK4_SY21 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(35,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SV1 ) )
| ~ ( ( SV1
!= ( sK3_SY30 @ SV1 ) ) ) ) )
= $true )
| ( ( ~ ( sK2_SY18 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(36,plain,
! [SV4: $i,SV2: $i] :
( ( ( SV2 != SV4 )
| ~ ( sK1_SY0 @ SV2 )
| ( sK2_SY18 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV5: $i,SV3: $i] :
( ( ( SV3 != SV5 )
| ~ ( sK2_SY18 @ SV5 )
| ( sK1_SY0 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(38,plain,
( ( ! [SX0: $i] :
( ~ ( sK1_SY0 @ SX0 )
| ( sK4_SY21 = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(39,plain,
( ( sK1_SY0 @ sK4_SY21 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(40,plain,
! [SV1: $i] :
( ( ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SV1 ) )
| ~ ( ( SV1
!= ( sK3_SY30 @ SV1 ) ) ) )
= $false )
| ( ( ~ ( sK2_SY18 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV4: $i,SV2: $i] :
( ( ( ( SV2 != SV4 ) )
= $true )
| ( ( ~ ( sK1_SY0 @ SV2 )
| ( sK2_SY18 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV5: $i,SV3: $i] :
( ( ( ( SV3 != SV5 ) )
= $true )
| ( ( ~ ( sK2_SY18 @ SV5 )
| ( sK1_SY0 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV6: $i] :
( ( ~ ( sK1_SY0 @ SV6 )
| ( sK4_SY21 = SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV1: $i] :
( ( ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SV1 ) ) )
= $false )
| ( ( ~ ( sK2_SY18 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV1: $i] :
( ( ( ~ ( ( SV1
!= ( sK3_SY30 @ SV1 ) ) ) )
= $false )
| ( ( ~ ( sK2_SY18 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV4: $i,SV2: $i] :
( ( ( SV2 = SV4 )
= $false )
| ( ( ~ ( sK1_SY0 @ SV2 )
| ( sK2_SY18 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV5: $i,SV3: $i] :
( ( ( SV3 = SV5 )
= $false )
| ( ( ~ ( sK2_SY18 @ SV5 )
| ( sK1_SY0 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV6: $i] :
( ( ( ~ ( sK1_SY0 @ SV6 ) )
= $true )
| ( ( sK4_SY21 = SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV1: $i] :
( ( ( sK2_SY18 @ ( sK3_SY30 @ SV1 ) )
= $true )
| ( ( ~ ( sK2_SY18 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(50,plain,
! [SV1: $i] :
( ( ( ( SV1
!= ( sK3_SY30 @ SV1 ) ) )
= $true )
| ( ( ~ ( sK2_SY18 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(51,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( sK1_SY0 @ SV2 ) )
= $true )
| ( ( sK2_SY18 @ SV4 )
= $true )
| ( ( SV2 = SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV3: $i,SV5: $i] :
( ( ( ~ ( sK2_SY18 @ SV5 ) )
= $true )
| ( ( sK1_SY0 @ SV3 )
= $true )
| ( ( SV3 = SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV6: $i] :
( ( ( sK1_SY0 @ SV6 )
= $false )
| ( ( sK4_SY21 = SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV1: $i] :
( ( ( sK2_SY18 @ SV1 )
= $false )
| ( ( sK2_SY18 @ ( sK3_SY30 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV1: $i] :
( ( ( SV1
= ( sK3_SY30 @ SV1 ) )
= $false )
| ( ( ~ ( sK2_SY18 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV4: $i,SV2: $i] :
( ( ( sK1_SY0 @ SV2 )
= $false )
| ( ( sK2_SY18 @ SV4 )
= $true )
| ( ( SV2 = SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV3: $i,SV5: $i] :
( ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( sK1_SY0 @ SV3 )
= $true )
| ( ( SV3 = SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV1: $i] :
( ( ( sK2_SY18 @ SV1 )
= $false )
| ( ( SV1
= ( sK3_SY30 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(59,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[39,58,57,56,54,53]) ).
thf(60,plain,
( ( ! [SY25: $i,SY26: $i] :
( ( SY25 != SY26 )
| ~ ( sK1_SY0 @ SY25 )
| ( sK2_SY18 @ SY26 ) )
& ! [SY25: $i,SY26: $i] :
( ( SY25 != SY26 )
| ~ ( sK2_SY18 @ SY26 )
| ( sK1_SY0 @ SY25 ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(61,plain,
( ( ! [SY32: $i] :
( ~ ( sK2_SY18 @ SY32 )
| ( sK6_SY29 = SY32 ) )
& ( sK2_SY18 @ sK6_SY29 )
& ! [SY21: $i] :
( ( ( sK1_SY0 @ ( sK5_SY22 @ SY21 ) )
& ( SY21
!= ( sK5_SY22 @ SY21 ) ) )
| ~ ( sK1_SY0 @ SY21 ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(62,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sK2_SY18 @ SX0 )
| ( sK6_SY29 = SX0 ) )
| ~ ( sK2_SY18 @ sK6_SY29 ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SX0 ) )
| ~ ( ( SX0
!= ( sK5_SY22 @ SX0 ) ) ) )
| ~ ( sK1_SY0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61,exu]) ).
thf(63,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK1_SY0 @ SX0 )
| ( sK2_SY18 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK2_SY18 @ SX1 )
| ( sK1_SY0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60,exu]) ).
thf(64,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sK2_SY18 @ SX0 )
| ( sK6_SY29 = SX0 ) )
| ~ ( sK2_SY18 @ sK6_SY29 ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SX0 ) )
| ~ ( ( SX0
!= ( sK5_SY22 @ SX0 ) ) ) )
| ~ ( sK1_SY0 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK1_SY0 @ SX0 )
| ( sK2_SY18 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK2_SY18 @ SX1 )
| ( sK1_SY0 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(66,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sK2_SY18 @ SX0 )
| ( sK6_SY29 = SX0 ) )
| ~ ( sK2_SY18 @ sK6_SY29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(67,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SX0 ) )
| ~ ( ( SX0
!= ( sK5_SY22 @ SX0 ) ) ) )
| ~ ( sK1_SY0 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(68,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK1_SY0 @ SX0 )
| ( sK2_SY18 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(69,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK2_SY18 @ SX1 )
| ( sK1_SY0 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(70,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( sK2_SY18 @ SX0 )
| ( sK6_SY29 = SX0 ) )
| ~ ( sK2_SY18 @ sK6_SY29 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(71,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SX0 ) )
| ~ ( ( SX0
!= ( sK5_SY22 @ SX0 ) ) ) )
| ~ ( sK1_SY0 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK1_SY0 @ SX0 )
| ( sK2_SY18 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( sK2_SY18 @ SX1 )
| ( sK1_SY0 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(74,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK2_SY18 @ SX0 )
| ( sK6_SY29 = SX0 ) )
| ~ ( sK2_SY18 @ sK6_SY29 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV7: $i] :
( ( ~ ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SV7 ) )
| ~ ( ( SV7
!= ( sK5_SY22 @ SV7 ) ) ) )
| ~ ( sK1_SY0 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV8: $i] :
( ( ! [SY35: $i] :
( ( SV8 != SY35 )
| ~ ( sK1_SY0 @ SV8 )
| ( sK2_SY18 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV9: $i] :
( ( ! [SY36: $i] :
( ( SV9 != SY36 )
| ~ ( sK2_SY18 @ SY36 )
| ( sK1_SY0 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(78,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK2_SY18 @ SX0 )
| ( sK6_SY29 = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(79,plain,
( ( ~ ( sK2_SY18 @ sK6_SY29 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(80,plain,
! [SV7: $i] :
( ( ( ~ ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SV7 ) )
| ~ ( ( SV7
!= ( sK5_SY22 @ SV7 ) ) ) ) )
= $true )
| ( ( ~ ( sK1_SY0 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV10: $i,SV8: $i] :
( ( ( SV8 != SV10 )
| ~ ( sK1_SY0 @ SV8 )
| ( sK2_SY18 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV11: $i,SV9: $i] :
( ( ( SV9 != SV11 )
| ~ ( sK2_SY18 @ SV11 )
| ( sK1_SY0 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(83,plain,
( ( ! [SX0: $i] :
( ~ ( sK2_SY18 @ SX0 )
| ( sK6_SY29 = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(84,plain,
( ( sK2_SY18 @ sK6_SY29 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(85,plain,
! [SV7: $i] :
( ( ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SV7 ) )
| ~ ( ( SV7
!= ( sK5_SY22 @ SV7 ) ) ) )
= $false )
| ( ( ~ ( sK1_SY0 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(86,plain,
! [SV10: $i,SV8: $i] :
( ( ( ( SV8 != SV10 ) )
= $true )
| ( ( ~ ( sK1_SY0 @ SV8 )
| ( sK2_SY18 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(87,plain,
! [SV11: $i,SV9: $i] :
( ( ( ( SV9 != SV11 ) )
= $true )
| ( ( ~ ( sK2_SY18 @ SV11 )
| ( sK1_SY0 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(88,plain,
! [SV12: $i] :
( ( ~ ( sK2_SY18 @ SV12 )
| ( sK6_SY29 = SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(89,plain,
! [SV7: $i] :
( ( ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SV7 ) ) )
= $false )
| ( ( ~ ( sK1_SY0 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(90,plain,
! [SV7: $i] :
( ( ( ~ ( ( SV7
!= ( sK5_SY22 @ SV7 ) ) ) )
= $false )
| ( ( ~ ( sK1_SY0 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(91,plain,
! [SV10: $i,SV8: $i] :
( ( ( SV8 = SV10 )
= $false )
| ( ( ~ ( sK1_SY0 @ SV8 )
| ( sK2_SY18 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(92,plain,
! [SV11: $i,SV9: $i] :
( ( ( SV9 = SV11 )
= $false )
| ( ( ~ ( sK2_SY18 @ SV11 )
| ( sK1_SY0 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(93,plain,
! [SV12: $i] :
( ( ( ~ ( sK2_SY18 @ SV12 ) )
= $true )
| ( ( sK6_SY29 = SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(94,plain,
! [SV7: $i] :
( ( ( sK1_SY0 @ ( sK5_SY22 @ SV7 ) )
= $true )
| ( ( ~ ( sK1_SY0 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(95,plain,
! [SV7: $i] :
( ( ( ( SV7
!= ( sK5_SY22 @ SV7 ) ) )
= $true )
| ( ( ~ ( sK1_SY0 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(96,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ( sK1_SY0 @ SV8 ) )
= $true )
| ( ( sK2_SY18 @ SV10 )
= $true )
| ( ( SV8 = SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(97,plain,
! [SV9: $i,SV11: $i] :
( ( ( ~ ( sK2_SY18 @ SV11 ) )
= $true )
| ( ( sK1_SY0 @ SV9 )
= $true )
| ( ( SV9 = SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV12: $i] :
( ( ( sK2_SY18 @ SV12 )
= $false )
| ( ( sK6_SY29 = SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV7: $i] :
( ( ( sK1_SY0 @ SV7 )
= $false )
| ( ( sK1_SY0 @ ( sK5_SY22 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV7: $i] :
( ( ( SV7
= ( sK5_SY22 @ SV7 ) )
= $false )
| ( ( ~ ( sK1_SY0 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(101,plain,
! [SV10: $i,SV8: $i] :
( ( ( sK1_SY0 @ SV8 )
= $false )
| ( ( sK2_SY18 @ SV10 )
= $true )
| ( ( SV8 = SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV9: $i,SV11: $i] :
( ( ( sK2_SY18 @ SV11 )
= $false )
| ( ( sK1_SY0 @ SV9 )
= $true )
| ( ( SV9 = SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV7: $i] :
( ( ( sK1_SY0 @ SV7 )
= $false )
| ( ( SV7
= ( sK5_SY22 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(104,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[84,103,102,101,99,98]) ).
thf(105,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[104,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU550^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n025.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 : Sat Jun 18 23:21:13 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: 175
% 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)....
% 0.20/0.42
% 0.20/0.42 ********************************
% 0.20/0.42 * All subproblems solved! *
% 0.20/0.42 ********************************
% 0.20/0.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:104,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.43
% 0.20/0.43 %**** Beginning of derivation protocol ****
% 0.20/0.43 % SZS output start CNFRefutation
% See solution above
% 0.20/0.43
% 0.20/0.43 %**** End of derivation protocol ****
% 0.20/0.43 %**** no. of clauses in derivation: 105 ****
% 0.20/0.43 %**** clause counter: 104 ****
% 0.20/0.43
% 0.20/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:104,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------