%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV214^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 10:49:45 AM UTC 2026
% Result : Theorem 0.05s 0.26s
% Output : CNFRefutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 1
% Syntax : Number of formulae : 146 ( 65 unt; 0 typ; 0 def)
% Number of atoms : 837 ( 570 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 1229 ( 334 ~; 264 |; 28 &; 582 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 394 ( 44 ^; 336 !; 14 ?; 394 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_iS,type,
iS: $tType ).
thf(tp_c0,type,
c0: iS ).
thf(tp_cP,type,
cP: iS > iS > iS ).
thf(tp_sK1_SV6,type,
sK1_SV6: iS ).
thf(tp_sK2_SY36,type,
sK2_SY36: ( iS > $o ) > iS ).
thf(tp_sK3_SY44,type,
sK3_SY44: ( iS > $o ) > iS ).
thf(tp_sK4_SY43,type,
sK4_SY43: iS ).
thf(tp_sK5_SV17,type,
sK5_SV17: iS ).
thf(tp_sK6_SY46,type,
sK6_SY46: ( iS > $o ) > iS ).
thf(tp_sK7_SY57,type,
sK7_SY57: ( iS > $o ) > iS ).
thf(tp_sK8_SY55,type,
sK8_SY55: iS ).
thf(1,conjecture,
( ( ! [Xx: iS,Xy: iS] :
( ( cP @ Xx @ Xy )
!= c0 )
& ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
( ( ( cP @ Xx @ Xu )
= ( cP @ Xy @ Xv ) )
=> ( ( Xx = Xy )
& ( Xu = Xv ) ) )
& ! [X: iS > $o] :
( ( ( X @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( X @ Xx )
& ( X @ Xy ) )
=> ( X @ ( cP @ Xx @ Xy ) ) ) )
=> ! [Xx: iS] : ( X @ Xx ) ) )
=> ( ( ( ^ [Xx: iS] :
( ( Xx = c0 )
| ? [Xy: iS] :
( c0
= ( cP @ Xx @ Xy ) ) ) )
= ( ^ [Xx: iS,Xy: iS] : ( Xx = Xy )
@ c0 ) )
& ( ( ^ [Xy: iS] :
( ( Xy = c0 )
| ? [Xx: iS] :
( c0
= ( cP @ Xx @ Xy ) ) ) )
= ( ^ [Xx: iS,Xy: iS] : ( Xx = Xy )
@ c0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_T_LR_LEM2_pme) ).
thf(2,negated_conjecture,
( ( ( ! [Xx: iS,Xy: iS] :
( ( cP @ Xx @ Xy )
!= c0 )
& ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
( ( ( cP @ Xx @ Xu )
= ( cP @ Xy @ Xv ) )
=> ( ( Xx = Xy )
& ( Xu = Xv ) ) )
& ! [X: iS > $o] :
( ( ( X @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( X @ Xx )
& ( X @ Xy ) )
=> ( X @ ( cP @ Xx @ Xy ) ) ) )
=> ! [Xx: iS] : ( X @ Xx ) ) )
=> ( ( ( ^ [Xx: iS] :
( ( Xx = c0 )
| ? [Xy: iS] :
( c0
= ( cP @ Xx @ Xy ) ) ) )
= ( ^ [Xx: iS,Xy: iS] : ( Xx = Xy )
@ c0 ) )
& ( ( ^ [Xy: iS] :
( ( Xy = c0 )
| ? [Xx: iS] :
( c0
= ( cP @ Xx @ Xy ) ) ) )
= ( ^ [Xx: iS,Xy: iS] : ( Xx = Xy )
@ c0 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Xx: iS,Xy: iS] :
( ( cP @ Xx @ Xy )
!= c0 )
& ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
( ( ( cP @ Xx @ Xu )
= ( cP @ Xy @ Xv ) )
=> ( ( Xx = Xy )
& ( Xu = Xv ) ) )
& ! [X: iS > $o] :
( ( ( X @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( X @ Xx )
& ( X @ Xy ) )
=> ( X @ ( cP @ Xx @ Xy ) ) ) )
=> ! [Xx: iS] : ( X @ Xx ) ) )
=> ( ( ( ^ [Xx: iS] :
( ( Xx = c0 )
| ? [Xy: iS] :
( c0
= ( cP @ Xx @ Xy ) ) ) )
= ( ^ [SY12: iS] : ( c0 = SY12 ) ) )
& ( ( ^ [Xy: iS] :
( ( Xy = c0 )
| ? [Xx: iS] :
( c0
= ( cP @ Xx @ Xy ) ) ) )
= ( ^ [SY15: iS] : ( c0 = SY15 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: iS,Xy: iS] :
( ( cP @ Xx @ Xy )
!= c0 ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
( ( ( cP @ Xx @ Xu )
= ( cP @ Xy @ Xv ) )
=> ( ( Xx = Xy )
& ( Xu = Xv ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [X: iS > $o] :
( ( ( X @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( X @ Xx )
& ( X @ Xy ) )
=> ( X @ ( cP @ Xx @ Xy ) ) ) )
=> ! [Xx: iS] : ( X @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ( ( ^ [Xx: iS] :
( ( Xx = c0 )
| ? [Xy: iS] :
( c0
= ( cP @ Xx @ Xy ) ) ) )
= ( ^ [SY12: iS] : ( c0 = SY12 ) ) )
& ( ( ^ [Xy: iS] :
( ( Xy = c0 )
| ? [Xx: iS] :
( c0
= ( cP @ Xx @ Xy ) ) ) )
= ( ^ [SY15: iS] : ( c0 = SY15 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ( ^ [Xx: iS] :
( ( Xx = c0 )
| ? [Xy: iS] :
( c0
= ( cP @ Xx @ Xy ) ) ) )
= ( ^ [SY12: iS] : ( c0 = SY12 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(9,plain,
( ( ( ^ [Xy: iS] :
( ( Xy = c0 )
| ? [Xx: iS] :
( c0
= ( cP @ Xx @ Xy ) ) ) )
= ( ^ [SY15: iS] : ( c0 = SY15 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(10,plain,
( ( ( ^ [Xx: iS] :
( ( Xx = c0 )
| ? [Xy: iS] :
( c0
= ( cP @ Xx @ Xy ) ) ) )
!= ( ^ [SY12: iS] : ( c0 = SY12 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ( ^ [Xy: iS] :
( ( Xy = c0 )
| ? [Xx: iS] :
( c0
= ( cP @ Xx @ Xy ) ) ) )
!= ( ^ [SY15: iS] : ( c0 = SY15 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [X: iS > $o] :
( ( ( X @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( X @ Xx )
& ( X @ Xy ) )
=> ( X @ ( cP @ Xx @ Xy ) ) ) )
=> ! [Xx: iS] : ( X @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(13,plain,
( ( ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
( ( ( cP @ Xx @ Xu )
= ( cP @ Xy @ Xv ) )
=> ( ( Xx = Xy )
& ( Xu = Xv ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [Xx: iS,Xy: iS] :
( ( cP @ Xx @ Xy )
!= c0 ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(15,plain,
( ( ( ^ [Xx: iS] :
( ( Xx = c0 )
| ? [Xy: iS] :
( c0
= ( cP @ Xx @ Xy ) ) ) )
!= ( ^ [SY12: iS] : ( c0 = SY12 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ! [SX0: iS,SX1: iS] :
( ( cP @ SX0 @ SX1 )
!= c0 ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [SX0: iS,SX1: iS,SX2: iS,SX3: iS] :
( ( ( cP @ SX0 @ SX2 )
!= ( cP @ SX1 @ SX3 ) )
| ~ ( ( SX0 != SX1 )
| ( SX2 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(18,plain,
( ( ! [SX0: iS > $o] :
( ~ ~ ( ~ ( SX0 @ c0 )
| ~ ! [SX1: iS,SX2: iS] :
( ~ ~ ( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 ) )
| ( SX0 @ ( cP @ SX1 @ SX2 ) ) ) )
| ! [SX1: iS] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(19,plain,
( ( ( ^ [SX0: iS] :
( ( SX0 = c0 )
| ~ ! [SX1: iS] :
( c0
!= ( cP @ SX0 @ SX1 ) ) ) )
!= ( ^ [SX0: iS] : ( c0 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(20,plain,
! [SV1: iS] :
( ( ! [SY32: iS] :
( ( cP @ SV1 @ SY32 )
!= c0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV2: iS] :
( ( ! [SY33: iS,SY34: iS,SY35: iS] :
( ( ( cP @ SV2 @ SY34 )
!= ( cP @ SY33 @ SY35 ) )
| ~ ( ( SV2 != SY33 )
| ( SY34 != SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV3: iS > $o] :
( ( ~ ~ ( ~ ( SV3 @ c0 )
| ~ ! [SY36: iS,SY37: iS] :
( ~ ~ ( ~ ( SV3 @ SY36 )
| ~ ( SV3 @ SY37 ) )
| ( SV3 @ ( cP @ SY36 @ SY37 ) ) ) )
| ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
( ( ( ^ [SX0: iS] :
( ( SX0 = c0 )
| ~ ! [SX1: iS] :
( c0
!= ( cP @ SX0 @ SX1 ) ) ) )
= ( ^ [SX0: iS] : ( c0 = SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV4: iS,SV1: iS] :
( ( ( cP @ SV1 @ SV4 )
!= c0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV5: iS,SV2: iS] :
( ( ! [SY39: iS,SY40: iS] :
( ( ( cP @ SV2 @ SY39 )
!= ( cP @ SV5 @ SY40 ) )
| ~ ( ( SV2 != SV5 )
| ( SY39 != SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV3: iS > $o] :
( ( ( ~ ~ ( ~ ( SV3 @ c0 )
| ~ ! [SY36: iS,SY37: iS] :
( ~ ~ ( ~ ( SV3 @ SY36 )
| ~ ( SV3 @ SY37 ) )
| ( SV3 @ ( cP @ SY36 @ SY37 ) ) ) ) )
= $true )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( ! [SV6: iS] :
( ( ( SV6 = c0 )
| ~ ! [SY41: iS] :
( c0
!= ( cP @ SV6 @ SY41 ) ) )
= ( c0 = SV6 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[23]) ).
thf(28,plain,
( ( ( ^ [SX0: iS] :
( ( SX0 = c0 )
| ~ ! [SX1: iS] :
( c0
!= ( cP @ SX0 @ SX1 ) ) ) )
= ( ^ [SX0: iS] : ( c0 = SX0 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[23]) ).
thf(29,plain,
! [SV4: iS,SV1: iS] :
( ( ( cP @ SV1 @ SV4 )
= c0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV5: iS,SV7: iS,SV2: iS] :
( ( ! [SY42: iS] :
( ( ( cP @ SV2 @ SV7 )
!= ( cP @ SV5 @ SY42 ) )
| ~ ( ( SV2 != SV5 )
| ( SV7 != SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV3: iS > $o] :
( ( ( ~ ( ~ ( SV3 @ c0 )
| ~ ! [SY36: iS,SY37: iS] :
( ~ ~ ( ~ ( SV3 @ SY36 )
| ~ ( SV3 @ SY37 ) )
| ( SV3 @ ( cP @ SY36 @ SY37 ) ) ) ) )
= $false )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(32,plain,
( ( ( ( sK1_SV6 = c0 )
| ~ ! [SY43: iS] :
( c0
!= ( cP @ sK1_SV6 @ SY43 ) ) )
= ( c0 = sK1_SV6 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(33,plain,
! [SV8: iS,SV5: iS,SV7: iS,SV2: iS] :
( ( ( ( cP @ SV2 @ SV7 )
!= ( cP @ SV5 @ SV8 ) )
| ~ ( ( SV2 != SV5 )
| ( SV7 != SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV3: iS > $o] :
( ( ( ~ ( SV3 @ c0 )
| ~ ! [SY36: iS,SY37: iS] :
( ~ ~ ( ~ ( SV3 @ SY36 )
| ~ ( SV3 @ SY37 ) )
| ( SV3 @ ( cP @ SY36 @ SY37 ) ) ) )
= $true )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(35,plain,
( ( ~ ( ( sK1_SV6 = c0 )
| ~ ! [SY43: iS] :
( c0
!= ( cP @ sK1_SV6 @ SY43 ) )
| ( c0 = sK1_SV6 ) )
| ~ ( ~ ( ( sK1_SV6 = c0 )
| ~ ! [SY43: iS] :
( c0
!= ( cP @ sK1_SV6 @ SY43 ) ) )
| ( c0 != sK1_SV6 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[32]) ).
thf(36,plain,
( ( ( ( sK1_SV6 = c0 )
| ~ ! [SY43: iS] :
( c0
!= ( cP @ sK1_SV6 @ SY43 ) ) )
= ( c0 = sK1_SV6 ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV8: iS,SV5: iS,SV7: iS,SV2: iS] :
( ( ( ( cP @ SV2 @ SV7 )
!= ( cP @ SV5 @ SV8 ) )
= $true )
| ( ( ~ ( ( SV2 != SV5 )
| ( SV7 != SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV3: iS > $o] :
( ( ( ~ ( SV3 @ c0 ) )
= $true )
| ( ( ~ ! [SY36: iS,SY37: iS] :
( ~ ~ ( ~ ( SV3 @ SY36 )
| ~ ( SV3 @ SY37 ) )
| ( SV3 @ ( cP @ SY36 @ SY37 ) ) ) )
= $true )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(39,plain,
( ( ~ ( ( sK1_SV6 = c0 )
| ~ ! [SY43: iS] :
( c0
!= ( cP @ sK1_SV6 @ SY43 ) )
| ( c0 = sK1_SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
( ( ~ ( ~ ( ( sK1_SV6 = c0 )
| ~ ! [SY43: iS] :
( c0
!= ( cP @ sK1_SV6 @ SY43 ) ) )
| ( c0 != sK1_SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(41,plain,
! [SV8: iS,SV5: iS,SV7: iS,SV2: iS] :
( ( ( ( cP @ SV2 @ SV7 )
= ( cP @ SV5 @ SV8 ) )
= $false )
| ( ( ~ ( ( SV2 != SV5 )
| ( SV7 != SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV3: iS > $o] :
( ( ( SV3 @ c0 )
= $false )
| ( ( ~ ! [SY36: iS,SY37: iS] :
( ~ ~ ( ~ ( SV3 @ SY36 )
| ~ ( SV3 @ SY37 ) )
| ( SV3 @ ( cP @ SY36 @ SY37 ) ) ) )
= $true )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
( ( ( sK1_SV6 = c0 )
| ~ ! [SY43: iS] :
( c0
!= ( cP @ sK1_SV6 @ SY43 ) )
| ( c0 = sK1_SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(44,plain,
( ( ~ ( ( sK1_SV6 = c0 )
| ~ ! [SY43: iS] :
( c0
!= ( cP @ sK1_SV6 @ SY43 ) ) )
| ( c0 != sK1_SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV8: iS,SV7: iS,SV5: iS,SV2: iS] :
( ( ( ( SV2 != SV5 )
| ( SV7 != SV8 ) )
= $false )
| ( ( ( cP @ SV2 @ SV7 )
= ( cP @ SV5 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV3: iS > $o] :
( ( ( ! [SY36: iS,SY37: iS] :
( ~ ~ ( ~ ( SV3 @ SY36 )
| ~ ( SV3 @ SY37 ) )
| ( SV3 @ ( cP @ SY36 @ SY37 ) ) ) )
= $false )
| ( ( SV3 @ c0 )
= $false )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
( ( ( ( sK1_SV6 = c0 )
| ~ ! [SY43: iS] :
( c0
!= ( cP @ sK1_SV6 @ SY43 ) ) )
= $true )
| ( ( c0 = sK1_SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(48,plain,
( ( ( ~ ( ( sK1_SV6 = c0 )
| ~ ! [SY43: iS] :
( c0
!= ( cP @ sK1_SV6 @ SY43 ) ) ) )
= $true )
| ( ( c0 != sK1_SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV8: iS,SV7: iS,SV5: iS,SV2: iS] :
( ( ( SV2 != SV5 )
= $false )
| ( ( ( cP @ SV2 @ SV7 )
= ( cP @ SV5 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV5: iS,SV2: iS,SV8: iS,SV7: iS] :
( ( ( SV7 != SV8 )
= $false )
| ( ( ( cP @ SV2 @ SV7 )
= ( cP @ SV5 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(51,plain,
! [SV3: iS > $o] :
( ( ( ! [SY44: iS] :
( ~ ~ ( ~ ( SV3 @ ( sK2_SY36 @ SV3 ) )
| ~ ( SV3 @ SY44 ) )
| ( SV3 @ ( cP @ ( sK2_SY36 @ SV3 ) @ SY44 ) ) ) )
= $false )
| ( ( SV3 @ c0 )
= $false )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(52,plain,
( ( ( sK1_SV6 = c0 )
= $true )
| ( ( ~ ! [SY43: iS] :
( c0
!= ( cP @ sK1_SV6 @ SY43 ) ) )
= $true )
| ( ( c0 = sK1_SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(53,plain,
( ( ( ( sK1_SV6 = c0 )
| ~ ! [SY43: iS] :
( c0
!= ( cP @ sK1_SV6 @ SY43 ) ) )
= $false )
| ( ( c0 != sK1_SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV8: iS,SV7: iS,SV5: iS,SV2: iS] :
( ( ( SV2 = SV5 )
= $true )
| ( ( ( cP @ SV2 @ SV7 )
= ( cP @ SV5 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(55,plain,
! [SV5: iS,SV2: iS,SV8: iS,SV7: iS] :
( ( ( SV7 = SV8 )
= $true )
| ( ( ( cP @ SV2 @ SV7 )
= ( cP @ SV5 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(56,plain,
! [SV3: iS > $o] :
( ( ( ~ ~ ( ~ ( SV3 @ ( sK2_SY36 @ SV3 ) )
| ~ ( SV3 @ ( sK3_SY44 @ SV3 ) ) )
| ( SV3 @ ( cP @ ( sK2_SY36 @ SV3 ) @ ( sK3_SY44 @ SV3 ) ) ) )
= $false )
| ( ( SV3 @ c0 )
= $false )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(57,plain,
( ( ( ! [SY43: iS] :
( c0
!= ( cP @ sK1_SV6 @ SY43 ) ) )
= $false )
| ( ( sK1_SV6 = c0 )
= $true )
| ( ( c0 = sK1_SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
( ( ( sK1_SV6 = c0 )
= $false )
| ( ( c0 != sK1_SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(59,plain,
( ( ( ~ ! [SY43: iS] :
( c0
!= ( cP @ sK1_SV6 @ SY43 ) ) )
= $false )
| ( ( c0 != sK1_SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(60,plain,
! [SV3: iS > $o] :
( ( ( ~ ~ ( ~ ( SV3 @ ( sK2_SY36 @ SV3 ) )
| ~ ( SV3 @ ( sK3_SY44 @ SV3 ) ) ) )
= $false )
| ( ( SV3 @ c0 )
= $false )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(61,plain,
! [SV3: iS > $o] :
( ( ( SV3 @ ( cP @ ( sK2_SY36 @ SV3 ) @ ( sK3_SY44 @ SV3 ) ) )
= $false )
| ( ( SV3 @ c0 )
= $false )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(62,plain,
( ( ( c0
!= ( cP @ sK1_SV6 @ sK4_SY43 ) )
= $false )
| ( ( sK1_SV6 = c0 )
= $true )
| ( ( c0 = sK1_SV6 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(63,plain,
( ( ( c0 = sK1_SV6 )
= $false )
| ( ( sK1_SV6 = c0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(64,plain,
( ( ( ! [SY43: iS] :
( c0
!= ( cP @ sK1_SV6 @ SY43 ) ) )
= $true )
| ( ( c0 != sK1_SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(65,plain,
! [SV3: iS > $o] :
( ( ( ~ ( ~ ( SV3 @ ( sK2_SY36 @ SV3 ) )
| ~ ( SV3 @ ( sK3_SY44 @ SV3 ) ) ) )
= $true )
| ( ( SV3 @ c0 )
= $false )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(66,plain,
! [SV9: iS,SV3: iS > $o] :
( ( ( SV3 @ SV9 )
= $true )
| ( ( SV3 @ c0 )
= $false )
| ( ( SV3 @ ( cP @ ( sK2_SY36 @ SV3 ) @ ( sK3_SY44 @ SV3 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(67,plain,
( ( ( c0
= ( cP @ sK1_SV6 @ sK4_SY43 ) )
= $true )
| ( ( sK1_SV6 = c0 )
= $true )
| ( ( c0 = sK1_SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(68,plain,
! [SV10: iS] :
( ( ( c0
!= ( cP @ sK1_SV6 @ SV10 ) )
= $true )
| ( ( c0 != sK1_SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV3: iS > $o] :
( ( ( ~ ( SV3 @ ( sK2_SY36 @ SV3 ) )
| ~ ( SV3 @ ( sK3_SY44 @ SV3 ) ) )
= $false )
| ( ( SV3 @ c0 )
= $false )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV10: iS] :
( ( ( c0
= ( cP @ sK1_SV6 @ SV10 ) )
= $false )
| ( ( c0 != sK1_SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV3: iS > $o] :
( ( ( ~ ( SV3 @ ( sK2_SY36 @ SV3 ) ) )
= $false )
| ( ( SV3 @ c0 )
= $false )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(72,plain,
! [SV3: iS > $o] :
( ( ( ~ ( SV3 @ ( sK3_SY44 @ SV3 ) ) )
= $false )
| ( ( SV3 @ c0 )
= $false )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(73,plain,
! [SV10: iS] :
( ( ( c0 = sK1_SV6 )
= $false )
| ( ( c0
= ( cP @ sK1_SV6 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(74,plain,
! [SV3: iS > $o] :
( ( ( SV3 @ ( sK2_SY36 @ SV3 ) )
= $true )
| ( ( SV3 @ c0 )
= $false )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(75,plain,
! [SV3: iS > $o] :
( ( ( SV3 @ ( sK3_SY44 @ SV3 ) )
= $true )
| ( ( SV3 @ c0 )
= $false )
| ( ( ! [SY38: iS] : ( SV3 @ SY38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(76,plain,
! [SV11: iS,SV3: iS > $o] :
( ( ( SV3 @ SV11 )
= $true )
| ( ( SV3 @ c0 )
= $false )
| ( ( SV3 @ ( sK2_SY36 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(77,plain,
! [SV12: iS,SV3: iS > $o] :
( ( ( SV3 @ SV12 )
= $true )
| ( ( SV3 @ c0 )
= $false )
| ( ( SV3 @ ( sK3_SY44 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(78,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,77,76,73,67,66,63,55,54,36,29]) ).
thf(79,plain,
( ( ! [X: iS > $o] :
( ( ( X @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( X @ Xx )
& ( X @ Xy ) )
=> ( X @ ( cP @ Xx @ Xy ) ) ) )
=> ! [Xx: iS] : ( X @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(80,plain,
( ( ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
( ( ( cP @ Xx @ Xu )
= ( cP @ Xy @ Xv ) )
=> ( ( Xx = Xy )
& ( Xu = Xv ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(81,plain,
( ( ! [Xx: iS,Xy: iS] :
( ( cP @ Xx @ Xy )
!= c0 ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(82,plain,
( ( ( ^ [Xy: iS] :
( ( Xy = c0 )
| ? [Xx: iS] :
( c0
= ( cP @ Xx @ Xy ) ) ) )
!= ( ^ [SY15: iS] : ( c0 = SY15 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(83,plain,
( ( ! [SX0: iS,SX1: iS] :
( ( cP @ SX0 @ SX1 )
!= c0 ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(84,plain,
( ( ! [SX0: iS > $o] :
( ~ ~ ( ~ ( SX0 @ c0 )
| ~ ! [SX1: iS,SX2: iS] :
( ~ ~ ( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 ) )
| ( SX0 @ ( cP @ SX1 @ SX2 ) ) ) )
| ! [SX1: iS] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(85,plain,
( ( ( ^ [SX0: iS] :
( ( SX0 = c0 )
| ~ ! [SX1: iS] :
( c0
!= ( cP @ SX1 @ SX0 ) ) ) )
!= ( ^ [SX0: iS] : ( c0 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(86,plain,
( ( ! [SX0: iS,SX1: iS,SX2: iS,SX3: iS] :
( ( ( cP @ SX0 @ SX2 )
!= ( cP @ SX1 @ SX3 ) )
| ~ ( ( SX0 != SX1 )
| ( SX2 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(87,plain,
! [SV13: iS] :
( ( ! [SY45: iS] :
( ( cP @ SV13 @ SY45 )
!= c0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV14: iS > $o] :
( ( ~ ~ ( ~ ( SV14 @ c0 )
| ~ ! [SY46: iS,SY47: iS] :
( ~ ~ ( ~ ( SV14 @ SY46 )
| ~ ( SV14 @ SY47 ) )
| ( SV14 @ ( cP @ SY46 @ SY47 ) ) ) )
| ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(89,plain,
( ( ( ^ [SX0: iS] :
( ( SX0 = c0 )
| ~ ! [SX1: iS] :
( c0
!= ( cP @ SX1 @ SX0 ) ) ) )
= ( ^ [SX0: iS] : ( c0 = SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(90,plain,
! [SV15: iS] :
( ( ! [SY49: iS,SY50: iS,SY51: iS] :
( ( ( cP @ SV15 @ SY50 )
!= ( cP @ SY49 @ SY51 ) )
| ~ ( ( SV15 != SY49 )
| ( SY50 != SY51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV16: iS,SV13: iS] :
( ( ( cP @ SV13 @ SV16 )
!= c0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(92,plain,
! [SV14: iS > $o] :
( ( ( ~ ~ ( ~ ( SV14 @ c0 )
| ~ ! [SY46: iS,SY47: iS] :
( ~ ~ ( ~ ( SV14 @ SY46 )
| ~ ( SV14 @ SY47 ) )
| ( SV14 @ ( cP @ SY46 @ SY47 ) ) ) ) )
= $true )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(93,plain,
( ( ! [SV17: iS] :
( ( ( SV17 = c0 )
| ~ ! [SY52: iS] :
( c0
!= ( cP @ SY52 @ SV17 ) ) )
= ( c0 = SV17 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[89]) ).
thf(94,plain,
( ( ( ^ [SX0: iS] :
( ( SX0 = c0 )
| ~ ! [SX1: iS] :
( c0
!= ( cP @ SX1 @ SX0 ) ) ) )
= ( ^ [SX0: iS] : ( c0 = SX0 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[89]) ).
thf(95,plain,
! [SV18: iS,SV15: iS] :
( ( ! [SY53: iS,SY54: iS] :
( ( ( cP @ SV15 @ SY53 )
!= ( cP @ SV18 @ SY54 ) )
| ~ ( ( SV15 != SV18 )
| ( SY53 != SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(96,plain,
! [SV16: iS,SV13: iS] :
( ( ( cP @ SV13 @ SV16 )
= c0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(97,plain,
! [SV14: iS > $o] :
( ( ( ~ ( ~ ( SV14 @ c0 )
| ~ ! [SY46: iS,SY47: iS] :
( ~ ~ ( ~ ( SV14 @ SY46 )
| ~ ( SV14 @ SY47 ) )
| ( SV14 @ ( cP @ SY46 @ SY47 ) ) ) ) )
= $false )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(98,plain,
( ( ( ( sK5_SV17 = c0 )
| ~ ! [SY55: iS] :
( c0
!= ( cP @ SY55 @ sK5_SV17 ) ) )
= ( c0 = sK5_SV17 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[93]) ).
thf(99,plain,
! [SV18: iS,SV19: iS,SV15: iS] :
( ( ! [SY56: iS] :
( ( ( cP @ SV15 @ SV19 )
!= ( cP @ SV18 @ SY56 ) )
| ~ ( ( SV15 != SV18 )
| ( SV19 != SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(100,plain,
! [SV14: iS > $o] :
( ( ( ~ ( SV14 @ c0 )
| ~ ! [SY46: iS,SY47: iS] :
( ~ ~ ( ~ ( SV14 @ SY46 )
| ~ ( SV14 @ SY47 ) )
| ( SV14 @ ( cP @ SY46 @ SY47 ) ) ) )
= $true )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(101,plain,
( ( ~ ( ( sK5_SV17 = c0 )
| ~ ! [SY55: iS] :
( c0
!= ( cP @ SY55 @ sK5_SV17 ) )
| ( c0 = sK5_SV17 ) )
| ~ ( ~ ( ( sK5_SV17 = c0 )
| ~ ! [SY55: iS] :
( c0
!= ( cP @ SY55 @ sK5_SV17 ) ) )
| ( c0 != sK5_SV17 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[98]) ).
thf(102,plain,
( ( ( ( sK5_SV17 = c0 )
| ~ ! [SY55: iS] :
( c0
!= ( cP @ SY55 @ sK5_SV17 ) ) )
= ( c0 = sK5_SV17 ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[98]) ).
thf(103,plain,
! [SV20: iS,SV18: iS,SV19: iS,SV15: iS] :
( ( ( ( cP @ SV15 @ SV19 )
!= ( cP @ SV18 @ SV20 ) )
| ~ ( ( SV15 != SV18 )
| ( SV19 != SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(104,plain,
! [SV14: iS > $o] :
( ( ( ~ ( SV14 @ c0 ) )
= $true )
| ( ( ~ ! [SY46: iS,SY47: iS] :
( ~ ~ ( ~ ( SV14 @ SY46 )
| ~ ( SV14 @ SY47 ) )
| ( SV14 @ ( cP @ SY46 @ SY47 ) ) ) )
= $true )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(105,plain,
( ( ~ ( ( sK5_SV17 = c0 )
| ~ ! [SY55: iS] :
( c0
!= ( cP @ SY55 @ sK5_SV17 ) )
| ( c0 = sK5_SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(106,plain,
( ( ~ ( ~ ( ( sK5_SV17 = c0 )
| ~ ! [SY55: iS] :
( c0
!= ( cP @ SY55 @ sK5_SV17 ) ) )
| ( c0 != sK5_SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(107,plain,
! [SV20: iS,SV18: iS,SV19: iS,SV15: iS] :
( ( ( ( cP @ SV15 @ SV19 )
!= ( cP @ SV18 @ SV20 ) )
= $true )
| ( ( ~ ( ( SV15 != SV18 )
| ( SV19 != SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV14: iS > $o] :
( ( ( SV14 @ c0 )
= $false )
| ( ( ~ ! [SY46: iS,SY47: iS] :
( ~ ~ ( ~ ( SV14 @ SY46 )
| ~ ( SV14 @ SY47 ) )
| ( SV14 @ ( cP @ SY46 @ SY47 ) ) ) )
= $true )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(109,plain,
( ( ( sK5_SV17 = c0 )
| ~ ! [SY55: iS] :
( c0
!= ( cP @ SY55 @ sK5_SV17 ) )
| ( c0 = sK5_SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(110,plain,
( ( ~ ( ( sK5_SV17 = c0 )
| ~ ! [SY55: iS] :
( c0
!= ( cP @ SY55 @ sK5_SV17 ) ) )
| ( c0 != sK5_SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(111,plain,
! [SV20: iS,SV18: iS,SV19: iS,SV15: iS] :
( ( ( ( cP @ SV15 @ SV19 )
= ( cP @ SV18 @ SV20 ) )
= $false )
| ( ( ~ ( ( SV15 != SV18 )
| ( SV19 != SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV14: iS > $o] :
( ( ( ! [SY46: iS,SY47: iS] :
( ~ ~ ( ~ ( SV14 @ SY46 )
| ~ ( SV14 @ SY47 ) )
| ( SV14 @ ( cP @ SY46 @ SY47 ) ) ) )
= $false )
| ( ( SV14 @ c0 )
= $false )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(113,plain,
( ( ( ( sK5_SV17 = c0 )
| ~ ! [SY55: iS] :
( c0
!= ( cP @ SY55 @ sK5_SV17 ) ) )
= $true )
| ( ( c0 = sK5_SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(114,plain,
( ( ( ~ ( ( sK5_SV17 = c0 )
| ~ ! [SY55: iS] :
( c0
!= ( cP @ SY55 @ sK5_SV17 ) ) ) )
= $true )
| ( ( c0 != sK5_SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(115,plain,
! [SV20: iS,SV19: iS,SV18: iS,SV15: iS] :
( ( ( ( SV15 != SV18 )
| ( SV19 != SV20 ) )
= $false )
| ( ( ( cP @ SV15 @ SV19 )
= ( cP @ SV18 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(116,plain,
! [SV14: iS > $o] :
( ( ( ! [SY57: iS] :
( ~ ~ ( ~ ( SV14 @ ( sK6_SY46 @ SV14 ) )
| ~ ( SV14 @ SY57 ) )
| ( SV14 @ ( cP @ ( sK6_SY46 @ SV14 ) @ SY57 ) ) ) )
= $false )
| ( ( SV14 @ c0 )
= $false )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[112]) ).
thf(117,plain,
( ( ( sK5_SV17 = c0 )
= $true )
| ( ( ~ ! [SY55: iS] :
( c0
!= ( cP @ SY55 @ sK5_SV17 ) ) )
= $true )
| ( ( c0 = sK5_SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(118,plain,
( ( ( ( sK5_SV17 = c0 )
| ~ ! [SY55: iS] :
( c0
!= ( cP @ SY55 @ sK5_SV17 ) ) )
= $false )
| ( ( c0 != sK5_SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(119,plain,
! [SV20: iS,SV19: iS,SV18: iS,SV15: iS] :
( ( ( SV15 != SV18 )
= $false )
| ( ( ( cP @ SV15 @ SV19 )
= ( cP @ SV18 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(120,plain,
! [SV18: iS,SV15: iS,SV20: iS,SV19: iS] :
( ( ( SV19 != SV20 )
= $false )
| ( ( ( cP @ SV15 @ SV19 )
= ( cP @ SV18 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(121,plain,
! [SV14: iS > $o] :
( ( ( ~ ~ ( ~ ( SV14 @ ( sK6_SY46 @ SV14 ) )
| ~ ( SV14 @ ( sK7_SY57 @ SV14 ) ) )
| ( SV14 @ ( cP @ ( sK6_SY46 @ SV14 ) @ ( sK7_SY57 @ SV14 ) ) ) )
= $false )
| ( ( SV14 @ c0 )
= $false )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[116]) ).
thf(122,plain,
( ( ( ! [SY55: iS] :
( c0
!= ( cP @ SY55 @ sK5_SV17 ) ) )
= $false )
| ( ( sK5_SV17 = c0 )
= $true )
| ( ( c0 = sK5_SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(123,plain,
( ( ( sK5_SV17 = c0 )
= $false )
| ( ( c0 != sK5_SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(124,plain,
( ( ( ~ ! [SY55: iS] :
( c0
!= ( cP @ SY55 @ sK5_SV17 ) ) )
= $false )
| ( ( c0 != sK5_SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(125,plain,
! [SV20: iS,SV19: iS,SV18: iS,SV15: iS] :
( ( ( SV15 = SV18 )
= $true )
| ( ( ( cP @ SV15 @ SV19 )
= ( cP @ SV18 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(126,plain,
! [SV18: iS,SV15: iS,SV20: iS,SV19: iS] :
( ( ( SV19 = SV20 )
= $true )
| ( ( ( cP @ SV15 @ SV19 )
= ( cP @ SV18 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(127,plain,
! [SV14: iS > $o] :
( ( ( ~ ~ ( ~ ( SV14 @ ( sK6_SY46 @ SV14 ) )
| ~ ( SV14 @ ( sK7_SY57 @ SV14 ) ) ) )
= $false )
| ( ( SV14 @ c0 )
= $false )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(128,plain,
! [SV14: iS > $o] :
( ( ( SV14 @ ( cP @ ( sK6_SY46 @ SV14 ) @ ( sK7_SY57 @ SV14 ) ) )
= $false )
| ( ( SV14 @ c0 )
= $false )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(129,plain,
( ( ( c0
!= ( cP @ sK8_SY55 @ sK5_SV17 ) )
= $false )
| ( ( sK5_SV17 = c0 )
= $true )
| ( ( c0 = sK5_SV17 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[122]) ).
thf(130,plain,
( ( ( c0 = sK5_SV17 )
= $false )
| ( ( sK5_SV17 = c0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(131,plain,
( ( ( ! [SY55: iS] :
( c0
!= ( cP @ SY55 @ sK5_SV17 ) ) )
= $true )
| ( ( c0 != sK5_SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(132,plain,
! [SV14: iS > $o] :
( ( ( ~ ( ~ ( SV14 @ ( sK6_SY46 @ SV14 ) )
| ~ ( SV14 @ ( sK7_SY57 @ SV14 ) ) ) )
= $true )
| ( ( SV14 @ c0 )
= $false )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(133,plain,
! [SV21: iS,SV14: iS > $o] :
( ( ( SV14 @ SV21 )
= $true )
| ( ( SV14 @ c0 )
= $false )
| ( ( SV14 @ ( cP @ ( sK6_SY46 @ SV14 ) @ ( sK7_SY57 @ SV14 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(134,plain,
( ( ( c0
= ( cP @ sK8_SY55 @ sK5_SV17 ) )
= $true )
| ( ( sK5_SV17 = c0 )
= $true )
| ( ( c0 = sK5_SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(135,plain,
! [SV22: iS] :
( ( ( c0
!= ( cP @ SV22 @ sK5_SV17 ) )
= $true )
| ( ( c0 != sK5_SV17 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(136,plain,
! [SV14: iS > $o] :
( ( ( ~ ( SV14 @ ( sK6_SY46 @ SV14 ) )
| ~ ( SV14 @ ( sK7_SY57 @ SV14 ) ) )
= $false )
| ( ( SV14 @ c0 )
= $false )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(137,plain,
! [SV22: iS] :
( ( ( c0
= ( cP @ SV22 @ sK5_SV17 ) )
= $false )
| ( ( c0 != sK5_SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(138,plain,
! [SV14: iS > $o] :
( ( ( ~ ( SV14 @ ( sK6_SY46 @ SV14 ) ) )
= $false )
| ( ( SV14 @ c0 )
= $false )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(139,plain,
! [SV14: iS > $o] :
( ( ( ~ ( SV14 @ ( sK7_SY57 @ SV14 ) ) )
= $false )
| ( ( SV14 @ c0 )
= $false )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(140,plain,
! [SV22: iS] :
( ( ( c0 = sK5_SV17 )
= $false )
| ( ( c0
= ( cP @ SV22 @ sK5_SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(141,plain,
! [SV14: iS > $o] :
( ( ( SV14 @ ( sK6_SY46 @ SV14 ) )
= $true )
| ( ( SV14 @ c0 )
= $false )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(142,plain,
! [SV14: iS > $o] :
( ( ( SV14 @ ( sK7_SY57 @ SV14 ) )
= $true )
| ( ( SV14 @ c0 )
= $false )
| ( ( ! [SY48: iS] : ( SV14 @ SY48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(143,plain,
! [SV23: iS,SV14: iS > $o] :
( ( ( SV14 @ SV23 )
= $true )
| ( ( SV14 @ c0 )
= $false )
| ( ( SV14 @ ( sK6_SY46 @ SV14 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(144,plain,
! [SV24: iS,SV14: iS > $o] :
( ( ( SV14 @ SV24 )
= $true )
| ( ( SV14 @ c0 )
= $false )
| ( ( SV14 @ ( sK7_SY57 @ SV14 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(145,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[94,144,143,140,134,133,130,126,125,102,96]) ).
thf(146,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[145,78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV214^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.18 % Computer : n017.cluster.edu
% 0.05/0.18 % Model : x86_64 x86_64
% 0.05/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.18 % Memory : 8046.5625MB
% 0.05/0.18 % OS : Linux 6.8.0-71-generic
% 0.05/0.18 % CPULimit : 300
% 0.05/0.18 % WCLimit : 300
% 0.05/0.18 % DateTime : Tue Oct 6 15:38:46 UTC 2026
% 0.05/0.18 % CPUTime :
% 0.05/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.26
% 0.05/0.26 No.of.Axioms: 0
% 0.05/0.26
% 0.05/0.26 Length.of.Defs: 0
% 0.05/0.26
% 0.05/0.26 Contains.Choice.Funs: false
% 0.05/0.26 ...
% 0.05/0.26
% 0.05/0.26 ********************************
% 0.05/0.26 * All subproblems solved! *
% 0.05/0.26 ********************************
% 0.05/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:145,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.05/0.26
% 0.05/0.26 %**** Beginning of derivation protocol ****
% 0.05/0.26 % SZS output start CNFRefutation
% See solution above
% 0.05/0.26
% 0.05/0.26 %**** End of derivation protocol ****
% 0.05/0.26 %**** no. of clauses in derivation: 146 ****
% 0.05/0.26 %**** clause counter: 145 ****
% 0.05/0.26
% 0.05/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:145,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------