TSTP Solution File: SYN551+2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN551+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n006.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 : Thu Jul 21 08:28:22 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 74 ( 51 unt; 6 typ; 0 def)
% Number of atoms : 387 ( 302 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 695 ( 176 ~; 122 |; 12 &; 364 @)
% ( 17 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 108 ( 0 ^ 94 !; 14 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_f,type,
f: $i > $i ).
thf(tp_g,type,
g: $i > $i ).
thf(tp_sK1_Y,type,
sK1_Y: $i > $i ).
thf(tp_sK2_X,type,
sK2_X: $i ).
thf(tp_sK3_Y,type,
sK3_Y: $i > $i ).
thf(tp_sK4_X,type,
sK4_X: $i ).
thf(1,conjecture,
( ? [X: $i] :
! [Y: $i] :
( ( Y
= ( f @ ( g @ Y ) ) )
<=> ( X = Y ) )
<=> ? [X: $i] :
! [Y: $i] :
( ( Y
= ( g @ ( f @ Y ) ) )
<=> ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_cute_thing) ).
thf(2,negated_conjecture,
( ( ? [X: $i] :
! [Y: $i] :
( ( Y
= ( f @ ( g @ Y ) ) )
<=> ( X = Y ) )
<=> ? [X: $i] :
! [Y: $i] :
( ( Y
= ( g @ ( f @ Y ) ) )
<=> ( X = Y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [X: $i] :
! [Y: $i] :
( ( Y
= ( f @ ( g @ Y ) ) )
<=> ( X = Y ) )
<=> ? [X: $i] :
! [Y: $i] :
( ( Y
= ( g @ ( f @ Y ) ) )
<=> ( X = Y ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [X: $i] :
! [Y: $i] :
( ( Y
= ( f @ ( g @ Y ) ) )
<=> ( X = Y ) )
=> ? [X: $i] :
! [Y: $i] :
( ( Y
= ( g @ ( f @ Y ) ) )
<=> ( X = Y ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(5,plain,
( ( ? [X: $i] :
! [Y: $i] :
( ( Y
= ( g @ ( f @ Y ) ) )
<=> ( X = Y ) )
=> ? [X: $i] :
! [Y: $i] :
( ( Y
= ( f @ ( g @ Y ) ) )
<=> ( X = Y ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(6,plain,
( ( ~ ( ? [X: $i] :
! [Y: $i] :
( ( Y
= ( f @ ( g @ Y ) ) )
<=> ( X = Y ) )
=> ? [X: $i] :
! [Y: $i] :
( ( Y
= ( g @ ( f @ Y ) ) )
<=> ( X = Y ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ( ? [X: $i] :
! [Y: $i] :
( ( Y
= ( g @ ( f @ Y ) ) )
<=> ( X = Y ) )
=> ? [X: $i] :
! [Y: $i] :
( ( Y
= ( f @ ( g @ Y ) ) )
<=> ( X = Y ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ! [SY4: $i] :
( ( SY4
!= ( f @ ( g @ SY4 ) ) )
| ( sK2_X = SY4 ) )
& ! [SY5: $i] :
( ( sK2_X != SY5 )
| ( SY5
= ( f @ ( g @ SY5 ) ) ) )
& ! [X: $i] :
( ( ( ( sK1_Y @ X )
!= ( g @ ( f @ ( sK1_Y @ X ) ) ) )
| ( X
!= ( sK1_Y @ X ) ) )
& ( ( ( sK1_Y @ X )
= ( g @ ( f @ ( sK1_Y @ X ) ) ) )
| ( X
= ( sK1_Y @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(9,plain,
( ( ! [SY6: $i] :
( ( SY6
!= ( g @ ( f @ SY6 ) ) )
| ( sK4_X = SY6 ) )
& ! [SY7: $i] :
( ( sK4_X != SY7 )
| ( SY7
= ( g @ ( f @ SY7 ) ) ) )
& ! [X: $i] :
( ( ( ( sK3_Y @ X )
!= ( f @ ( g @ ( sK3_Y @ X ) ) ) )
| ( X
!= ( sK3_Y @ X ) ) )
& ( ( ( sK3_Y @ X )
= ( f @ ( g @ ( sK3_Y @ X ) ) ) )
| ( X
= ( sK3_Y @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(10,plain,
( ( ! [SY4: $i] :
( ( SY4
!= ( f @ ( g @ SY4 ) ) )
| ( sK2_X = SY4 ) )
& ! [SY5: $i] :
( ( sK2_X != SY5 )
| ( SY5
= ( f @ ( g @ SY5 ) ) ) )
& ! [X: $i] :
( ( ( ( sK1_Y @ X )
!= ( g @ ( f @ ( sK1_Y @ X ) ) ) )
| ( X
!= ( sK1_Y @ X ) ) )
& ( ( ( sK1_Y @ X )
= ( g @ ( f @ ( sK1_Y @ X ) ) ) )
| ( X
= ( sK1_Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0
!= ( f @ ( g @ SX0 ) ) )
| ( sK2_X = SX0 ) )
| ~ ! [SX0: $i] :
( ( sK2_X != SX0 )
| ( SX0
= ( f @ ( g @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ( ( sK1_Y @ SX0 )
!= ( g @ ( f @ ( sK1_Y @ SX0 ) ) ) )
| ( SX0
!= ( sK1_Y @ SX0 ) ) )
| ~ ( ( ( sK1_Y @ SX0 )
= ( g @ ( f @ ( sK1_Y @ SX0 ) ) ) )
| ( SX0
= ( sK1_Y @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0
!= ( f @ ( g @ SX0 ) ) )
| ( sK2_X = SX0 ) )
| ~ ! [SX0: $i] :
( ( sK2_X != SX0 )
| ( SX0
= ( f @ ( g @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ( ( sK1_Y @ SX0 )
!= ( g @ ( f @ ( sK1_Y @ SX0 ) ) ) )
| ( SX0
!= ( sK1_Y @ SX0 ) ) )
| ~ ( ( ( sK1_Y @ SX0 )
= ( g @ ( f @ ( sK1_Y @ SX0 ) ) ) )
| ( SX0
= ( sK1_Y @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(13,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0
!= ( f @ ( g @ SX0 ) ) )
| ( sK2_X = SX0 ) )
| ~ ! [SX0: $i] :
( ( sK2_X != SX0 )
| ( SX0
= ( f @ ( g @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( ( ( sK1_Y @ SX0 )
!= ( g @ ( f @ ( sK1_Y @ SX0 ) ) ) )
| ( SX0
!= ( sK1_Y @ SX0 ) ) )
| ~ ( ( ( sK1_Y @ SX0 )
= ( g @ ( f @ ( sK1_Y @ SX0 ) ) ) )
| ( SX0
= ( sK1_Y @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0
!= ( f @ ( g @ SX0 ) ) )
| ( sK2_X = SX0 ) )
| ~ ! [SX0: $i] :
( ( sK2_X != SX0 )
| ( SX0
= ( f @ ( g @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( ( sK1_Y @ SX0 )
!= ( g @ ( f @ ( sK1_Y @ SX0 ) ) ) )
| ( SX0
!= ( sK1_Y @ SX0 ) ) )
| ~ ( ( ( sK1_Y @ SX0 )
= ( g @ ( f @ ( sK1_Y @ SX0 ) ) ) )
| ( SX0
= ( sK1_Y @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ! [SX0: $i] :
( ( SX0
!= ( f @ ( g @ SX0 ) ) )
| ( sK2_X = SX0 ) )
| ~ ! [SX0: $i] :
( ( sK2_X != SX0 )
| ( SX0
= ( f @ ( g @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: $i] :
( ( ~ ( ~ ( ( ( sK1_Y @ SV1 )
!= ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
| ( SV1
!= ( sK1_Y @ SV1 ) ) )
| ~ ( ( ( sK1_Y @ SV1 )
= ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
| ( SV1
= ( sK1_Y @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ! [SX0: $i] :
( ( SX0
!= ( f @ ( g @ SX0 ) ) )
| ( sK2_X = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ! [SX0: $i] :
( ( sK2_X != SX0 )
| ( SX0
= ( f @ ( g @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: $i] :
( ( ~ ( ( ( sK1_Y @ SV1 )
!= ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
| ( SV1
!= ( sK1_Y @ SV1 ) ) )
| ~ ( ( ( sK1_Y @ SV1 )
= ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
| ( SV1
= ( sK1_Y @ SV1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ! [SX0: $i] :
( ( SX0
!= ( f @ ( g @ SX0 ) ) )
| ( sK2_X = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ! [SX0: $i] :
( ( sK2_X != SX0 )
| ( SX0
= ( f @ ( g @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: $i] :
( ( ~ ( ( ( sK1_Y @ SV1 )
!= ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
| ( SV1
!= ( sK1_Y @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: $i] :
( ( ~ ( ( ( sK1_Y @ SV1 )
= ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
| ( SV1
= ( sK1_Y @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: $i] :
( ( ( SV2
!= ( f @ ( g @ SV2 ) ) )
| ( sK2_X = SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV3: $i] :
( ( ( sK2_X != SV3 )
| ( SV3
= ( f @ ( g @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV1: $i] :
( ( ( ( sK1_Y @ SV1 )
!= ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
| ( SV1
!= ( sK1_Y @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
! [SV1: $i] :
( ( ( ( sK1_Y @ SV1 )
= ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
| ( SV1
= ( sK1_Y @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(30,plain,
! [SV2: $i] :
( ( ( ( SV2
!= ( f @ ( g @ SV2 ) ) ) )
= $true )
| ( ( sK2_X = SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV3: $i] :
( ( ( ( sK2_X != SV3 ) )
= $true )
| ( ( SV3
= ( f @ ( g @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV1: $i] :
( ( ( ( ( sK1_Y @ SV1 )
!= ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) ) )
= $true )
| ( ( ( SV1
!= ( sK1_Y @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV1: $i] :
( ( ( ( sK1_Y @ SV1 )
= ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
= $true )
| ( ( SV1
= ( sK1_Y @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV2: $i] :
( ( ( SV2
= ( f @ ( g @ SV2 ) ) )
= $false )
| ( ( sK2_X = SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV3: $i] :
( ( ( sK2_X = SV3 )
= $false )
| ( ( SV3
= ( f @ ( g @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV1: $i] :
( ( ( ( sK1_Y @ SV1 )
= ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
= $false )
| ( ( ( SV1
!= ( sK1_Y @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV1: $i] :
( ( ( SV1
= ( sK1_Y @ SV1 ) )
= $false )
| ( ( ( sK1_Y @ SV1 )
= ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(38,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[33,37,35,34]) ).
thf(39,plain,
( ( ! [SY6: $i] :
( ( SY6
!= ( g @ ( f @ SY6 ) ) )
| ( sK4_X = SY6 ) )
& ! [SY7: $i] :
( ( sK4_X != SY7 )
| ( SY7
= ( g @ ( f @ SY7 ) ) ) )
& ! [X: $i] :
( ( ( ( sK3_Y @ X )
!= ( f @ ( g @ ( sK3_Y @ X ) ) ) )
| ( X
!= ( sK3_Y @ X ) ) )
& ( ( ( sK3_Y @ X )
= ( f @ ( g @ ( sK3_Y @ X ) ) ) )
| ( X
= ( sK3_Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(40,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0
!= ( g @ ( f @ SX0 ) ) )
| ( sK4_X = SX0 ) )
| ~ ! [SX0: $i] :
( ( sK4_X != SX0 )
| ( SX0
= ( g @ ( f @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ( ( sK3_Y @ SX0 )
!= ( f @ ( g @ ( sK3_Y @ SX0 ) ) ) )
| ( SX0
!= ( sK3_Y @ SX0 ) ) )
| ~ ( ( ( sK3_Y @ SX0 )
= ( f @ ( g @ ( sK3_Y @ SX0 ) ) ) )
| ( SX0
= ( sK3_Y @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(41,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0
!= ( g @ ( f @ SX0 ) ) )
| ( sK4_X = SX0 ) )
| ~ ! [SX0: $i] :
( ( sK4_X != SX0 )
| ( SX0
= ( g @ ( f @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ( ( sK3_Y @ SX0 )
!= ( f @ ( g @ ( sK3_Y @ SX0 ) ) ) )
| ( SX0
!= ( sK3_Y @ SX0 ) ) )
| ~ ( ( ( sK3_Y @ SX0 )
= ( f @ ( g @ ( sK3_Y @ SX0 ) ) ) )
| ( SX0
= ( sK3_Y @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(42,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0
!= ( g @ ( f @ SX0 ) ) )
| ( sK4_X = SX0 ) )
| ~ ! [SX0: $i] :
( ( sK4_X != SX0 )
| ( SX0
= ( g @ ( f @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(43,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( ( ( sK3_Y @ SX0 )
!= ( f @ ( g @ ( sK3_Y @ SX0 ) ) ) )
| ( SX0
!= ( sK3_Y @ SX0 ) ) )
| ~ ( ( ( sK3_Y @ SX0 )
= ( f @ ( g @ ( sK3_Y @ SX0 ) ) ) )
| ( SX0
= ( sK3_Y @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(44,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0
!= ( g @ ( f @ SX0 ) ) )
| ( sK4_X = SX0 ) )
| ~ ! [SX0: $i] :
( ( sK4_X != SX0 )
| ( SX0
= ( g @ ( f @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(45,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( ( sK3_Y @ SX0 )
!= ( f @ ( g @ ( sK3_Y @ SX0 ) ) ) )
| ( SX0
!= ( sK3_Y @ SX0 ) ) )
| ~ ( ( ( sK3_Y @ SX0 )
= ( f @ ( g @ ( sK3_Y @ SX0 ) ) ) )
| ( SX0
= ( sK3_Y @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(46,plain,
( ( ~ ! [SX0: $i] :
( ( SX0
!= ( g @ ( f @ SX0 ) ) )
| ( sK4_X = SX0 ) )
| ~ ! [SX0: $i] :
( ( sK4_X != SX0 )
| ( SX0
= ( g @ ( f @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV4: $i] :
( ( ~ ( ~ ( ( ( sK3_Y @ SV4 )
!= ( f @ ( g @ ( sK3_Y @ SV4 ) ) ) )
| ( SV4
!= ( sK3_Y @ SV4 ) ) )
| ~ ( ( ( sK3_Y @ SV4 )
= ( f @ ( g @ ( sK3_Y @ SV4 ) ) ) )
| ( SV4
= ( sK3_Y @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(48,plain,
( ( ~ ! [SX0: $i] :
( ( SX0
!= ( g @ ( f @ SX0 ) ) )
| ( sK4_X = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(49,plain,
( ( ~ ! [SX0: $i] :
( ( sK4_X != SX0 )
| ( SX0
= ( g @ ( f @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(50,plain,
! [SV4: $i] :
( ( ~ ( ( ( sK3_Y @ SV4 )
!= ( f @ ( g @ ( sK3_Y @ SV4 ) ) ) )
| ( SV4
!= ( sK3_Y @ SV4 ) ) )
| ~ ( ( ( sK3_Y @ SV4 )
= ( f @ ( g @ ( sK3_Y @ SV4 ) ) ) )
| ( SV4
= ( sK3_Y @ SV4 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(51,plain,
( ( ! [SX0: $i] :
( ( SX0
!= ( g @ ( f @ SX0 ) ) )
| ( sK4_X = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(52,plain,
( ( ! [SX0: $i] :
( ( sK4_X != SX0 )
| ( SX0
= ( g @ ( f @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(53,plain,
! [SV4: $i] :
( ( ~ ( ( ( sK3_Y @ SV4 )
!= ( f @ ( g @ ( sK3_Y @ SV4 ) ) ) )
| ( SV4
!= ( sK3_Y @ SV4 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(54,plain,
! [SV4: $i] :
( ( ~ ( ( ( sK3_Y @ SV4 )
= ( f @ ( g @ ( sK3_Y @ SV4 ) ) ) )
| ( SV4
= ( sK3_Y @ SV4 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(55,plain,
! [SV5: $i] :
( ( ( SV5
!= ( g @ ( f @ SV5 ) ) )
| ( sK4_X = SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV6: $i] :
( ( ( sK4_X != SV6 )
| ( SV6
= ( g @ ( f @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV4: $i] :
( ( ( ( sK3_Y @ SV4 )
!= ( f @ ( g @ ( sK3_Y @ SV4 ) ) ) )
| ( SV4
!= ( sK3_Y @ SV4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(58,plain,
! [SV4: $i] :
( ( ( ( sK3_Y @ SV4 )
= ( f @ ( g @ ( sK3_Y @ SV4 ) ) ) )
| ( SV4
= ( sK3_Y @ SV4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV5: $i] :
( ( ( ( SV5
!= ( g @ ( f @ SV5 ) ) ) )
= $true )
| ( ( sK4_X = SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV6: $i] :
( ( ( ( sK4_X != SV6 ) )
= $true )
| ( ( SV6
= ( g @ ( f @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV4: $i] :
( ( ( ( ( sK3_Y @ SV4 )
!= ( f @ ( g @ ( sK3_Y @ SV4 ) ) ) ) )
= $true )
| ( ( ( SV4
!= ( sK3_Y @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV4: $i] :
( ( ( ( sK3_Y @ SV4 )
= ( f @ ( g @ ( sK3_Y @ SV4 ) ) ) )
= $true )
| ( ( SV4
= ( sK3_Y @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV5: $i] :
( ( ( SV5
= ( g @ ( f @ SV5 ) ) )
= $false )
| ( ( sK4_X = SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV6: $i] :
( ( ( sK4_X = SV6 )
= $false )
| ( ( SV6
= ( g @ ( f @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV4: $i] :
( ( ( ( sK3_Y @ SV4 )
= ( f @ ( g @ ( sK3_Y @ SV4 ) ) ) )
= $false )
| ( ( ( SV4
!= ( sK3_Y @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV4: $i] :
( ( ( SV4
= ( sK3_Y @ SV4 ) )
= $false )
| ( ( ( sK3_Y @ SV4 )
= ( f @ ( g @ ( sK3_Y @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(67,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[62,66,64,63]) ).
thf(68,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[67,38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN551+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.08/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jul 11 13:19:35 EDT 2022
% 0.14/0.35 % 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
% 0.14/0.36 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.20/0.43
% 0.20/0.43 ********************************
% 0.20/0.43 * All subproblems solved! *
% 0.20/0.43 ********************************
% 0.20/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:67,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: 68 ****
% 0.20/0.43 %**** clause counter: 67 ****
% 0.20/0.43
% 0.20/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:67,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------