TSTP Solution File: SET047^1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET047^1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n012.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 02:58:36 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 30
% Syntax : Number of formulae : 91 ( 29 unt; 18 typ; 10 def)
% Number of atoms : 531 ( 129 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 1226 ( 197 ~; 173 |; 2 &; 851 @)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 146 ( 37 ^ 107 !; 2 ?; 146 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_element,type,
element: $i > $i > mworld > $o ).
thf(tp_mactual,type,
mactual: mworld ).
thf(tp_mand,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mbox,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(tp_mdia,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(tp_mequiv,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mexists_di,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(tp_mforall_di,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(tp_mimplies,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mlocal,type,
mlocal: ( mworld > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(tp_mor,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mrel,type,
mrel: mworld > mworld > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY3,type,
sK2_SY3: $i ).
thf(tp_sK3_SY5,type,
sK3_SY5: $i > $i > $i ).
thf(tp_set_equal,type,
set_equal: $i > $i > mworld > $o ).
thf(mand,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv) ).
thf(mexists_di,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
? [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_di) ).
thf(mforall_di,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di) ).
thf(mimplies,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(1,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] :
( mequiv @ ( set_equal @ X @ Y )
@ ( mforall_di
@ ^ [Z: $i] : ( mequiv @ ( element @ Z @ X ) @ ( element @ Z @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel43_1) ).
thf(2,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] : ( mequiv @ ( set_equal @ X @ Y ) @ ( set_equal @ Y @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel43) ).
thf(3,negated_conjecture,
( ( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] : ( mequiv @ ( set_equal @ X @ Y ) @ ( set_equal @ Y @ X ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ~ ( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] : ( mequiv @ ( set_equal @ X @ Y ) @ ( set_equal @ Y @ X ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] :
( mequiv @ ( set_equal @ X @ Y )
@ ( mforall_di
@ ^ [Z: $i] : ( mequiv @ ( element @ Z @ X ) @ ( element @ Z @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(6,plain,
( ( ~ ( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] : ( mequiv @ ( set_equal @ X @ Y ) @ ( set_equal @ Y @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( set_equal @ SX0 @ SX1 @ mactual )
| ( set_equal @ SX1 @ SX0 @ mactual ) )
| ~ ( ~ ( set_equal @ SX1 @ SX0 @ mactual )
| ( set_equal @ SX0 @ SX1 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(8,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( set_equal @ SX0 @ SX1 @ mactual )
| ! [SX2: $i] :
~ ( ~ ( ~ ( element @ SX2 @ SX0 @ mactual )
| ( element @ SX2 @ SX1 @ mactual ) )
| ~ ( ~ ( element @ SX2 @ SX1 @ mactual )
| ( element @ SX2 @ SX0 @ mactual ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( element @ SX2 @ SX0 @ mactual )
| ( element @ SX2 @ SX1 @ mactual ) )
| ~ ( ~ ( element @ SX2 @ SX1 @ mactual )
| ( element @ SX2 @ SX0 @ mactual ) ) )
| ( set_equal @ SX0 @ SX1 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(9,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( set_equal @ SX0 @ SX1 @ mactual )
| ( set_equal @ SX1 @ SX0 @ mactual ) )
| ~ ( ~ ( set_equal @ SX1 @ SX0 @ mactual )
| ( set_equal @ SX0 @ SX1 @ mactual ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7]) ).
thf(10,plain,
! [SV1: $i] :
( ( ! [SY0: $i] :
~ ( ~ ( ~ ( set_equal @ SV1 @ SY0 @ mactual )
| ! [SY1: $i] :
~ ( ~ ( ~ ( element @ SY1 @ SV1 @ mactual )
| ( element @ SY1 @ SY0 @ mactual ) )
| ~ ( ~ ( element @ SY1 @ SY0 @ mactual )
| ( element @ SY1 @ SV1 @ mactual ) ) ) )
| ~ ( ~ ! [SY2: $i] :
~ ( ~ ( ~ ( element @ SY2 @ SV1 @ mactual )
| ( element @ SY2 @ SY0 @ mactual ) )
| ~ ( ~ ( element @ SY2 @ SY0 @ mactual )
| ( element @ SY2 @ SV1 @ mactual ) ) )
| ( set_equal @ SV1 @ SY0 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [SY3: $i] :
~ ( ~ ( ~ ( set_equal @ sK1_SX0 @ SY3 @ mactual )
| ( set_equal @ SY3 @ sK1_SX0 @ mactual ) )
| ~ ( ~ ( set_equal @ SY3 @ sK1_SX0 @ mactual )
| ( set_equal @ sK1_SX0 @ SY3 @ mactual ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(12,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( ~ ( ~ ( set_equal @ SV1 @ SV2 @ mactual )
| ! [SY4: $i] :
~ ( ~ ( ~ ( element @ SY4 @ SV1 @ mactual )
| ( element @ SY4 @ SV2 @ mactual ) )
| ~ ( ~ ( element @ SY4 @ SV2 @ mactual )
| ( element @ SY4 @ SV1 @ mactual ) ) ) )
| ~ ( ~ ! [SY5: $i] :
~ ( ~ ( ~ ( element @ SY5 @ SV1 @ mactual )
| ( element @ SY5 @ SV2 @ mactual ) )
| ~ ( ~ ( element @ SY5 @ SV2 @ mactual )
| ( element @ SY5 @ SV1 @ mactual ) ) )
| ( set_equal @ SV1 @ SV2 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ( ~ ( ~ ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual )
| ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual ) )
| ~ ( ~ ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
| ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( ~ ( set_equal @ SV1 @ SV2 @ mactual )
| ! [SY4: $i] :
~ ( ~ ( ~ ( element @ SY4 @ SV1 @ mactual )
| ( element @ SY4 @ SV2 @ mactual ) )
| ~ ( ~ ( element @ SY4 @ SV2 @ mactual )
| ( element @ SY4 @ SV1 @ mactual ) ) ) )
| ~ ( ~ ! [SY5: $i] :
~ ( ~ ( ~ ( element @ SY5 @ SV1 @ mactual )
| ( element @ SY5 @ SV2 @ mactual ) )
| ~ ( ~ ( element @ SY5 @ SV2 @ mactual )
| ( element @ SY5 @ SV1 @ mactual ) ) )
| ( set_equal @ SV1 @ SV2 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( ~ ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual )
| ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual ) )
| ~ ( ~ ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
| ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( ~ ( set_equal @ SV1 @ SV2 @ mactual )
| ! [SY4: $i] :
~ ( ~ ( ~ ( element @ SY4 @ SV1 @ mactual )
| ( element @ SY4 @ SV2 @ mactual ) )
| ~ ( ~ ( element @ SY4 @ SV2 @ mactual )
| ( element @ SY4 @ SV1 @ mactual ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( ~ ! [SY5: $i] :
~ ( ~ ( ~ ( element @ SY5 @ SV1 @ mactual )
| ( element @ SY5 @ SV2 @ mactual ) )
| ~ ( ~ ( element @ SY5 @ SV2 @ mactual )
| ( element @ SY5 @ SV1 @ mactual ) ) )
| ( set_equal @ SV1 @ SV2 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( ( ~ ( ~ ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual )
| ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual ) ) )
= $true )
| ( ( ~ ( ~ ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
| ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( set_equal @ SV1 @ SV2 @ mactual )
| ! [SY4: $i] :
~ ( ~ ( ~ ( element @ SY4 @ SV1 @ mactual )
| ( element @ SY4 @ SV2 @ mactual ) )
| ~ ( ~ ( element @ SY4 @ SV2 @ mactual )
| ( element @ SY4 @ SV1 @ mactual ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ! [SY5: $i] :
~ ( ~ ( ~ ( element @ SY5 @ SV1 @ mactual )
| ( element @ SY5 @ SV2 @ mactual ) )
| ~ ( ~ ( element @ SY5 @ SV2 @ mactual )
| ( element @ SY5 @ SV1 @ mactual ) ) )
| ( set_equal @ SV1 @ SV2 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ( ~ ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual )
| ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual ) )
= $false )
| ( ( ~ ( ~ ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
| ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( set_equal @ SV1 @ SV2 @ mactual ) )
= $true )
| ( ( ! [SY4: $i] :
~ ( ~ ( ~ ( element @ SY4 @ SV1 @ mactual )
| ( element @ SY4 @ SV2 @ mactual ) )
| ~ ( ~ ( element @ SY4 @ SV2 @ mactual )
| ( element @ SY4 @ SV1 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ! [SY5: $i] :
~ ( ~ ( ~ ( element @ SY5 @ SV1 @ mactual )
| ( element @ SY5 @ SV2 @ mactual ) )
| ~ ( ~ ( element @ SY5 @ SV2 @ mactual )
| ( element @ SY5 @ SV1 @ mactual ) ) ) )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ( ~ ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual ) )
= $false )
| ( ( ~ ( ~ ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
| ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
= $false )
| ( ( ~ ( ~ ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
| ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: $i,SV1: $i] :
( ( ( set_equal @ SV1 @ SV2 @ mactual )
= $false )
| ( ( ! [SY4: $i] :
~ ( ~ ( ~ ( element @ SY4 @ SV1 @ mactual )
| ( element @ SY4 @ SV2 @ mactual ) )
| ~ ( ~ ( element @ SY4 @ SV2 @ mactual )
| ( element @ SY4 @ SV1 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: $i,SV1: $i] :
( ( ( ! [SY5: $i] :
~ ( ~ ( ~ ( element @ SY5 @ SV1 @ mactual )
| ( element @ SY5 @ SV2 @ mactual ) )
| ~ ( ~ ( element @ SY5 @ SV2 @ mactual )
| ( element @ SY5 @ SV1 @ mactual ) ) ) )
= $false )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual )
= $true )
| ( ( ~ ( ~ ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
| ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ( ~ ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
| ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual ) )
= $false )
| ( ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ( ~ ( element @ SV3 @ SV1 @ mactual )
| ( element @ SV3 @ SV2 @ mactual ) )
| ~ ( ~ ( element @ SV3 @ SV2 @ mactual )
| ( element @ SV3 @ SV1 @ mactual ) ) ) )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( ~ ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual )
| ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual ) )
| ~ ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
| ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual ) ) ) )
= $false )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(32,plain,
( ( ( ~ ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
| ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual ) )
= $false )
| ( ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( ( ~ ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual ) )
= $false )
| ( ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual )
= $false )
| ( ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(35,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ( element @ SV3 @ SV1 @ mactual )
| ( element @ SV3 @ SV2 @ mactual ) )
| ~ ( ~ ( element @ SV3 @ SV2 @ mactual )
| ( element @ SV3 @ SV1 @ mactual ) ) )
= $false )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(36,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual )
| ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual ) )
| ~ ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
| ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual ) ) )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(37,plain,
( ( ( ~ ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual ) )
= $false )
| ( ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(38,plain,
( ( ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual )
= $false )
| ( ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(39,plain,
( ( ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
= $true )
| ( ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(40,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ( element @ SV3 @ SV1 @ mactual )
| ( element @ SV3 @ SV2 @ mactual ) ) )
= $false )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(41,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( ~ ( element @ SV3 @ SV2 @ mactual )
| ( element @ SV3 @ SV1 @ mactual ) ) )
= $false )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(42,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual )
| ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
| ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual ) ) )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(43,plain,
( ( ( set_equal @ sK2_SY3 @ sK1_SX0 @ mactual )
= $true )
| ( ( set_equal @ sK1_SX0 @ sK2_SY3 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(44,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( element @ SV3 @ SV1 @ mactual )
| ( element @ SV3 @ SV2 @ mactual ) )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( element @ SV3 @ SV2 @ mactual )
| ( element @ SV3 @ SV1 @ mactual ) )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual )
| ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
| ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual ) ) )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( element @ SV3 @ SV1 @ mactual ) )
= $true )
| ( ( element @ SV3 @ SV2 @ mactual )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( element @ SV3 @ SV2 @ mactual ) )
= $true )
| ( ( element @ SV3 @ SV1 @ mactual )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
| ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual ) ) )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(50,plain,
! [SV1: $i,SV2: $i] :
( ( ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
= $false )
| ( ( ~ ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
| ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual ) ) )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( element @ SV3 @ SV1 @ mactual )
= $false )
| ( ( element @ SV3 @ SV2 @ mactual )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( element @ SV3 @ SV2 @ mactual )
= $false )
| ( ( element @ SV3 @ SV1 @ mactual )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV1: $i,SV2: $i] :
( ( ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual )
= $true )
| ( ( ~ ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
| ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual ) ) )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(54,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
| ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual ) )
= $false )
| ( ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
= $false )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
| ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual ) )
= $false )
| ( ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual ) )
= $false )
| ( ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
= $false )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(57,plain,
! [SV1: $i,SV2: $i] :
( ( ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual )
= $false )
| ( ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
= $false )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(58,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual ) )
= $false )
| ( ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(59,plain,
! [SV1: $i,SV2: $i] :
( ( ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual )
= $false )
| ( ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV1: $i,SV2: $i] :
( ( ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
= $true )
| ( ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
= $false )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(61,plain,
! [SV1: $i,SV2: $i] :
( ( ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV2 @ mactual )
= $true )
| ( ( element @ ( sK3_SY5 @ SV2 @ SV1 ) @ SV1 @ mactual )
= $true )
| ( ( set_equal @ SV1 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(62,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[34,61,60,59,57,52,51,43,39,38]) ).
thf(63,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET047^1 : TPTP v8.1.0. Released v8.1.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 21:07:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.35
% 0.19/0.35 No.of.Axioms: 1
% 0.19/0.35
% 0.19/0.35 Length.of.Defs: 1574
% 0.19/0.35
% 0.19/0.35 Contains.Choice.Funs: false
% 0.19/0.35 (rf:0,axioms:1,ps:3,u:6,ude:false,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:3,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.19/0.41
% 0.19/0.41 ********************************
% 0.19/0.41 * All subproblems solved! *
% 0.19/0.41 ********************************
% 0.19/0.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:false,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:62,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.41
% 0.19/0.41 %**** Beginning of derivation protocol ****
% 0.19/0.41 % SZS output start CNFRefutation
% See solution above
% 0.19/0.41
% 0.19/0.41 %**** End of derivation protocol ****
% 0.19/0.41 %**** no. of clauses in derivation: 63 ****
% 0.19/0.41 %**** clause counter: 62 ****
% 0.19/0.41
% 0.19/0.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:false,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:62,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------