%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET047^1 : TPTP v9.3.1. Released v8.1.0.
% 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 : n002.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 10:39:08 AM UTC 2026
% Result : Theorem 0.10s 0.23s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 111 ( 63 unt; 0 typ; 10 def)
% Number of atoms : 717 ( 170 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 1859 ( 276 ~; 235 |; 15 &;1321 @)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 254 ( 30 ^; 222 !; 2 ?; 254 :)
% 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_SY13,type,
sK1_SY13: $i ).
thf(tp_sK2_SY48,type,
sK2_SY48: $i ).
thf(tp_sK3_SY44,type,
sK3_SY44: $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_def) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_def) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv_def) ).
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_def) ).
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_def) ).
thf(mimplies,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def) ).
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,
( ( ! [SY13: $i,SY14: $i] :
( ( set_equal @ SY13 @ SY14 @ mactual )
<=> ( set_equal @ SY14 @ SY13 @ mactual ) ) )
= $false ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(5,plain,
( ( ! [SY42: $i,SY43: $i] :
( ( set_equal @ SY42 @ SY43 @ mactual )
<=> ! [SY44: $i] :
( ( element @ SY44 @ SY42 @ mactual )
<=> ( element @ SY44 @ SY43 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(6,plain,
( ( ! [SY48: $i] :
( ( set_equal @ sK1_SY13 @ SY48 @ mactual )
<=> ( set_equal @ SY48 @ sK1_SY13 @ mactual ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(7,plain,
( ( ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual )
<=> ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual )
=> ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(9,plain,
( ( ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual )
=> ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(10,plain,
( ( ~ ( ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual )
=> ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual )
=> ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(12,plain,
( ( ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual )
& ~ ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(13,plain,
( ( ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual )
& ~ ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(14,plain,
( ( ! [SY42: $i,SY43: $i] :
( ( ( ~ ( element @ ( sK3_SY44 @ SY43 @ SY42 ) @ SY42 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SY43 @ SY42 ) @ SY43 @ mactual ) )
& ( ( element @ ( sK3_SY44 @ SY43 @ SY42 ) @ SY42 @ mactual )
| ( element @ ( sK3_SY44 @ SY43 @ SY42 ) @ SY43 @ mactual ) ) )
| ( set_equal @ SY42 @ SY43 @ mactual ) )
& ! [SY42: $i,SY43: $i] :
( ~ ( set_equal @ SY42 @ SY43 @ mactual )
| ( ! [SY44: $i] :
( ~ ( element @ SY44 @ SY42 @ mactual )
| ( element @ SY44 @ SY43 @ mactual ) )
& ! [SY44: $i] :
( ~ ( element @ SY44 @ SY43 @ mactual )
| ( element @ SY44 @ SY42 @ mactual ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(15,plain,
( ( ! [SY42: $i,SY43: $i] :
( ( ( ~ ( element @ ( sK3_SY44 @ SY43 @ SY42 ) @ SY42 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SY43 @ SY42 ) @ SY43 @ mactual ) )
& ( ( element @ ( sK3_SY44 @ SY43 @ SY42 ) @ SY42 @ mactual )
| ( element @ ( sK3_SY44 @ SY43 @ SY42 ) @ SY43 @ mactual ) ) )
| ( set_equal @ SY42 @ SY43 @ mactual ) )
& ! [SY42: $i,SY43: $i] :
( ~ ( set_equal @ SY42 @ SY43 @ mactual )
| ( ! [SY44: $i] :
( ~ ( element @ SY44 @ SY42 @ mactual )
| ( element @ SY44 @ SY43 @ mactual ) )
& ! [SY44: $i] :
( ~ ( element @ SY44 @ SY43 @ mactual )
| ( element @ SY44 @ SY42 @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(16,plain,
( ( ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual )
& ~ ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ~ ( ~ ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual )
| ~ ~ ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(18,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) ) )
| ( set_equal @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( set_equal @ SX0 @ SX1 @ mactual )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX0 @ mactual )
| ( element @ SX2 @ SX1 @ mactual ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX1 @ mactual )
| ( element @ SX2 @ SX0 @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(19,plain,
( ( ~ ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual )
| ~ ~ ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) ) )
| ( set_equal @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( set_equal @ SX0 @ SX1 @ mactual )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX0 @ mactual )
| ( element @ SX2 @ SX1 @ mactual ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX1 @ mactual )
| ( element @ SX2 @ SX0 @ mactual ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(22,plain,
( ( ~ ~ ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) ) )
| ( set_equal @ SX0 @ SX1 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( set_equal @ SX0 @ SX1 @ mactual )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX0 @ mactual )
| ( element @ SX2 @ SX1 @ mactual ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX1 @ mactual )
| ( element @ SX2 @ SX0 @ mactual ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) ) )
| ( set_equal @ SX0 @ SX1 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(28,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( set_equal @ SX0 @ SX1 @ mactual )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX0 @ mactual )
| ( element @ SX2 @ SX1 @ mactual ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX1 @ mactual )
| ( element @ SX2 @ SX0 @ mactual ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV1: $i] :
( ( ! [SY49: $i] :
( ~ ( ~ ( ~ ( element @ ( sK3_SY44 @ SY49 @ SV1 ) @ SV1 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SY49 @ SV1 ) @ SY49 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SY49 @ SV1 ) @ SV1 @ mactual )
| ( element @ ( sK3_SY44 @ SY49 @ SV1 ) @ SY49 @ mactual ) ) )
| ( set_equal @ SV1 @ SY49 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV2: $i] :
( ( ! [SY50: $i] :
( ~ ( set_equal @ SV2 @ SY50 @ mactual )
| ~ ( ~ ! [SY51: $i] :
( ~ ( element @ SY51 @ SV2 @ mactual )
| ( element @ SY51 @ SY50 @ mactual ) )
| ~ ! [SY52: $i] :
( ~ ( element @ SY52 @ SY50 @ mactual )
| ( element @ SY52 @ SV2 @ mactual ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV1 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV3 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV1 @ mactual )
| ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV3 @ mactual ) ) )
| ( set_equal @ SV1 @ SV3 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV4: $i,SV2: $i] :
( ( ~ ( set_equal @ SV2 @ SV4 @ mactual )
| ~ ( ~ ! [SY53: $i] :
( ~ ( element @ SY53 @ SV2 @ mactual )
| ( element @ SY53 @ SV4 @ mactual ) )
| ~ ! [SY54: $i] :
( ~ ( element @ SY54 @ SV4 @ mactual )
| ( element @ SY54 @ SV2 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ( ~ ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV1 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV3 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV1 @ mactual )
| ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV3 @ mactual ) ) ) )
= $true )
| ( ( set_equal @ SV1 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( set_equal @ SV2 @ SV4 @ mactual ) )
= $true )
| ( ( ~ ( ~ ! [SY53: $i] :
( ~ ( element @ SY53 @ SV2 @ mactual )
| ( element @ SY53 @ SV4 @ mactual ) )
| ~ ! [SY54: $i] :
( ~ ( element @ SY54 @ SV4 @ mactual )
| ( element @ SY54 @ SV2 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV1 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV3 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV1 @ mactual )
| ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV3 @ mactual ) ) )
= $false )
| ( ( set_equal @ SV1 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV4: $i,SV2: $i] :
( ( ( set_equal @ SV2 @ SV4 @ mactual )
= $false )
| ( ( ~ ( ~ ! [SY53: $i] :
( ~ ( element @ SY53 @ SV2 @ mactual )
| ( element @ SY53 @ SV4 @ mactual ) )
| ~ ! [SY54: $i] :
( ~ ( element @ SY54 @ SV4 @ mactual )
| ( element @ SY54 @ SV2 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV1 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV3 @ mactual ) ) )
= $false )
| ( ( set_equal @ SV1 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(39,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV1 @ mactual )
| ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV3 @ mactual ) ) )
= $false )
| ( ( set_equal @ SV1 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(40,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ! [SY53: $i] :
( ~ ( element @ SY53 @ SV2 @ mactual )
| ( element @ SY53 @ SV4 @ mactual ) )
| ~ ! [SY54: $i] :
( ~ ( element @ SY54 @ SV4 @ mactual )
| ( element @ SY54 @ SV2 @ mactual ) ) )
= $false )
| ( ( set_equal @ SV2 @ SV4 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV1 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV3 @ mactual ) )
= $true )
| ( ( set_equal @ SV1 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV1: $i,SV3: $i] :
( ( ( ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV1 @ mactual )
| ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV3 @ mactual ) )
= $true )
| ( ( set_equal @ SV1 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(43,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ! [SY53: $i] :
( ~ ( element @ SY53 @ SV2 @ mactual )
| ( element @ SY53 @ SV4 @ mactual ) ) )
= $false )
| ( ( set_equal @ SV2 @ SV4 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(44,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ! [SY54: $i] :
( ~ ( element @ SY54 @ SV4 @ mactual )
| ( element @ SY54 @ SV2 @ mactual ) ) )
= $false )
| ( ( set_equal @ SV2 @ SV4 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV1 @ mactual ) )
= $true )
| ( ( ~ ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV3 @ mactual ) )
= $true )
| ( ( set_equal @ SV1 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV1: $i,SV3: $i] :
( ( ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV1 @ mactual )
= $true )
| ( ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV3 @ mactual )
= $true )
| ( ( set_equal @ SV1 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV4: $i,SV2: $i] :
( ( ( ! [SY53: $i] :
( ~ ( element @ SY53 @ SV2 @ mactual )
| ( element @ SY53 @ SV4 @ mactual ) ) )
= $true )
| ( ( set_equal @ SV2 @ SV4 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(48,plain,
! [SV2: $i,SV4: $i] :
( ( ( ! [SY54: $i] :
( ~ ( element @ SY54 @ SV4 @ mactual )
| ( element @ SY54 @ SV2 @ mactual ) ) )
= $true )
| ( ( set_equal @ SV2 @ SV4 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(49,plain,
! [SV1: $i,SV3: $i] :
( ( ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV1 @ mactual )
= $false )
| ( ( ~ ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV3 @ mactual ) )
= $true )
| ( ( set_equal @ SV1 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( element @ SV5 @ SV2 @ mactual )
| ( element @ SV5 @ SV4 @ mactual ) )
= $true )
| ( ( set_equal @ SV2 @ SV4 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( ~ ( element @ SV6 @ SV4 @ mactual )
| ( element @ SV6 @ SV2 @ mactual ) )
= $true )
| ( ( set_equal @ SV2 @ SV4 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV1: $i,SV3: $i] :
( ( ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV3 @ mactual )
= $false )
| ( ( element @ ( sK3_SY44 @ SV3 @ SV1 ) @ SV1 @ mactual )
= $false )
| ( ( set_equal @ SV1 @ SV3 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( element @ SV5 @ SV2 @ mactual ) )
= $true )
| ( ( element @ SV5 @ SV4 @ mactual )
= $true )
| ( ( set_equal @ SV2 @ SV4 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( ~ ( element @ SV6 @ SV4 @ mactual ) )
= $true )
| ( ( element @ SV6 @ SV2 @ mactual )
= $true )
| ( ( set_equal @ SV2 @ SV4 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ( element @ SV5 @ SV2 @ mactual )
= $false )
| ( ( element @ SV5 @ SV4 @ mactual )
= $true )
| ( ( set_equal @ SV2 @ SV4 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( element @ SV6 @ SV4 @ mactual )
= $false )
| ( ( element @ SV6 @ SV2 @ mactual )
= $true )
| ( ( set_equal @ SV2 @ SV4 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,56,55,52,46,29]) ).
thf(58,plain,
( ( ! [SY42: $i,SY43: $i] :
( ( ( ~ ( element @ ( sK3_SY44 @ SY43 @ SY42 ) @ SY42 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SY43 @ SY42 ) @ SY43 @ mactual ) )
& ( ( element @ ( sK3_SY44 @ SY43 @ SY42 ) @ SY42 @ mactual )
| ( element @ ( sK3_SY44 @ SY43 @ SY42 ) @ SY43 @ mactual ) ) )
| ( set_equal @ SY42 @ SY43 @ mactual ) )
& ! [SY42: $i,SY43: $i] :
( ~ ( set_equal @ SY42 @ SY43 @ mactual )
| ( ! [SY44: $i] :
( ~ ( element @ SY44 @ SY42 @ mactual )
| ( element @ SY44 @ SY43 @ mactual ) )
& ! [SY44: $i] :
( ~ ( element @ SY44 @ SY43 @ mactual )
| ( element @ SY44 @ SY42 @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(59,plain,
( ( ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual )
& ~ ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(60,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) ) )
| ( set_equal @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( set_equal @ SX0 @ SX1 @ mactual )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX0 @ mactual )
| ( element @ SX2 @ SX1 @ mactual ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX1 @ mactual )
| ( element @ SX2 @ SX0 @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(61,plain,
( ( ~ ( ~ ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual )
| ~ ~ ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(62,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) ) )
| ( set_equal @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( set_equal @ SX0 @ SX1 @ mactual )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX0 @ mactual )
| ( element @ SX2 @ SX1 @ mactual ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX1 @ mactual )
| ( element @ SX2 @ SX0 @ mactual ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(63,plain,
( ( ~ ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual )
| ~ ~ ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) ) )
| ( set_equal @ SX0 @ SX1 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(65,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( set_equal @ SX0 @ SX1 @ mactual )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX0 @ mactual )
| ( element @ SX2 @ SX1 @ mactual ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX1 @ mactual )
| ( element @ SX2 @ SX0 @ mactual ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(66,plain,
( ( ~ ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(67,plain,
( ( ~ ~ ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(68,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ( element @ ( sK3_SY44 @ SX1 @ SX0 ) @ SX1 @ mactual ) ) )
| ( set_equal @ SX0 @ SX1 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(69,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( set_equal @ SX0 @ SX1 @ mactual )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX0 @ mactual )
| ( element @ SX2 @ SX1 @ mactual ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ SX1 @ mactual )
| ( element @ SX2 @ SX0 @ mactual ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(70,plain,
( ( set_equal @ sK2_SY48 @ sK1_SY13 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(71,plain,
( ( ~ ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(72,plain,
! [SV7: $i] :
( ( ! [SY55: $i] :
( ~ ( ~ ( ~ ( element @ ( sK3_SY44 @ SY55 @ SV7 ) @ SV7 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SY55 @ SV7 ) @ SY55 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SY55 @ SV7 ) @ SV7 @ mactual )
| ( element @ ( sK3_SY44 @ SY55 @ SV7 ) @ SY55 @ mactual ) ) )
| ( set_equal @ SV7 @ SY55 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV8: $i] :
( ( ! [SY56: $i] :
( ~ ( set_equal @ SV8 @ SY56 @ mactual )
| ~ ( ~ ! [SY57: $i] :
( ~ ( element @ SY57 @ SV8 @ mactual )
| ( element @ SY57 @ SY56 @ mactual ) )
| ~ ! [SY58: $i] :
( ~ ( element @ SY58 @ SY56 @ mactual )
| ( element @ SY58 @ SV8 @ mactual ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(74,plain,
( ( set_equal @ sK1_SY13 @ sK2_SY48 @ mactual )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV7: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV7 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV9 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV7 @ mactual )
| ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV9 @ mactual ) ) )
| ( set_equal @ SV7 @ SV9 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(76,plain,
! [SV10: $i,SV8: $i] :
( ( ~ ( set_equal @ SV8 @ SV10 @ mactual )
| ~ ( ~ ! [SY59: $i] :
( ~ ( element @ SY59 @ SV8 @ mactual )
| ( element @ SY59 @ SV10 @ mactual ) )
| ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ SV10 @ mactual )
| ( element @ SY60 @ SV8 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(77,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( ~ ( ~ ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV7 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV9 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV7 @ mactual )
| ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV9 @ mactual ) ) ) )
= $true )
| ( ( set_equal @ SV7 @ SV9 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(78,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ( set_equal @ SV8 @ SV10 @ mactual ) )
= $true )
| ( ( ~ ( ~ ! [SY59: $i] :
( ~ ( element @ SY59 @ SV8 @ mactual )
| ( element @ SY59 @ SV10 @ mactual ) )
| ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ SV10 @ mactual )
| ( element @ SY60 @ SV8 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(79,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( ~ ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV7 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV9 @ mactual ) )
| ~ ( ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV7 @ mactual )
| ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV9 @ mactual ) ) )
= $false )
| ( ( set_equal @ SV7 @ SV9 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(80,plain,
! [SV10: $i,SV8: $i] :
( ( ( set_equal @ SV8 @ SV10 @ mactual )
= $false )
| ( ( ~ ( ~ ! [SY59: $i] :
( ~ ( element @ SY59 @ SV8 @ mactual )
| ( element @ SY59 @ SV10 @ mactual ) )
| ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ SV10 @ mactual )
| ( element @ SY60 @ SV8 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(81,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( ~ ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV7 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV9 @ mactual ) ) )
= $false )
| ( ( set_equal @ SV7 @ SV9 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(82,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV7 @ mactual )
| ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV9 @ mactual ) ) )
= $false )
| ( ( set_equal @ SV7 @ SV9 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(83,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ! [SY59: $i] :
( ~ ( element @ SY59 @ SV8 @ mactual )
| ( element @ SY59 @ SV10 @ mactual ) )
| ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ SV10 @ mactual )
| ( element @ SY60 @ SV8 @ mactual ) ) )
= $false )
| ( ( set_equal @ SV8 @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(84,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV7 @ mactual )
| ~ ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV9 @ mactual ) )
= $true )
| ( ( set_equal @ SV7 @ SV9 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(85,plain,
! [SV7: $i,SV9: $i] :
( ( ( ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV7 @ mactual )
| ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV9 @ mactual ) )
= $true )
| ( ( set_equal @ SV7 @ SV9 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(86,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ! [SY59: $i] :
( ~ ( element @ SY59 @ SV8 @ mactual )
| ( element @ SY59 @ SV10 @ mactual ) ) )
= $false )
| ( ( set_equal @ SV8 @ SV10 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(87,plain,
! [SV8: $i,SV10: $i] :
( ( ( ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ SV10 @ mactual )
| ( element @ SY60 @ SV8 @ mactual ) ) )
= $false )
| ( ( set_equal @ SV8 @ SV10 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(88,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV7 @ mactual ) )
= $true )
| ( ( ~ ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV9 @ mactual ) )
= $true )
| ( ( set_equal @ SV7 @ SV9 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(89,plain,
! [SV7: $i,SV9: $i] :
( ( ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV7 @ mactual )
= $true )
| ( ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV9 @ mactual )
= $true )
| ( ( set_equal @ SV7 @ SV9 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(90,plain,
! [SV10: $i,SV8: $i] :
( ( ( ! [SY59: $i] :
( ~ ( element @ SY59 @ SV8 @ mactual )
| ( element @ SY59 @ SV10 @ mactual ) ) )
= $true )
| ( ( set_equal @ SV8 @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(91,plain,
! [SV8: $i,SV10: $i] :
( ( ( ! [SY60: $i] :
( ~ ( element @ SY60 @ SV10 @ mactual )
| ( element @ SY60 @ SV8 @ mactual ) ) )
= $true )
| ( ( set_equal @ SV8 @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(92,plain,
! [SV7: $i,SV9: $i] :
( ( ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV7 @ mactual )
= $false )
| ( ( ~ ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV9 @ mactual ) )
= $true )
| ( ( set_equal @ SV7 @ SV9 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(93,plain,
! [SV10: $i,SV8: $i,SV11: $i] :
( ( ( ~ ( element @ SV11 @ SV8 @ mactual )
| ( element @ SV11 @ SV10 @ mactual ) )
= $true )
| ( ( set_equal @ SV8 @ SV10 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(94,plain,
! [SV8: $i,SV10: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ SV10 @ mactual )
| ( element @ SV12 @ SV8 @ mactual ) )
= $true )
| ( ( set_equal @ SV8 @ SV10 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(95,plain,
! [SV7: $i,SV9: $i] :
( ( ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV9 @ mactual )
= $false )
| ( ( element @ ( sK3_SY44 @ SV9 @ SV7 ) @ SV7 @ mactual )
= $false )
| ( ( set_equal @ SV7 @ SV9 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(96,plain,
! [SV10: $i,SV8: $i,SV11: $i] :
( ( ( ~ ( element @ SV11 @ SV8 @ mactual ) )
= $true )
| ( ( element @ SV11 @ SV10 @ mactual )
= $true )
| ( ( set_equal @ SV8 @ SV10 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(97,plain,
! [SV8: $i,SV10: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ SV10 @ mactual ) )
= $true )
| ( ( element @ SV12 @ SV8 @ mactual )
= $true )
| ( ( set_equal @ SV8 @ SV10 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(98,plain,
! [SV10: $i,SV8: $i,SV11: $i] :
( ( ( element @ SV11 @ SV8 @ mactual )
= $false )
| ( ( element @ SV11 @ SV10 @ mactual )
= $true )
| ( ( set_equal @ SV8 @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(99,plain,
! [SV8: $i,SV10: $i,SV12: $i] :
( ( ( element @ SV12 @ SV10 @ mactual )
= $false )
| ( ( element @ SV12 @ SV8 @ mactual )
= $true )
| ( ( set_equal @ SV8 @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(100,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[70,99,98,95,89,74]) ).
thf(101,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[100,57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET047^1 : TPTP v9.3.1. Released v8.1.0.
% 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
% 0.10/0.17 % Computer : n002.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 14:31:57 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.23
% 0.10/0.23 No.of.Axioms: 1
% 0.10/0.23
% 0.10/0.23 Length.of.Defs: 1614
% 0.10/0.23
% 0.10/0.23 Contains.Choice.Funs: false
% 0.10/0.23 ....
% 0.10/0.23
% 0.10/0.23 ********************************
% 0.10/0.23 * All subproblems solved! *
% 0.10/0.23 ********************************
% 0.10/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:100,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.23
% 0.10/0.23 %**** Beginning of derivation protocol ****
% 0.10/0.23 % SZS output start CNFRefutation
% See solution above
% 0.10/0.23
% 0.10/0.23 %**** End of derivation protocol ****
% 0.10/0.23 %**** no. of clauses in derivation: 101 ****
% 0.10/0.23 %**** clause counter: 100 ****
% 0.10/0.23
% 0.10/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:100,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------