%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET924^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 10:42:34 AM UTC 2026
% Result : Theorem 0.07s 0.29s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 150 ( 108 unt; 0 typ; 10 def)
% Number of atoms : 667 ( 175 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 1538 ( 144 ~; 108 |; 9 &;1261 @)
% ( 5 <=>; 11 =>; 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 : 22 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 292 ( 42 ^; 248 !; 2 ?; 292 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_empty,type,
empty: $i > mworld > $o ).
thf(tp_in,type,
in: $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_qmltpeq,type,
qmltpeq: $i > $i > mworld > $o ).
thf(tp_sK1_SY14,type,
sK1_SY14: $i ).
thf(tp_sK2_SY147,type,
sK2_SY147: $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(mand,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor_def) ).
thf(1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
thf(4,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(8,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_substitution_1) ).
thf(9,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_substitution_2) ).
thf(10,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_substitution_1) ).
thf(12,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(13,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(14,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(15,negated_conjecture,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,plain,
( ( ! [SY14: $i,SY15: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ SY14 ) @ SY15 ) @ ( singleton @ SY14 ) @ mactual )
<=> ~ ( in @ SY14 @ SY15 @ mactual ) ) )
= $false ),
inference(unfold_def,[status(thm)],[15,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(17,plain,
( ( ! [SY32: $i,SY33: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ SY32 ) @ SY33 ) @ ( singleton @ SY32 ) @ mactual )
<=> ~ ( in @ SY32 @ SY33 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(18,plain,
( ( ! [SY50: $i,SY51: $i] :
( ( in @ SY50 @ SY51 @ mactual )
=> ~ ( in @ SY51 @ SY50 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(19,plain,
( ( ! [SY67: $i,SY68: $i] :
( ( qmltpeq @ SY67 @ SY68 @ mactual )
=> ( qmltpeq @ ( singleton @ SY67 ) @ ( singleton @ SY68 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(20,plain,
( ( ! [SY92: $i,SY93: $i,SY94: $i] :
( ( qmltpeq @ SY92 @ SY93 @ mactual )
=> ( qmltpeq @ ( set_difference @ SY94 @ SY92 ) @ ( set_difference @ SY94 @ SY93 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(21,plain,
( ( ! [SY119: $i,SY120: $i,SY121: $i] :
( ( qmltpeq @ SY119 @ SY120 @ mactual )
=> ( qmltpeq @ ( set_difference @ SY119 @ SY121 ) @ ( set_difference @ SY120 @ SY121 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(22,plain,
( ( ! [SY138: $i,SY139: $i] :
( ( qmltpeq @ SY138 @ SY139 @ mactual )
=> ( qmltpeq @ SY139 @ SY138 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(23,plain,
( ( ! [SY145: $i] : ( qmltpeq @ SY145 @ SY145 @ mactual ) )
= $true ),
inference(unfold_def,[status(thm)],[13,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(24,plain,
( ( ! [SY147: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual )
<=> ~ ( in @ sK1_SY14 @ SY147 @ mactual ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(25,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual )
<=> ~ ( in @ sK1_SY14 @ sK2_SY147 @ mactual ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(26,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual )
=> ~ ( in @ sK1_SY14 @ sK2_SY147 @ mactual ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[25]) ).
thf(27,plain,
( ( ~ ( in @ sK1_SY14 @ sK2_SY147 @ mactual )
=> ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[25]) ).
thf(28,plain,
( ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual )
=> ~ ( in @ sK1_SY14 @ sK2_SY147 @ mactual ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(29,plain,
( ( ~ ( ~ ( in @ sK1_SY14 @ sK2_SY147 @ mactual )
=> ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(30,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual )
& ( in @ sK1_SY14 @ sK2_SY147 @ mactual ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(31,plain,
( ( ~ ( in @ sK1_SY14 @ sK2_SY147 @ mactual )
& ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(32,plain,
( ( ! [SY32: $i,SY33: $i] :
( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY32 ) @ SY33 ) @ ( singleton @ SY32 ) @ mactual )
| ~ ( in @ SY32 @ SY33 @ mactual ) )
& ! [SY32: $i,SY33: $i] :
( ( in @ SY32 @ SY33 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY32 ) @ SY33 ) @ ( singleton @ SY32 ) @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(33,plain,
( ( ! [SY50: $i,SY51: $i] :
( ~ ( in @ SY50 @ SY51 @ mactual )
| ~ ( in @ SY51 @ SY50 @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(34,plain,
( ( ! [SY67: $i,SY68: $i] :
( ~ ( qmltpeq @ SY67 @ SY68 @ mactual )
| ( qmltpeq @ ( singleton @ SY67 ) @ ( singleton @ SY68 ) @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(35,plain,
( ( ! [SY92: $i,SY93: $i] :
( ~ ( qmltpeq @ SY92 @ SY93 @ mactual )
| ! [SY94: $i] : ( qmltpeq @ ( set_difference @ SY94 @ SY92 ) @ ( set_difference @ SY94 @ SY93 ) @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(36,plain,
( ( ! [SY119: $i,SY120: $i] :
( ~ ( qmltpeq @ SY119 @ SY120 @ mactual )
| ! [SY121: $i] : ( qmltpeq @ ( set_difference @ SY119 @ SY121 ) @ ( set_difference @ SY120 @ SY121 ) @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(37,plain,
( ( ! [SY138: $i,SY139: $i] :
( ~ ( qmltpeq @ SY138 @ SY139 @ mactual )
| ( qmltpeq @ SY139 @ SY138 @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(38,plain,
( ( ! [SY145: $i] : ( qmltpeq @ SY145 @ SY145 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(39,plain,
( ( ! [SY138: $i,SY139: $i] :
( ~ ( qmltpeq @ SY138 @ SY139 @ mactual )
| ( qmltpeq @ SY139 @ SY138 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(40,plain,
( ( ! [SY119: $i,SY120: $i] :
( ~ ( qmltpeq @ SY119 @ SY120 @ mactual )
| ! [SY121: $i] : ( qmltpeq @ ( set_difference @ SY119 @ SY121 ) @ ( set_difference @ SY120 @ SY121 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(41,plain,
( ( ! [SY92: $i,SY93: $i] :
( ~ ( qmltpeq @ SY92 @ SY93 @ mactual )
| ! [SY94: $i] : ( qmltpeq @ ( set_difference @ SY94 @ SY92 ) @ ( set_difference @ SY94 @ SY93 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(42,plain,
( ( ! [SY67: $i,SY68: $i] :
( ~ ( qmltpeq @ SY67 @ SY68 @ mactual )
| ( qmltpeq @ ( singleton @ SY67 ) @ ( singleton @ SY68 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(43,plain,
( ( ! [SY50: $i,SY51: $i] :
( ~ ( in @ SY50 @ SY51 @ mactual )
| ~ ( in @ SY51 @ SY50 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(44,plain,
( ( ! [SY32: $i,SY33: $i] :
( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY32 ) @ SY33 ) @ ( singleton @ SY32 ) @ mactual )
| ~ ( in @ SY32 @ SY33 @ mactual ) )
& ! [SY32: $i,SY33: $i] :
( ( in @ SY32 @ SY33 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY32 ) @ SY33 ) @ ( singleton @ SY32 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(45,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual )
& ( in @ sK1_SY14 @ sK2_SY147 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(46,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual )
| ~ ( in @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(47,plain,
( ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual )
| ~ ( in @ sK1_SY14 @ sK2_SY147 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(48,plain,
! [SV1: $i] :
( ( qmltpeq @ SV1 @ SV1 @ mactual )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(49,plain,
! [SV2: $i] :
( ( ! [SY148: $i] :
( ~ ( qmltpeq @ SV2 @ SY148 @ mactual )
| ( qmltpeq @ SY148 @ SV2 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(50,plain,
! [SV3: $i] :
( ( ! [SY149: $i] :
( ~ ( qmltpeq @ SV3 @ SY149 @ mactual )
| ! [SY150: $i] : ( qmltpeq @ ( set_difference @ SV3 @ SY150 ) @ ( set_difference @ SY149 @ SY150 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(51,plain,
! [SV4: $i] :
( ( ! [SY151: $i] :
( ~ ( qmltpeq @ SV4 @ SY151 @ mactual )
| ! [SY152: $i] : ( qmltpeq @ ( set_difference @ SY152 @ SV4 ) @ ( set_difference @ SY152 @ SY151 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(52,plain,
! [SV5: $i] :
( ( ! [SY153: $i] :
( ~ ( qmltpeq @ SV5 @ SY153 @ mactual )
| ( qmltpeq @ ( singleton @ SV5 ) @ ( singleton @ SY153 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(53,plain,
! [SV6: $i] :
( ( ! [SY154: $i] :
( ~ ( in @ SV6 @ SY154 @ mactual )
| ~ ( in @ SY154 @ SV6 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(54,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual )
| ~ ( in @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(55,plain,
( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual )
| ~ ( in @ sK1_SY14 @ sK2_SY147 @ mactual ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(56,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( qmltpeq @ SV2 @ SV7 @ mactual )
| ( qmltpeq @ SV7 @ SV2 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(57,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ( qmltpeq @ SV3 @ SV8 @ mactual )
| ! [SY155: $i] : ( qmltpeq @ ( set_difference @ SV3 @ SY155 ) @ ( set_difference @ SV8 @ SY155 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(58,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( qmltpeq @ SV4 @ SV9 @ mactual )
| ! [SY156: $i] : ( qmltpeq @ ( set_difference @ SY156 @ SV4 ) @ ( set_difference @ SY156 @ SV9 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(59,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( qmltpeq @ SV5 @ SV10 @ mactual )
| ( qmltpeq @ ( singleton @ SV5 ) @ ( singleton @ SV10 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(60,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ SV11 @ mactual )
| ~ ( in @ SV11 @ SV6 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(61,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual )
| ~ ( in @ SX0 @ SX1 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(62,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(63,plain,
( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(64,plain,
( ( ~ ( in @ sK1_SY14 @ sK2_SY147 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(65,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( qmltpeq @ SV2 @ SV7 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV7 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(66,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ( qmltpeq @ SV3 @ SV8 @ mactual ) )
= $true )
| ( ( ! [SY155: $i] : ( qmltpeq @ ( set_difference @ SV3 @ SY155 ) @ ( set_difference @ SV8 @ SY155 ) @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( qmltpeq @ SV4 @ SV9 @ mactual ) )
= $true )
| ( ( ! [SY156: $i] : ( qmltpeq @ ( set_difference @ SY156 @ SV4 ) @ ( set_difference @ SY156 @ SV9 ) @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(68,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( qmltpeq @ SV5 @ SV10 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( singleton @ SV5 ) @ ( singleton @ SV10 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(69,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV11 @ mactual ) )
= $true )
| ( ( ~ ( in @ SV11 @ SV6 @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(70,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual )
| ~ ( in @ SX0 @ SX1 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(72,plain,
( ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(73,plain,
( ( in @ sK1_SY14 @ sK2_SY147 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(74,plain,
! [SV7: $i,SV2: $i] :
( ( ( qmltpeq @ SV2 @ SV7 @ mactual )
= $false )
| ( ( qmltpeq @ SV7 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(75,plain,
! [SV8: $i,SV3: $i] :
( ( ( qmltpeq @ SV3 @ SV8 @ mactual )
= $false )
| ( ( ! [SY155: $i] : ( qmltpeq @ ( set_difference @ SV3 @ SY155 ) @ ( set_difference @ SV8 @ SY155 ) @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(76,plain,
! [SV9: $i,SV4: $i] :
( ( ( qmltpeq @ SV4 @ SV9 @ mactual )
= $false )
| ( ( ! [SY156: $i] : ( qmltpeq @ ( set_difference @ SY156 @ SV4 ) @ ( set_difference @ SY156 @ SV9 ) @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(77,plain,
! [SV10: $i,SV5: $i] :
( ( ( qmltpeq @ SV5 @ SV10 @ mactual )
= $false )
| ( ( qmltpeq @ ( singleton @ SV5 ) @ ( singleton @ SV10 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(78,plain,
! [SV11: $i,SV6: $i] :
( ( ( in @ SV6 @ SV11 @ mactual )
= $false )
| ( ( ~ ( in @ SV11 @ SV6 @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV12: $i] :
( ( ! [SY157: $i] :
( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV12 ) @ SY157 ) @ ( singleton @ SV12 ) @ mactual )
| ~ ( in @ SV12 @ SY157 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV13: $i] :
( ( ! [SY158: $i] :
( ( in @ SV13 @ SY158 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV13 ) @ SY158 ) @ ( singleton @ SV13 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV8: $i,SV14: $i,SV3: $i] :
( ( ( qmltpeq @ ( set_difference @ SV3 @ SV14 ) @ ( set_difference @ SV8 @ SV14 ) @ mactual )
= $true )
| ( ( qmltpeq @ SV3 @ SV8 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(82,plain,
! [SV9: $i,SV4: $i,SV15: $i] :
( ( ( qmltpeq @ ( set_difference @ SV15 @ SV4 ) @ ( set_difference @ SV15 @ SV9 ) @ mactual )
= $true )
| ( ( qmltpeq @ SV4 @ SV9 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(83,plain,
! [SV6: $i,SV11: $i] :
( ( ( in @ SV11 @ SV6 @ mactual )
= $false )
| ( ( in @ SV6 @ SV11 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(84,plain,
! [SV16: $i,SV12: $i] :
( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV12 ) @ SV16 ) @ ( singleton @ SV12 ) @ mactual )
| ~ ( in @ SV12 @ SV16 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(85,plain,
! [SV17: $i,SV13: $i] :
( ( ( in @ SV13 @ SV17 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV13 ) @ SV17 ) @ ( singleton @ SV13 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(86,plain,
! [SV16: $i,SV12: $i] :
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV12 ) @ SV16 ) @ ( singleton @ SV12 ) @ mactual ) )
= $true )
| ( ( ~ ( in @ SV12 @ SV16 @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(87,plain,
! [SV17: $i,SV13: $i] :
( ( ( in @ SV13 @ SV17 @ mactual )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV13 ) @ SV17 ) @ ( singleton @ SV13 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(88,plain,
! [SV16: $i,SV12: $i] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ SV12 ) @ SV16 ) @ ( singleton @ SV12 ) @ mactual )
= $false )
| ( ( ~ ( in @ SV12 @ SV16 @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(89,plain,
! [SV16: $i,SV12: $i] :
( ( ( in @ SV12 @ SV16 @ mactual )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV12 ) @ SV16 ) @ ( singleton @ SV12 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(90,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[48,89,87,83,82,81,77,74,73,72]) ).
thf(91,plain,
( ( ! [SY145: $i] : ( qmltpeq @ SY145 @ SY145 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(92,plain,
( ( ! [SY138: $i,SY139: $i] :
( ~ ( qmltpeq @ SY138 @ SY139 @ mactual )
| ( qmltpeq @ SY139 @ SY138 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(93,plain,
( ( ! [SY119: $i,SY120: $i] :
( ~ ( qmltpeq @ SY119 @ SY120 @ mactual )
| ! [SY121: $i] : ( qmltpeq @ ( set_difference @ SY119 @ SY121 ) @ ( set_difference @ SY120 @ SY121 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(94,plain,
( ( ! [SY92: $i,SY93: $i] :
( ~ ( qmltpeq @ SY92 @ SY93 @ mactual )
| ! [SY94: $i] : ( qmltpeq @ ( set_difference @ SY94 @ SY92 ) @ ( set_difference @ SY94 @ SY93 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(95,plain,
( ( ! [SY67: $i,SY68: $i] :
( ~ ( qmltpeq @ SY67 @ SY68 @ mactual )
| ( qmltpeq @ ( singleton @ SY67 ) @ ( singleton @ SY68 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(96,plain,
( ( ! [SY50: $i,SY51: $i] :
( ~ ( in @ SY50 @ SY51 @ mactual )
| ~ ( in @ SY51 @ SY50 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(97,plain,
( ( ! [SY32: $i,SY33: $i] :
( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY32 ) @ SY33 ) @ ( singleton @ SY32 ) @ mactual )
| ~ ( in @ SY32 @ SY33 @ mactual ) )
& ! [SY32: $i,SY33: $i] :
( ( in @ SY32 @ SY33 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY32 ) @ SY33 ) @ ( singleton @ SY32 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(98,plain,
( ( ~ ( in @ sK1_SY14 @ sK2_SY147 @ mactual )
& ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(99,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual )
| ~ ( in @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(100,plain,
( ( ~ ( ~ ~ ( in @ sK1_SY14 @ sK2_SY147 @ mactual )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(101,plain,
! [SV18: $i] :
( ( qmltpeq @ SV18 @ SV18 @ mactual )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(102,plain,
! [SV19: $i] :
( ( ! [SY159: $i] :
( ~ ( qmltpeq @ SV19 @ SY159 @ mactual )
| ( qmltpeq @ SY159 @ SV19 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(103,plain,
! [SV20: $i] :
( ( ! [SY160: $i] :
( ~ ( qmltpeq @ SV20 @ SY160 @ mactual )
| ! [SY161: $i] : ( qmltpeq @ ( set_difference @ SV20 @ SY161 ) @ ( set_difference @ SY160 @ SY161 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(104,plain,
! [SV21: $i] :
( ( ! [SY162: $i] :
( ~ ( qmltpeq @ SV21 @ SY162 @ mactual )
| ! [SY163: $i] : ( qmltpeq @ ( set_difference @ SY163 @ SV21 ) @ ( set_difference @ SY163 @ SY162 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(105,plain,
! [SV22: $i] :
( ( ! [SY164: $i] :
( ~ ( qmltpeq @ SV22 @ SY164 @ mactual )
| ( qmltpeq @ ( singleton @ SV22 ) @ ( singleton @ SY164 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(106,plain,
! [SV23: $i] :
( ( ! [SY165: $i] :
( ~ ( in @ SV23 @ SY165 @ mactual )
| ~ ( in @ SY165 @ SV23 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(107,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual )
| ~ ( in @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(108,plain,
( ( ~ ~ ( in @ sK1_SY14 @ sK2_SY147 @ mactual )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(109,plain,
! [SV24: $i,SV19: $i] :
( ( ~ ( qmltpeq @ SV19 @ SV24 @ mactual )
| ( qmltpeq @ SV24 @ SV19 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(110,plain,
! [SV25: $i,SV20: $i] :
( ( ~ ( qmltpeq @ SV20 @ SV25 @ mactual )
| ! [SY166: $i] : ( qmltpeq @ ( set_difference @ SV20 @ SY166 ) @ ( set_difference @ SV25 @ SY166 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(111,plain,
! [SV26: $i,SV21: $i] :
( ( ~ ( qmltpeq @ SV21 @ SV26 @ mactual )
| ! [SY167: $i] : ( qmltpeq @ ( set_difference @ SY167 @ SV21 ) @ ( set_difference @ SY167 @ SV26 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(112,plain,
! [SV27: $i,SV22: $i] :
( ( ~ ( qmltpeq @ SV22 @ SV27 @ mactual )
| ( qmltpeq @ ( singleton @ SV22 ) @ ( singleton @ SV27 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(113,plain,
! [SV28: $i,SV23: $i] :
( ( ~ ( in @ SV23 @ SV28 @ mactual )
| ~ ( in @ SV28 @ SV23 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(114,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual )
| ~ ( in @ SX0 @ SX1 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(115,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(116,plain,
( ( ~ ~ ( in @ sK1_SY14 @ sK2_SY147 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(117,plain,
( ( ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(118,plain,
! [SV24: $i,SV19: $i] :
( ( ( ~ ( qmltpeq @ SV19 @ SV24 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV24 @ SV19 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(119,plain,
! [SV25: $i,SV20: $i] :
( ( ( ~ ( qmltpeq @ SV20 @ SV25 @ mactual ) )
= $true )
| ( ( ! [SY166: $i] : ( qmltpeq @ ( set_difference @ SV20 @ SY166 ) @ ( set_difference @ SV25 @ SY166 ) @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(120,plain,
! [SV26: $i,SV21: $i] :
( ( ( ~ ( qmltpeq @ SV21 @ SV26 @ mactual ) )
= $true )
| ( ( ! [SY167: $i] : ( qmltpeq @ ( set_difference @ SY167 @ SV21 ) @ ( set_difference @ SY167 @ SV26 ) @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(121,plain,
! [SV27: $i,SV22: $i] :
( ( ( ~ ( qmltpeq @ SV22 @ SV27 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( singleton @ SV22 ) @ ( singleton @ SV27 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(122,plain,
! [SV28: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV28 @ mactual ) )
= $true )
| ( ( ~ ( in @ SV28 @ SV23 @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(123,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual )
| ~ ( in @ SX0 @ SX1 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(125,plain,
( ( ~ ( in @ sK1_SY14 @ sK2_SY147 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(126,plain,
( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(127,plain,
! [SV24: $i,SV19: $i] :
( ( ( qmltpeq @ SV19 @ SV24 @ mactual )
= $false )
| ( ( qmltpeq @ SV24 @ SV19 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(128,plain,
! [SV25: $i,SV20: $i] :
( ( ( qmltpeq @ SV20 @ SV25 @ mactual )
= $false )
| ( ( ! [SY166: $i] : ( qmltpeq @ ( set_difference @ SV20 @ SY166 ) @ ( set_difference @ SV25 @ SY166 ) @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(129,plain,
! [SV26: $i,SV21: $i] :
( ( ( qmltpeq @ SV21 @ SV26 @ mactual )
= $false )
| ( ( ! [SY167: $i] : ( qmltpeq @ ( set_difference @ SY167 @ SV21 ) @ ( set_difference @ SY167 @ SV26 ) @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(130,plain,
! [SV27: $i,SV22: $i] :
( ( ( qmltpeq @ SV22 @ SV27 @ mactual )
= $false )
| ( ( qmltpeq @ ( singleton @ SV22 ) @ ( singleton @ SV27 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(131,plain,
! [SV28: $i,SV23: $i] :
( ( ( in @ SV23 @ SV28 @ mactual )
= $false )
| ( ( ~ ( in @ SV28 @ SV23 @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(132,plain,
! [SV29: $i] :
( ( ! [SY168: $i] :
( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SY168 ) @ ( singleton @ SV29 ) @ mactual )
| ~ ( in @ SV29 @ SY168 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(133,plain,
! [SV30: $i] :
( ( ! [SY169: $i] :
( ( in @ SV30 @ SY169 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV30 ) @ SY169 ) @ ( singleton @ SV30 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(134,plain,
( ( in @ sK1_SY14 @ sK2_SY147 @ mactual )
= $false ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(135,plain,
( ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY14 ) @ sK2_SY147 ) @ ( singleton @ sK1_SY14 ) @ mactual )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(136,plain,
! [SV25: $i,SV31: $i,SV20: $i] :
( ( ( qmltpeq @ ( set_difference @ SV20 @ SV31 ) @ ( set_difference @ SV25 @ SV31 ) @ mactual )
= $true )
| ( ( qmltpeq @ SV20 @ SV25 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(137,plain,
! [SV26: $i,SV21: $i,SV32: $i] :
( ( ( qmltpeq @ ( set_difference @ SV32 @ SV21 ) @ ( set_difference @ SV32 @ SV26 ) @ mactual )
= $true )
| ( ( qmltpeq @ SV21 @ SV26 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(138,plain,
! [SV23: $i,SV28: $i] :
( ( ( in @ SV28 @ SV23 @ mactual )
= $false )
| ( ( in @ SV23 @ SV28 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(139,plain,
! [SV33: $i,SV29: $i] :
( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV33 ) @ ( singleton @ SV29 ) @ mactual )
| ~ ( in @ SV29 @ SV33 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(140,plain,
! [SV34: $i,SV30: $i] :
( ( ( in @ SV30 @ SV34 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV30 ) @ SV34 ) @ ( singleton @ SV30 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(141,plain,
! [SV33: $i,SV29: $i] :
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV33 ) @ ( singleton @ SV29 ) @ mactual ) )
= $true )
| ( ( ~ ( in @ SV29 @ SV33 @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(142,plain,
! [SV34: $i,SV30: $i] :
( ( ( in @ SV30 @ SV34 @ mactual )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV30 ) @ SV34 ) @ ( singleton @ SV30 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(143,plain,
! [SV33: $i,SV29: $i] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV33 ) @ ( singleton @ SV29 ) @ mactual )
= $false )
| ( ( ~ ( in @ SV29 @ SV33 @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(144,plain,
! [SV33: $i,SV29: $i] :
( ( ( in @ SV29 @ SV33 @ mactual )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV33 ) @ ( singleton @ SV29 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(145,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[101,144,142,138,137,136,135,134,130,127]) ).
thf(146,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[145,90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET924^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n010.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 14:56:25 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.29
% 0.07/0.29 No.of.Axioms: 13
% 0.07/0.29
% 0.07/0.29 Length.of.Defs: 1624
% 0.07/0.29
% 0.07/0.29 Contains.Choice.Funs: false
% 0.07/0.29 .....
% 0.07/0.29
% 0.07/0.29 ********************************
% 0.07/0.29 * All subproblems solved! *
% 0.07/0.29 ********************************
% 0.07/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,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:145,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.07/0.29
% 0.07/0.29 %**** Beginning of derivation protocol ****
% 0.07/0.29 % SZS output start CNFRefutation
% See solution above
% 0.07/0.30
% 0.07/0.30 %**** End of derivation protocol ****
% 0.07/0.30 %**** no. of clauses in derivation: 140 ****
% 0.07/0.30 %**** clause counter: 145 ****
% 0.07/0.30
% 0.07/0.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,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:145,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------