TSTP Solution File: SYO359^5 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO359^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 17:33:33 EDT 2022
% Result : Theorem 0.22s 0.46s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 17
% Syntax : Number of formulae : 143 ( 28 unt; 16 typ; 0 def)
% Number of atoms : 1263 ( 391 equ; 0 cnn)
% Maximal formula atoms : 7 ( 9 avg)
% Number of connectives : 908 ( 150 ~; 324 |; 6 &; 404 @)
% ( 8 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 110 ( 0 ^ 110 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_b,type,
b: $tType ).
thf(tp_gtype,type,
gtype: $tType ).
thf(tp_f,type,
f: b > $o ).
thf(tp_g,type,
g: b > $o ).
thf(tp_h,type,
h: ( b > $o ) > gtype ).
thf(tp_sK10_E,type,
sK10_E: b > b ).
thf(tp_sK11_E,type,
sK11_E: b > b ).
thf(tp_sK1_Xx,type,
sK1_Xx: b ).
thf(tp_sK2_REN,type,
sK2_REN: $o ).
thf(tp_sK3_SV14,type,
sK3_SV14: b ).
thf(tp_sK4_E,type,
sK4_E: b ).
thf(tp_sK5_E,type,
sK5_E: b ).
thf(tp_sK6_SV18,type,
sK6_SV18: b > b ).
thf(tp_sK7_SV19,type,
sK7_SV19: b > b ).
thf(tp_sK8_SV20,type,
sK8_SV20: b > b ).
thf(tp_sK9_SV21,type,
sK9_SV21: b > b ).
thf(1,conjecture,
( ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ! [Xq: ( b > $o ) > $o] :
( ( Xq @ f )
=> ( Xq @ g ) ) )
=> ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ( ( h @ f )
= ( h @ g ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXT1) ).
thf(2,negated_conjecture,
( ( ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ! [Xq: ( b > $o ) > $o] :
( ( Xq @ f )
=> ( Xq @ g ) ) )
=> ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ( ( h @ f )
= ( h @ g ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ! [Xq: ( b > $o ) > $o] :
( ( Xq @ f )
=> ( Xq @ g ) ) )
=> ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ( ( h @ f )
= ( h @ g ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ! [Xq: ( b > $o ) > $o] :
( ( Xq @ f )
=> ( Xq @ g ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ( h @ f )
= ( h @ g ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ( ( h @ f )
!= ( h @ g ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( sK2_REN
| ! [Xq: ( b > $o ) > $o] :
( ~ ( Xq @ f )
| ( Xq @ g ) ) )
& ( sK2_REN
=> ( ( ~ ( f @ sK1_Xx )
| ~ ( g @ sK1_Xx ) )
& ( ( f @ sK1_Xx )
| ( g @ sK1_Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [Xx: b] :
( ~ ( f @ Xx )
| ( g @ Xx ) )
& ! [Xx: b] :
( ~ ( g @ Xx )
| ( f @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(10,plain,
( ( ! [Xx: b] :
( ~ ( f @ Xx )
| ( g @ Xx ) )
& ! [Xx: b] :
( ~ ( g @ Xx )
| ( f @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( ( sK2_REN
| ! [Xq: ( b > $o ) > $o] :
( ~ ( Xq @ f )
| ( Xq @ g ) ) )
& ( sK2_REN
=> ( ( ~ ( f @ sK1_Xx )
| ~ ( g @ sK1_Xx ) )
& ( ( f @ sK1_Xx )
| ( g @ sK1_Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ( ( h @ f )
!= ( h @ g ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( ~ ( ~ ( sK2_REN
| ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
| ~ ( ~ sK2_REN
| ~ ( ~ ( ~ ( f @ sK1_Xx )
| ~ ( g @ sK1_Xx ) )
| ~ ( ( f @ sK1_Xx )
| ( g @ sK1_Xx ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ( ~ ! [SX0: b] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ~ ! [SX0: b] :
( ~ ( g @ SX0 )
| ( f @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(15,plain,
( ( ( h @ f )
= ( h @ g ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ~ ( sK2_REN
| ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
| ~ ( ~ sK2_REN
| ~ ( ~ ( ~ ( f @ sK1_Xx )
| ~ ( g @ sK1_Xx ) )
| ~ ( ( f @ sK1_Xx )
| ( g @ sK1_Xx ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ! [SX0: b] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ~ ! [SX0: b] :
( ~ ( g @ SX0 )
| ( f @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ( sK2_REN
| ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( ~ sK2_REN
| ~ ( ~ ( ~ ( f @ sK1_Xx )
| ~ ( g @ sK1_Xx ) )
| ~ ( ( f @ sK1_Xx )
| ( g @ sK1_Xx ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ! [SX0: b] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ! [SX0: b] :
( ~ ( g @ SX0 )
| ( f @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
( ( sK2_REN
| ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(23,plain,
( ( ~ sK2_REN
| ~ ( ~ ( ~ ( f @ sK1_Xx )
| ~ ( g @ sK1_Xx ) )
| ~ ( ( f @ sK1_Xx )
| ( g @ sK1_Xx ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( ! [SX0: b] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ! [SX0: b] :
( ~ ( g @ SX0 )
| ( f @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( sK2_REN = $true )
| ( ( ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( ( ~ sK2_REN )
= $true )
| ( ( ~ ( ~ ( ~ ( f @ sK1_Xx )
| ~ ( g @ sK1_Xx ) )
| ~ ( ( f @ sK1_Xx )
| ( g @ sK1_Xx ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV1: b] :
( ( ~ ( f @ SV1 )
| ( g @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV2: b] :
( ( ~ ( g @ SV2 )
| ( f @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV3: ( b > $o ) > $o] :
( ( ( ~ ( SV3 @ f )
| ( SV3 @ g ) )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
( ( sK2_REN = $false )
| ( ( ~ ( ~ ( ~ ( f @ sK1_Xx )
| ~ ( g @ sK1_Xx ) )
| ~ ( ( f @ sK1_Xx )
| ( g @ sK1_Xx ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV1: b] :
( ( ( ~ ( f @ SV1 ) )
= $true )
| ( ( g @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV2: b] :
( ( ( ~ ( g @ SV2 ) )
= $true )
| ( ( f @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV3: ( b > $o ) > $o] :
( ( ( ~ ( SV3 @ f ) )
= $true )
| ( ( SV3 @ g )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(35,plain,
( ( ( ~ ( ~ ( f @ sK1_Xx )
| ~ ( g @ sK1_Xx ) )
| ~ ( ( f @ sK1_Xx )
| ( g @ sK1_Xx ) ) )
= $false )
| ( sK2_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV1: b] :
( ( ( f @ SV1 )
= $false )
| ( ( g @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV2: b] :
( ( ( g @ SV2 )
= $false )
| ( ( f @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV3: ( b > $o ) > $o] :
( ( ( SV3 @ f )
= $false )
| ( ( SV3 @ g )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(39,plain,
( ( ( ~ ( ~ ( f @ sK1_Xx )
| ~ ( g @ sK1_Xx ) ) )
= $false )
| ( sK2_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
( ( ( ~ ( ( f @ sK1_Xx )
| ( g @ sK1_Xx ) ) )
= $false )
| ( sK2_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(41,plain,
( ( ( ~ ( f @ sK1_Xx )
| ~ ( g @ sK1_Xx ) )
= $true )
| ( sK2_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(42,plain,
( ( ( ( f @ sK1_Xx )
| ( g @ sK1_Xx ) )
= $true )
| ( sK2_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(43,plain,
( ( ( ~ ( f @ sK1_Xx ) )
= $true )
| ( ( ~ ( g @ sK1_Xx ) )
= $true )
| ( sK2_REN = $false ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(44,plain,
( ( ( f @ sK1_Xx )
= $true )
| ( ( g @ sK1_Xx )
= $true )
| ( sK2_REN = $false ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(45,plain,
( ( ( f @ sK1_Xx )
= $false )
| ( ( ~ ( g @ sK1_Xx ) )
= $true )
| ( sK2_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
( ( ( g @ sK1_Xx )
= $false )
| ( ( f @ sK1_Xx )
= $false )
| ( sK2_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(47,plain,
( ( ( f = f )
= $false )
| ( ( g = f )
= $true )
| ( sK2_REN = $true ) ),
inference(replace_leibnizEQ,[status(thm)],[38:[bind(SV3,$thf( ^ [SV4: b > $o] : ( SV4 = f ) ))]]) ).
thf(48,plain,
( ( ( g = f )
= $true )
| ( sK2_REN = $true ) ),
inference(sim,[status(thm)],[47]) ).
thf(51,plain,
! [SV6: ( b > $o ) > $o] :
( ( ( ~ ( SV6 @ f ) )
= $false )
| ( ( ~ ( SV6 @ g ) )
= $true )
| ( sK2_REN = $true ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV3,$thf( ^ [SV5: b > $o] : ~ ( SV6 @ SV5 ) ))]]) ).
thf(53,plain,
( ( ( f = f )
= $false )
| ( ( g = f )
= $true )
| ( sK2_REN = $true ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV3,$thf( ^ [SV10: b > $o] : ( SV10 = f ) ))]]) ).
thf(54,plain,
( ( sK2_REN = $true )
| ( ( ( g = f )
= sK2_REN )
= $false ) ),
inference(fac_restr,[status(thm)],[48]) ).
thf(55,plain,
! [SV11: b] :
( ( sK2_REN = $true )
| ( ( ( g @ SV11 )
= ( f @ SV11 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[48]) ).
thf(56,plain,
! [SV11: b] :
( ( ( g @ SV11 )
= $true )
| ( ( f @ SV11 )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[55]) ).
thf(57,plain,
! [SV11: b] :
( ( ( g @ SV11 )
= $false )
| ( ( f @ SV11 )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[55]) ).
thf(58,plain,
( ( ( ~ ( ( g = f )
| sK2_REN )
| ~ ( ( g != f )
| ~ sK2_REN ) )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[54]) ).
thf(60,plain,
( ( ( ~ ( ( g = f )
| sK2_REN ) )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(62,plain,
( ( ( ( g = f )
| sK2_REN )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(64,plain,
( ( ( g = f )
= $true )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(66,plain,
( ( ( ! [SV12: b] :
( ( g @ SV12 )
= ( f @ SV12 ) ) )
= $true )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[64]) ).
thf(67,plain,
( ( ( g = f )
= $true )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV13: b] :
( ( ( ( g @ SV13 )
= ( f @ SV13 ) )
= $true )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV13: b] :
( ( ( ~ ( ( g @ SV13 )
| ( f @ SV13 ) )
| ~ ( ~ ( g @ SV13 )
| ~ ( f @ SV13 ) ) )
= $true )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[69]) ).
thf(73,plain,
! [SV13: b] :
( ( ( ( g @ SV13 )
= ( f @ SV13 ) )
= $true )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV13: b] :
( ( ( ~ ( ( g @ SV13 )
| ( f @ SV13 ) ) )
= $true )
| ( ( ~ ( ~ ( g @ SV13 )
| ~ ( f @ SV13 ) ) )
= $true )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV13: b] :
( ( ( ( g @ SV13 )
| ( f @ SV13 ) )
= $false )
| ( ( ~ ( ~ ( g @ SV13 )
| ~ ( f @ SV13 ) ) )
= $true )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(83,plain,
! [SV13: b] :
( ( ( g @ SV13 )
= $false )
| ( ( ~ ( ~ ( g @ SV13 )
| ~ ( f @ SV13 ) ) )
= $true )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(84,plain,
! [SV13: b] :
( ( ( f @ SV13 )
= $false )
| ( ( ~ ( ~ ( g @ SV13 )
| ~ ( f @ SV13 ) ) )
= $true )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(87,plain,
! [SV13: b] :
( ( ( ~ ( g @ SV13 )
| ~ ( f @ SV13 ) )
= $false )
| ( ( g @ SV13 )
= $false )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV13: b] :
( ( ( ~ ( g @ SV13 )
| ~ ( f @ SV13 ) )
= $false )
| ( ( f @ SV13 )
= $false )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(92,plain,
! [SV13: b] :
( ( ( ~ ( f @ SV13 ) )
= $false )
| ( ( g @ SV13 )
= $false )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(93,plain,
! [SV13: b] :
( ( ( ~ ( g @ SV13 ) )
= $false )
| ( ( f @ SV13 )
= $false )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(98,plain,
! [SV13: b] :
( ( ( f @ SV13 )
= $true )
| ( ( g @ SV13 )
= $false )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(99,plain,
! [SV13: b] :
( ( ( g @ SV13 )
= $true )
| ( ( f @ SV13 )
= $false )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(103,plain,
! [SV15: b] :
( ( sK2_REN = $true )
| ( sK2_REN = $true )
| ( ( ( g @ SV15 )
= ( f @ SV15 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[67]) ).
thf(104,plain,
! [SV13: b] :
( ( sK2_REN = $true )
| ( sK2_REN = $true )
| ( ( g @ SV13 )
= $true )
| ( ( f @ SV13 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[73]) ).
thf(105,plain,
! [SV13: b] :
( ( sK2_REN = $true )
| ( sK2_REN = $true )
| ( ( g @ SV13 )
= $false )
| ( ( f @ SV13 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[73]) ).
thf(106,plain,
! [SV15: b] :
( ( ( g @ SV15 )
= $true )
| ( ( f @ SV15 )
= $false )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[103]) ).
thf(107,plain,
! [SV15: b] :
( ( ( g @ SV15 )
= $false )
| ( ( f @ SV15 )
= $true )
| ( sK2_REN = $true )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[103]) ).
thf(110,plain,
( ( ( f @ sK5_E )
= $true )
| ( ( g @ sK5_E )
= $true ) ),
inference(extuni,[status(esa)],[15]) ).
thf(111,plain,
( ( ( f @ sK5_E )
= $false )
| ( ( g @ sK5_E )
= $false ) ),
inference(extuni,[status(esa)],[15]) ).
thf(113,plain,
! [SV17: b] :
( ( sK2_REN = $true )
| ( ( ( g @ SV17 )
= ( f @ SV17 ) )
= $true )
| ( ( f = f )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[53]) ).
thf(116,plain,
! [SV17: b] :
( ( ( f = f )
= $false )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[113]) ).
thf(117,plain,
! [SV17: b] :
( ( ( f = f )
= $false )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[113]) ).
thf(118,plain,
! [SV6: ( b > $o ) > $o] :
( ( ( SV6 @ f )
= $true )
| ( ( ~ ( SV6 @ g ) )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(123,plain,
! [SV17: b] :
( ( ( ! [SV20: b] :
( ( f @ SV20 )
= ( f @ SV20 ) ) )
= $false )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[117]) ).
thf(124,plain,
! [SV17: b] :
( ( ( f = f )
= $false )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[117]) ).
thf(125,plain,
! [SV17: b] :
( ( ( ! [SV21: b] :
( ( f @ SV21 )
= ( f @ SV21 ) ) )
= $false )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[116]) ).
thf(126,plain,
! [SV17: b] :
( ( ( f = f )
= $false )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[116]) ).
thf(127,plain,
! [SV6: ( b > $o ) > $o] :
( ( ( SV6 @ g )
= $false )
| ( ( SV6 @ f )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(130,plain,
! [SV17: b] :
( ( ( ( f @ ( sK8_SV20 @ SV17 ) )
= ( f @ ( sK8_SV20 @ SV17 ) ) )
= $false )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_forall_neg,[status(esa)],[123]) ).
thf(131,plain,
! [SV17: b] :
( ( ( ( f @ ( sK9_SV21 @ SV17 ) )
= ( f @ ( sK9_SV21 @ SV17 ) ) )
= $false )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_forall_neg,[status(esa)],[125]) ).
thf(136,plain,
! [SV17: b] :
( ( ( ~ ( ( f @ ( sK8_SV20 @ SV17 ) )
| ( f @ ( sK8_SV20 @ SV17 ) ) )
| ~ ( ~ ( f @ ( sK8_SV20 @ SV17 ) )
| ~ ( f @ ( sK8_SV20 @ SV17 ) ) ) )
= $false )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[130]) ).
thf(137,plain,
! [SV17: b] :
( ( ( ( f @ ( sK8_SV20 @ SV17 ) )
= ( f @ ( sK8_SV20 @ SV17 ) ) )
= $false )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[130]) ).
thf(138,plain,
! [SV17: b] :
( ( ( ~ ( ( f @ ( sK9_SV21 @ SV17 ) )
| ( f @ ( sK9_SV21 @ SV17 ) ) )
| ~ ( ~ ( f @ ( sK9_SV21 @ SV17 ) )
| ~ ( f @ ( sK9_SV21 @ SV17 ) ) ) )
= $false )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[131]) ).
thf(139,plain,
! [SV17: b] :
( ( ( ( f @ ( sK9_SV21 @ SV17 ) )
= ( f @ ( sK9_SV21 @ SV17 ) ) )
= $false )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[131]) ).
thf(144,plain,
! [SV17: b] :
( ( ( ~ ( ( f @ ( sK8_SV20 @ SV17 ) )
| ( f @ ( sK8_SV20 @ SV17 ) ) ) )
= $false )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(145,plain,
! [SV17: b] :
( ( ( ~ ( ~ ( f @ ( sK8_SV20 @ SV17 ) )
| ~ ( f @ ( sK8_SV20 @ SV17 ) ) ) )
= $false )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(146,plain,
! [SV17: b] :
( ( ( ~ ( ( f @ ( sK9_SV21 @ SV17 ) )
| ( f @ ( sK9_SV21 @ SV17 ) ) ) )
= $false )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(147,plain,
! [SV17: b] :
( ( ( ~ ( ~ ( f @ ( sK9_SV21 @ SV17 ) )
| ~ ( f @ ( sK9_SV21 @ SV17 ) ) ) )
= $false )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(152,plain,
! [SV17: b] :
( ( ( ( f @ ( sK8_SV20 @ SV17 ) )
| ( f @ ( sK8_SV20 @ SV17 ) ) )
= $true )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(153,plain,
! [SV17: b] :
( ( ( ~ ( f @ ( sK8_SV20 @ SV17 ) )
| ~ ( f @ ( sK8_SV20 @ SV17 ) ) )
= $true )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(154,plain,
! [SV17: b] :
( ( ( ( f @ ( sK9_SV21 @ SV17 ) )
| ( f @ ( sK9_SV21 @ SV17 ) ) )
= $true )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(155,plain,
! [SV17: b] :
( ( ( ~ ( f @ ( sK9_SV21 @ SV17 ) )
| ~ ( f @ ( sK9_SV21 @ SV17 ) ) )
= $true )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(160,plain,
! [SV17: b] :
( ( ( f @ ( sK8_SV20 @ SV17 ) )
= $true )
| ( ( f @ ( sK8_SV20 @ SV17 ) )
= $true )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(161,plain,
! [SV17: b] :
( ( ( ~ ( f @ ( sK8_SV20 @ SV17 ) ) )
= $true )
| ( ( ~ ( f @ ( sK8_SV20 @ SV17 ) ) )
= $true )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(162,plain,
! [SV17: b] :
( ( ( f @ ( sK9_SV21 @ SV17 ) )
= $true )
| ( ( f @ ( sK9_SV21 @ SV17 ) )
= $true )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(163,plain,
! [SV17: b] :
( ( ( ~ ( f @ ( sK9_SV21 @ SV17 ) ) )
= $true )
| ( ( ~ ( f @ ( sK9_SV21 @ SV17 ) ) )
= $true )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(166,plain,
! [SV17: b] :
( ( ( f @ ( sK8_SV20 @ SV17 ) )
= $false )
| ( ( ~ ( f @ ( sK8_SV20 @ SV17 ) ) )
= $true )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(167,plain,
! [SV17: b] :
( ( ( f @ ( sK9_SV21 @ SV17 ) )
= $false )
| ( ( ~ ( f @ ( sK9_SV21 @ SV17 ) ) )
= $true )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(170,plain,
! [SV17: b] :
( ( ( f @ ( sK8_SV20 @ SV17 ) )
= $false )
| ( ( f @ ( sK8_SV20 @ SV17 ) )
= $false )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(171,plain,
! [SV17: b] :
( ( ( f @ ( sK9_SV21 @ SV17 ) )
= $false )
| ( ( f @ ( sK9_SV21 @ SV17 ) )
= $false )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(176,plain,
! [SV17: b] :
( ( sK2_REN = $true )
| ( ( f @ SV17 )
= $true )
| ( ( g @ SV17 )
= $false ) ),
inference(extuni,[status(esa)],[137]) ).
thf(177,plain,
! [SV17: b] :
( ( sK2_REN = $true )
| ( ( f @ SV17 )
= $true )
| ( ( g @ SV17 )
= $false ) ),
inference(extuni,[status(esa)],[124]) ).
thf(178,plain,
! [SV17: b] :
( ( sK2_REN = $true )
| ( ( f @ SV17 )
= $false )
| ( ( g @ SV17 )
= $true ) ),
inference(extuni,[status(esa)],[139]) ).
thf(179,plain,
! [SV17: b] :
( ( sK2_REN = $true )
| ( ( f @ SV17 )
= $false )
| ( ( g @ SV17 )
= $true ) ),
inference(extuni,[status(esa)],[126]) ).
thf(180,plain,
! [SV13: b] :
( ( ( f @ SV13 )
= $true )
| ( ( g @ SV13 )
= $false )
| ( sK2_REN = $true ) ),
inference(sim,[status(thm)],[98]) ).
thf(181,plain,
! [SV13: b] :
( ( ( g @ SV13 )
= $true )
| ( ( f @ SV13 )
= $false )
| ( sK2_REN = $true ) ),
inference(sim,[status(thm)],[99]) ).
thf(182,plain,
! [SV13: b] :
( ( sK2_REN = $true )
| ( ( g @ SV13 )
= $false )
| ( ( f @ SV13 )
= $true ) ),
inference(sim,[status(thm)],[105]) ).
thf(183,plain,
! [SV13: b] :
( ( sK2_REN = $true )
| ( ( g @ SV13 )
= $true )
| ( ( f @ SV13 )
= $false ) ),
inference(sim,[status(thm)],[104]) ).
thf(184,plain,
! [SV15: b] :
( ( ( g @ SV15 )
= $false )
| ( ( f @ SV15 )
= $true )
| ( sK2_REN = $true ) ),
inference(sim,[status(thm)],[107]) ).
thf(185,plain,
! [SV15: b] :
( ( ( g @ SV15 )
= $true )
| ( ( f @ SV15 )
= $false )
| ( sK2_REN = $true ) ),
inference(sim,[status(thm)],[106]) ).
thf(186,plain,
! [SV17: b] :
( ( ( f @ ( sK8_SV20 @ SV17 ) )
= $true )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(sim,[status(thm)],[160]) ).
thf(187,plain,
! [SV17: b] :
( ( ( f @ ( sK8_SV20 @ SV17 ) )
= $false )
| ( ( g @ SV17 )
= $false )
| ( ( f @ SV17 )
= $true )
| ( sK2_REN = $true ) ),
inference(sim,[status(thm)],[170]) ).
thf(188,plain,
! [SV17: b] :
( ( ( f @ ( sK9_SV21 @ SV17 ) )
= $true )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(sim,[status(thm)],[162]) ).
thf(189,plain,
! [SV17: b] :
( ( ( f @ ( sK9_SV21 @ SV17 ) )
= $false )
| ( ( g @ SV17 )
= $true )
| ( ( f @ SV17 )
= $false )
| ( sK2_REN = $true ) ),
inference(sim,[status(thm)],[171]) ).
thf(190,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,189,188,187,186,185,184,183,182,181,180,179,178,177,176,127,111,110,57,56,48,46,44,38,37,36]) ).
thf(191,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYO359^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.16/0.36 % Computer : n027.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 600
% 0.16/0.36 % DateTime : Sat Jul 9 04:04:46 EDT 2022
% 0.16/0.36 % CPUTime :
% 0.16/0.36
% 0.16/0.36 No.of.Axioms: 0
% 0.16/0.36
% 0.16/0.36 Length.of.Defs: 0
% 0.16/0.36
% 0.16/0.36 Contains.Choice.Funs: false
% 0.16/0.37 (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.22/0.46
% 0.22/0.46 ********************************
% 0.22/0.46 * All subproblems solved! *
% 0.22/0.46 ********************************
% 0.22/0.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:190,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.22/0.47
% 0.22/0.47 %**** Beginning of derivation protocol ****
% 0.22/0.47 % SZS output start CNFRefutation
% See solution above
% 0.22/0.47
% 0.22/0.47 %**** End of derivation protocol ****
% 0.22/0.47 %**** no. of clauses in derivation: 127 ****
% 0.22/0.47 %**** clause counter: 190 ****
% 0.22/0.47
% 0.22/0.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:190,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------