TSTP Solution File: SET633+3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET633+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:03:47 EDT 2022
% Result : Theorem 0.21s 0.47s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 149 ( 87 unt; 10 typ; 0 def)
% Number of atoms : 812 ( 247 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 1727 ( 290 ~; 249 |; 24 &;1146 @)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 386 ( 0 ^ 386 !; 0 ?; 386 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SY22,type,
sK2_SY22: $i ).
thf(tp_sK3_SY24,type,
sK3_SY24: $i ).
thf(tp_sK4_D,type,
sK4_D: $i > $i > $i ).
thf(tp_sK5_D,type,
sK5_D: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_symmetric_difference,type,
symmetric_difference: $i > $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(1,axiom,
! [B: $i] : ( subset @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(2,axiom,
! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
thf(3,axiom,
! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( symmetric_difference @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
thf(4,axiom,
! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(5,axiom,
! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(6,axiom,
! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( difference @ B @ C ) )
<=> ( ( member @ D @ B )
& ~ ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
thf(7,axiom,
! [B: $i,C: $i,D: $i] :
( ( ( subset @ B @ C )
& ( subset @ D @ C ) )
=> ( subset @ ( union @ B @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_subset) ).
thf(8,axiom,
! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( union @ ( difference @ B @ C ) @ ( difference @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
thf(9,conjecture,
! [B: $i,C: $i,D: $i] :
( ( ( subset @ ( difference @ B @ C ) @ D )
& ( subset @ ( difference @ C @ B ) @ D ) )
=> ( subset @ ( symmetric_difference @ B @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th115) ).
thf(10,negated_conjecture,
( ( ! [B: $i,C: $i,D: $i] :
( ( ( subset @ ( difference @ B @ C ) @ D )
& ( subset @ ( difference @ C @ B ) @ D ) )
=> ( subset @ ( symmetric_difference @ B @ C ) @ D ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( ( subset @ ( difference @ B @ C ) @ D )
& ( subset @ ( difference @ C @ B ) @ D ) )
=> ( subset @ ( symmetric_difference @ B @ C ) @ D ) ) )
= $false ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( symmetric_difference @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( difference @ B @ C ) )
<=> ( ( member @ D @ B )
& ~ ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( ( subset @ B @ C )
& ( subset @ D @ C ) )
=> ( subset @ ( union @ B @ D ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( union @ ( difference @ B @ C ) @ ( difference @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(20,plain,
( ( ! [SY22: $i,SY23: $i] :
( ( ( subset @ ( difference @ sK1_B @ SY22 ) @ SY23 )
& ( subset @ ( difference @ SY22 @ sK1_B ) @ SY23 ) )
=> ( subset @ ( symmetric_difference @ sK1_B @ SY22 ) @ SY23 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(21,plain,
( ( ! [SY24: $i] :
( ( ( subset @ ( difference @ sK1_B @ sK2_SY22 ) @ SY24 )
& ( subset @ ( difference @ sK2_SY22 @ sK1_B ) @ SY24 ) )
=> ( subset @ ( symmetric_difference @ sK1_B @ sK2_SY22 ) @ SY24 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(22,plain,
( ( ( ( subset @ ( difference @ sK1_B @ sK2_SY22 ) @ sK3_SY24 )
& ( subset @ ( difference @ sK2_SY22 @ sK1_B ) @ sK3_SY24 ) )
=> ( subset @ ( symmetric_difference @ sK1_B @ sK2_SY22 ) @ sK3_SY24 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(23,plain,
( ( subset @ ( difference @ sK1_B @ sK2_SY22 ) @ sK3_SY24 )
= $true ),
inference(standard_cnf,[status(thm)],[22]) ).
thf(24,plain,
( ( subset @ ( difference @ sK2_SY22 @ sK1_B ) @ sK3_SY24 )
= $true ),
inference(standard_cnf,[status(thm)],[22]) ).
thf(25,plain,
( ( subset @ ( symmetric_difference @ sK1_B @ sK2_SY22 ) @ sK3_SY24 )
= $false ),
inference(standard_cnf,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ( subset @ ( symmetric_difference @ sK1_B @ sK2_SY22 ) @ sK3_SY24 ) )
= $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [B: $i,C: $i] :
( ( ( ~ ( member @ ( sK4_D @ C @ B ) @ B )
| ~ ( member @ ( sK4_D @ C @ B ) @ C ) )
& ( ( member @ ( sK4_D @ C @ B ) @ B )
| ( member @ ( sK4_D @ C @ B ) @ C ) ) )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) )
& ! [D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(28,plain,
( ( ! [B: $i,C: $i] :
( ( ( member @ ( sK5_D @ C @ B ) @ B )
& ~ ( member @ ( sK5_D @ C @ B ) @ C ) )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(29,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C )
| ( member @ D @ ( difference @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( difference @ B @ C ) )
| ( member @ D @ B ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( difference @ B @ C ) )
| ~ ( member @ D @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(30,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ~ ( subset @ B @ C )
| ~ ( subset @ D @ C )
| ( subset @ ( union @ B @ D ) @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(31,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( union @ ( difference @ B @ C ) @ ( difference @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(32,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ~ ( subset @ B @ C )
| ~ ( subset @ D @ C )
| ( subset @ ( union @ B @ D ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(33,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C )
| ( member @ D @ ( difference @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( difference @ B @ C ) )
| ( member @ D @ B ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( difference @ B @ C ) )
| ~ ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(34,plain,
( ( ! [B: $i,C: $i] :
( ( ( member @ ( sK5_D @ C @ B ) @ B )
& ~ ( member @ ( sK5_D @ C @ B ) @ C ) )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(35,plain,
( ( ! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(36,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( symmetric_difference @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(37,plain,
( ( ! [B: $i,C: $i] :
( ( ( ~ ( member @ ( sK4_D @ C @ B ) @ B )
| ~ ( member @ ( sK4_D @ C @ B ) @ C ) )
& ( ( member @ ( sK4_D @ C @ B ) @ B )
| ( member @ ( sK4_D @ C @ B ) @ C ) ) )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) )
& ! [D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(38,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(39,plain,
( ( subset @ ( difference @ sK2_SY22 @ sK1_B ) @ sK3_SY24 )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(40,plain,
( ( subset @ ( difference @ sK1_B @ sK2_SY22 ) @ sK3_SY24 )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(41,plain,
( ( ~ ( subset @ ( symmetric_difference @ sK1_B @ sK2_SY22 ) @ sK3_SY24 ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(42,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(43,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 )
| ( member @ SX2 @ ( difference @ SX0 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( difference @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( difference @ SX0 @ SX1 ) )
| ~ ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(44,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(45,plain,
! [SV1: $i] :
( ( ! [SY25: $i] :
( ( symmetric_difference @ SV1 @ SY25 )
= ( union @ ( difference @ SV1 @ SY25 ) @ ( difference @ SY25 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(46,plain,
! [SV2: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ~ ( subset @ SV2 @ SY26 )
| ~ ( subset @ SY27 @ SY26 )
| ( subset @ ( union @ SV2 @ SY27 ) @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(47,plain,
! [SV3: $i] :
( ( ! [SY28: $i] :
( ( union @ SV3 @ SY28 )
= ( union @ SY28 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(48,plain,
! [SV4: $i] :
( ( ! [SY29: $i] :
( ( symmetric_difference @ SV4 @ SY29 )
= ( symmetric_difference @ SY29 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(49,plain,
! [SV5: $i] :
( ( subset @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(50,plain,
( ( subset @ ( symmetric_difference @ sK1_B @ sK2_SY22 ) @ sK3_SY24 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(51,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(52,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY30: $i,SY31: $i] :
( ~ ( member @ SY31 @ SV6 )
| ( member @ SY31 @ SY30 )
| ( member @ SY31 @ ( difference @ SV6 @ SY30 ) ) )
| ~ ~ ( ~ ! [SY32: $i,SY33: $i] :
( ~ ( member @ SY33 @ ( difference @ SV6 @ SY32 ) )
| ( member @ SY33 @ SV6 ) )
| ~ ! [SY34: $i,SY35: $i] :
( ~ ( member @ SY35 @ ( difference @ SV6 @ SY34 ) )
| ~ ( member @ SY35 @ SY34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(53,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(54,plain,
! [SV7: $i,SV1: $i] :
( ( ( symmetric_difference @ SV1 @ SV7 )
= ( union @ ( difference @ SV1 @ SV7 ) @ ( difference @ SV7 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(55,plain,
! [SV8: $i,SV2: $i] :
( ( ! [SY36: $i] :
( ~ ( subset @ SV2 @ SV8 )
| ~ ( subset @ SY36 @ SV8 )
| ( subset @ ( union @ SV2 @ SY36 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(56,plain,
! [SV9: $i,SV3: $i] :
( ( ( union @ SV3 @ SV9 )
= ( union @ SV9 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(57,plain,
! [SV10: $i,SV4: $i] :
( ( ( symmetric_difference @ SV4 @ SV10 )
= ( symmetric_difference @ SV10 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(58,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(59,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(60,plain,
! [SV6: $i] :
( ( ~ ! [SY30: $i,SY31: $i] :
( ~ ( member @ SY31 @ SV6 )
| ( member @ SY31 @ SY30 )
| ( member @ SY31 @ ( difference @ SV6 @ SY30 ) ) )
| ~ ~ ( ~ ! [SY32: $i,SY33: $i] :
( ~ ( member @ SY33 @ ( difference @ SV6 @ SY32 ) )
| ( member @ SY33 @ SV6 ) )
| ~ ! [SY34: $i,SY35: $i] :
( ~ ( member @ SY35 @ ( difference @ SV6 @ SY34 ) )
| ~ ( member @ SY35 @ SY34 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(61,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(62,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(63,plain,
! [SV11: $i,SV8: $i,SV2: $i] :
( ( ~ ( subset @ SV2 @ SV8 )
| ~ ( subset @ SV11 @ SV8 )
| ( subset @ ( union @ SV2 @ SV11 ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(64,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(65,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(66,plain,
! [SV6: $i] :
( ( ~ ! [SY30: $i,SY31: $i] :
( ~ ( member @ SY31 @ SV6 )
| ( member @ SY31 @ SY30 )
| ( member @ SY31 @ ( difference @ SV6 @ SY30 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(67,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ! [SY32: $i,SY33: $i] :
( ~ ( member @ SY33 @ ( difference @ SV6 @ SY32 ) )
| ( member @ SY33 @ SV6 ) )
| ~ ! [SY34: $i,SY35: $i] :
( ~ ( member @ SY35 @ ( difference @ SV6 @ SY34 ) )
| ~ ( member @ SY35 @ SY34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(68,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(69,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(70,plain,
! [SV11: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( subset @ SV2 @ SV8 )
| ~ ( subset @ SV11 @ SV8 ) )
= $true )
| ( ( subset @ ( union @ SV2 @ SV11 ) @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(71,plain,
! [SV12: $i] :
( ( ! [SY37: $i] :
( ~ ( ~ ( ~ ( member @ ( sK4_D @ SY37 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK4_D @ SY37 @ SV12 ) @ SY37 ) )
| ~ ( ( member @ ( sK4_D @ SY37 @ SV12 ) @ SV12 )
| ( member @ ( sK4_D @ SY37 @ SV12 ) @ SY37 ) ) )
| ( SV12 = SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(72,plain,
! [SV13: $i] :
( ( ! [SY38: $i] :
( ( SV13 != SY38 )
| ~ ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV13 )
| ( member @ SY39 @ SY38 ) )
| ~ ! [SY40: $i] :
( ~ ( member @ SY40 @ SY38 )
| ( member @ SY40 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(73,plain,
! [SV6: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ~ ( member @ SY31 @ SV6 )
| ( member @ SY31 @ SY30 )
| ( member @ SY31 @ ( difference @ SV6 @ SY30 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(74,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY32: $i,SY33: $i] :
( ~ ( member @ SY33 @ ( difference @ SV6 @ SY32 ) )
| ( member @ SY33 @ SV6 ) )
| ~ ! [SY34: $i,SY35: $i] :
( ~ ( member @ SY35 @ ( difference @ SV6 @ SY34 ) )
| ~ ( member @ SY35 @ SY34 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(75,plain,
! [SV14: $i] :
( ( ! [SY41: $i] :
( ~ ( ~ ( member @ ( sK5_D @ SY41 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK5_D @ SY41 @ SV14 ) @ SY41 ) )
| ( subset @ SV14 @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(76,plain,
! [SV15: $i] :
( ( ! [SY42: $i] :
( ~ ( subset @ SV15 @ SY42 )
| ! [SY43: $i] :
( ~ ( member @ SY43 @ SV15 )
| ( member @ SY43 @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(77,plain,
! [SV11: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( subset @ SV2 @ SV8 ) )
= $true )
| ( ( ~ ( subset @ SV11 @ SV8 ) )
= $true )
| ( ( subset @ ( union @ SV2 @ SV11 ) @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(78,plain,
! [SV12: $i,SV16: $i] :
( ( ~ ( ~ ( ~ ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV16 ) )
| ~ ( ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV12 )
| ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV16 ) ) )
| ( SV12 = SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(79,plain,
! [SV17: $i,SV13: $i] :
( ( ( SV13 != SV17 )
| ~ ( ~ ! [SY44: $i] :
( ~ ( member @ SY44 @ SV13 )
| ( member @ SY44 @ SV17 ) )
| ~ ! [SY45: $i] :
( ~ ( member @ SY45 @ SV17 )
| ( member @ SY45 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(80,plain,
! [SV18: $i,SV6: $i] :
( ( ! [SY46: $i] :
( ~ ( member @ SY46 @ SV6 )
| ( member @ SY46 @ SV18 )
| ( member @ SY46 @ ( difference @ SV6 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(81,plain,
! [SV6: $i] :
( ( ~ ! [SY32: $i,SY33: $i] :
( ~ ( member @ SY33 @ ( difference @ SV6 @ SY32 ) )
| ( member @ SY33 @ SV6 ) )
| ~ ! [SY34: $i,SY35: $i] :
( ~ ( member @ SY35 @ ( difference @ SV6 @ SY34 ) )
| ~ ( member @ SY35 @ SY34 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(82,plain,
! [SV14: $i,SV19: $i] :
( ( ~ ( ~ ( member @ ( sK5_D @ SV19 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK5_D @ SV19 @ SV14 ) @ SV19 ) )
| ( subset @ SV14 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(83,plain,
! [SV20: $i,SV15: $i] :
( ( ~ ( subset @ SV15 @ SV20 )
| ! [SY47: $i] :
( ~ ( member @ SY47 @ SV15 )
| ( member @ SY47 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(84,plain,
! [SV11: $i,SV8: $i,SV2: $i] :
( ( ( subset @ SV2 @ SV8 )
= $false )
| ( ( ~ ( subset @ SV11 @ SV8 ) )
= $true )
| ( ( subset @ ( union @ SV2 @ SV11 ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(85,plain,
! [SV12: $i,SV16: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV16 ) )
| ~ ( ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV12 )
| ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV16 ) ) ) )
= $true )
| ( ( SV12 = SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV17: $i,SV13: $i] :
( ( ( ( SV13 != SV17 ) )
= $true )
| ( ( ~ ( ~ ! [SY44: $i] :
( ~ ( member @ SY44 @ SV13 )
| ( member @ SY44 @ SV17 ) )
| ~ ! [SY45: $i] :
( ~ ( member @ SY45 @ SV17 )
| ( member @ SY45 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV18: $i,SV6: $i,SV21: $i] :
( ( ~ ( member @ SV21 @ SV6 )
| ( member @ SV21 @ SV18 )
| ( member @ SV21 @ ( difference @ SV6 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV6: $i] :
( ( ~ ! [SY32: $i,SY33: $i] :
( ~ ( member @ SY33 @ ( difference @ SV6 @ SY32 ) )
| ( member @ SY33 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(89,plain,
! [SV6: $i] :
( ( ~ ! [SY34: $i,SY35: $i] :
( ~ ( member @ SY35 @ ( difference @ SV6 @ SY34 ) )
| ~ ( member @ SY35 @ SY34 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(90,plain,
! [SV14: $i,SV19: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_D @ SV19 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK5_D @ SV19 @ SV14 ) @ SV19 ) ) )
= $true )
| ( ( subset @ SV14 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV20: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV20 ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( member @ SY47 @ SV15 )
| ( member @ SY47 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV2: $i,SV8: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV8 )
= $false )
| ( ( subset @ SV2 @ SV8 )
= $false )
| ( ( subset @ ( union @ SV2 @ SV11 ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV12: $i,SV16: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV16 ) )
| ~ ( ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV12 )
| ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV16 ) ) )
= $false )
| ( ( SV12 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV17: $i,SV13: $i] :
( ( ( SV13 = SV17 )
= $false )
| ( ( ~ ( ~ ! [SY44: $i] :
( ~ ( member @ SY44 @ SV13 )
| ( member @ SY44 @ SV17 ) )
| ~ ! [SY45: $i] :
( ~ ( member @ SY45 @ SV17 )
| ( member @ SY45 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV18: $i,SV6: $i,SV21: $i] :
( ( ( ~ ( member @ SV21 @ SV6 )
| ( member @ SV21 @ SV18 ) )
= $true )
| ( ( member @ SV21 @ ( difference @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV6: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ~ ( member @ SY33 @ ( difference @ SV6 @ SY32 ) )
| ( member @ SY33 @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(97,plain,
! [SV6: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ~ ( member @ SY35 @ ( difference @ SV6 @ SY34 ) )
| ~ ( member @ SY35 @ SY34 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(98,plain,
! [SV14: $i,SV19: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV19 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK5_D @ SV19 @ SV14 ) @ SV19 ) )
= $false )
| ( ( subset @ SV14 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(99,plain,
! [SV20: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV20 )
= $false )
| ( ( ! [SY47: $i] :
( ~ ( member @ SY47 @ SV15 )
| ( member @ SY47 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(100,plain,
! [SV12: $i,SV16: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV16 ) ) )
= $false )
| ( ( SV12 = SV16 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(101,plain,
! [SV12: $i,SV16: $i] :
( ( ( ~ ( ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV12 )
| ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV16 ) ) )
= $false )
| ( ( SV12 = SV16 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(102,plain,
! [SV17: $i,SV13: $i] :
( ( ( ~ ! [SY44: $i] :
( ~ ( member @ SY44 @ SV13 )
| ( member @ SY44 @ SV17 ) )
| ~ ! [SY45: $i] :
( ~ ( member @ SY45 @ SV17 )
| ( member @ SY45 @ SV13 ) ) )
= $false )
| ( ( SV13 = SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(103,plain,
! [SV18: $i,SV6: $i,SV21: $i] :
( ( ( ~ ( member @ SV21 @ SV6 ) )
= $true )
| ( ( member @ SV21 @ SV18 )
= $true )
| ( ( member @ SV21 @ ( difference @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(104,plain,
! [SV22: $i,SV6: $i] :
( ( ! [SY48: $i] :
( ~ ( member @ SY48 @ ( difference @ SV6 @ SV22 ) )
| ( member @ SY48 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(105,plain,
! [SV23: $i,SV6: $i] :
( ( ! [SY49: $i] :
( ~ ( member @ SY49 @ ( difference @ SV6 @ SV23 ) )
| ~ ( member @ SY49 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(106,plain,
! [SV14: $i,SV19: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV19 @ SV14 ) @ SV14 ) )
= $false )
| ( ( subset @ SV14 @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(107,plain,
! [SV14: $i,SV19: $i] :
( ( ( ~ ~ ( member @ ( sK5_D @ SV19 @ SV14 ) @ SV19 ) )
= $false )
| ( ( subset @ SV14 @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(108,plain,
! [SV20: $i,SV15: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV15 )
| ( member @ SV24 @ SV20 ) )
= $true )
| ( ( subset @ SV15 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(109,plain,
! [SV12: $i,SV16: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV16 ) )
= $true )
| ( ( SV12 = SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(110,plain,
! [SV12: $i,SV16: $i] :
( ( ( ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV12 )
| ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV16 ) )
= $true )
| ( ( SV12 = SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(111,plain,
! [SV17: $i,SV13: $i] :
( ( ( ~ ! [SY44: $i] :
( ~ ( member @ SY44 @ SV13 )
| ( member @ SY44 @ SV17 ) ) )
= $false )
| ( ( SV13 = SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(112,plain,
! [SV13: $i,SV17: $i] :
( ( ( ~ ! [SY45: $i] :
( ~ ( member @ SY45 @ SV17 )
| ( member @ SY45 @ SV13 ) ) )
= $false )
| ( ( SV13 = SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(113,plain,
! [SV18: $i,SV6: $i,SV21: $i] :
( ( ( member @ SV21 @ SV6 )
= $false )
| ( ( member @ SV21 @ SV18 )
= $true )
| ( ( member @ SV21 @ ( difference @ SV6 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(114,plain,
! [SV22: $i,SV6: $i,SV25: $i] :
( ( ~ ( member @ SV25 @ ( difference @ SV6 @ SV22 ) )
| ( member @ SV25 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(115,plain,
! [SV23: $i,SV6: $i,SV26: $i] :
( ( ~ ( member @ SV26 @ ( difference @ SV6 @ SV23 ) )
| ~ ( member @ SV26 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV14: $i,SV19: $i] :
( ( ( member @ ( sK5_D @ SV19 @ SV14 ) @ SV14 )
= $true )
| ( ( subset @ SV14 @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(117,plain,
! [SV14: $i,SV19: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV19 @ SV14 ) @ SV19 ) )
= $true )
| ( ( subset @ SV14 @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(118,plain,
! [SV20: $i,SV15: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV15 ) )
= $true )
| ( ( member @ SV24 @ SV20 )
= $true )
| ( ( subset @ SV15 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(119,plain,
! [SV12: $i,SV16: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV12 ) )
= $true )
| ( ( ~ ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV16 ) )
= $true )
| ( ( SV12 = SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV12: $i,SV16: $i] :
( ( ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV12 )
= $true )
| ( ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV16 )
= $true )
| ( ( SV12 = SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV17: $i,SV13: $i] :
( ( ( ! [SY44: $i] :
( ~ ( member @ SY44 @ SV13 )
| ( member @ SY44 @ SV17 ) ) )
= $true )
| ( ( SV13 = SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(122,plain,
! [SV13: $i,SV17: $i] :
( ( ( ! [SY45: $i] :
( ~ ( member @ SY45 @ SV17 )
| ( member @ SY45 @ SV13 ) ) )
= $true )
| ( ( SV13 = SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(123,plain,
! [SV22: $i,SV6: $i,SV25: $i] :
( ( ( ~ ( member @ SV25 @ ( difference @ SV6 @ SV22 ) ) )
= $true )
| ( ( member @ SV25 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(124,plain,
! [SV23: $i,SV6: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ ( difference @ SV6 @ SV23 ) ) )
= $true )
| ( ( ~ ( member @ SV26 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(125,plain,
! [SV14: $i,SV19: $i] :
( ( ( member @ ( sK5_D @ SV19 @ SV14 ) @ SV19 )
= $false )
| ( ( subset @ SV14 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(126,plain,
! [SV20: $i,SV15: $i,SV24: $i] :
( ( ( member @ SV24 @ SV15 )
= $false )
| ( ( member @ SV24 @ SV20 )
= $true )
| ( ( subset @ SV15 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(127,plain,
! [SV12: $i,SV16: $i] :
( ( ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV12 )
= $false )
| ( ( ~ ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV16 ) )
= $true )
| ( ( SV12 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(128,plain,
! [SV17: $i,SV13: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ SV13 )
| ( member @ SV27 @ SV17 ) )
= $true )
| ( ( SV13 = SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(129,plain,
! [SV13: $i,SV17: $i,SV28: $i] :
( ( ( ~ ( member @ SV28 @ SV17 )
| ( member @ SV28 @ SV13 ) )
= $true )
| ( ( SV13 = SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(130,plain,
! [SV22: $i,SV6: $i,SV25: $i] :
( ( ( member @ SV25 @ ( difference @ SV6 @ SV22 ) )
= $false )
| ( ( member @ SV25 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(131,plain,
! [SV23: $i,SV6: $i,SV26: $i] :
( ( ( member @ SV26 @ ( difference @ SV6 @ SV23 ) )
= $false )
| ( ( ~ ( member @ SV26 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(132,plain,
! [SV12: $i,SV16: $i] :
( ( ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV16 )
= $false )
| ( ( member @ ( sK4_D @ SV16 @ SV12 ) @ SV12 )
= $false )
| ( ( SV12 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(133,plain,
! [SV17: $i,SV13: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ SV13 ) )
= $true )
| ( ( member @ SV27 @ SV17 )
= $true )
| ( ( SV13 = SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(134,plain,
! [SV13: $i,SV17: $i,SV28: $i] :
( ( ( ~ ( member @ SV28 @ SV17 ) )
= $true )
| ( ( member @ SV28 @ SV13 )
= $true )
| ( ( SV13 = SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(135,plain,
! [SV6: $i,SV23: $i,SV26: $i] :
( ( ( member @ SV26 @ SV23 )
= $false )
| ( ( member @ SV26 @ ( difference @ SV6 @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(136,plain,
! [SV17: $i,SV13: $i,SV27: $i] :
( ( ( member @ SV27 @ SV13 )
= $false )
| ( ( member @ SV27 @ SV17 )
= $true )
| ( ( SV13 = SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(137,plain,
! [SV13: $i,SV17: $i,SV28: $i] :
( ( ( member @ SV28 @ SV17 )
= $false )
| ( ( member @ SV28 @ SV13 )
= $true )
| ( ( SV13 = SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(138,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[39,137,136,135,132,130,126,125,120,116,113,92,57,56,54,50,49,40]) ).
thf(139,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET633+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 9 22:09:16 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 8
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:8,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:10,loop_count:0,foatp_calls:0,translation:fof_full).........
% 0.21/0.47
% 0.21/0.47 ********************************
% 0.21/0.47 * All subproblems solved! *
% 0.21/0.47 ********************************
% 0.21/0.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:138,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.47
% 0.21/0.47 %**** Beginning of derivation protocol ****
% 0.21/0.47 % SZS output start CNFRefutation
% See solution above
% 0.21/0.48
% 0.21/0.48 %**** End of derivation protocol ****
% 0.21/0.48 %**** no. of clauses in derivation: 139 ****
% 0.21/0.48 %**** clause counter: 138 ****
% 0.21/0.48
% 0.21/0.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:138,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------