%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET642+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 10:40:43 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 146 ( 63 unt; 0 typ; 0 def)
% Number of atoms : 1208 ( 299 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 2255 ( 277 ~; 366 |; 0 &;1514 @)
% ( 3 <=>; 95 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 7 con; 0-2 aty)
% Number of variables : 353 ( 0 ^; 347 !; 6 ?; 353 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cross_product,type,
cross_product: $i > $i > $i ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_ilf_type,type,
ilf_type: $i > $i > $o ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_member_type,type,
member_type: $i > $i ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_power_set,type,
power_set: $i > $i ).
thf(tp_relation_like,type,
relation_like: $i > $o ).
thf(tp_relation_type,type,
relation_type: $i > $i > $i ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY41,type,
sK3_SY41: $i ).
thf(tp_sK4_SY32,type,
sK4_SY32: $i > $i ).
thf(tp_sK5_SY45,type,
sK5_SY45: $i ).
thf(tp_sK6_SY49,type,
sK6_SY49: $i > $i > $i ).
thf(tp_sK7_SY44,type,
sK7_SY44: $i > $i > $i ).
thf(tp_set_type,type,
set_type: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_type,type,
subset_type: $i > $i ).
thf(1,axiom,
! [B: $i] : ( ilf_type @ B @ set_type ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
thf(2,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( ordered_pair @ B @ C ) @ set_type ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18) ).
thf(11,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( subset @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).
thf(12,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( subset_type @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).
thf(14,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( cross_product @ B @ C ) @ set_type ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
thf(15,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( subset @ B @ C )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
=> ( member @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
thf(16,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ? [D: $i] : ( ilf_type @ D @ ( relation_type @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
thf(18,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( subset @ B @ ( cross_product @ C @ D ) )
=> ( ilf_type @ B @ ( relation_type @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
thf(19,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ ( relation_type @ C @ D ) )
=> ( ( subset @ B @ E )
=> ( subset @ B @ ( cross_product @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
thf(20,conjecture,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ ( relation_type @ C @ D ) )
=> ( ( subset @ B @ E )
=> ( ilf_type @ B @ ( relation_type @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_4) ).
thf(21,negated_conjecture,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ ( relation_type @ C @ D ) )
=> ( ( subset @ B @ E )
=> ( ilf_type @ B @ ( relation_type @ C @ D ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[20]) ).
thf(22,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ ( relation_type @ C @ D ) )
=> ( ( subset @ B @ E )
=> ( ilf_type @ B @ ( relation_type @ C @ D ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [B: $i] : ( ilf_type @ B @ set_type ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(24,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( ordered_pair @ B @ C ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(25,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( subset @ B @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(26,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( subset_type @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(27,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( cross_product @ B @ C ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(28,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( subset @ B @ C )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
=> ( member @ D @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(29,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ? [D: $i] : ( ilf_type @ D @ ( relation_type @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(30,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( subset @ B @ ( cross_product @ C @ D ) )
=> ( ilf_type @ B @ ( relation_type @ C @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(31,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ ( relation_type @ C @ D ) )
=> ( ( subset @ B @ E )
=> ( subset @ B @ ( cross_product @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(32,plain,
( ( ( ilf_type @ sK1_B @ set_type )
=> ! [SY25: $i] :
( ( ilf_type @ SY25 @ set_type )
=> ! [SY26: $i] :
( ( ilf_type @ SY26 @ set_type )
=> ! [SY27: $i] :
( ( ilf_type @ SY27 @ ( relation_type @ SY25 @ SY26 ) )
=> ( ( subset @ sK1_B @ SY27 )
=> ( ilf_type @ sK1_B @ ( relation_type @ SY25 @ SY26 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(33,plain,
( ( ilf_type @ sK1_B @ set_type )
= $true ),
inference(standard_cnf,[status(thm)],[32]) ).
thf(34,plain,
( ( ! [SY25: $i] :
( ( ilf_type @ SY25 @ set_type )
=> ! [SY26: $i] :
( ( ilf_type @ SY26 @ set_type )
=> ! [SY27: $i] :
( ( ilf_type @ SY27 @ ( relation_type @ SY25 @ SY26 ) )
=> ( ( subset @ sK1_B @ SY27 )
=> ( ilf_type @ sK1_B @ ( relation_type @ SY25 @ SY26 ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[32]) ).
thf(35,plain,
( ( ~ ! [SY25: $i] :
( ( ilf_type @ SY25 @ set_type )
=> ! [SY26: $i] :
( ( ilf_type @ SY26 @ set_type )
=> ! [SY27: $i] :
( ( ilf_type @ SY27 @ ( relation_type @ SY25 @ SY26 ) )
=> ( ( subset @ sK1_B @ SY27 )
=> ( ilf_type @ sK1_B @ ( relation_type @ SY25 @ SY26 ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[34]) ).
thf(36,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ ( relation_type @ C @ D ) )
=> ( ( subset @ B @ E )
=> ( subset @ B @ ( cross_product @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(37,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( subset @ B @ ( cross_product @ C @ D ) )
=> ( ilf_type @ B @ ( relation_type @ C @ D ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(38,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ? [D: $i] : ( ilf_type @ D @ ( relation_type @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(39,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( subset @ B @ C )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
=> ( member @ D @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(40,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( cross_product @ B @ C ) @ set_type ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(41,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( subset_type @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(42,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( subset @ B @ B ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(43,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( ordered_pair @ B @ C ) @ set_type ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(44,plain,
( ( ! [B: $i] : ( ilf_type @ B @ set_type ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(45,plain,
( ( ilf_type @ sK1_B @ set_type )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(46,plain,
( ( ~ ! [SY25: $i] :
( ( ilf_type @ SY25 @ set_type )
=> ! [SY26: $i] :
( ( ilf_type @ SY26 @ set_type )
=> ! [SY27: $i] :
( ( ilf_type @ SY27 @ ( relation_type @ SY25 @ SY26 ) )
=> ( ( subset @ sK1_B @ SY27 )
=> ( ilf_type @ sK1_B @ ( relation_type @ SY25 @ SY26 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(47,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ( ilf_type @ ( ordered_pair @ SX0 @ SX1 ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(48,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(49,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ ( relation_type @ SX0 @ SX1 ) )
| ~ ( subset @ sK1_B @ SX2 )
| ( ilf_type @ sK1_B @ ( relation_type @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(50,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ( subset @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(51,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ! [SX1: $i] :
~ ( ilf_type @ SX1 @ ( subset_type @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(52,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ! [SX3: $i] :
( ~ ( ilf_type @ SX3 @ ( relation_type @ SX1 @ SX2 ) )
| ~ ( subset @ SX0 @ SX3 )
| ( subset @ SX0 @ ( cross_product @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(53,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( subset @ SX0 @ ( cross_product @ SX1 @ SX2 ) )
| ( ilf_type @ SX0 @ ( relation_type @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(54,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ! [SX2: $i] :
~ ( ilf_type @ SX2 @ ( relation_type @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(55,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ( ilf_type @ ( cross_product @ SX0 @ SX1 ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(56,plain,
! [SV1: $i] :
( ( ilf_type @ SV1 @ set_type )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(57,plain,
! [SV2: $i] :
( ( ~ ( ilf_type @ SV2 @ set_type )
| ! [SY28: $i] :
( ~ ( ilf_type @ SY28 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV2 @ SY28 ) @ set_type ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(58,plain,
! [SV3: $i] :
( ( ~ ( ilf_type @ SV3 @ set_type )
| ! [SY29: $i] :
( ~ ( ilf_type @ SY29 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV3 @ SY29 )
| ! [SY30: $i] :
( ~ ( ilf_type @ SY30 @ set_type )
| ~ ( member @ SY30 @ SV3 )
| ( member @ SY30 @ SY29 ) ) )
| ~ ( ~ ! [SY31: $i] :
( ~ ( ilf_type @ SY31 @ set_type )
| ~ ( member @ SY31 @ SV3 )
| ( member @ SY31 @ SY29 ) )
| ( subset @ SV3 @ SY29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(59,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ ( relation_type @ SX0 @ SX1 ) )
| ~ ( subset @ sK1_B @ SX2 )
| ( ilf_type @ sK1_B @ ( relation_type @ SX0 @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(60,plain,
! [SV4: $i] :
( ( ~ ( ilf_type @ SV4 @ set_type )
| ( subset @ SV4 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(61,plain,
! [SV5: $i] :
( ( ~ ( ilf_type @ SV5 @ set_type )
| ~ ! [SY32: $i] :
~ ( ilf_type @ SY32 @ ( subset_type @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(62,plain,
! [SV6: $i] :
( ( ~ ( ilf_type @ SV6 @ set_type )
| ! [SY33: $i] :
( ~ ( ilf_type @ SY33 @ set_type )
| ! [SY34: $i] :
( ~ ( ilf_type @ SY34 @ set_type )
| ! [SY35: $i] :
( ~ ( ilf_type @ SY35 @ ( relation_type @ SY33 @ SY34 ) )
| ~ ( subset @ SV6 @ SY35 )
| ( subset @ SV6 @ ( cross_product @ SY33 @ SY34 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(63,plain,
! [SV7: $i] :
( ( ~ ( ilf_type @ SV7 @ set_type )
| ! [SY36: $i] :
( ~ ( ilf_type @ SY36 @ set_type )
| ! [SY37: $i] :
( ~ ( ilf_type @ SY37 @ set_type )
| ~ ( subset @ SV7 @ ( cross_product @ SY36 @ SY37 ) )
| ( ilf_type @ SV7 @ ( relation_type @ SY36 @ SY37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(64,plain,
! [SV8: $i] :
( ( ~ ( ilf_type @ SV8 @ set_type )
| ! [SY38: $i] :
( ~ ( ilf_type @ SY38 @ set_type )
| ~ ! [SY39: $i] :
~ ( ilf_type @ SY39 @ ( relation_type @ SY38 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(65,plain,
! [SV9: $i] :
( ( ~ ( ilf_type @ SV9 @ set_type )
| ! [SY40: $i] :
( ~ ( ilf_type @ SY40 @ set_type )
| ( ilf_type @ ( cross_product @ SV9 @ SY40 ) @ set_type ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(66,plain,
! [SV2: $i] :
( ( ( ~ ( ilf_type @ SV2 @ set_type ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( ilf_type @ SY28 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV2 @ SY28 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV3: $i] :
( ( ( ~ ( ilf_type @ SV3 @ set_type ) )
= $true )
| ( ( ! [SY29: $i] :
( ~ ( ilf_type @ SY29 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV3 @ SY29 )
| ! [SY30: $i] :
( ~ ( ilf_type @ SY30 @ set_type )
| ~ ( member @ SY30 @ SV3 )
| ( member @ SY30 @ SY29 ) ) )
| ~ ( ~ ! [SY31: $i] :
( ~ ( ilf_type @ SY31 @ set_type )
| ~ ( member @ SY31 @ SV3 )
| ( member @ SY31 @ SY29 ) )
| ( subset @ SV3 @ SY29 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(68,plain,
( ( ~ ( ilf_type @ sK2_SX0 @ set_type )
| ! [SY41: $i] :
( ~ ( ilf_type @ SY41 @ set_type )
| ! [SY42: $i] :
( ~ ( ilf_type @ SY42 @ ( relation_type @ sK2_SX0 @ SY41 ) )
| ~ ( subset @ sK1_B @ SY42 )
| ( ilf_type @ sK1_B @ ( relation_type @ sK2_SX0 @ SY41 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(69,plain,
! [SV4: $i] :
( ( ( ~ ( ilf_type @ SV4 @ set_type ) )
= $true )
| ( ( subset @ SV4 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(70,plain,
! [SV5: $i] :
( ( ( ~ ( ilf_type @ SV5 @ set_type ) )
= $true )
| ( ( ~ ! [SY32: $i] :
~ ( ilf_type @ SY32 @ ( subset_type @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(71,plain,
! [SV6: $i] :
( ( ( ~ ( ilf_type @ SV6 @ set_type ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( ilf_type @ SY33 @ set_type )
| ! [SY34: $i] :
( ~ ( ilf_type @ SY34 @ set_type )
| ! [SY35: $i] :
( ~ ( ilf_type @ SY35 @ ( relation_type @ SY33 @ SY34 ) )
| ~ ( subset @ SV6 @ SY35 )
| ( subset @ SV6 @ ( cross_product @ SY33 @ SY34 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(72,plain,
! [SV7: $i] :
( ( ( ~ ( ilf_type @ SV7 @ set_type ) )
= $true )
| ( ( ! [SY36: $i] :
( ~ ( ilf_type @ SY36 @ set_type )
| ! [SY37: $i] :
( ~ ( ilf_type @ SY37 @ set_type )
| ~ ( subset @ SV7 @ ( cross_product @ SY36 @ SY37 ) )
| ( ilf_type @ SV7 @ ( relation_type @ SY36 @ SY37 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(73,plain,
! [SV8: $i] :
( ( ( ~ ( ilf_type @ SV8 @ set_type ) )
= $true )
| ( ( ! [SY38: $i] :
( ~ ( ilf_type @ SY38 @ set_type )
| ~ ! [SY39: $i] :
~ ( ilf_type @ SY39 @ ( relation_type @ SY38 @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(74,plain,
! [SV9: $i] :
( ( ( ~ ( ilf_type @ SV9 @ set_type ) )
= $true )
| ( ( ! [SY40: $i] :
( ~ ( ilf_type @ SY40 @ set_type )
| ( ilf_type @ ( cross_product @ SV9 @ SY40 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(75,plain,
! [SV2: $i] :
( ( ( ilf_type @ SV2 @ set_type )
= $false )
| ( ( ! [SY28: $i] :
( ~ ( ilf_type @ SY28 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV2 @ SY28 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(76,plain,
! [SV3: $i] :
( ( ( ilf_type @ SV3 @ set_type )
= $false )
| ( ( ! [SY29: $i] :
( ~ ( ilf_type @ SY29 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV3 @ SY29 )
| ! [SY30: $i] :
( ~ ( ilf_type @ SY30 @ set_type )
| ~ ( member @ SY30 @ SV3 )
| ( member @ SY30 @ SY29 ) ) )
| ~ ( ~ ! [SY31: $i] :
( ~ ( ilf_type @ SY31 @ set_type )
| ~ ( member @ SY31 @ SV3 )
| ( member @ SY31 @ SY29 ) )
| ( subset @ SV3 @ SY29 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(77,plain,
( ( ~ ( ilf_type @ sK2_SX0 @ set_type ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(78,plain,
( ( ! [SY41: $i] :
( ~ ( ilf_type @ SY41 @ set_type )
| ! [SY42: $i] :
( ~ ( ilf_type @ SY42 @ ( relation_type @ sK2_SX0 @ SY41 ) )
| ~ ( subset @ sK1_B @ SY42 )
| ( ilf_type @ sK1_B @ ( relation_type @ sK2_SX0 @ SY41 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(79,plain,
! [SV4: $i] :
( ( ( ilf_type @ SV4 @ set_type )
= $false )
| ( ( subset @ SV4 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(80,plain,
! [SV5: $i] :
( ( ( ilf_type @ SV5 @ set_type )
= $false )
| ( ( ~ ! [SY32: $i] :
~ ( ilf_type @ SY32 @ ( subset_type @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(81,plain,
! [SV6: $i] :
( ( ( ilf_type @ SV6 @ set_type )
= $false )
| ( ( ! [SY33: $i] :
( ~ ( ilf_type @ SY33 @ set_type )
| ! [SY34: $i] :
( ~ ( ilf_type @ SY34 @ set_type )
| ! [SY35: $i] :
( ~ ( ilf_type @ SY35 @ ( relation_type @ SY33 @ SY34 ) )
| ~ ( subset @ SV6 @ SY35 )
| ( subset @ SV6 @ ( cross_product @ SY33 @ SY34 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV7: $i] :
( ( ( ilf_type @ SV7 @ set_type )
= $false )
| ( ( ! [SY36: $i] :
( ~ ( ilf_type @ SY36 @ set_type )
| ! [SY37: $i] :
( ~ ( ilf_type @ SY37 @ set_type )
| ~ ( subset @ SV7 @ ( cross_product @ SY36 @ SY37 ) )
| ( ilf_type @ SV7 @ ( relation_type @ SY36 @ SY37 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(83,plain,
! [SV8: $i] :
( ( ( ilf_type @ SV8 @ set_type )
= $false )
| ( ( ! [SY38: $i] :
( ~ ( ilf_type @ SY38 @ set_type )
| ~ ! [SY39: $i] :
~ ( ilf_type @ SY39 @ ( relation_type @ SY38 @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(84,plain,
! [SV9: $i] :
( ( ( ilf_type @ SV9 @ set_type )
= $false )
| ( ( ! [SY40: $i] :
( ~ ( ilf_type @ SY40 @ set_type )
| ( ilf_type @ ( cross_product @ SV9 @ SY40 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(85,plain,
! [SV2: $i,SV10: $i] :
( ( ( ~ ( ilf_type @ SV10 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV2 @ SV10 ) @ set_type ) )
= $true )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV3: $i,SV11: $i] :
( ( ( ~ ( ilf_type @ SV11 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV3 @ SV11 )
| ! [SY43: $i] :
( ~ ( ilf_type @ SY43 @ set_type )
| ~ ( member @ SY43 @ SV3 )
| ( member @ SY43 @ SV11 ) ) )
| ~ ( ~ ! [SY44: $i] :
( ~ ( ilf_type @ SY44 @ set_type )
| ~ ( member @ SY44 @ SV3 )
| ( member @ SY44 @ SV11 ) )
| ( subset @ SV3 @ SV11 ) ) ) )
= $true )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(87,plain,
( ( ilf_type @ sK2_SX0 @ set_type )
= $true ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(88,plain,
( ( ~ ( ilf_type @ sK3_SY41 @ set_type )
| ! [SY45: $i] :
( ~ ( ilf_type @ SY45 @ ( relation_type @ sK2_SX0 @ sK3_SY41 ) )
| ~ ( subset @ sK1_B @ SY45 )
| ( ilf_type @ sK1_B @ ( relation_type @ sK2_SX0 @ sK3_SY41 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[78]) ).
thf(89,plain,
! [SV5: $i] :
( ( ( ! [SY32: $i] :
~ ( ilf_type @ SY32 @ ( subset_type @ SV5 ) ) )
= $false )
| ( ( ilf_type @ SV5 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( ilf_type @ SV12 @ set_type )
| ! [SY46: $i] :
( ~ ( ilf_type @ SY46 @ set_type )
| ! [SY47: $i] :
( ~ ( ilf_type @ SY47 @ ( relation_type @ SV12 @ SY46 ) )
| ~ ( subset @ SV6 @ SY47 )
| ( subset @ SV6 @ ( cross_product @ SV12 @ SY46 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV7: $i,SV13: $i] :
( ( ( ~ ( ilf_type @ SV13 @ set_type )
| ! [SY48: $i] :
( ~ ( ilf_type @ SY48 @ set_type )
| ~ ( subset @ SV7 @ ( cross_product @ SV13 @ SY48 ) )
| ( ilf_type @ SV7 @ ( relation_type @ SV13 @ SY48 ) ) ) )
= $true )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ( ilf_type @ SV14 @ set_type )
| ~ ! [SY49: $i] :
~ ( ilf_type @ SY49 @ ( relation_type @ SV14 @ SV8 ) ) )
= $true )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(93,plain,
! [SV9: $i,SV15: $i] :
( ( ( ~ ( ilf_type @ SV15 @ set_type )
| ( ilf_type @ ( cross_product @ SV9 @ SV15 ) @ set_type ) )
= $true )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(94,plain,
! [SV2: $i,SV10: $i] :
( ( ( ~ ( ilf_type @ SV10 @ set_type ) )
= $true )
| ( ( ilf_type @ ( ordered_pair @ SV2 @ SV10 ) @ set_type )
= $true )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV3: $i,SV11: $i] :
( ( ( ~ ( ilf_type @ SV11 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subset @ SV3 @ SV11 )
| ! [SY43: $i] :
( ~ ( ilf_type @ SY43 @ set_type )
| ~ ( member @ SY43 @ SV3 )
| ( member @ SY43 @ SV11 ) ) )
| ~ ( ~ ! [SY44: $i] :
( ~ ( ilf_type @ SY44 @ set_type )
| ~ ( member @ SY44 @ SV3 )
| ( member @ SY44 @ SV11 ) )
| ( subset @ SV3 @ SV11 ) ) ) )
= $true )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(96,plain,
( ( ~ ( ilf_type @ sK3_SY41 @ set_type ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(97,plain,
( ( ! [SY45: $i] :
( ~ ( ilf_type @ SY45 @ ( relation_type @ sK2_SX0 @ sK3_SY41 ) )
| ~ ( subset @ sK1_B @ SY45 )
| ( ilf_type @ sK1_B @ ( relation_type @ sK2_SX0 @ sK3_SY41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(98,plain,
! [SV5: $i] :
( ( ( ~ ( ilf_type @ ( sK4_SY32 @ SV5 ) @ ( subset_type @ SV5 ) ) )
= $false )
| ( ( ilf_type @ SV5 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[89]) ).
thf(99,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( ilf_type @ SV12 @ set_type ) )
= $true )
| ( ( ! [SY46: $i] :
( ~ ( ilf_type @ SY46 @ set_type )
| ! [SY47: $i] :
( ~ ( ilf_type @ SY47 @ ( relation_type @ SV12 @ SY46 ) )
| ~ ( subset @ SV6 @ SY47 )
| ( subset @ SV6 @ ( cross_product @ SV12 @ SY46 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(100,plain,
! [SV7: $i,SV13: $i] :
( ( ( ~ ( ilf_type @ SV13 @ set_type ) )
= $true )
| ( ( ! [SY48: $i] :
( ~ ( ilf_type @ SY48 @ set_type )
| ~ ( subset @ SV7 @ ( cross_product @ SV13 @ SY48 ) )
| ( ilf_type @ SV7 @ ( relation_type @ SV13 @ SY48 ) ) ) )
= $true )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(101,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ( ilf_type @ SV14 @ set_type ) )
= $true )
| ( ( ~ ! [SY49: $i] :
~ ( ilf_type @ SY49 @ ( relation_type @ SV14 @ SV8 ) ) )
= $true )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(102,plain,
! [SV9: $i,SV15: $i] :
( ( ( ~ ( ilf_type @ SV15 @ set_type ) )
= $true )
| ( ( ilf_type @ ( cross_product @ SV9 @ SV15 ) @ set_type )
= $true )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(103,plain,
! [SV2: $i,SV10: $i] :
( ( ( ilf_type @ SV10 @ set_type )
= $false )
| ( ( ilf_type @ ( ordered_pair @ SV2 @ SV10 ) @ set_type )
= $true )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(104,plain,
! [SV3: $i,SV11: $i] :
( ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( subset @ SV3 @ SV11 )
| ! [SY43: $i] :
( ~ ( ilf_type @ SY43 @ set_type )
| ~ ( member @ SY43 @ SV3 )
| ( member @ SY43 @ SV11 ) ) )
| ~ ( ~ ! [SY44: $i] :
( ~ ( ilf_type @ SY44 @ set_type )
| ~ ( member @ SY44 @ SV3 )
| ( member @ SY44 @ SV11 ) )
| ( subset @ SV3 @ SV11 ) ) ) )
= $true )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(105,plain,
( ( ilf_type @ sK3_SY41 @ set_type )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(106,plain,
( ( ~ ( ilf_type @ sK5_SY45 @ ( relation_type @ sK2_SX0 @ sK3_SY41 ) )
| ~ ( subset @ sK1_B @ sK5_SY45 )
| ( ilf_type @ sK1_B @ ( relation_type @ sK2_SX0 @ sK3_SY41 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[97]) ).
thf(107,plain,
! [SV5: $i] :
( ( ( ilf_type @ ( sK4_SY32 @ SV5 ) @ ( subset_type @ SV5 ) )
= $true )
| ( ( ilf_type @ SV5 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(108,plain,
! [SV6: $i,SV12: $i] :
( ( ( ilf_type @ SV12 @ set_type )
= $false )
| ( ( ! [SY46: $i] :
( ~ ( ilf_type @ SY46 @ set_type )
| ! [SY47: $i] :
( ~ ( ilf_type @ SY47 @ ( relation_type @ SV12 @ SY46 ) )
| ~ ( subset @ SV6 @ SY47 )
| ( subset @ SV6 @ ( cross_product @ SV12 @ SY46 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(109,plain,
! [SV7: $i,SV13: $i] :
( ( ( ilf_type @ SV13 @ set_type )
= $false )
| ( ( ! [SY48: $i] :
( ~ ( ilf_type @ SY48 @ set_type )
| ~ ( subset @ SV7 @ ( cross_product @ SV13 @ SY48 ) )
| ( ilf_type @ SV7 @ ( relation_type @ SV13 @ SY48 ) ) ) )
= $true )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(110,plain,
! [SV8: $i,SV14: $i] :
( ( ( ilf_type @ SV14 @ set_type )
= $false )
| ( ( ~ ! [SY49: $i] :
~ ( ilf_type @ SY49 @ ( relation_type @ SV14 @ SV8 ) ) )
= $true )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(111,plain,
! [SV9: $i,SV15: $i] :
( ( ( ilf_type @ SV15 @ set_type )
= $false )
| ( ( ilf_type @ ( cross_product @ SV9 @ SV15 ) @ set_type )
= $true )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(112,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ( ~ ( subset @ SV3 @ SV11 )
| ! [SY43: $i] :
( ~ ( ilf_type @ SY43 @ set_type )
| ~ ( member @ SY43 @ SV3 )
| ( member @ SY43 @ SV11 ) ) )
| ~ ( ~ ! [SY44: $i] :
( ~ ( ilf_type @ SY44 @ set_type )
| ~ ( member @ SY44 @ SV3 )
| ( member @ SY44 @ SV11 ) )
| ( subset @ SV3 @ SV11 ) ) )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(113,plain,
( ( ~ ( ilf_type @ sK5_SY45 @ ( relation_type @ sK2_SX0 @ sK3_SY41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(114,plain,
( ( ~ ( subset @ sK1_B @ sK5_SY45 )
| ( ilf_type @ sK1_B @ ( relation_type @ sK2_SX0 @ sK3_SY41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(115,plain,
! [SV6: $i,SV12: $i,SV16: $i] :
( ( ( ~ ( ilf_type @ SV16 @ set_type )
| ! [SY50: $i] :
( ~ ( ilf_type @ SY50 @ ( relation_type @ SV12 @ SV16 ) )
| ~ ( subset @ SV6 @ SY50 )
| ( subset @ SV6 @ ( cross_product @ SV12 @ SV16 ) ) ) )
= $true )
| ( ( ilf_type @ SV12 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(116,plain,
! [SV13: $i,SV7: $i,SV17: $i] :
( ( ( ~ ( ilf_type @ SV17 @ set_type )
| ~ ( subset @ SV7 @ ( cross_product @ SV13 @ SV17 ) )
| ( ilf_type @ SV7 @ ( relation_type @ SV13 @ SV17 ) ) )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(117,plain,
! [SV8: $i,SV14: $i] :
( ( ( ! [SY49: $i] :
~ ( ilf_type @ SY49 @ ( relation_type @ SV14 @ SV8 ) ) )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(118,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ( ~ ( subset @ SV3 @ SV11 )
| ! [SY43: $i] :
( ~ ( ilf_type @ SY43 @ set_type )
| ~ ( member @ SY43 @ SV3 )
| ( member @ SY43 @ SV11 ) ) ) )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(119,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ( ~ ! [SY44: $i] :
( ~ ( ilf_type @ SY44 @ set_type )
| ~ ( member @ SY44 @ SV3 )
| ( member @ SY44 @ SV11 ) )
| ( subset @ SV3 @ SV11 ) ) )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(120,plain,
( ( ilf_type @ sK5_SY45 @ ( relation_type @ sK2_SX0 @ sK3_SY41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(121,plain,
( ( ~ ( subset @ sK1_B @ sK5_SY45 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(122,plain,
( ( ilf_type @ sK1_B @ ( relation_type @ sK2_SX0 @ sK3_SY41 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(123,plain,
! [SV6: $i,SV12: $i,SV16: $i] :
( ( ( ~ ( ilf_type @ SV16 @ set_type ) )
= $true )
| ( ( ! [SY50: $i] :
( ~ ( ilf_type @ SY50 @ ( relation_type @ SV12 @ SV16 ) )
| ~ ( subset @ SV6 @ SY50 )
| ( subset @ SV6 @ ( cross_product @ SV12 @ SV16 ) ) ) )
= $true )
| ( ( ilf_type @ SV12 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(124,plain,
! [SV13: $i,SV7: $i,SV17: $i] :
( ( ( ~ ( ilf_type @ SV17 @ set_type ) )
= $true )
| ( ( ~ ( subset @ SV7 @ ( cross_product @ SV13 @ SV17 ) )
| ( ilf_type @ SV7 @ ( relation_type @ SV13 @ SV17 ) ) )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(125,plain,
! [SV14: $i,SV8: $i] :
( ( ( ~ ( ilf_type @ ( sK6_SY49 @ SV8 @ SV14 ) @ ( relation_type @ SV14 @ SV8 ) ) )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[117]) ).
thf(126,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV11 )
| ! [SY43: $i] :
( ~ ( ilf_type @ SY43 @ set_type )
| ~ ( member @ SY43 @ SV3 )
| ( member @ SY43 @ SV11 ) ) )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(127,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ! [SY44: $i] :
( ~ ( ilf_type @ SY44 @ set_type )
| ~ ( member @ SY44 @ SV3 )
| ( member @ SY44 @ SV11 ) )
| ( subset @ SV3 @ SV11 ) )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(128,plain,
( ( subset @ sK1_B @ sK5_SY45 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(129,plain,
! [SV6: $i,SV12: $i,SV16: $i] :
( ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ! [SY50: $i] :
( ~ ( ilf_type @ SY50 @ ( relation_type @ SV12 @ SV16 ) )
| ~ ( subset @ SV6 @ SY50 )
| ( subset @ SV6 @ ( cross_product @ SV12 @ SV16 ) ) ) )
= $true )
| ( ( ilf_type @ SV12 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(130,plain,
! [SV13: $i,SV7: $i,SV17: $i] :
( ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( ~ ( subset @ SV7 @ ( cross_product @ SV13 @ SV17 ) )
| ( ilf_type @ SV7 @ ( relation_type @ SV13 @ SV17 ) ) )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(131,plain,
! [SV14: $i,SV8: $i] :
( ( ( ilf_type @ ( sK6_SY49 @ SV8 @ SV14 ) @ ( relation_type @ SV14 @ SV8 ) )
= $true )
| ( ( ilf_type @ SV14 @ set_type )
= $false )
| ( ( ilf_type @ SV8 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(132,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV11 ) )
= $true )
| ( ( ! [SY43: $i] :
( ~ ( ilf_type @ SY43 @ set_type )
| ~ ( member @ SY43 @ SV3 )
| ( member @ SY43 @ SV11 ) ) )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(133,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ! [SY44: $i] :
( ~ ( ilf_type @ SY44 @ set_type )
| ~ ( member @ SY44 @ SV3 )
| ( member @ SY44 @ SV11 ) ) )
= $true )
| ( ( subset @ SV3 @ SV11 )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(134,plain,
! [SV6: $i,SV16: $i,SV12: $i,SV18: $i] :
( ( ( ~ ( ilf_type @ SV18 @ ( relation_type @ SV12 @ SV16 ) )
| ~ ( subset @ SV6 @ SV18 )
| ( subset @ SV6 @ ( cross_product @ SV12 @ SV16 ) ) )
= $true )
| ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(135,plain,
! [SV17: $i,SV13: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ ( cross_product @ SV13 @ SV17 ) ) )
= $true )
| ( ( ilf_type @ SV7 @ ( relation_type @ SV13 @ SV17 ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( ilf_type @ SV13 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(136,plain,
! [SV11: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV11 )
= $false )
| ( ( ! [SY43: $i] :
( ~ ( ilf_type @ SY43 @ set_type )
| ~ ( member @ SY43 @ SV3 )
| ( member @ SY43 @ SV11 ) ) )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(137,plain,
! [SV11: $i,SV3: $i] :
( ( ( ! [SY44: $i] :
( ~ ( ilf_type @ SY44 @ set_type )
| ~ ( member @ SY44 @ SV3 )
| ( member @ SY44 @ SV11 ) ) )
= $false )
| ( ( subset @ SV3 @ SV11 )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(138,plain,
! [SV6: $i,SV16: $i,SV12: $i,SV18: $i] :
( ( ( ~ ( ilf_type @ SV18 @ ( relation_type @ SV12 @ SV16 ) ) )
= $true )
| ( ( ~ ( subset @ SV6 @ SV18 )
| ( subset @ SV6 @ ( cross_product @ SV12 @ SV16 ) ) )
= $true )
| ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(139,plain,
! [SV17: $i,SV13: $i,SV7: $i] :
( ( ( subset @ SV7 @ ( cross_product @ SV13 @ SV17 ) )
= $false )
| ( ( ilf_type @ SV7 @ ( relation_type @ SV13 @ SV17 ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( ilf_type @ SV13 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(140,plain,
! [SV11: $i,SV3: $i,SV19: $i] :
( ( ( ~ ( ilf_type @ SV19 @ set_type )
| ~ ( member @ SV19 @ SV3 )
| ( member @ SV19 @ SV11 ) )
= $true )
| ( ( subset @ SV3 @ SV11 )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(141,plain,
! [SV3: $i,SV11: $i] :
( ( ( ~ ( ilf_type @ ( sK7_SY44 @ SV11 @ SV3 ) @ set_type )
| ~ ( member @ ( sK7_SY44 @ SV11 @ SV3 ) @ SV3 )
| ( member @ ( sK7_SY44 @ SV11 @ SV3 ) @ SV11 ) )
= $false )
| ( ( subset @ SV3 @ SV11 )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[137]) ).
thf(142,plain,
! [SV6: $i,SV16: $i,SV12: $i,SV18: $i] :
( ( ( ilf_type @ SV18 @ ( relation_type @ SV12 @ SV16 ) )
= $false )
| ( ( ~ ( subset @ SV6 @ SV18 )
| ( subset @ SV6 @ ( cross_product @ SV12 @ SV16 ) ) )
= $true )
| ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(143,plain,
! [SV11: $i,SV3: $i,SV19: $i] :
( ( ( ~ ( ilf_type @ SV19 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV19 @ SV3 )
| ( member @ SV19 @ SV11 ) )
= $true )
| ( ( subset @ SV3 @ SV11 )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(144,plain,
! [SV3: $i,SV11: $i] :
( ( ( ~ ( ilf_type @ ( sK7_SY44 @ SV11 @ SV3 ) @ set_type ) )
= $false )
| ( ( subset @ SV3 @ SV11 )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(145,plain,
! [SV3: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK7_SY44 @ SV11 @ SV3 ) @ SV3 )
| ( member @ ( sK7_SY44 @ SV11 @ SV3 ) @ SV11 ) )
= $false )
| ( ( subset @ SV3 @ SV11 )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(146,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV18 ) )
= $true )
| ( ( subset @ SV6 @ ( cross_product @ SV12 @ SV16 ) )
= $true )
| ( ( ilf_type @ SV18 @ ( relation_type @ SV12 @ SV16 ) )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(147,plain,
! [SV11: $i,SV3: $i,SV19: $i] :
( ( ( ilf_type @ SV19 @ set_type )
= $false )
| ( ( ~ ( member @ SV19 @ SV3 )
| ( member @ SV19 @ SV11 ) )
= $true )
| ( ( subset @ SV3 @ SV11 )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(148,plain,
! [SV3: $i,SV11: $i] :
( ( ( ilf_type @ ( sK7_SY44 @ SV11 @ SV3 ) @ set_type )
= $true )
| ( ( subset @ SV3 @ SV11 )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(149,plain,
! [SV3: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK7_SY44 @ SV11 @ SV3 ) @ SV3 ) )
= $false )
| ( ( subset @ SV3 @ SV11 )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(150,plain,
! [SV3: $i,SV11: $i] :
( ( ( member @ ( sK7_SY44 @ SV11 @ SV3 ) @ SV11 )
= $false )
| ( ( subset @ SV3 @ SV11 )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(151,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV18 )
= $false )
| ( ( subset @ SV6 @ ( cross_product @ SV12 @ SV16 ) )
= $true )
| ( ( ilf_type @ SV18 @ ( relation_type @ SV12 @ SV16 ) )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(152,plain,
! [SV11: $i,SV3: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ SV3 ) )
= $true )
| ( ( member @ SV19 @ SV11 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false )
| ( ( subset @ SV3 @ SV11 )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(153,plain,
! [SV3: $i,SV11: $i] :
( ( ( member @ ( sK7_SY44 @ SV11 @ SV3 ) @ SV3 )
= $true )
| ( ( subset @ SV3 @ SV11 )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(154,plain,
! [SV11: $i,SV3: $i,SV19: $i] :
( ( ( member @ SV19 @ SV3 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false )
| ( ( subset @ SV3 @ SV11 )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(155,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[45,154,153,151,150,148,139,131,128,122,120,111,107,105,103,87,79,56]) ).
thf(156,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET642+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n011.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 14:47:51 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.24
% 0.08/0.24 No.of.Axioms: 9
% 0.08/0.24
% 0.08/0.24 Length.of.Defs: 0
% 0.08/0.24
% 0.08/0.24 Contains.Choice.Funs: false
% 0.08/0.24 .....
% 0.08/0.24
% 0.08/0.24 ********************************
% 0.08/0.24 * All subproblems solved! *
% 0.08/0.24 ********************************
% 0.08/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:155,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.24
% 0.08/0.24 %**** Beginning of derivation protocol ****
% 0.08/0.24 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25
% 0.08/0.25 %**** End of derivation protocol ****
% 0.08/0.25 %**** no. of clauses in derivation: 146 ****
% 0.08/0.25 %**** clause counter: 155 ****
% 0.08/0.25
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:155,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------