%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PUZ064-2 : TPTP v9.3.1. Released v3.2.0.
% 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 : n019.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 10:36:51 AM UTC 2026
% Result : Unsatisfiable 127.66s 25.84s
% Output : CNFRefutation 127.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 30
% Syntax : Number of formulae : 188 ( 155 unt; 0 typ; 0 def)
% Number of atoms : 712 ( 304 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 1970 ( 114 ~; 134 |; 0 &;1722 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 473 ( 0 ^; 473 !; 0 ?; 473 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Main_OsubsetI__1,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(tp_c_Mutil_Otiling,type,
c_Mutil_Otiling: $i > $i > $i ).
thf(tp_c_Relation_OImage,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(tp_c_Relation_Odiag,type,
c_Relation_Odiag: $i > $i > $i ).
thf(tp_c_UNIV,type,
c_UNIV: $i ).
thf(tp_c_emptyset,type,
c_emptyset: $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_inter,type,
c_inter: $i > $i > $i > $i ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_c_minus,type,
c_minus: $i > $i > $i > $i ).
thf(tp_c_uminus,type,
c_uminus: $i > $i > $i ).
thf(tp_c_union,type,
c_union: $i > $i > $i > $i ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_set,type,
tc_set: $i > $i ).
thf(tp_v_A,type,
v_A: $i ).
thf(tp_v_a,type,
v_a: $i ).
thf(tp_v_t,type,
v_t: $i ).
thf(tp_v_u,type,
v_u: $i ).
thf(1,axiom,
! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(2,axiom,
! [V_B: $i,V_A: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( V_A = V_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(3,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_A @ T_a )
| ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(4,axiom,
! [V_A: $i,T_a: $i] : ( c_lessequals @ c_emptyset @ V_A @ ( tc_set @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(5,axiom,
! [V_c: $i,T_a: $i] :
~ ( c_in @ V_c @ c_emptyset @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(6,axiom,
! [V_y: $i,T_a: $i] :
( ( c_uminus @ ( c_uminus @ V_y @ ( tc_set @ T_a ) ) @ ( tc_set @ T_a ) )
= V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
thf(7,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
thf(8,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ~ ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
thf(9,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ~ ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
thf(10,axiom,
! [V_y: $i,T_a: $i] :
( ( c_union @ V_y @ c_emptyset @ T_a )
= V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
thf(11,axiom,
! [V_y: $i,T_a: $i] :
( ( c_union @ c_emptyset @ V_y @ T_a )
= V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
thf(12,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_union @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ T_a )
= ( c_union @ V_A @ ( c_union @ V_B @ V_C @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__assoc_0) ).
thf(13,axiom,
! [V_y: $i,T_a: $i] :
( ( c_union @ V_y @ V_y @ T_a )
= V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
thf(14,axiom,
! [V_B: $i,T_a: $i] :
( ( c_union @ c_UNIV @ V_B @ T_a )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
thf(15,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_union @ V_A @ ( c_minus @ V_B @ V_A @ ( tc_set @ T_a ) ) @ T_a )
= ( c_union @ V_A @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
thf(16,axiom,
! [V_B: $i,V_A: $i,T_a: $i] :
( ( c_union @ ( c_minus @ V_B @ V_A @ ( tc_set @ T_a ) ) @ V_A @ T_a )
= ( c_union @ V_B @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
thf(17,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
thf(18,axiom,
! [V_y: $i,T_a: $i] :
( ( c_inter @ c_UNIV @ V_y @ T_a )
= V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
thf(19,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_minus @ V_A @ ( c_uminus @ V_B @ ( tc_set @ T_a ) ) @ ( tc_set @ T_a ) )
= ( c_inter @ V_A @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
thf(20,axiom,
! [T_a: $i] :
( ( c_uminus @ c_UNIV @ ( tc_set @ T_a ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
thf(21,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_uminus @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ ( tc_set @ T_a ) )
= ( c_union @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
thf(22,axiom,
! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Relation_OImage @ ( c_Relation_Odiag @ V_A @ T_a ) @ V_B @ T_a @ T_a )
= ( c_inter @ V_A @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
thf(23,axiom,
! [V_a: $i,V_A: $i,T_a: $i,V_t: $i] :
( ~ ( c_in @ V_a @ V_A @ ( tc_set @ T_a ) )
| ~ ( c_in @ V_t @ ( c_Mutil_Otiling @ V_A @ T_a ) @ ( tc_set @ T_a ) )
| ( ( c_inter @ V_a @ V_t @ T_a )
!= c_emptyset )
| ( c_in @ ( c_union @ V_a @ V_t @ T_a ) @ ( c_Mutil_Otiling @ V_A @ T_a ) @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Mutil_Otiling_OUn_0) ).
thf(24,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(25,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[24]) ).
thf(26,negated_conjecture,
( ( c_in @ ( c_union @ v_t @ v_u @ t_a ) @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) )
| ( ( c_inter @ v_t @ v_u @ t_a )
!= c_emptyset )
| ~ ( c_in @ v_u @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(27,negated_conjecture,
~ ( c_in @ ( c_union @ ( c_union @ v_a @ v_t @ t_a ) @ v_u @ t_a ) @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(28,negated_conjecture,
( ( c_inter @ ( c_union @ v_a @ v_t @ t_a ) @ v_u @ t_a )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(29,negated_conjecture,
c_in @ v_u @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(30,negated_conjecture,
( ( c_inter @ v_a @ v_t @ t_a )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(31,negated_conjecture,
c_in @ v_a @ v_A @ ( tc_set @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(32,plain,
$false = $false,
inference(unfold_def,[status(thm)],[25]) ).
thf(33,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(34,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( V_A = V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(35,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_A @ T_a )
| ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(36,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ c_emptyset @ V_A @ ( tc_set @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(37,plain,
( ( ! [V_c: $i,T_a: $i] :
~ ( c_in @ V_c @ c_emptyset @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(38,plain,
( ( ! [V_y: $i,T_a: $i] :
( ( c_uminus @ ( c_uminus @ V_y @ ( tc_set @ T_a ) ) @ ( tc_set @ T_a ) )
= V_y ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(39,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(40,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ~ ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(41,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ~ ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(42,plain,
( ( ! [V_y: $i,T_a: $i] :
( ( c_union @ V_y @ c_emptyset @ T_a )
= V_y ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(43,plain,
( ( ! [V_y: $i,T_a: $i] :
( ( c_union @ c_emptyset @ V_y @ T_a )
= V_y ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(44,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_union @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ T_a )
= ( c_union @ V_A @ ( c_union @ V_B @ V_C @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(45,plain,
( ( ! [V_y: $i,T_a: $i] :
( ( c_union @ V_y @ V_y @ T_a )
= V_y ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(46,plain,
( ( ! [V_B: $i,T_a: $i] :
( ( c_union @ c_UNIV @ V_B @ T_a )
= c_UNIV ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(47,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_union @ V_A @ ( c_minus @ V_B @ V_A @ ( tc_set @ T_a ) ) @ T_a )
= ( c_union @ V_A @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(48,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ( c_union @ ( c_minus @ V_B @ V_A @ ( tc_set @ T_a ) ) @ V_A @ T_a )
= ( c_union @ V_B @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(49,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(50,plain,
( ( ! [V_y: $i,T_a: $i] :
( ( c_inter @ c_UNIV @ V_y @ T_a )
= V_y ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(51,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_minus @ V_A @ ( c_uminus @ V_B @ ( tc_set @ T_a ) ) @ ( tc_set @ T_a ) )
= ( c_inter @ V_A @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(52,plain,
( ( ! [T_a: $i] :
( ( c_uminus @ c_UNIV @ ( tc_set @ T_a ) )
= c_emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(53,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_uminus @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ ( tc_set @ T_a ) )
= ( c_union @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(54,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Relation_OImage @ ( c_Relation_Odiag @ V_A @ T_a ) @ V_B @ T_a @ T_a )
= ( c_inter @ V_A @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(55,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_t: $i] :
( ~ ( c_in @ V_a @ V_A @ ( tc_set @ T_a ) )
| ~ ( c_in @ V_t @ ( c_Mutil_Otiling @ V_A @ T_a ) @ ( tc_set @ T_a ) )
| ( ( c_inter @ V_a @ V_t @ T_a )
!= c_emptyset )
| ( c_in @ ( c_union @ V_a @ V_t @ T_a ) @ ( c_Mutil_Otiling @ V_A @ T_a ) @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(56,plain,
( ( ( c_in @ ( c_union @ v_t @ v_u @ t_a ) @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) )
| ( ( c_inter @ v_t @ v_u @ t_a )
!= c_emptyset )
| ~ ( c_in @ v_u @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(57,plain,
( ( ~ ( c_in @ ( c_union @ ( c_union @ v_a @ v_t @ t_a ) @ v_u @ t_a ) @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(58,plain,
( ( ( c_inter @ ( c_union @ v_a @ v_t @ t_a ) @ v_u @ t_a )
= c_emptyset )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(59,plain,
( ( c_in @ v_u @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(60,plain,
( ( ( c_inter @ v_a @ v_t @ t_a )
= c_emptyset )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(61,plain,
( ( c_in @ v_a @ v_A @ ( tc_set @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(62,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(63,plain,
( ( c_in @ v_a @ v_A @ ( tc_set @ t_a ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(64,plain,
( ( ( c_inter @ v_a @ v_t @ t_a )
= c_emptyset )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(65,plain,
( ( c_in @ v_u @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(66,plain,
( ( ( c_inter @ ( c_union @ v_a @ v_t @ t_a ) @ v_u @ t_a )
= c_emptyset )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(67,plain,
( ( ~ ( c_in @ ( c_union @ ( c_union @ v_a @ v_t @ t_a ) @ v_u @ t_a ) @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(68,plain,
( ( ( c_in @ ( c_union @ v_t @ v_u @ t_a ) @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) )
| ( ( c_inter @ v_t @ v_u @ t_a )
!= c_emptyset )
| ~ ( c_in @ v_u @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(69,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_t: $i] :
( ~ ( c_in @ V_a @ V_A @ ( tc_set @ T_a ) )
| ~ ( c_in @ V_t @ ( c_Mutil_Otiling @ V_A @ T_a ) @ ( tc_set @ T_a ) )
| ( ( c_inter @ V_a @ V_t @ T_a )
!= c_emptyset )
| ( c_in @ ( c_union @ V_a @ V_t @ T_a ) @ ( c_Mutil_Otiling @ V_A @ T_a ) @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(70,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Relation_OImage @ ( c_Relation_Odiag @ V_A @ T_a ) @ V_B @ T_a @ T_a )
= ( c_inter @ V_A @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(71,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_uminus @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ ( tc_set @ T_a ) )
= ( c_union @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(72,plain,
( ( ! [T_a: $i] :
( ( c_uminus @ c_UNIV @ ( tc_set @ T_a ) )
= c_emptyset ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(73,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_minus @ V_A @ ( c_uminus @ V_B @ ( tc_set @ T_a ) ) @ ( tc_set @ T_a ) )
= ( c_inter @ V_A @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(74,plain,
( ( ! [V_y: $i,T_a: $i] :
( ( c_inter @ c_UNIV @ V_y @ T_a )
= V_y ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(75,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(76,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ( c_union @ ( c_minus @ V_B @ V_A @ ( tc_set @ T_a ) ) @ V_A @ T_a )
= ( c_union @ V_B @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(77,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_union @ V_A @ ( c_minus @ V_B @ V_A @ ( tc_set @ T_a ) ) @ T_a )
= ( c_union @ V_A @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(78,plain,
( ( ! [V_B: $i,T_a: $i] :
( ( c_union @ c_UNIV @ V_B @ T_a )
= c_UNIV ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(79,plain,
( ( ! [V_y: $i,T_a: $i] :
( ( c_union @ V_y @ V_y @ T_a )
= V_y ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(80,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_union @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ T_a )
= ( c_union @ V_A @ ( c_union @ V_B @ V_C @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(81,plain,
( ( ! [V_y: $i,T_a: $i] :
( ( c_union @ c_emptyset @ V_y @ T_a )
= V_y ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(82,plain,
( ( ! [V_y: $i,T_a: $i] :
( ( c_union @ V_y @ c_emptyset @ T_a )
= V_y ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(83,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ~ ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(84,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ~ ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(85,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(86,plain,
( ( ! [V_y: $i,T_a: $i] :
( ( c_uminus @ ( c_uminus @ V_y @ ( tc_set @ T_a ) ) @ ( tc_set @ T_a ) )
= V_y ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(87,plain,
( ( ! [V_c: $i,T_a: $i] :
~ ( c_in @ V_c @ c_emptyset @ T_a ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(88,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ c_emptyset @ V_A @ ( tc_set @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(89,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_A @ T_a )
| ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(90,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( V_A = V_B ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(91,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(92,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[62]) ).
thf(93,plain,
( ( ( c_in @ ( c_union @ v_t @ v_u @ t_a ) @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) )
| ( ( c_inter @ v_t @ v_u @ t_a )
!= c_emptyset )
| ~ ( c_in @ v_u @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(94,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_in @ SX0 @ SX1 @ ( tc_set @ SX2 ) )
| ~ ( c_in @ SX3 @ ( c_Mutil_Otiling @ SX1 @ SX2 ) @ ( tc_set @ SX2 ) )
| ( ( c_inter @ SX0 @ SX3 @ SX2 )
!= c_emptyset )
| ( c_in @ ( c_union @ SX0 @ SX3 @ SX2 ) @ ( c_Mutil_Otiling @ SX1 @ SX2 ) @ ( tc_set @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(95,plain,
( ( c_in @ ( c_union @ ( c_union @ v_a @ v_t @ t_a ) @ v_u @ t_a ) @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(96,plain,
! [SV1: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ( c_Relation_OImage @ ( c_Relation_Odiag @ SV1 @ SY64 ) @ SY65 @ SY64 @ SY64 )
= ( c_inter @ SV1 @ SY65 @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(97,plain,
! [SV2: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ( c_uminus @ ( c_minus @ SV2 @ SY66 @ ( tc_set @ SY67 ) ) @ ( tc_set @ SY67 ) )
= ( c_union @ ( c_uminus @ SV2 @ ( tc_set @ SY67 ) ) @ SY66 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(98,plain,
! [SV3: $i] :
( ( ( c_uminus @ c_UNIV @ ( tc_set @ SV3 ) )
= c_emptyset )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(99,plain,
! [SV4: $i] :
( ( ! [SY68: $i,SY69: $i] :
( ( c_minus @ SV4 @ ( c_uminus @ SY68 @ ( tc_set @ SY69 ) ) @ ( tc_set @ SY69 ) )
= ( c_inter @ SV4 @ SY68 @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(100,plain,
! [SV5: $i] :
( ( ! [SY70: $i] :
( ( c_inter @ c_UNIV @ SV5 @ SY70 )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(101,plain,
! [SV6: $i] :
( ( ! [SY71: $i,SY72: $i,SY73: $i] :
( ~ ( c_in @ SV6 @ ( c_inter @ SY71 @ SY72 @ SY73 ) @ SY73 )
| ( c_in @ SV6 @ SY72 @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(102,plain,
! [SV7: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ( c_union @ ( c_minus @ SV7 @ SY74 @ ( tc_set @ SY75 ) ) @ SY74 @ SY75 )
= ( c_union @ SV7 @ SY74 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(103,plain,
! [SV8: $i] :
( ( ! [SY76: $i,SY77: $i] :
( ( c_union @ SV8 @ ( c_minus @ SY76 @ SV8 @ ( tc_set @ SY77 ) ) @ SY77 )
= ( c_union @ SV8 @ SY76 @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(104,plain,
! [SV9: $i] :
( ( ! [SY78: $i] :
( ( c_union @ c_UNIV @ SV9 @ SY78 )
= c_UNIV ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(105,plain,
! [SV10: $i] :
( ( ! [SY79: $i] :
( ( c_union @ SV10 @ SV10 @ SY79 )
= SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(106,plain,
! [SV11: $i] :
( ( ! [SY80: $i,SY81: $i,SY82: $i] :
( ( c_union @ ( c_union @ SV11 @ SY80 @ SY81 ) @ SY82 @ SY81 )
= ( c_union @ SV11 @ ( c_union @ SY80 @ SY82 @ SY81 ) @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(107,plain,
! [SV12: $i] :
( ( ! [SY83: $i] :
( ( c_union @ c_emptyset @ SV12 @ SY83 )
= SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(108,plain,
! [SV13: $i] :
( ( ! [SY84: $i] :
( ( c_union @ SV13 @ c_emptyset @ SY84 )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(109,plain,
! [SV14: $i] :
( ( ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ( c_lessequals @ ( c_union @ SV14 @ SY85 @ SY86 ) @ SY87 @ ( tc_set @ SY86 ) )
| ( c_lessequals @ SV14 @ SY87 @ ( tc_set @ SY86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(110,plain,
! [SV15: $i] :
( ( ! [SY88: $i,SY89: $i,SY90: $i] :
( ~ ( c_lessequals @ ( c_union @ SV15 @ SY88 @ SY89 ) @ SY90 @ ( tc_set @ SY89 ) )
| ( c_lessequals @ SY88 @ SY90 @ ( tc_set @ SY89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(111,plain,
! [SV16: $i] :
( ( ! [SY91: $i,SY92: $i,SY93: $i] :
( ~ ( c_lessequals @ SV16 @ SY91 @ ( tc_set @ SY92 ) )
| ~ ( c_lessequals @ SY93 @ SY91 @ ( tc_set @ SY92 ) )
| ( c_lessequals @ ( c_union @ SY93 @ SV16 @ SY92 ) @ SY91 @ ( tc_set @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(112,plain,
! [SV17: $i] :
( ( ! [SY94: $i] :
( ( c_uminus @ ( c_uminus @ SV17 @ ( tc_set @ SY94 ) ) @ ( tc_set @ SY94 ) )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(113,plain,
! [SV18: $i] :
( ( ! [SY95: $i] :
~ ( c_in @ SV18 @ c_emptyset @ SY95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(114,plain,
! [SV19: $i] :
( ( ! [SY96: $i] : ( c_lessequals @ c_emptyset @ SV19 @ ( tc_set @ SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(115,plain,
! [SV20: $i] :
( ( ! [SY97: $i,SY98: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ SV20 @ SY97 @ SY98 ) @ SV20 @ SY98 )
| ( c_lessequals @ SV20 @ SY97 @ ( tc_set @ SY98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(116,plain,
! [SV21: $i] :
( ( ! [SY99: $i,SY100: $i] :
( ~ ( c_lessequals @ SV21 @ SY99 @ ( tc_set @ SY100 ) )
| ~ ( c_lessequals @ SY99 @ SV21 @ ( tc_set @ SY100 ) )
| ( SY99 = SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(117,plain,
! [SV22: $i] :
( ( ! [SY101: $i] : ( c_lessequals @ SV22 @ SV22 @ ( tc_set @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(118,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(119,plain,
( ( ( c_in @ ( c_union @ v_t @ v_u @ t_a ) @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) )
= $true )
| ( ( ( ( c_inter @ v_t @ v_u @ t_a )
!= c_emptyset )
| ~ ( c_in @ v_u @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(120,plain,
! [SV23: $i] :
( ( ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ( c_in @ SV23 @ SY102 @ ( tc_set @ SY103 ) )
| ~ ( c_in @ SY104 @ ( c_Mutil_Otiling @ SY102 @ SY103 ) @ ( tc_set @ SY103 ) )
| ( ( c_inter @ SV23 @ SY104 @ SY103 )
!= c_emptyset )
| ( c_in @ ( c_union @ SV23 @ SY104 @ SY103 ) @ ( c_Mutil_Otiling @ SY102 @ SY103 ) @ ( tc_set @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(121,plain,
! [SV24: $i,SV1: $i] :
( ( ! [SY105: $i] :
( ( c_Relation_OImage @ ( c_Relation_Odiag @ SV1 @ SV24 ) @ SY105 @ SV24 @ SV24 )
= ( c_inter @ SV1 @ SY105 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(122,plain,
! [SV25: $i,SV2: $i] :
( ( ! [SY106: $i] :
( ( c_uminus @ ( c_minus @ SV2 @ SV25 @ ( tc_set @ SY106 ) ) @ ( tc_set @ SY106 ) )
= ( c_union @ ( c_uminus @ SV2 @ ( tc_set @ SY106 ) ) @ SV25 @ SY106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(123,plain,
! [SV26: $i,SV4: $i] :
( ( ! [SY107: $i] :
( ( c_minus @ SV4 @ ( c_uminus @ SV26 @ ( tc_set @ SY107 ) ) @ ( tc_set @ SY107 ) )
= ( c_inter @ SV4 @ SV26 @ SY107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(124,plain,
! [SV27: $i,SV5: $i] :
( ( ( c_inter @ c_UNIV @ SV5 @ SV27 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(125,plain,
! [SV28: $i,SV6: $i] :
( ( ! [SY108: $i,SY109: $i] :
( ~ ( c_in @ SV6 @ ( c_inter @ SV28 @ SY108 @ SY109 ) @ SY109 )
| ( c_in @ SV6 @ SY108 @ SY109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(126,plain,
! [SV29: $i,SV7: $i] :
( ( ! [SY110: $i] :
( ( c_union @ ( c_minus @ SV7 @ SV29 @ ( tc_set @ SY110 ) ) @ SV29 @ SY110 )
= ( c_union @ SV7 @ SV29 @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(127,plain,
! [SV30: $i,SV8: $i] :
( ( ! [SY111: $i] :
( ( c_union @ SV8 @ ( c_minus @ SV30 @ SV8 @ ( tc_set @ SY111 ) ) @ SY111 )
= ( c_union @ SV8 @ SV30 @ SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(128,plain,
! [SV31: $i,SV9: $i] :
( ( ( c_union @ c_UNIV @ SV9 @ SV31 )
= c_UNIV )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(129,plain,
! [SV32: $i,SV10: $i] :
( ( ( c_union @ SV10 @ SV10 @ SV32 )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(130,plain,
! [SV33: $i,SV11: $i] :
( ( ! [SY112: $i,SY113: $i] :
( ( c_union @ ( c_union @ SV11 @ SV33 @ SY112 ) @ SY113 @ SY112 )
= ( c_union @ SV11 @ ( c_union @ SV33 @ SY113 @ SY112 ) @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(131,plain,
! [SV34: $i,SV12: $i] :
( ( ( c_union @ c_emptyset @ SV12 @ SV34 )
= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(132,plain,
! [SV35: $i,SV13: $i] :
( ( ( c_union @ SV13 @ c_emptyset @ SV35 )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(133,plain,
! [SV36: $i,SV14: $i] :
( ( ! [SY114: $i,SY115: $i] :
( ~ ( c_lessequals @ ( c_union @ SV14 @ SV36 @ SY114 ) @ SY115 @ ( tc_set @ SY114 ) )
| ( c_lessequals @ SV14 @ SY115 @ ( tc_set @ SY114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(134,plain,
! [SV37: $i,SV15: $i] :
( ( ! [SY116: $i,SY117: $i] :
( ~ ( c_lessequals @ ( c_union @ SV15 @ SV37 @ SY116 ) @ SY117 @ ( tc_set @ SY116 ) )
| ( c_lessequals @ SV37 @ SY117 @ ( tc_set @ SY116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(135,plain,
! [SV38: $i,SV16: $i] :
( ( ! [SY118: $i,SY119: $i] :
( ~ ( c_lessequals @ SV16 @ SV38 @ ( tc_set @ SY118 ) )
| ~ ( c_lessequals @ SY119 @ SV38 @ ( tc_set @ SY118 ) )
| ( c_lessequals @ ( c_union @ SY119 @ SV16 @ SY118 ) @ SV38 @ ( tc_set @ SY118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(136,plain,
! [SV39: $i,SV17: $i] :
( ( ( c_uminus @ ( c_uminus @ SV17 @ ( tc_set @ SV39 ) ) @ ( tc_set @ SV39 ) )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(137,plain,
! [SV40: $i,SV18: $i] :
( ( ~ ( c_in @ SV18 @ c_emptyset @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(138,plain,
! [SV41: $i,SV19: $i] :
( ( c_lessequals @ c_emptyset @ SV19 @ ( tc_set @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(139,plain,
! [SV42: $i,SV20: $i] :
( ( ! [SY120: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ SV20 @ SV42 @ SY120 ) @ SV20 @ SY120 )
| ( c_lessequals @ SV20 @ SV42 @ ( tc_set @ SY120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(140,plain,
! [SV43: $i,SV21: $i] :
( ( ! [SY121: $i] :
( ~ ( c_lessequals @ SV21 @ SV43 @ ( tc_set @ SY121 ) )
| ~ ( c_lessequals @ SV43 @ SV21 @ ( tc_set @ SY121 ) )
| ( SV43 = SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(141,plain,
! [SV44: $i,SV22: $i] :
( ( c_lessequals @ SV22 @ SV22 @ ( tc_set @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(142,plain,
( ( ( ( c_inter @ v_t @ v_u @ t_a )
!= c_emptyset )
= $true )
| ( ( ~ ( c_in @ v_u @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_union @ v_t @ v_u @ t_a ) @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(143,plain,
! [SV45: $i,SV23: $i] :
( ( ! [SY122: $i,SY123: $i] :
( ~ ( c_in @ SV23 @ SV45 @ ( tc_set @ SY122 ) )
| ~ ( c_in @ SY123 @ ( c_Mutil_Otiling @ SV45 @ SY122 ) @ ( tc_set @ SY122 ) )
| ( ( c_inter @ SV23 @ SY123 @ SY122 )
!= c_emptyset )
| ( c_in @ ( c_union @ SV23 @ SY123 @ SY122 ) @ ( c_Mutil_Otiling @ SV45 @ SY122 ) @ ( tc_set @ SY122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(144,plain,
! [SV46: $i,SV24: $i,SV1: $i] :
( ( ( c_Relation_OImage @ ( c_Relation_Odiag @ SV1 @ SV24 ) @ SV46 @ SV24 @ SV24 )
= ( c_inter @ SV1 @ SV46 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(145,plain,
! [SV47: $i,SV25: $i,SV2: $i] :
( ( ( c_uminus @ ( c_minus @ SV2 @ SV25 @ ( tc_set @ SV47 ) ) @ ( tc_set @ SV47 ) )
= ( c_union @ ( c_uminus @ SV2 @ ( tc_set @ SV47 ) ) @ SV25 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(146,plain,
! [SV48: $i,SV26: $i,SV4: $i] :
( ( ( c_minus @ SV4 @ ( c_uminus @ SV26 @ ( tc_set @ SV48 ) ) @ ( tc_set @ SV48 ) )
= ( c_inter @ SV4 @ SV26 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(147,plain,
! [SV49: $i,SV28: $i,SV6: $i] :
( ( ! [SY124: $i] :
( ~ ( c_in @ SV6 @ ( c_inter @ SV28 @ SV49 @ SY124 ) @ SY124 )
| ( c_in @ SV6 @ SV49 @ SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(148,plain,
! [SV50: $i,SV29: $i,SV7: $i] :
( ( ( c_union @ ( c_minus @ SV7 @ SV29 @ ( tc_set @ SV50 ) ) @ SV29 @ SV50 )
= ( c_union @ SV7 @ SV29 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(149,plain,
! [SV51: $i,SV30: $i,SV8: $i] :
( ( ( c_union @ SV8 @ ( c_minus @ SV30 @ SV8 @ ( tc_set @ SV51 ) ) @ SV51 )
= ( c_union @ SV8 @ SV30 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(150,plain,
! [SV52: $i,SV33: $i,SV11: $i] :
( ( ! [SY125: $i] :
( ( c_union @ ( c_union @ SV11 @ SV33 @ SV52 ) @ SY125 @ SV52 )
= ( c_union @ SV11 @ ( c_union @ SV33 @ SY125 @ SV52 ) @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(151,plain,
! [SV53: $i,SV36: $i,SV14: $i] :
( ( ! [SY126: $i] :
( ~ ( c_lessequals @ ( c_union @ SV14 @ SV36 @ SV53 ) @ SY126 @ ( tc_set @ SV53 ) )
| ( c_lessequals @ SV14 @ SY126 @ ( tc_set @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(152,plain,
! [SV54: $i,SV37: $i,SV15: $i] :
( ( ! [SY127: $i] :
( ~ ( c_lessequals @ ( c_union @ SV15 @ SV37 @ SV54 ) @ SY127 @ ( tc_set @ SV54 ) )
| ( c_lessequals @ SV37 @ SY127 @ ( tc_set @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(153,plain,
! [SV55: $i,SV38: $i,SV16: $i] :
( ( ! [SY128: $i] :
( ~ ( c_lessequals @ SV16 @ SV38 @ ( tc_set @ SV55 ) )
| ~ ( c_lessequals @ SY128 @ SV38 @ ( tc_set @ SV55 ) )
| ( c_lessequals @ ( c_union @ SY128 @ SV16 @ SV55 ) @ SV38 @ ( tc_set @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(154,plain,
! [SV40: $i,SV18: $i] :
( ( c_in @ SV18 @ c_emptyset @ SV40 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(155,plain,
! [SV56: $i,SV42: $i,SV20: $i] :
( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV20 @ SV42 @ SV56 ) @ SV20 @ SV56 )
| ( c_lessequals @ SV20 @ SV42 @ ( tc_set @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(156,plain,
! [SV57: $i,SV43: $i,SV21: $i] :
( ( ~ ( c_lessequals @ SV21 @ SV43 @ ( tc_set @ SV57 ) )
| ~ ( c_lessequals @ SV43 @ SV21 @ ( tc_set @ SV57 ) )
| ( SV43 = SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(157,plain,
( ( ( ( c_inter @ v_t @ v_u @ t_a )
= c_emptyset )
= $false )
| ( ( ~ ( c_in @ v_u @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_union @ v_t @ v_u @ t_a ) @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(158,plain,
! [SV58: $i,SV45: $i,SV23: $i] :
( ( ! [SY129: $i] :
( ~ ( c_in @ SV23 @ SV45 @ ( tc_set @ SV58 ) )
| ~ ( c_in @ SY129 @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) )
| ( ( c_inter @ SV23 @ SY129 @ SV58 )
!= c_emptyset )
| ( c_in @ ( c_union @ SV23 @ SY129 @ SV58 ) @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(159,plain,
! [SV59: $i,SV49: $i,SV28: $i,SV6: $i] :
( ( ~ ( c_in @ SV6 @ ( c_inter @ SV28 @ SV49 @ SV59 ) @ SV59 )
| ( c_in @ SV6 @ SV49 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(160,plain,
! [SV60: $i,SV52: $i,SV33: $i,SV11: $i] :
( ( ( c_union @ ( c_union @ SV11 @ SV33 @ SV52 ) @ SV60 @ SV52 )
= ( c_union @ SV11 @ ( c_union @ SV33 @ SV60 @ SV52 ) @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(161,plain,
! [SV61: $i,SV53: $i,SV36: $i,SV14: $i] :
( ( ~ ( c_lessequals @ ( c_union @ SV14 @ SV36 @ SV53 ) @ SV61 @ ( tc_set @ SV53 ) )
| ( c_lessequals @ SV14 @ SV61 @ ( tc_set @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(162,plain,
! [SV62: $i,SV54: $i,SV37: $i,SV15: $i] :
( ( ~ ( c_lessequals @ ( c_union @ SV15 @ SV37 @ SV54 ) @ SV62 @ ( tc_set @ SV54 ) )
| ( c_lessequals @ SV37 @ SV62 @ ( tc_set @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(163,plain,
! [SV63: $i,SV55: $i,SV38: $i,SV16: $i] :
( ( ~ ( c_lessequals @ SV16 @ SV38 @ ( tc_set @ SV55 ) )
| ~ ( c_lessequals @ SV63 @ SV38 @ ( tc_set @ SV55 ) )
| ( c_lessequals @ ( c_union @ SV63 @ SV16 @ SV55 ) @ SV38 @ ( tc_set @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(164,plain,
! [SV56: $i,SV42: $i,SV20: $i] :
( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV20 @ SV42 @ SV56 ) @ SV20 @ SV56 )
= $true )
| ( ( c_lessequals @ SV20 @ SV42 @ ( tc_set @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(165,plain,
! [SV57: $i,SV43: $i,SV21: $i] :
( ( ( ~ ( c_lessequals @ SV21 @ SV43 @ ( tc_set @ SV57 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV43 @ SV21 @ ( tc_set @ SV57 ) )
| ( SV43 = SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(166,plain,
( ( ( c_in @ v_u @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) )
= $false )
| ( ( ( c_inter @ v_t @ v_u @ t_a )
= c_emptyset )
= $false )
| ( ( c_in @ ( c_union @ v_t @ v_u @ t_a ) @ ( c_Mutil_Otiling @ v_A @ t_a ) @ ( tc_set @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(167,plain,
! [SV64: $i,SV58: $i,SV45: $i,SV23: $i] :
( ( ~ ( c_in @ SV23 @ SV45 @ ( tc_set @ SV58 ) )
| ~ ( c_in @ SV64 @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) )
| ( ( c_inter @ SV23 @ SV64 @ SV58 )
!= c_emptyset )
| ( c_in @ ( c_union @ SV23 @ SV64 @ SV58 ) @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(168,plain,
! [SV59: $i,SV49: $i,SV28: $i,SV6: $i] :
( ( ( ~ ( c_in @ SV6 @ ( c_inter @ SV28 @ SV49 @ SV59 ) @ SV59 ) )
= $true )
| ( ( c_in @ SV6 @ SV49 @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(169,plain,
! [SV61: $i,SV53: $i,SV36: $i,SV14: $i] :
( ( ( ~ ( c_lessequals @ ( c_union @ SV14 @ SV36 @ SV53 ) @ SV61 @ ( tc_set @ SV53 ) ) )
= $true )
| ( ( c_lessequals @ SV14 @ SV61 @ ( tc_set @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(170,plain,
! [SV62: $i,SV54: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( c_lessequals @ ( c_union @ SV15 @ SV37 @ SV54 ) @ SV62 @ ( tc_set @ SV54 ) ) )
= $true )
| ( ( c_lessequals @ SV37 @ SV62 @ ( tc_set @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(171,plain,
! [SV63: $i,SV55: $i,SV38: $i,SV16: $i] :
( ( ( ~ ( c_lessequals @ SV16 @ SV38 @ ( tc_set @ SV55 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV63 @ SV38 @ ( tc_set @ SV55 ) )
| ( c_lessequals @ ( c_union @ SV63 @ SV16 @ SV55 ) @ SV38 @ ( tc_set @ SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(172,plain,
! [SV57: $i,SV43: $i,SV21: $i] :
( ( ( c_lessequals @ SV21 @ SV43 @ ( tc_set @ SV57 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV43 @ SV21 @ ( tc_set @ SV57 ) )
| ( SV43 = SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(173,plain,
! [SV64: $i,SV58: $i,SV45: $i,SV23: $i] :
( ( ( ~ ( c_in @ SV23 @ SV45 @ ( tc_set @ SV58 ) ) )
= $true )
| ( ( ~ ( c_in @ SV64 @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) )
| ( ( c_inter @ SV23 @ SV64 @ SV58 )
!= c_emptyset )
| ( c_in @ ( c_union @ SV23 @ SV64 @ SV58 ) @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(174,plain,
! [SV59: $i,SV49: $i,SV28: $i,SV6: $i] :
( ( ( c_in @ SV6 @ ( c_inter @ SV28 @ SV49 @ SV59 ) @ SV59 )
= $false )
| ( ( c_in @ SV6 @ SV49 @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(175,plain,
! [SV61: $i,SV53: $i,SV36: $i,SV14: $i] :
( ( ( c_lessequals @ ( c_union @ SV14 @ SV36 @ SV53 ) @ SV61 @ ( tc_set @ SV53 ) )
= $false )
| ( ( c_lessequals @ SV14 @ SV61 @ ( tc_set @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(176,plain,
! [SV62: $i,SV54: $i,SV37: $i,SV15: $i] :
( ( ( c_lessequals @ ( c_union @ SV15 @ SV37 @ SV54 ) @ SV62 @ ( tc_set @ SV54 ) )
= $false )
| ( ( c_lessequals @ SV37 @ SV62 @ ( tc_set @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(177,plain,
! [SV63: $i,SV55: $i,SV38: $i,SV16: $i] :
( ( ( c_lessequals @ SV16 @ SV38 @ ( tc_set @ SV55 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV63 @ SV38 @ ( tc_set @ SV55 ) )
| ( c_lessequals @ ( c_union @ SV63 @ SV16 @ SV55 ) @ SV38 @ ( tc_set @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(178,plain,
! [SV57: $i,SV21: $i,SV43: $i] :
( ( ( ~ ( c_lessequals @ SV43 @ SV21 @ ( tc_set @ SV57 ) ) )
= $true )
| ( ( SV43 = SV21 )
= $true )
| ( ( c_lessequals @ SV21 @ SV43 @ ( tc_set @ SV57 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(179,plain,
! [SV64: $i,SV58: $i,SV45: $i,SV23: $i] :
( ( ( c_in @ SV23 @ SV45 @ ( tc_set @ SV58 ) )
= $false )
| ( ( ~ ( c_in @ SV64 @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) )
| ( ( c_inter @ SV23 @ SV64 @ SV58 )
!= c_emptyset )
| ( c_in @ ( c_union @ SV23 @ SV64 @ SV58 ) @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(180,plain,
! [SV16: $i,SV55: $i,SV38: $i,SV63: $i] :
( ( ( ~ ( c_lessequals @ SV63 @ SV38 @ ( tc_set @ SV55 ) ) )
= $true )
| ( ( c_lessequals @ ( c_union @ SV63 @ SV16 @ SV55 ) @ SV38 @ ( tc_set @ SV55 ) )
= $true )
| ( ( c_lessequals @ SV16 @ SV38 @ ( tc_set @ SV55 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(181,plain,
! [SV57: $i,SV21: $i,SV43: $i] :
( ( ( c_lessequals @ SV43 @ SV21 @ ( tc_set @ SV57 ) )
= $false )
| ( ( SV43 = SV21 )
= $true )
| ( ( c_lessequals @ SV21 @ SV43 @ ( tc_set @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(182,plain,
! [SV23: $i,SV58: $i,SV45: $i,SV64: $i] :
( ( ( ~ ( c_in @ SV64 @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) ) )
= $true )
| ( ( ( ( c_inter @ SV23 @ SV64 @ SV58 )
!= c_emptyset )
| ( c_in @ ( c_union @ SV23 @ SV64 @ SV58 ) @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) ) )
= $true )
| ( ( c_in @ SV23 @ SV45 @ ( tc_set @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(183,plain,
! [SV16: $i,SV55: $i,SV38: $i,SV63: $i] :
( ( ( c_lessequals @ SV63 @ SV38 @ ( tc_set @ SV55 ) )
= $false )
| ( ( c_lessequals @ ( c_union @ SV63 @ SV16 @ SV55 ) @ SV38 @ ( tc_set @ SV55 ) )
= $true )
| ( ( c_lessequals @ SV16 @ SV38 @ ( tc_set @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(184,plain,
! [SV23: $i,SV58: $i,SV45: $i,SV64: $i] :
( ( ( c_in @ SV64 @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) )
= $false )
| ( ( ( ( c_inter @ SV23 @ SV64 @ SV58 )
!= c_emptyset )
| ( c_in @ ( c_union @ SV23 @ SV64 @ SV58 ) @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) ) )
= $true )
| ( ( c_in @ SV23 @ SV45 @ ( tc_set @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(185,plain,
! [SV45: $i,SV58: $i,SV64: $i,SV23: $i] :
( ( ( ( c_inter @ SV23 @ SV64 @ SV58 )
!= c_emptyset )
= $true )
| ( ( c_in @ ( c_union @ SV23 @ SV64 @ SV58 ) @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) )
= $true )
| ( ( c_in @ SV64 @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) )
= $false )
| ( ( c_in @ SV23 @ SV45 @ ( tc_set @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(186,plain,
! [SV45: $i,SV58: $i,SV64: $i,SV23: $i] :
( ( ( ( c_inter @ SV23 @ SV64 @ SV58 )
= c_emptyset )
= $false )
| ( ( c_in @ ( c_union @ SV23 @ SV64 @ SV58 ) @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) )
= $true )
| ( ( c_in @ SV64 @ ( c_Mutil_Otiling @ SV45 @ SV58 ) @ ( tc_set @ SV58 ) )
= $false )
| ( ( c_in @ SV23 @ SV45 @ ( tc_set @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(187,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[63,186,183,181,176,175,174,166,164,160,154,149,148,146,145,144,141,138,136,132,131,129,128,124,118,98,95,66,65,64]) ).
thf(188,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ064-2 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.09/0.17 % Computer : n019.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 13:59:01 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 127.66/25.84
% 127.66/25.84 No.of.Axioms: 29
% 127.66/25.84
% 127.66/25.84 Length.of.Defs: 0
% 127.66/25.84
% 127.66/25.84 Contains.Choice.Funs: false
% 127.66/25.84 .....
% 127.66/25.84
% 127.66/25.84 ********************************
% 127.66/25.84 * All subproblems solved! *
% 127.66/25.84 ********************************
% 127.66/25.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:29,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:187,loop_count:0,foatp_calls:1,translation:fof_full)
% 127.66/25.84
% 127.66/25.84 %**** Beginning of derivation protocol ****
% 127.66/25.84 % SZS output start CNFRefutation
% See solution above
% 127.66/25.84
% 127.66/25.84 %**** End of derivation protocol ****
% 127.66/25.84 %**** no. of clauses in derivation: 188 ****
% 127.66/25.84 %**** clause counter: 187 ****
% 127.66/25.84
% 127.66/25.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:29,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:187,loop_count:0,foatp_calls:1,translation:fof_full)
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