%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LAT276-2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 10:27:11 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 88 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 486 ( 131 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1826 ( 104 ~; 148 |; 0 &;1574 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 119 ( 0 ^; 119 !; 0 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Pair,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tp_c_Tarski_Olub,type,
c_Tarski_Olub: $i > $i > $i > $i ).
thf(tp_c_Tarski_Opotype_Oorder,type,
c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).
thf(tp_c_Tarski_Opotype_Opset,type,
c_Tarski_Opotype_Opset: $i > $i > $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_Product__Type_Ounit,type,
tc_Product__Type_Ounit: $i ).
thf(tp_tc_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_tc_set,type,
tc_set: $i > $i ).
thf(tp_v_A,type,
v_A: $i ).
thf(tp_v_S,type,
v_S: $i ).
thf(tp_v_cl,type,
v_cl: $i ).
thf(tp_v_r,type,
v_r: $i ).
thf(tp_v_sko__4mP,type,
v_sko__4mP: $i > $i > $i > $i ).
thf(tp_v_xa,type,
v_xa: $i ).
thf(1,axiom,
( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
thf(2,axiom,
! [V_x: $i,V_S: $i] :
( ~ ( c_in @ V_x @ V_S @ t_a )
| ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ V_x @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0) ).
thf(3,axiom,
! [V_L: $i,V_S: $i] :
( ~ ( c_in @ V_L @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ V_L @ V_S @ v_r ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1) ).
thf(4,axiom,
! [V_L: $i,V_S: $i] :
( ~ ( c_in @ V_L @ v_A @ t_a )
| ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mP @ V_L @ V_S @ v_r ) @ V_S @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0) ).
thf(5,axiom,
( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
thf(6,axiom,
! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(7,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(8,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,negated_conjecture,
! [V_U: $i] :
( ( c_in @ ( c_Pair @ V_U @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_U @ v_S @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_9) ).
thf(10,negated_conjecture,
( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(11,negated_conjecture,
( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ v_xa @ v_S @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(12,negated_conjecture,
( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(13,negated_conjecture,
! [V_V: $i] :
( ( c_in @ ( c_Pair @ V_V @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_V @ v_S @ t_a )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_10) ).
thf(14,negated_conjecture,
c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(15,plain,
$false = $false,
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,plain,
( ( ! [V_x: $i,V_S: $i] :
( ~ ( c_in @ V_x @ V_S @ t_a )
| ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ V_x @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(18,plain,
( ( ! [V_L: $i,V_S: $i] :
( ~ ( c_in @ V_L @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ V_L @ V_S @ v_r ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [V_L: $i,V_S: $i] :
( ~ ( c_in @ V_L @ v_A @ t_a )
| ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mP @ V_L @ V_S @ v_r ) @ V_S @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(20,plain,
( ( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(22,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( c_Pair @ V_U @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_U @ v_S @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(23,plain,
( ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(24,plain,
( ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ v_xa @ v_S @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(25,plain,
( ( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(26,plain,
( ( ! [V_V: $i] :
( ( c_in @ ( c_Pair @ V_V @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_V @ v_S @ t_a )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(27,plain,
( ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(28,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(29,plain,
( ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(30,plain,
( ( ! [V_V: $i] :
( ( c_in @ ( c_Pair @ V_V @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_V @ v_S @ t_a )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(31,plain,
( ( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(32,plain,
( ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ v_xa @ v_S @ t_a ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(33,plain,
( ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(34,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( c_Pair @ V_U @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_U @ v_S @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(35,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(36,plain,
( ( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(37,plain,
( ( ! [V_L: $i,V_S: $i] :
( ~ ( c_in @ V_L @ v_A @ t_a )
| ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mP @ V_L @ V_S @ v_r ) @ V_S @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(38,plain,
( ( ! [V_L: $i,V_S: $i] :
( ~ ( c_in @ V_L @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ V_L @ V_S @ v_r ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(39,plain,
( ( ! [V_x: $i,V_S: $i] :
( ~ ( c_in @ V_x @ V_S @ t_a )
| ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ V_x @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(40,plain,
( ( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(41,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[28]) ).
thf(42,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ SV1 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1 @ v_S @ t_a )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(43,plain,
( ( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
= $true )
| ( ( c_in @ v_xa @ v_S @ t_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(44,plain,
( ( ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ v_xa @ v_S @ t_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(45,plain,
( ( ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(46,plain,
! [SV2: $i] :
( ( ( c_in @ ( c_Pair @ SV2 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV2 @ v_S @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(47,plain,
! [SV3: $i] :
( ( ! [SY12: $i,SY13: $i,SY14: $i] :
( ~ ( c_in @ SV3 @ SY12 @ SY13 )
| ~ ( c_lessequals @ SY12 @ SY14 @ ( tc_set @ SY13 ) )
| ( c_in @ SV3 @ SY14 @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(48,plain,
! [SV4: $i] :
( ( ! [SY15: $i] :
( ~ ( c_in @ SV4 @ v_A @ t_a )
| ~ ( c_lessequals @ SY15 @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SY15 @ v_cl @ t_a ) @ SV4 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mP @ SV4 @ SY15 @ v_r ) @ SY15 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(49,plain,
! [SV5: $i] :
( ( ! [SY16: $i] :
( ~ ( c_in @ SV5 @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SY16 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_lessequals @ SY16 @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SY16 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(50,plain,
! [SV6: $i] :
( ( ! [SY17: $i] :
( ~ ( c_in @ SV6 @ SY17 @ t_a )
| ~ ( c_lessequals @ SY17 @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ SV6 @ ( c_Tarski_Olub @ SY17 @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(51,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(52,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ SV1 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ~ ( c_in @ SV1 @ v_S @ t_a )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(53,plain,
( ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ v_xa @ v_S @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(54,plain,
( ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(55,plain,
! [SV2: $i] :
( ( ( c_in @ ( c_Pair @ SV2 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ~ ( c_in @ SV2 @ v_S @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(56,plain,
! [SV7: $i,SV3: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ~ ( c_in @ SV3 @ SV7 @ SY18 )
| ~ ( c_lessequals @ SV7 @ SY19 @ ( tc_set @ SY18 ) )
| ( c_in @ SV3 @ SY19 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(57,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( c_in @ SV4 @ v_A @ t_a )
| ~ ( c_lessequals @ SV8 @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV8 @ v_cl @ t_a ) @ SV4 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mP @ SV4 @ SV8 @ v_r ) @ SV8 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(58,plain,
! [SV9: $i,SV5: $i] :
( ( ~ ( c_in @ SV5 @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SV9 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_lessequals @ SV9 @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV9 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV10: $i,SV6: $i] :
( ( ~ ( c_in @ SV6 @ SV10 @ t_a )
| ~ ( c_lessequals @ SV10 @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ SV6 @ ( c_Tarski_Olub @ SV10 @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV1: $i] :
( ( ( ~ ( c_in @ SV1 @ v_S @ t_a ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(61,plain,
( ( ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(62,plain,
! [SV2: $i] :
( ( ( ~ ( c_in @ SV2 @ v_S @ t_a ) )
= $true )
| ( ( c_in @ v_xa @ v_S @ t_a )
= $true )
| ( ( c_in @ ( c_Pair @ SV2 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(63,plain,
! [SV11: $i,SV7: $i,SV3: $i] :
( ( ! [SY20: $i] :
( ~ ( c_in @ SV3 @ SV7 @ SV11 )
| ~ ( c_lessequals @ SV7 @ SY20 @ ( tc_set @ SV11 ) )
| ( c_in @ SV3 @ SY20 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(64,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( c_in @ SV4 @ v_A @ t_a ) )
= $true )
| ( ( ~ ( c_lessequals @ SV8 @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV8 @ v_cl @ t_a ) @ SV4 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mP @ SV4 @ SV8 @ v_r ) @ SV8 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(65,plain,
! [SV9: $i,SV5: $i] :
( ( ( ~ ( c_in @ SV5 @ v_A @ t_a ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SV9 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_lessequals @ SV9 @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV9 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(66,plain,
! [SV10: $i,SV6: $i] :
( ( ( ~ ( c_in @ SV6 @ SV10 @ t_a ) )
= $true )
| ( ( ~ ( c_lessequals @ SV10 @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ SV6 @ ( c_Tarski_Olub @ SV10 @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(67,plain,
! [SV1: $i] :
( ( ( c_in @ SV1 @ v_S @ t_a )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(68,plain,
! [SV2: $i] :
( ( ( c_in @ SV2 @ v_S @ t_a )
= $false )
| ( ( c_in @ v_xa @ v_S @ t_a )
= $true )
| ( ( c_in @ ( c_Pair @ SV2 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV12: $i,SV11: $i,SV7: $i,SV3: $i] :
( ( ~ ( c_in @ SV3 @ SV7 @ SV11 )
| ~ ( c_lessequals @ SV7 @ SV12 @ ( tc_set @ SV11 ) )
| ( c_in @ SV3 @ SV12 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV8: $i,SV4: $i] :
( ( ( c_in @ SV4 @ v_A @ t_a )
= $false )
| ( ( ~ ( c_lessequals @ SV8 @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV8 @ v_cl @ t_a ) @ SV4 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mP @ SV4 @ SV8 @ v_r ) @ SV8 @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV9: $i,SV5: $i] :
( ( ( c_in @ SV5 @ v_A @ t_a )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SV9 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_lessequals @ SV9 @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV9 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV10: $i,SV6: $i] :
( ( ( c_in @ SV6 @ SV10 @ t_a )
= $false )
| ( ( ~ ( c_lessequals @ SV10 @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ SV6 @ ( c_Tarski_Olub @ SV10 @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(73,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ SV1 @ v_S @ t_a )
= $false )
| ( ( c_in @ ( c_Pair @ SV1 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV12: $i,SV11: $i,SV7: $i,SV3: $i] :
( ( ( ~ ( c_in @ SV3 @ SV7 @ SV11 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV7 @ SV12 @ ( tc_set @ SV11 ) )
| ( c_in @ SV3 @ SV12 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(75,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( c_lessequals @ SV8 @ v_A @ ( tc_set @ t_a ) ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV8 @ v_cl @ t_a ) @ SV4 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mP @ SV4 @ SV8 @ v_r ) @ SV8 @ t_a ) )
= $true )
| ( ( c_in @ SV4 @ v_A @ t_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV9: $i,SV5: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SV9 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV9 @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV9 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ SV5 @ v_A @ t_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( c_lessequals @ SV10 @ v_A @ ( tc_set @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV6 @ ( c_Tarski_Olub @ SV10 @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_in @ SV6 @ SV10 @ t_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV12: $i,SV11: $i,SV7: $i,SV3: $i] :
( ( ( c_in @ SV3 @ SV7 @ SV11 )
= $false )
| ( ( ~ ( c_lessequals @ SV7 @ SV12 @ ( tc_set @ SV11 ) )
| ( c_in @ SV3 @ SV12 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV4: $i,SV8: $i] :
( ( ( c_lessequals @ SV8 @ v_A @ ( tc_set @ t_a ) )
= $false )
| ( ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV8 @ v_cl @ t_a ) @ SV4 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mP @ SV4 @ SV8 @ v_r ) @ SV8 @ t_a ) )
= $true )
| ( ( c_in @ SV4 @ v_A @ t_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV9: $i,SV5: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SV9 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_lessequals @ SV9 @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV9 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ SV5 @ v_A @ t_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV6: $i,SV10: $i] :
( ( ( c_lessequals @ SV10 @ v_A @ ( tc_set @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV6 @ ( c_Tarski_Olub @ SV10 @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_in @ SV6 @ SV10 @ t_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV3: $i,SV11: $i,SV12: $i,SV7: $i] :
( ( ( ~ ( c_lessequals @ SV7 @ SV12 @ ( tc_set @ SV11 ) ) )
= $true )
| ( ( c_in @ SV3 @ SV12 @ SV11 )
= $true )
| ( ( c_in @ SV3 @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV4: $i,SV8: $i] :
( ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV8 @ v_cl @ t_a ) @ SV4 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_in @ ( v_sko__4mP @ SV4 @ SV8 @ v_r ) @ SV8 @ t_a )
= $true )
| ( ( c_lessequals @ SV8 @ v_A @ ( tc_set @ t_a ) )
= $false )
| ( ( c_in @ SV4 @ v_A @ t_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV5: $i,SV9: $i] :
( ( ( ~ ( c_lessequals @ SV9 @ v_A @ ( tc_set @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV9 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SV9 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ SV5 @ v_A @ t_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV3: $i,SV11: $i,SV12: $i,SV7: $i] :
( ( ( c_lessequals @ SV7 @ SV12 @ ( tc_set @ SV11 ) )
= $false )
| ( ( c_in @ SV3 @ SV12 @ SV11 )
= $true )
| ( ( c_in @ SV3 @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(86,plain,
! [SV5: $i,SV9: $i] :
( ( ( c_lessequals @ SV9 @ v_A @ ( tc_set @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV9 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SV9 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ SV5 @ v_A @ t_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(87,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[29,86,85,83,81,73,68,61,53,51,43,40,36]) ).
thf(88,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT276-2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n006.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 11:53:52 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
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% 0.07/0.25 No.of.Axioms: 12
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% 0.07/0.25 Length.of.Defs: 0
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% 0.07/0.25 Contains.Choice.Funs: false
% 0.07/0.25 .
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% 0.07/0.25 ********************************
% 0.07/0.25 * All subproblems solved! *
% 0.07/0.25 ********************************
% 0.07/0.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:12,ps:3,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:87,loop_count:0,foatp_calls:1,translation:fof_full)
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% 0.07/0.25 %**** Beginning of derivation protocol ****
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
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% 0.07/0.25 %**** End of derivation protocol ****
% 0.07/0.25 %**** no. of clauses in derivation: 88 ****
% 0.07/0.25 %**** clause counter: 87 ****
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% 0.07/0.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:12,ps:3,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:87,loop_count:0,foatp_calls:1,translation:fof_full)
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