TSTP Solution File: LAT274-2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LAT274-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 05:45:26 EDT 2022
% Result : Unsatisfiable 0.47s 0.68s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 35
% Syntax : Number of formulae : 178 ( 82 unt; 19 typ; 0 def)
% Number of atoms : 1088 ( 324 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 4121 ( 208 ~; 403 |; 0 &;3510 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 11 con; 0-4 aty)
% Number of variables : 565 ( 0 ^ 565 !; 0 ?; 565 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Pair,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tp_c_Tarski_Ointerval,type,
c_Tarski_Ointerval: $i > $i > $i > $i > $i ).
thf(tp_c_Tarski_OisLub,type,
c_Tarski_OisLub: $i > $i > $i > $i > $o ).
thf(tp_c_emptyset,type,
c_emptyset: $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_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_L,type,
v_L: $i ).
thf(tp_v_S,type,
v_S: $i ).
thf(tp_v_a,type,
v_a: $i ).
thf(tp_v_b,type,
v_b: $i ).
thf(tp_v_cl,type,
v_cl: $i ).
thf(tp_v_r,type,
v_r: $i ).
thf(tp_v_sko__4mi,type,
v_sko__4mi: $i > $i > $i > $i ).
thf(tp_v_sko__4mj,type,
v_sko__4mj: $i > $i > $i > $i ).
thf(tp_v_sko__4mk,type,
v_sko__4mk: $i > $i > $i > $i ).
thf(1,axiom,
! [V_S: $i,V_L: $i,V_z: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ~ ( c_in @ V_z @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1) ).
thf(2,axiom,
! [V_S: $i,V_L: $i,V_z: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ~ ( c_in @ V_z @ v_A @ t_a )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_S @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0) ).
thf(3,axiom,
! [V_S: $i,V_L: $i,V_y: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ~ ( c_in @ V_y @ V_S @ t_a )
| ( c_in @ ( c_Pair @ V_y @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0) ).
thf(4,axiom,
! [V_x: $i,V_b: $i,T_a: $i,V_r: $i,V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0) ).
thf(5,axiom,
! [V_x: $i,V_S: $i,T_a: $i,V_r: $i,V_a: $i,V_b: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0) ).
thf(6,axiom,
! [V_x: $i,V_S: $i,T_a: $i,V_r: $i,V_a: $i,V_b: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0) ).
thf(7,axiom,
! [V_a: $i,V_S: $i,V_L: $i,V_A: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ 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 @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( V_S = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3) ).
thf(8,axiom,
! [V_a: $i,V_S: $i,V_A: $i,V_L: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ 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 @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_S @ t_a )
| ( V_S = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2) ).
thf(9,axiom,
! [V_L: $i,V_S: $i,V_A: $i,V_a: $i] :
( ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ 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 @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ V_S @ t_a )
| ( V_S = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1) ).
thf(10,axiom,
! [V_S: $i,V_A: $i,V_a: $i,V_L: $i] :
( ~ ( c_lessequals @ V_S @ V_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ V_S @ t_a )
| ( c_in @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_S @ t_a )
| ( V_S = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0) ).
thf(11,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(12,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[11]) ).
thf(13,negated_conjecture,
~ ( c_in @ v_L @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(14,negated_conjecture,
c_Tarski_OisLub @ v_S @ v_cl @ v_L @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(15,negated_conjecture,
v_S != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(16,negated_conjecture,
c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(17,negated_conjecture,
c_in @ v_b @ v_A @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(18,plain,
$false = $false,
inference(unfold_def,[status(thm)],[12]) ).
thf(19,plain,
( ( ! [V_S: $i,V_L: $i,V_z: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ~ ( c_in @ V_z @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(20,plain,
( ( ! [V_S: $i,V_L: $i,V_z: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ~ ( c_in @ V_z @ v_A @ t_a )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_S @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(21,plain,
( ( ! [V_S: $i,V_L: $i,V_y: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ~ ( c_in @ V_y @ V_S @ t_a )
| ( c_in @ ( c_Pair @ V_y @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [V_x: $i,V_b: $i,T_a: $i,V_r: $i,V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(23,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i,V_r: $i,V_a: $i,V_b: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(24,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i,V_r: $i,V_a: $i,V_b: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(25,plain,
( ( ! [V_a: $i,V_S: $i,V_L: $i,V_A: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ 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 @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( V_S = c_emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(26,plain,
( ( ! [V_a: $i,V_S: $i,V_A: $i,V_L: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ 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 @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_S @ t_a )
| ( V_S = c_emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(27,plain,
( ( ! [V_L: $i,V_S: $i,V_A: $i,V_a: $i] :
( ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ 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 @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ V_S @ t_a )
| ( V_S = c_emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(28,plain,
( ( ! [V_S: $i,V_A: $i,V_a: $i,V_L: $i] :
( ~ ( c_lessequals @ V_S @ V_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ V_S @ t_a )
| ( c_in @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_S @ t_a )
| ( V_S = c_emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(29,plain,
( ( ~ ( c_in @ v_L @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(30,plain,
( ( c_Tarski_OisLub @ v_S @ v_cl @ v_L @ t_a )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(31,plain,
( ( ( v_S != c_emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(32,plain,
( ( c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(33,plain,
( ( c_in @ v_b @ v_A @ t_a )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(34,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(35,plain,
( ( ! [V_S: $i,V_L: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ! [V_z: $i] :
( ~ ( c_in @ V_z @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(36,plain,
( ( ! [V_S: $i,V_L: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ! [V_z: $i] :
( ~ ( c_in @ V_z @ v_A @ t_a )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_S @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(37,plain,
( ( ! [V_S: $i,V_L: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ! [V_y: $i] :
( ~ ( c_in @ V_y @ V_S @ t_a )
| ( c_in @ ( c_Pair @ V_y @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(38,plain,
( ( ! [V_x: $i,V_b: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(39,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ! [V_a: $i,V_b: $i] :
( ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(40,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ! [V_a: $i] :
( ! [V_b: $i] :
~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(41,plain,
( ( ! [V_a: $i,V_S: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [V_L: $i] :
( ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_S @ V_A @ ( tc_set @ t_a ) )
| ( V_S = c_emptyset )
| ( c_in @ ( c_Pair @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(42,plain,
( ( ! [V_a: $i,V_S: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_S @ V_A @ ( tc_set @ t_a ) )
| ! [V_L: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( V_S = c_emptyset )
| ( c_in @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_S @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(43,plain,
( ( ! [V_L: $i,V_S: $i] :
( ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_S @ V_A @ ( tc_set @ t_a ) )
| ! [V_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( V_S = c_emptyset )
| ( c_in @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ V_S @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(44,plain,
( ( ! [V_S: $i,V_A: $i] :
( ~ ( c_lessequals @ V_S @ V_A @ ( tc_set @ t_a ) )
| ! [V_a: $i,V_L: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ V_S @ t_a )
| ( V_S = c_emptyset )
| ( c_in @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_S @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(45,plain,
( ( ( v_S != c_emptyset ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(46,plain,
( ( c_in @ v_b @ v_A @ t_a )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(47,plain,
( ( c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(48,plain,
( ( ( v_S != c_emptyset ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(49,plain,
( ( c_Tarski_OisLub @ v_S @ v_cl @ v_L @ t_a )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(50,plain,
( ( ~ ( c_in @ v_L @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ t_a ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(51,plain,
( ( ! [V_S: $i,V_A: $i] :
( ~ ( c_lessequals @ V_S @ V_A @ ( tc_set @ t_a ) )
| ! [V_a: $i,V_L: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ V_S @ t_a )
| ( V_S = c_emptyset )
| ( c_in @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_S @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(52,plain,
( ( ! [V_L: $i,V_S: $i] :
( ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_S @ V_A @ ( tc_set @ t_a ) )
| ! [V_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( V_S = c_emptyset )
| ( c_in @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ V_S @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(53,plain,
( ( ! [V_a: $i,V_S: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_S @ V_A @ ( tc_set @ t_a ) )
| ! [V_L: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( V_S = c_emptyset )
| ( c_in @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_S @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(54,plain,
( ( ! [V_a: $i,V_S: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [V_L: $i] :
( ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_S @ V_A @ ( tc_set @ t_a ) )
| ( V_S = c_emptyset )
| ( c_in @ ( c_Pair @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(55,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ! [V_a: $i] :
( ! [V_b: $i] :
~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(56,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ V_x @ V_S @ T_a )
| ! [V_a: $i,V_b: $i] :
( ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(57,plain,
( ( ! [V_x: $i,V_b: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(58,plain,
( ( ! [V_S: $i,V_L: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ! [V_y: $i] :
( ~ ( c_in @ V_y @ V_S @ t_a )
| ( c_in @ ( c_Pair @ V_y @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(59,plain,
( ( ! [V_S: $i,V_L: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ! [V_z: $i] :
( ~ ( c_in @ V_z @ v_A @ t_a )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_S @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(60,plain,
( ( ! [V_S: $i,V_L: $i] :
( ~ ( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a )
| ! [V_z: $i] :
( ~ ( c_in @ V_z @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(61,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(62,plain,
( ( v_S = c_emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(63,plain,
( ( c_in @ v_L @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ t_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(64,plain,
! [SV1: $i] :
( ( ! [SY42: $i] :
( ~ ( c_lessequals @ SV1 @ SY42 @ ( tc_set @ t_a ) )
| ! [SY43: $i,SY44: $i] :
( ( c_in @ ( c_Pair @ SY43 @ SY44 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mj @ SV1 @ SY43 @ v_r ) @ SV1 @ t_a )
| ( SV1 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SY44 @ SV1 @ v_r ) @ SV1 @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(65,plain,
! [SV2: $i] :
( ( ! [SY45: $i] :
( ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV2 @ SY45 @ v_r ) @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [V_A: $i] :
~ ( c_lessequals @ SY45 @ V_A @ ( tc_set @ t_a ) )
| ! [SY47: $i] :
( ( c_in @ ( c_Pair @ SY47 @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SY45 = c_emptyset )
| ( c_in @ ( v_sko__4mj @ SY45 @ SY47 @ v_r ) @ SY45 @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(66,plain,
! [SV3: $i] :
( ( ! [SY48: $i] :
( ~ ( c_in @ ( c_Pair @ SV3 @ ( v_sko__4mj @ SY48 @ SV3 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [V_A: $i] :
~ ( c_lessequals @ SY48 @ V_A @ ( tc_set @ t_a ) )
| ! [SY50: $i] :
( ( c_in @ ( c_Pair @ SV3 @ SY50 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SY48 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SY50 @ SY48 @ v_r ) @ SY48 @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(67,plain,
! [SV4: $i] :
( ( ! [SY51: $i] :
( ~ ( c_in @ ( c_Pair @ SV4 @ ( v_sko__4mj @ SY51 @ SV4 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [SY52: $i] :
( ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ SY52 @ SY51 @ v_r ) @ SY52 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [V_A: $i] :
~ ( c_lessequals @ SY51 @ V_A @ ( tc_set @ t_a ) )
| ( SY51 = c_emptyset )
| ( c_in @ ( c_Pair @ SV4 @ SY52 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(68,plain,
! [SV5: $i] :
( ( ! [SY54: $i,SY55: $i,SY56: $i] :
( ~ ( c_in @ SV5 @ SY54 @ SY55 )
| ! [SY57: $i] :
( ! [V_b: $i] :
~ ( c_lessequals @ SY54 @ ( c_Tarski_Ointerval @ SY56 @ SY57 @ V_b @ SY55 ) @ ( tc_set @ SY55 ) )
| ( c_in @ ( c_Pair @ SY57 @ SV5 @ SY55 @ SY55 ) @ SY56 @ ( tc_prod @ SY55 @ SY55 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(69,plain,
! [SV6: $i] :
( ( ! [SY59: $i,SY60: $i,SY61: $i] :
( ~ ( c_in @ SV6 @ SY59 @ SY60 )
| ! [SY62: $i,SY63: $i] :
( ~ ( c_lessequals @ SY59 @ ( c_Tarski_Ointerval @ SY61 @ SY62 @ SY63 @ SY60 ) @ ( tc_set @ SY60 ) )
| ( c_in @ ( c_Pair @ SV6 @ SY63 @ SY60 @ SY60 ) @ SY61 @ ( tc_prod @ SY60 @ SY60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(70,plain,
! [SV7: $i] :
( ( ! [SY64: $i,SY65: $i,SY66: $i] :
( ~ ( c_in @ ( c_Pair @ SV7 @ SY64 @ SY65 @ SY65 ) @ SY66 @ ( tc_prod @ SY65 @ SY65 ) )
| ! [SY67: $i] :
( ~ ( c_in @ ( c_Pair @ SY67 @ SV7 @ SY65 @ SY65 ) @ SY66 @ ( tc_prod @ SY65 @ SY65 ) )
| ( c_in @ SV7 @ ( c_Tarski_Ointerval @ SY66 @ SY67 @ SY64 @ SY65 ) @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(71,plain,
! [SV8: $i] :
( ( ! [SY68: $i] :
( ~ ( c_Tarski_OisLub @ SV8 @ v_cl @ SY68 @ t_a )
| ! [SY69: $i] :
( ~ ( c_in @ SY69 @ SV8 @ t_a )
| ( c_in @ ( c_Pair @ SY69 @ SY68 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(72,plain,
! [SV9: $i] :
( ( ! [SY70: $i] :
( ~ ( c_Tarski_OisLub @ SV9 @ v_cl @ SY70 @ t_a )
| ! [SY71: $i] :
( ~ ( c_in @ SY71 @ v_A @ t_a )
| ( c_in @ ( c_Pair @ SY70 @ SY71 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ SV9 @ v_r @ SY71 ) @ SV9 @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(73,plain,
! [SV10: $i] :
( ( ! [SY72: $i] :
( ~ ( c_Tarski_OisLub @ SV10 @ v_cl @ SY72 @ t_a )
| ! [SY73: $i] :
( ~ ( c_in @ SY73 @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV10 @ v_r @ SY73 ) @ SY73 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SY72 @ SY73 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(74,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(75,plain,
! [SV11: $i,SV1: $i] :
( ( ~ ( c_lessequals @ SV1 @ SV11 @ ( tc_set @ t_a ) )
| ! [SY43: $i,SY44: $i] :
( ( c_in @ ( c_Pair @ SY43 @ SY44 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mj @ SV1 @ SY43 @ v_r ) @ SV1 @ t_a )
| ( SV1 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SY44 @ SV1 @ v_r ) @ SV1 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(76,plain,
! [SV12: $i,SV2: $i] :
( ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV2 @ SV12 @ v_r ) @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [SY76: $i] :
~ ( c_lessequals @ SV12 @ SY76 @ ( tc_set @ t_a ) )
| ! [SY77: $i] :
( ( c_in @ ( c_Pair @ SY77 @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SV12 = c_emptyset )
| ( c_in @ ( v_sko__4mj @ SV12 @ SY77 @ v_r ) @ SV12 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(77,plain,
! [SV13: $i,SV3: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV3 @ ( v_sko__4mj @ SV13 @ SV3 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [SY78: $i] :
~ ( c_lessequals @ SV13 @ SY78 @ ( tc_set @ t_a ) )
| ! [SY79: $i] :
( ( c_in @ ( c_Pair @ SV3 @ SY79 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SV13 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SY79 @ SV13 @ v_r ) @ SV13 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(78,plain,
! [SV14: $i,SV4: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV4 @ ( v_sko__4mj @ SV14 @ SV4 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [SY80: $i] :
( ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ SY80 @ SV14 @ v_r ) @ SY80 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [SY81: $i] :
~ ( c_lessequals @ SV14 @ SY81 @ ( tc_set @ t_a ) )
| ( SV14 = c_emptyset )
| ( c_in @ ( c_Pair @ SV4 @ SY80 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(79,plain,
! [SV15: $i,SV5: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ~ ( c_in @ SV5 @ SV15 @ SY82 )
| ! [SY84: $i] :
( ! [SY85: $i] :
~ ( c_lessequals @ SV15 @ ( c_Tarski_Ointerval @ SY83 @ SY84 @ SY85 @ SY82 ) @ ( tc_set @ SY82 ) )
| ( c_in @ ( c_Pair @ SY84 @ SV5 @ SY82 @ SY82 ) @ SY83 @ ( tc_prod @ SY82 @ SY82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(80,plain,
! [SV16: $i,SV6: $i] :
( ( ! [SY86: $i,SY87: $i] :
( ~ ( c_in @ SV6 @ SV16 @ SY86 )
| ! [SY88: $i,SY89: $i] :
( ~ ( c_lessequals @ SV16 @ ( c_Tarski_Ointerval @ SY87 @ SY88 @ SY89 @ SY86 ) @ ( tc_set @ SY86 ) )
| ( c_in @ ( c_Pair @ SV6 @ SY89 @ SY86 @ SY86 ) @ SY87 @ ( tc_prod @ SY86 @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(81,plain,
! [SV17: $i,SV7: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ~ ( c_in @ ( c_Pair @ SV7 @ SV17 @ SY90 @ SY90 ) @ SY91 @ ( tc_prod @ SY90 @ SY90 ) )
| ! [SY92: $i] :
( ~ ( c_in @ ( c_Pair @ SY92 @ SV7 @ SY90 @ SY90 ) @ SY91 @ ( tc_prod @ SY90 @ SY90 ) )
| ( c_in @ SV7 @ ( c_Tarski_Ointerval @ SY91 @ SY92 @ SV17 @ SY90 ) @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(82,plain,
! [SV18: $i,SV8: $i] :
( ( ~ ( c_Tarski_OisLub @ SV8 @ v_cl @ SV18 @ t_a )
| ! [SY93: $i] :
( ~ ( c_in @ SY93 @ SV8 @ t_a )
| ( c_in @ ( c_Pair @ SY93 @ SV18 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(83,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ( c_Tarski_OisLub @ SV9 @ v_cl @ SV19 @ t_a )
| ! [SY94: $i] :
( ~ ( c_in @ SY94 @ v_A @ t_a )
| ( c_in @ ( c_Pair @ SV19 @ SY94 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ SV9 @ v_r @ SY94 ) @ SV9 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(84,plain,
! [SV20: $i,SV10: $i] :
( ( ~ ( c_Tarski_OisLub @ SV10 @ v_cl @ SV20 @ t_a )
| ! [SY95: $i] :
( ~ ( c_in @ SY95 @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV10 @ v_r @ SY95 ) @ SY95 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV20 @ SY95 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(85,plain,
! [SV11: $i,SV1: $i] :
( ( ( ~ ( c_lessequals @ SV1 @ SV11 @ ( tc_set @ t_a ) ) )
= $true )
| ( ( ! [SY43: $i,SY44: $i] :
( ( c_in @ ( c_Pair @ SY43 @ SY44 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mj @ SV1 @ SY43 @ v_r ) @ SV1 @ t_a )
| ( SV1 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SY44 @ SV1 @ v_r ) @ SV1 @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV12: $i,SV2: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV2 @ SV12 @ v_r ) @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ! [SY76: $i] :
~ ( c_lessequals @ SV12 @ SY76 @ ( tc_set @ t_a ) )
| ! [SY77: $i] :
( ( c_in @ ( c_Pair @ SY77 @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SV12 = c_emptyset )
| ( c_in @ ( v_sko__4mj @ SV12 @ SY77 @ v_r ) @ SV12 @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(87,plain,
! [SV13: $i,SV3: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV3 @ ( v_sko__4mj @ SV13 @ SV3 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ! [SY78: $i] :
~ ( c_lessequals @ SV13 @ SY78 @ ( tc_set @ t_a ) )
| ! [SY79: $i] :
( ( c_in @ ( c_Pair @ SV3 @ SY79 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SV13 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SY79 @ SV13 @ v_r ) @ SV13 @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(88,plain,
! [SV14: $i,SV4: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV4 @ ( v_sko__4mj @ SV14 @ SV4 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ! [SY80: $i] :
( ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ SY80 @ SV14 @ v_r ) @ SY80 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [SY81: $i] :
~ ( c_lessequals @ SV14 @ SY81 @ ( tc_set @ t_a ) )
| ( SV14 = c_emptyset )
| ( c_in @ ( c_Pair @ SV4 @ SY80 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(89,plain,
! [SV21: $i,SV15: $i,SV5: $i] :
( ( ! [SY96: $i] :
( ~ ( c_in @ SV5 @ SV15 @ SV21 )
| ! [SY97: $i] :
( ! [SY98: $i] :
~ ( c_lessequals @ SV15 @ ( c_Tarski_Ointerval @ SY96 @ SY97 @ SY98 @ SV21 ) @ ( tc_set @ SV21 ) )
| ( c_in @ ( c_Pair @ SY97 @ SV5 @ SV21 @ SV21 ) @ SY96 @ ( tc_prod @ SV21 @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(90,plain,
! [SV22: $i,SV16: $i,SV6: $i] :
( ( ! [SY99: $i] :
( ~ ( c_in @ SV6 @ SV16 @ SV22 )
| ! [SY100: $i,SY101: $i] :
( ~ ( c_lessequals @ SV16 @ ( c_Tarski_Ointerval @ SY99 @ SY100 @ SY101 @ SV22 ) @ ( tc_set @ SV22 ) )
| ( c_in @ ( c_Pair @ SV6 @ SY101 @ SV22 @ SV22 ) @ SY99 @ ( tc_prod @ SV22 @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(91,plain,
! [SV23: $i,SV17: $i,SV7: $i] :
( ( ! [SY102: $i] :
( ~ ( c_in @ ( c_Pair @ SV7 @ SV17 @ SV23 @ SV23 ) @ SY102 @ ( tc_prod @ SV23 @ SV23 ) )
| ! [SY103: $i] :
( ~ ( c_in @ ( c_Pair @ SY103 @ SV7 @ SV23 @ SV23 ) @ SY102 @ ( tc_prod @ SV23 @ SV23 ) )
| ( c_in @ SV7 @ ( c_Tarski_Ointerval @ SY102 @ SY103 @ SV17 @ SV23 ) @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(92,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ( c_Tarski_OisLub @ SV8 @ v_cl @ SV18 @ t_a ) )
= $true )
| ( ( ! [SY93: $i] :
( ~ ( c_in @ SY93 @ SV8 @ t_a )
| ( c_in @ ( c_Pair @ SY93 @ SV18 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(93,plain,
! [SV19: $i,SV9: $i] :
( ( ( ~ ( c_Tarski_OisLub @ SV9 @ v_cl @ SV19 @ t_a ) )
= $true )
| ( ( ! [SY94: $i] :
( ~ ( c_in @ SY94 @ v_A @ t_a )
| ( c_in @ ( c_Pair @ SV19 @ SY94 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ SV9 @ v_r @ SY94 ) @ SV9 @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(94,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ( c_Tarski_OisLub @ SV10 @ v_cl @ SV20 @ t_a ) )
= $true )
| ( ( ! [SY95: $i] :
( ~ ( c_in @ SY95 @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV10 @ v_r @ SY95 ) @ SY95 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV20 @ SY95 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(95,plain,
! [SV11: $i,SV1: $i] :
( ( ( c_lessequals @ SV1 @ SV11 @ ( tc_set @ t_a ) )
= $false )
| ( ( ! [SY43: $i,SY44: $i] :
( ( c_in @ ( c_Pair @ SY43 @ SY44 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mj @ SV1 @ SY43 @ v_r ) @ SV1 @ t_a )
| ( SV1 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SY44 @ SV1 @ v_r ) @ SV1 @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(96,plain,
! [SV12: $i,SV2: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV2 @ SV12 @ v_r ) @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ! [SY76: $i] :
~ ( c_lessequals @ SV12 @ SY76 @ ( tc_set @ t_a ) )
| ! [SY77: $i] :
( ( c_in @ ( c_Pair @ SY77 @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SV12 = c_emptyset )
| ( c_in @ ( v_sko__4mj @ SV12 @ SY77 @ v_r ) @ SV12 @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(97,plain,
! [SV13: $i,SV3: $i] :
( ( ( c_in @ ( c_Pair @ SV3 @ ( v_sko__4mj @ SV13 @ SV3 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ! [SY78: $i] :
~ ( c_lessequals @ SV13 @ SY78 @ ( tc_set @ t_a ) )
| ! [SY79: $i] :
( ( c_in @ ( c_Pair @ SV3 @ SY79 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SV13 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SY79 @ SV13 @ v_r ) @ SV13 @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(98,plain,
! [SV14: $i,SV4: $i] :
( ( ( c_in @ ( c_Pair @ SV4 @ ( v_sko__4mj @ SV14 @ SV4 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ! [SY80: $i] :
( ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ SY80 @ SV14 @ v_r ) @ SY80 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [SY81: $i] :
~ ( c_lessequals @ SV14 @ SY81 @ ( tc_set @ t_a ) )
| ( SV14 = c_emptyset )
| ( c_in @ ( c_Pair @ SV4 @ SY80 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(99,plain,
! [SV24: $i,SV21: $i,SV15: $i,SV5: $i] :
( ( ~ ( c_in @ SV5 @ SV15 @ SV21 )
| ! [SY104: $i] :
( ! [SY105: $i] :
~ ( c_lessequals @ SV15 @ ( c_Tarski_Ointerval @ SV24 @ SY104 @ SY105 @ SV21 ) @ ( tc_set @ SV21 ) )
| ( c_in @ ( c_Pair @ SY104 @ SV5 @ SV21 @ SV21 ) @ SV24 @ ( tc_prod @ SV21 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(100,plain,
! [SV25: $i,SV22: $i,SV16: $i,SV6: $i] :
( ( ~ ( c_in @ SV6 @ SV16 @ SV22 )
| ! [SY106: $i,SY107: $i] :
( ~ ( c_lessequals @ SV16 @ ( c_Tarski_Ointerval @ SV25 @ SY106 @ SY107 @ SV22 ) @ ( tc_set @ SV22 ) )
| ( c_in @ ( c_Pair @ SV6 @ SY107 @ SV22 @ SV22 ) @ SV25 @ ( tc_prod @ SV22 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(101,plain,
! [SV26: $i,SV23: $i,SV17: $i,SV7: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV7 @ SV17 @ SV23 @ SV23 ) @ SV26 @ ( tc_prod @ SV23 @ SV23 ) )
| ! [SY108: $i] :
( ~ ( c_in @ ( c_Pair @ SY108 @ SV7 @ SV23 @ SV23 ) @ SV26 @ ( tc_prod @ SV23 @ SV23 ) )
| ( c_in @ SV7 @ ( c_Tarski_Ointerval @ SV26 @ SY108 @ SV17 @ SV23 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(102,plain,
! [SV18: $i,SV8: $i] :
( ( ( c_Tarski_OisLub @ SV8 @ v_cl @ SV18 @ t_a )
= $false )
| ( ( ! [SY93: $i] :
( ~ ( c_in @ SY93 @ SV8 @ t_a )
| ( c_in @ ( c_Pair @ SY93 @ SV18 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(103,plain,
! [SV19: $i,SV9: $i] :
( ( ( c_Tarski_OisLub @ SV9 @ v_cl @ SV19 @ t_a )
= $false )
| ( ( ! [SY94: $i] :
( ~ ( c_in @ SY94 @ v_A @ t_a )
| ( c_in @ ( c_Pair @ SV19 @ SY94 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ SV9 @ v_r @ SY94 ) @ SV9 @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(104,plain,
! [SV20: $i,SV10: $i] :
( ( ( c_Tarski_OisLub @ SV10 @ v_cl @ SV20 @ t_a )
= $false )
| ( ( ! [SY95: $i] :
( ~ ( c_in @ SY95 @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV10 @ v_r @ SY95 ) @ SY95 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV20 @ SY95 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(105,plain,
! [SV11: $i,SV1: $i,SV27: $i] :
( ( ( ! [SY109: $i] :
( ( c_in @ ( c_Pair @ SV27 @ SY109 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mj @ SV1 @ SV27 @ v_r ) @ SV1 @ t_a )
| ( SV1 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SY109 @ SV1 @ v_r ) @ SV1 @ t_a ) ) )
= $true )
| ( ( c_lessequals @ SV1 @ SV11 @ ( tc_set @ t_a ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(106,plain,
! [SV2: $i,SV12: $i] :
( ( ( ! [SY76: $i] :
~ ( c_lessequals @ SV12 @ SY76 @ ( tc_set @ t_a ) ) )
= $true )
| ( ( ! [SY77: $i] :
( ( c_in @ ( c_Pair @ SY77 @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SV12 = c_emptyset )
| ( c_in @ ( v_sko__4mj @ SV12 @ SY77 @ v_r ) @ SV12 @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV2 @ SV12 @ v_r ) @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(107,plain,
! [SV3: $i,SV13: $i] :
( ( ( ! [SY78: $i] :
~ ( c_lessequals @ SV13 @ SY78 @ ( tc_set @ t_a ) ) )
= $true )
| ( ( ! [SY79: $i] :
( ( c_in @ ( c_Pair @ SV3 @ SY79 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SV13 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SY79 @ SV13 @ v_r ) @ SV13 @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV3 @ ( v_sko__4mj @ SV13 @ SV3 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(108,plain,
! [SV4: $i,SV14: $i,SV28: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV28 @ SV14 @ v_r ) @ SV28 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ! [SY81: $i] :
~ ( c_lessequals @ SV14 @ SY81 @ ( tc_set @ t_a ) )
| ( SV14 = c_emptyset )
| ( c_in @ ( c_Pair @ SV4 @ SV28 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV4 @ ( v_sko__4mj @ SV14 @ SV4 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(109,plain,
! [SV24: $i,SV21: $i,SV15: $i,SV5: $i] :
( ( ( ~ ( c_in @ SV5 @ SV15 @ SV21 ) )
= $true )
| ( ( ! [SY104: $i] :
( ! [SY105: $i] :
~ ( c_lessequals @ SV15 @ ( c_Tarski_Ointerval @ SV24 @ SY104 @ SY105 @ SV21 ) @ ( tc_set @ SV21 ) )
| ( c_in @ ( c_Pair @ SY104 @ SV5 @ SV21 @ SV21 ) @ SV24 @ ( tc_prod @ SV21 @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(110,plain,
! [SV25: $i,SV22: $i,SV16: $i,SV6: $i] :
( ( ( ~ ( c_in @ SV6 @ SV16 @ SV22 ) )
= $true )
| ( ( ! [SY106: $i,SY107: $i] :
( ~ ( c_lessequals @ SV16 @ ( c_Tarski_Ointerval @ SV25 @ SY106 @ SY107 @ SV22 ) @ ( tc_set @ SV22 ) )
| ( c_in @ ( c_Pair @ SV6 @ SY107 @ SV22 @ SV22 ) @ SV25 @ ( tc_prod @ SV22 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(111,plain,
! [SV26: $i,SV23: $i,SV17: $i,SV7: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV7 @ SV17 @ SV23 @ SV23 ) @ SV26 @ ( tc_prod @ SV23 @ SV23 ) ) )
= $true )
| ( ( ! [SY108: $i] :
( ~ ( c_in @ ( c_Pair @ SY108 @ SV7 @ SV23 @ SV23 ) @ SV26 @ ( tc_prod @ SV23 @ SV23 ) )
| ( c_in @ SV7 @ ( c_Tarski_Ointerval @ SV26 @ SY108 @ SV17 @ SV23 ) @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(112,plain,
! [SV18: $i,SV8: $i,SV29: $i] :
( ( ( ~ ( c_in @ SV29 @ SV8 @ t_a )
| ( c_in @ ( c_Pair @ SV29 @ SV18 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_Tarski_OisLub @ SV8 @ v_cl @ SV18 @ t_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(113,plain,
! [SV9: $i,SV19: $i,SV30: $i] :
( ( ( ~ ( c_in @ SV30 @ v_A @ t_a )
| ( c_in @ ( c_Pair @ SV19 @ SV30 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ SV9 @ v_r @ SV30 ) @ SV9 @ t_a ) )
= $true )
| ( ( c_Tarski_OisLub @ SV9 @ v_cl @ SV19 @ t_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(114,plain,
! [SV20: $i,SV10: $i,SV31: $i] :
( ( ( ~ ( c_in @ SV31 @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV10 @ v_r @ SV31 ) @ SV31 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV20 @ SV31 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_Tarski_OisLub @ SV10 @ v_cl @ SV20 @ t_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(115,plain,
! [SV11: $i,SV1: $i,SV32: $i,SV27: $i] :
( ( ( ( c_in @ ( c_Pair @ SV27 @ SV32 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mj @ SV1 @ SV27 @ v_r ) @ SV1 @ t_a )
| ( SV1 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SV32 @ SV1 @ v_r ) @ SV1 @ t_a ) )
= $true )
| ( ( c_lessequals @ SV1 @ SV11 @ ( tc_set @ t_a ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV2: $i,SV33: $i,SV12: $i] :
( ( ( ~ ( c_lessequals @ SV12 @ SV33 @ ( tc_set @ t_a ) ) )
= $true )
| ( ( ! [SY77: $i] :
( ( c_in @ ( c_Pair @ SY77 @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SV12 = c_emptyset )
| ( c_in @ ( v_sko__4mj @ SV12 @ SY77 @ v_r ) @ SV12 @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV2 @ SV12 @ v_r ) @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(117,plain,
! [SV3: $i,SV34: $i,SV13: $i] :
( ( ( ~ ( c_lessequals @ SV13 @ SV34 @ ( tc_set @ t_a ) ) )
= $true )
| ( ( ! [SY79: $i] :
( ( c_in @ ( c_Pair @ SV3 @ SY79 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SV13 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SY79 @ SV13 @ v_r ) @ SV13 @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV3 @ ( v_sko__4mj @ SV13 @ SV3 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(118,plain,
! [SV4: $i,SV14: $i,SV28: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV28 @ SV14 @ v_r ) @ SV28 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ! [SY81: $i] :
~ ( c_lessequals @ SV14 @ SY81 @ ( tc_set @ t_a ) )
| ( SV14 = c_emptyset )
| ( c_in @ ( c_Pair @ SV4 @ SV28 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV4 @ ( v_sko__4mj @ SV14 @ SV4 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(119,plain,
! [SV24: $i,SV21: $i,SV15: $i,SV5: $i] :
( ( ( c_in @ SV5 @ SV15 @ SV21 )
= $false )
| ( ( ! [SY104: $i] :
( ! [SY105: $i] :
~ ( c_lessequals @ SV15 @ ( c_Tarski_Ointerval @ SV24 @ SY104 @ SY105 @ SV21 ) @ ( tc_set @ SV21 ) )
| ( c_in @ ( c_Pair @ SY104 @ SV5 @ SV21 @ SV21 ) @ SV24 @ ( tc_prod @ SV21 @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV25: $i,SV22: $i,SV16: $i,SV6: $i] :
( ( ( c_in @ SV6 @ SV16 @ SV22 )
= $false )
| ( ( ! [SY106: $i,SY107: $i] :
( ~ ( c_lessequals @ SV16 @ ( c_Tarski_Ointerval @ SV25 @ SY106 @ SY107 @ SV22 ) @ ( tc_set @ SV22 ) )
| ( c_in @ ( c_Pair @ SV6 @ SY107 @ SV22 @ SV22 ) @ SV25 @ ( tc_prod @ SV22 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV26: $i,SV23: $i,SV17: $i,SV7: $i] :
( ( ( c_in @ ( c_Pair @ SV7 @ SV17 @ SV23 @ SV23 ) @ SV26 @ ( tc_prod @ SV23 @ SV23 ) )
= $false )
| ( ( ! [SY108: $i] :
( ~ ( c_in @ ( c_Pair @ SY108 @ SV7 @ SV23 @ SV23 ) @ SV26 @ ( tc_prod @ SV23 @ SV23 ) )
| ( c_in @ SV7 @ ( c_Tarski_Ointerval @ SV26 @ SY108 @ SV17 @ SV23 ) @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(122,plain,
! [SV18: $i,SV8: $i,SV29: $i] :
( ( ( ~ ( c_in @ SV29 @ SV8 @ t_a ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV29 @ SV18 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_Tarski_OisLub @ SV8 @ v_cl @ SV18 @ t_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV9: $i,SV19: $i,SV30: $i] :
( ( ( ~ ( c_in @ SV30 @ v_A @ t_a ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV19 @ SV30 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ SV9 @ v_r @ SV30 ) @ SV9 @ t_a ) )
= $true )
| ( ( c_Tarski_OisLub @ SV9 @ v_cl @ SV19 @ t_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV20: $i,SV10: $i,SV31: $i] :
( ( ( ~ ( c_in @ SV31 @ v_A @ t_a ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV10 @ v_r @ SV31 ) @ SV31 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV20 @ SV31 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_Tarski_OisLub @ SV10 @ v_cl @ SV20 @ t_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(125,plain,
! [SV11: $i,SV1: $i,SV32: $i,SV27: $i] :
( ( ( c_in @ ( c_Pair @ SV27 @ SV32 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ( c_in @ ( v_sko__4mj @ SV1 @ SV27 @ v_r ) @ SV1 @ t_a )
| ( SV1 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SV32 @ SV1 @ v_r ) @ SV1 @ t_a ) )
= $true )
| ( ( c_lessequals @ SV1 @ SV11 @ ( tc_set @ t_a ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV2: $i,SV33: $i,SV12: $i] :
( ( ( c_lessequals @ SV12 @ SV33 @ ( tc_set @ t_a ) )
= $false )
| ( ( ! [SY77: $i] :
( ( c_in @ ( c_Pair @ SY77 @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SV12 = c_emptyset )
| ( c_in @ ( v_sko__4mj @ SV12 @ SY77 @ v_r ) @ SV12 @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV2 @ SV12 @ v_r ) @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(127,plain,
! [SV3: $i,SV34: $i,SV13: $i] :
( ( ( c_lessequals @ SV13 @ SV34 @ ( tc_set @ t_a ) )
= $false )
| ( ( ! [SY79: $i] :
( ( c_in @ ( c_Pair @ SV3 @ SY79 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SV13 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SY79 @ SV13 @ v_r ) @ SV13 @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV3 @ ( v_sko__4mj @ SV13 @ SV3 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(128,plain,
! [SV4: $i,SV14: $i,SV28: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV28 @ SV14 @ v_r ) @ SV28 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ! [SY81: $i] :
~ ( c_lessequals @ SV14 @ SY81 @ ( tc_set @ t_a ) )
| ( SV14 = c_emptyset )
| ( c_in @ ( c_Pair @ SV4 @ SV28 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV4 @ ( v_sko__4mj @ SV14 @ SV4 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(129,plain,
! [SV5: $i,SV21: $i,SV35: $i,SV24: $i,SV15: $i] :
( ( ( ! [SY111: $i] :
~ ( c_lessequals @ SV15 @ ( c_Tarski_Ointerval @ SV24 @ SV35 @ SY111 @ SV21 ) @ ( tc_set @ SV21 ) )
| ( c_in @ ( c_Pair @ SV35 @ SV5 @ SV21 @ SV21 ) @ SV24 @ ( tc_prod @ SV21 @ SV21 ) ) )
= $true )
| ( ( c_in @ SV5 @ SV15 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(130,plain,
! [SV6: $i,SV22: $i,SV36: $i,SV25: $i,SV16: $i] :
( ( ( ! [SY112: $i] :
( ~ ( c_lessequals @ SV16 @ ( c_Tarski_Ointerval @ SV25 @ SV36 @ SY112 @ SV22 ) @ ( tc_set @ SV22 ) )
| ( c_in @ ( c_Pair @ SV6 @ SY112 @ SV22 @ SV22 ) @ SV25 @ ( tc_prod @ SV22 @ SV22 ) ) ) )
= $true )
| ( ( c_in @ SV6 @ SV16 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(131,plain,
! [SV17: $i,SV26: $i,SV23: $i,SV7: $i,SV37: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV37 @ SV7 @ SV23 @ SV23 ) @ SV26 @ ( tc_prod @ SV23 @ SV23 ) )
| ( c_in @ SV7 @ ( c_Tarski_Ointerval @ SV26 @ SV37 @ SV17 @ SV23 ) @ SV23 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV7 @ SV17 @ SV23 @ SV23 ) @ SV26 @ ( tc_prod @ SV23 @ SV23 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(132,plain,
! [SV18: $i,SV8: $i,SV29: $i] :
( ( ( c_in @ SV29 @ SV8 @ t_a )
= $false )
| ( ( c_in @ ( c_Pair @ SV29 @ SV18 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_Tarski_OisLub @ SV8 @ v_cl @ SV18 @ t_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(133,plain,
! [SV9: $i,SV19: $i,SV30: $i] :
( ( ( c_in @ SV30 @ v_A @ t_a )
= $false )
| ( ( ( c_in @ ( c_Pair @ SV19 @ SV30 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mi @ SV9 @ v_r @ SV30 ) @ SV9 @ t_a ) )
= $true )
| ( ( c_Tarski_OisLub @ SV9 @ v_cl @ SV19 @ t_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV20: $i,SV10: $i,SV31: $i] :
( ( ( c_in @ SV31 @ v_A @ t_a )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV10 @ v_r @ SV31 ) @ SV31 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV20 @ SV31 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_Tarski_OisLub @ SV10 @ v_cl @ SV20 @ t_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(135,plain,
! [SV11: $i,SV32: $i,SV27: $i,SV1: $i] :
( ( ( c_in @ ( v_sko__4mj @ SV1 @ SV27 @ v_r ) @ SV1 @ t_a )
= $true )
| ( ( ( SV1 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SV32 @ SV1 @ v_r ) @ SV1 @ t_a ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV27 @ SV32 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_lessequals @ SV1 @ SV11 @ ( tc_set @ t_a ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(136,plain,
! [SV33: $i,SV12: $i,SV2: $i,SV38: $i] :
( ( ( ( c_in @ ( c_Pair @ SV38 @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SV12 = c_emptyset )
| ( c_in @ ( v_sko__4mj @ SV12 @ SV38 @ v_r ) @ SV12 @ t_a ) )
= $true )
| ( ( c_lessequals @ SV12 @ SV33 @ ( tc_set @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV2 @ SV12 @ v_r ) @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(137,plain,
! [SV34: $i,SV13: $i,SV39: $i,SV3: $i] :
( ( ( ( c_in @ ( c_Pair @ SV3 @ SV39 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( SV13 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SV39 @ SV13 @ v_r ) @ SV13 @ t_a ) )
= $true )
| ( ( c_lessequals @ SV13 @ SV34 @ ( tc_set @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV3 @ ( v_sko__4mj @ SV13 @ SV3 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(138,plain,
! [SV28: $i,SV4: $i,SV14: $i] :
( ( ( ! [SY81: $i] :
~ ( c_lessequals @ SV14 @ SY81 @ ( tc_set @ t_a ) ) )
= $true )
| ( ( ( SV14 = c_emptyset )
| ( c_in @ ( c_Pair @ SV4 @ SV28 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV28 @ SV14 @ v_r ) @ SV28 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV4 @ ( v_sko__4mj @ SV14 @ SV4 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(139,plain,
! [SV5: $i,SV21: $i,SV35: $i,SV24: $i,SV15: $i] :
( ( ( ! [SY111: $i] :
~ ( c_lessequals @ SV15 @ ( c_Tarski_Ointerval @ SV24 @ SV35 @ SY111 @ SV21 ) @ ( tc_set @ SV21 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV35 @ SV5 @ SV21 @ SV21 ) @ SV24 @ ( tc_prod @ SV21 @ SV21 ) )
= $true )
| ( ( c_in @ SV5 @ SV15 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(140,plain,
! [SV6: $i,SV22: $i,SV40: $i,SV36: $i,SV25: $i,SV16: $i] :
( ( ( ~ ( c_lessequals @ SV16 @ ( c_Tarski_Ointerval @ SV25 @ SV36 @ SV40 @ SV22 ) @ ( tc_set @ SV22 ) )
| ( c_in @ ( c_Pair @ SV6 @ SV40 @ SV22 @ SV22 ) @ SV25 @ ( tc_prod @ SV22 @ SV22 ) ) )
= $true )
| ( ( c_in @ SV6 @ SV16 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(141,plain,
! [SV17: $i,SV26: $i,SV23: $i,SV7: $i,SV37: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV37 @ SV7 @ SV23 @ SV23 ) @ SV26 @ ( tc_prod @ SV23 @ SV23 ) ) )
= $true )
| ( ( c_in @ SV7 @ ( c_Tarski_Ointerval @ SV26 @ SV37 @ SV17 @ SV23 ) @ SV23 )
= $true )
| ( ( c_in @ ( c_Pair @ SV7 @ SV17 @ SV23 @ SV23 ) @ SV26 @ ( tc_prod @ SV23 @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(142,plain,
! [SV9: $i,SV30: $i,SV19: $i] :
( ( ( c_in @ ( c_Pair @ SV19 @ SV30 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_in @ ( v_sko__4mi @ SV9 @ v_r @ SV30 ) @ SV9 @ t_a )
= $true )
| ( ( c_in @ SV30 @ v_A @ t_a )
= $false )
| ( ( c_Tarski_OisLub @ SV9 @ v_cl @ SV19 @ t_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(143,plain,
! [SV20: $i,SV31: $i,SV10: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV10 @ v_r @ SV31 ) @ SV31 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV20 @ SV31 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_in @ SV31 @ v_A @ t_a )
= $false )
| ( ( c_Tarski_OisLub @ SV10 @ v_cl @ SV20 @ t_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(144,plain,
! [SV11: $i,SV27: $i,SV32: $i,SV1: $i] :
( ( ( SV1 = c_emptyset )
= $true )
| ( ( c_in @ ( v_sko__4mk @ SV32 @ SV1 @ v_r ) @ SV1 @ t_a )
= $true )
| ( ( c_in @ ( v_sko__4mj @ SV1 @ SV27 @ v_r ) @ SV1 @ t_a )
= $true )
| ( ( c_in @ ( c_Pair @ SV27 @ SV32 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_lessequals @ SV1 @ SV11 @ ( tc_set @ t_a ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(145,plain,
! [SV33: $i,SV12: $i,SV2: $i,SV38: $i] :
( ( ( c_in @ ( c_Pair @ SV38 @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ( SV12 = c_emptyset )
| ( c_in @ ( v_sko__4mj @ SV12 @ SV38 @ v_r ) @ SV12 @ t_a ) )
= $true )
| ( ( c_lessequals @ SV12 @ SV33 @ ( tc_set @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV2 @ SV12 @ v_r ) @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(146,plain,
! [SV34: $i,SV13: $i,SV39: $i,SV3: $i] :
( ( ( c_in @ ( c_Pair @ SV3 @ SV39 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ( SV13 = c_emptyset )
| ( c_in @ ( v_sko__4mk @ SV39 @ SV13 @ v_r ) @ SV13 @ t_a ) )
= $true )
| ( ( c_lessequals @ SV13 @ SV34 @ ( tc_set @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV3 @ ( v_sko__4mj @ SV13 @ SV3 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(147,plain,
! [SV28: $i,SV4: $i,SV41: $i,SV14: $i] :
( ( ( ~ ( c_lessequals @ SV14 @ SV41 @ ( tc_set @ t_a ) ) )
= $true )
| ( ( ( SV14 = c_emptyset )
| ( c_in @ ( c_Pair @ SV4 @ SV28 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV28 @ SV14 @ v_r ) @ SV28 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV4 @ ( v_sko__4mj @ SV14 @ SV4 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(148,plain,
! [SV5: $i,SV21: $i,SV42: $i,SV35: $i,SV24: $i,SV15: $i] :
( ( ( ~ ( c_lessequals @ SV15 @ ( c_Tarski_Ointerval @ SV24 @ SV35 @ SV42 @ SV21 ) @ ( tc_set @ SV21 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV35 @ SV5 @ SV21 @ SV21 ) @ SV24 @ ( tc_prod @ SV21 @ SV21 ) )
= $true )
| ( ( c_in @ SV5 @ SV15 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(149,plain,
! [SV6: $i,SV22: $i,SV40: $i,SV36: $i,SV25: $i,SV16: $i] :
( ( ( ~ ( c_lessequals @ SV16 @ ( c_Tarski_Ointerval @ SV25 @ SV36 @ SV40 @ SV22 ) @ ( tc_set @ SV22 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV6 @ SV40 @ SV22 @ SV22 ) @ SV25 @ ( tc_prod @ SV22 @ SV22 ) )
= $true )
| ( ( c_in @ SV6 @ SV16 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(150,plain,
! [SV17: $i,SV26: $i,SV23: $i,SV7: $i,SV37: $i] :
( ( ( c_in @ ( c_Pair @ SV37 @ SV7 @ SV23 @ SV23 ) @ SV26 @ ( tc_prod @ SV23 @ SV23 ) )
= $false )
| ( ( c_in @ SV7 @ ( c_Tarski_Ointerval @ SV26 @ SV37 @ SV17 @ SV23 ) @ SV23 )
= $true )
| ( ( c_in @ ( c_Pair @ SV7 @ SV17 @ SV23 @ SV23 ) @ SV26 @ ( tc_prod @ SV23 @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(151,plain,
! [SV20: $i,SV31: $i,SV10: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__4mi @ SV10 @ v_r @ SV31 ) @ SV31 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV20 @ SV31 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_in @ SV31 @ v_A @ t_a )
= $false )
| ( ( c_Tarski_OisLub @ SV10 @ v_cl @ SV20 @ t_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(152,plain,
! [SV33: $i,SV2: $i,SV38: $i,SV12: $i] :
( ( ( SV12 = c_emptyset )
= $true )
| ( ( c_in @ ( v_sko__4mj @ SV12 @ SV38 @ v_r ) @ SV12 @ t_a )
= $true )
| ( ( c_in @ ( c_Pair @ SV38 @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_lessequals @ SV12 @ SV33 @ ( tc_set @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV2 @ SV12 @ v_r ) @ SV2 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(153,plain,
! [SV34: $i,SV3: $i,SV39: $i,SV13: $i] :
( ( ( SV13 = c_emptyset )
= $true )
| ( ( c_in @ ( v_sko__4mk @ SV39 @ SV13 @ v_r ) @ SV13 @ t_a )
= $true )
| ( ( c_in @ ( c_Pair @ SV3 @ SV39 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_lessequals @ SV13 @ SV34 @ ( tc_set @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV3 @ ( v_sko__4mj @ SV13 @ SV3 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(154,plain,
! [SV28: $i,SV4: $i,SV41: $i,SV14: $i] :
( ( ( c_lessequals @ SV14 @ SV41 @ ( tc_set @ t_a ) )
= $false )
| ( ( ( SV14 = c_emptyset )
| ( c_in @ ( c_Pair @ SV4 @ SV28 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV28 @ SV14 @ v_r ) @ SV28 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV4 @ ( v_sko__4mj @ SV14 @ SV4 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(155,plain,
! [SV5: $i,SV21: $i,SV42: $i,SV35: $i,SV24: $i,SV15: $i] :
( ( ( c_lessequals @ SV15 @ ( c_Tarski_Ointerval @ SV24 @ SV35 @ SV42 @ SV21 ) @ ( tc_set @ SV21 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV35 @ SV5 @ SV21 @ SV21 ) @ SV24 @ ( tc_prod @ SV21 @ SV21 ) )
= $true )
| ( ( c_in @ SV5 @ SV15 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(156,plain,
! [SV6: $i,SV22: $i,SV40: $i,SV36: $i,SV25: $i,SV16: $i] :
( ( ( c_lessequals @ SV16 @ ( c_Tarski_Ointerval @ SV25 @ SV36 @ SV40 @ SV22 ) @ ( tc_set @ SV22 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV6 @ SV40 @ SV22 @ SV22 ) @ SV25 @ ( tc_prod @ SV22 @ SV22 ) )
= $true )
| ( ( c_in @ SV6 @ SV16 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(157,plain,
! [SV41: $i,SV28: $i,SV4: $i,SV14: $i] :
( ( ( SV14 = c_emptyset )
= $true )
| ( ( c_in @ ( c_Pair @ SV4 @ SV28 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_lessequals @ SV14 @ SV41 @ ( tc_set @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( v_sko__4mk @ SV28 @ SV14 @ v_r ) @ SV28 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV4 @ ( v_sko__4mj @ SV14 @ SV4 @ v_r ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(158,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[46,157,156,155,153,152,151,150,144,142,132,74,63,62,49,47]) ).
thf(159,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LAT274-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 30 05:47:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.37
% 0.12/0.37 No.of.Axioms: 15
% 0.12/0.37
% 0.12/0.37 Length.of.Defs: 0
% 0.12/0.37
% 0.12/0.37 Contains.Choice.Funs: false
% 0.12/0.41 (rf:0,axioms:15,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:17,loop_count:0,foatp_calls:0,translation:fof_full)............
% 0.47/0.68
% 0.47/0.68 ********************************
% 0.47/0.68 * All subproblems solved! *
% 0.47/0.68 ********************************
% 0.47/0.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:158,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.47/0.69
% 0.47/0.69 %**** Beginning of derivation protocol ****
% 0.47/0.69 % SZS output start CNFRefutation
% See solution above
% 0.47/0.69
% 0.47/0.69 %**** End of derivation protocol ****
% 0.47/0.69 %**** no. of clauses in derivation: 159 ****
% 0.47/0.69 %**** clause counter: 158 ****
% 0.47/0.69
% 0.47/0.69 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:158,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------