TSTP Solution File: LCL442-2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL442-2 : 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 : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:23:20 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 25
% Syntax : Number of formulae : 110 ( 54 unt; 12 typ; 0 def)
% Number of atoms : 447 ( 120 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1875 ( 84 ~; 109 |; 0 &;1682 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 208 ( 0 ^ 208 !; 0 ?; 208 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_PropLog_Oeval,type,
c_PropLog_Oeval: $i > $i > $i > $o ).
thf(tp_c_PropLog_Ohyps,type,
c_PropLog_Ohyps: $i > $i > $i > $i ).
thf(tp_c_PropLog_Opl_Ofalse,type,
c_PropLog_Opl_Ofalse: $i ).
thf(tp_c_PropLog_Opl_Oop_A_N_62,type,
c_PropLog_Opl_Oop_A_N_62: $i > $i > $i > $i ).
thf(tp_c_PropLog_Othms,type,
c_PropLog_Othms: $i > $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_union,type,
c_union: $i > $i > $i > $i ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_PropLog_Opl,type,
tc_PropLog_Opl: $i > $i ).
thf(tp_v_pl1,type,
v_pl1: $i ).
thf(tp_v_pl2,type,
v_pl2: $i ).
thf(tp_v_tt,type,
v_tt: $i ).
thf(1,axiom,
! [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
( ~ ( c_in @ V_q @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ V_q @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oweaken__right_0) ).
thf(2,axiom,
! [V_p: $i,V_G: $i,T_a: $i,V_A: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_G @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_union @ V_A @ V_G @ ( tc_PropLog_Opl @ T_a ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left__Un2_0) ).
thf(3,axiom,
! [V_p: $i,V_G: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_G @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_union @ V_G @ V_B @ ( tc_PropLog_Opl @ T_a ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left__Un1_0) ).
thf(4,axiom,
! [V_p: $i,V_H: $i,T_a: $i,V_q: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_q @ c_PropLog_Opl_Ofalse @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ V_q @ T_a ) @ c_PropLog_Opl_Ofalse @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oimp__false_0) ).
thf(5,axiom,
! [V_p: $i,T_a: $i,V_H: $i,V_q: $i] :
( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ c_PropLog_Opl_Ofalse @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ V_q @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Ofalse__imp_0) ).
thf(6,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(7,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,negated_conjecture,
( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
| ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
| ~ ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_9) ).
thf(9,negated_conjecture,
( ~ ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
| ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(10,negated_conjecture,
( ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a )
| ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(11,negated_conjecture,
( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl2 @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
| ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(12,negated_conjecture,
( ( c_in @ v_pl2 @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
| ~ ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(13,negated_conjecture,
( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
| ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(14,negated_conjecture,
( ( c_in @ v_pl1 @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
| ~ ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(15,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(16,plain,
( ( ! [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
( ~ ( c_in @ V_q @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ V_q @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,plain,
( ( ! [V_p: $i,V_G: $i,T_a: $i,V_A: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_G @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_union @ V_A @ V_G @ ( tc_PropLog_Opl @ T_a ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(18,plain,
( ( ! [V_p: $i,V_G: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_G @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_union @ V_G @ V_B @ ( tc_PropLog_Opl @ T_a ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [V_p: $i,V_H: $i,T_a: $i,V_q: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_q @ c_PropLog_Opl_Ofalse @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ V_q @ T_a ) @ c_PropLog_Opl_Ofalse @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(20,plain,
( ( ! [V_p: $i,T_a: $i,V_H: $i,V_q: $i] :
( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ c_PropLog_Opl_Ofalse @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ V_q @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
| ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
| ~ ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(22,plain,
( ( ~ ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
| ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(23,plain,
( ( ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a )
| ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(24,plain,
( ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl2 @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
| ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(25,plain,
( ( ( c_in @ v_pl2 @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
| ~ ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(26,plain,
( ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
| ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(27,plain,
( ( ( c_in @ v_pl1 @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
| ~ ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(28,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(29,plain,
( ( ! [V_q: $i,V_H: $i,T_a: $i] :
( ~ ( c_in @ V_q @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ! [V_p: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ V_q @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(30,plain,
( ( ! [V_p: $i,V_G: $i,T_a: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_G @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ! [V_A: $i] : ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_union @ V_A @ V_G @ ( tc_PropLog_Opl @ T_a ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(31,plain,
( ( ! [V_p: $i,V_G: $i,T_a: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_G @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ! [V_B: $i] : ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_union @ V_G @ V_B @ ( tc_PropLog_Opl @ T_a ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(32,plain,
( ( ! [V_p: $i,V_H: $i,T_a: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ! [V_q: $i] :
( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_q @ c_PropLog_Opl_Ofalse @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ V_q @ T_a ) @ c_PropLog_Opl_Ofalse @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(33,plain,
( ( ! [V_p: $i,T_a: $i,V_H: $i] :
( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ c_PropLog_Opl_Ofalse @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ! [V_q: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ V_q @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(34,plain,
( ( ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl2 @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(35,plain,
( ( ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(36,plain,
( ( ( c_in @ v_pl1 @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
| ~ ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(37,plain,
( ( ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(38,plain,
( ( ( c_in @ v_pl2 @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
| ~ ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(39,plain,
( ( ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl2 @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(40,plain,
( ( ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a )
| ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(41,plain,
( ( ~ ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
| ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(42,plain,
( ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
| ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
| ~ ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(43,plain,
( ( ! [V_p: $i,T_a: $i,V_H: $i] :
( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ c_PropLog_Opl_Ofalse @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ! [V_q: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ V_q @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(44,plain,
( ( ! [V_p: $i,V_H: $i,T_a: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ! [V_q: $i] :
( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_q @ c_PropLog_Opl_Ofalse @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ V_q @ T_a ) @ c_PropLog_Opl_Ofalse @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(45,plain,
( ( ! [V_p: $i,V_G: $i,T_a: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_G @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ! [V_B: $i] : ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_union @ V_G @ V_B @ ( tc_PropLog_Opl @ T_a ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(46,plain,
( ( ! [V_p: $i,V_G: $i,T_a: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_G @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ! [V_A: $i] : ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_union @ V_A @ V_G @ ( tc_PropLog_Opl @ T_a ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(47,plain,
( ( ! [V_q: $i,V_H: $i,T_a: $i] :
( ~ ( c_in @ V_q @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ! [V_p: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ V_q @ T_a ) @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(48,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(49,plain,
( ( ( c_in @ v_pl1 @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $true )
| ( ( ~ ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(50,plain,
( ( ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a )
= $true )
| ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(51,plain,
( ( ( c_in @ v_pl2 @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $true )
| ( ( ~ ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(52,plain,
( ( ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
= $true )
| ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl2 @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(53,plain,
( ( ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a )
= $true )
| ( ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(54,plain,
( ( ( ~ ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a ) )
= $true )
| ( ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(55,plain,
( ( ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true )
| ( ( ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
| ~ ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(56,plain,
! [SV1: $i] :
( ( ! [SY20: $i,SY21: $i] :
( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ c_PropLog_Opl_Ofalse @ SY20 ) @ ( c_PropLog_Othms @ SY21 @ SY20 ) @ ( tc_PropLog_Opl @ SY20 ) )
| ! [SY22: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ SY22 @ SY20 ) @ ( c_PropLog_Othms @ SY21 @ SY20 ) @ ( tc_PropLog_Opl @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(57,plain,
! [SV2: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ( c_in @ SV2 @ ( c_PropLog_Othms @ SY23 @ SY24 ) @ ( tc_PropLog_Opl @ SY24 ) )
| ! [SY25: $i] :
( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SY25 @ c_PropLog_Opl_Ofalse @ SY24 ) @ ( c_PropLog_Othms @ SY23 @ SY24 ) @ ( tc_PropLog_Opl @ SY24 ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ SV2 @ SY25 @ SY24 ) @ c_PropLog_Opl_Ofalse @ SY24 ) @ ( c_PropLog_Othms @ SY23 @ SY24 ) @ ( tc_PropLog_Opl @ SY24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(58,plain,
! [SV3: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ~ ( c_in @ SV3 @ ( c_PropLog_Othms @ SY26 @ SY27 ) @ ( tc_PropLog_Opl @ SY27 ) )
| ! [SY28: $i] : ( c_in @ SV3 @ ( c_PropLog_Othms @ ( c_union @ SY26 @ SY28 @ ( tc_PropLog_Opl @ SY27 ) ) @ SY27 ) @ ( tc_PropLog_Opl @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(59,plain,
! [SV4: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ( c_in @ SV4 @ ( c_PropLog_Othms @ SY29 @ SY30 ) @ ( tc_PropLog_Opl @ SY30 ) )
| ! [SY31: $i] : ( c_in @ SV4 @ ( c_PropLog_Othms @ ( c_union @ SY31 @ SY29 @ ( tc_PropLog_Opl @ SY30 ) ) @ SY30 ) @ ( tc_PropLog_Opl @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(60,plain,
! [SV5: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ~ ( c_in @ SV5 @ ( c_PropLog_Othms @ SY32 @ SY33 ) @ ( tc_PropLog_Opl @ SY33 ) )
| ! [SY34: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SY34 @ SV5 @ SY33 ) @ ( c_PropLog_Othms @ SY32 @ SY33 ) @ ( tc_PropLog_Opl @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(61,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(62,plain,
( ( ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a )
= $false )
| ( ( c_in @ v_pl1 @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(63,plain,
( ( ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
= $false )
| ( ( c_in @ v_pl2 @ ( c_PropLog_Othms @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(64,plain,
( ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $false )
| ( ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(65,plain,
( ( ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
= $false )
| ( ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(66,plain,
( ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $false )
| ( ( ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
| ~ ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(67,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY35: $i] :
( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ c_PropLog_Opl_Ofalse @ SV6 ) @ ( c_PropLog_Othms @ SY35 @ SV6 ) @ ( tc_PropLog_Opl @ SV6 ) )
| ! [SY36: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ SY36 @ SV6 ) @ ( c_PropLog_Othms @ SY35 @ SV6 ) @ ( tc_PropLog_Opl @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(68,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY37: $i] :
( ~ ( c_in @ SV2 @ ( c_PropLog_Othms @ SV7 @ SY37 ) @ ( tc_PropLog_Opl @ SY37 ) )
| ! [SY38: $i] :
( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SY38 @ c_PropLog_Opl_Ofalse @ SY37 ) @ ( c_PropLog_Othms @ SV7 @ SY37 ) @ ( tc_PropLog_Opl @ SY37 ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ SV2 @ SY38 @ SY37 ) @ c_PropLog_Opl_Ofalse @ SY37 ) @ ( c_PropLog_Othms @ SV7 @ SY37 ) @ ( tc_PropLog_Opl @ SY37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(69,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY39: $i] :
( ~ ( c_in @ SV3 @ ( c_PropLog_Othms @ SV8 @ SY39 ) @ ( tc_PropLog_Opl @ SY39 ) )
| ! [SY40: $i] : ( c_in @ SV3 @ ( c_PropLog_Othms @ ( c_union @ SV8 @ SY40 @ ( tc_PropLog_Opl @ SY39 ) ) @ SY39 ) @ ( tc_PropLog_Opl @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(70,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY41: $i] :
( ~ ( c_in @ SV4 @ ( c_PropLog_Othms @ SV9 @ SY41 ) @ ( tc_PropLog_Opl @ SY41 ) )
| ! [SY42: $i] : ( c_in @ SV4 @ ( c_PropLog_Othms @ ( c_union @ SY42 @ SV9 @ ( tc_PropLog_Opl @ SY41 ) ) @ SY41 ) @ ( tc_PropLog_Opl @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(71,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY43: $i] :
( ~ ( c_in @ SV5 @ ( c_PropLog_Othms @ SV10 @ SY43 ) @ ( tc_PropLog_Opl @ SY43 ) )
| ! [SY44: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SY44 @ SV5 @ SY43 ) @ ( c_PropLog_Othms @ SV10 @ SY43 ) @ ( tc_PropLog_Opl @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(72,plain,
( ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $false )
| ( ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(73,plain,
( ( ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
= $true )
| ( ( ~ ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a ) )
= $true )
| ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(74,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ c_PropLog_Opl_Ofalse @ SV6 ) @ ( c_PropLog_Othms @ SV11 @ SV6 ) @ ( tc_PropLog_Opl @ SV6 ) )
| ! [SY45: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ SY45 @ SV6 ) @ ( c_PropLog_Othms @ SV11 @ SV6 ) @ ( tc_PropLog_Opl @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(75,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ~ ( c_in @ SV2 @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) )
| ! [SY46: $i] :
( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SY46 @ c_PropLog_Opl_Ofalse @ SV12 ) @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ SV2 @ SY46 @ SV12 ) @ c_PropLog_Opl_Ofalse @ SV12 ) @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(76,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ~ ( c_in @ SV3 @ ( c_PropLog_Othms @ SV8 @ SV13 ) @ ( tc_PropLog_Opl @ SV13 ) )
| ! [SY47: $i] : ( c_in @ SV3 @ ( c_PropLog_Othms @ ( c_union @ SV8 @ SY47 @ ( tc_PropLog_Opl @ SV13 ) ) @ SV13 ) @ ( tc_PropLog_Opl @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(77,plain,
! [SV14: $i,SV9: $i,SV4: $i] :
( ( ~ ( c_in @ SV4 @ ( c_PropLog_Othms @ SV9 @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) )
| ! [SY48: $i] : ( c_in @ SV4 @ ( c_PropLog_Othms @ ( c_union @ SY48 @ SV9 @ ( tc_PropLog_Opl @ SV14 ) ) @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(78,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ~ ( c_in @ SV5 @ ( c_PropLog_Othms @ SV10 @ SV15 ) @ ( tc_PropLog_Opl @ SV15 ) )
| ! [SY49: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SY49 @ SV5 @ SV15 ) @ ( c_PropLog_Othms @ SV10 @ SV15 ) @ ( tc_PropLog_Opl @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(79,plain,
( ( ( c_PropLog_Oeval @ v_tt @ v_pl1 @ t_a )
= $false )
| ( ( c_PropLog_Oeval @ v_tt @ v_pl2 @ t_a )
= $true )
| ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ v_pl1 @ v_pl2 @ t_a ) @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ ( c_union @ ( c_PropLog_Ohyps @ v_pl1 @ v_tt @ t_a ) @ ( c_PropLog_Ohyps @ v_pl2 @ v_tt @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(80,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ c_PropLog_Opl_Ofalse @ SV6 ) @ ( c_PropLog_Othms @ SV11 @ SV6 ) @ ( tc_PropLog_Opl @ SV6 ) ) )
= $true )
| ( ( ! [SY45: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ SY45 @ SV6 ) @ ( c_PropLog_Othms @ SV11 @ SV6 ) @ ( tc_PropLog_Opl @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(81,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( c_in @ SV2 @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) ) )
= $true )
| ( ( ! [SY46: $i] :
( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SY46 @ c_PropLog_Opl_Ofalse @ SV12 ) @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ SV2 @ SY46 @ SV12 ) @ c_PropLog_Opl_Ofalse @ SV12 ) @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(82,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( c_in @ SV3 @ ( c_PropLog_Othms @ SV8 @ SV13 ) @ ( tc_PropLog_Opl @ SV13 ) ) )
= $true )
| ( ( ! [SY47: $i] : ( c_in @ SV3 @ ( c_PropLog_Othms @ ( c_union @ SV8 @ SY47 @ ( tc_PropLog_Opl @ SV13 ) ) @ SV13 ) @ ( tc_PropLog_Opl @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(83,plain,
! [SV14: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( c_in @ SV4 @ ( c_PropLog_Othms @ SV9 @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) ) )
= $true )
| ( ( ! [SY48: $i] : ( c_in @ SV4 @ ( c_PropLog_Othms @ ( c_union @ SY48 @ SV9 @ ( tc_PropLog_Opl @ SV14 ) ) @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(84,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( c_in @ SV5 @ ( c_PropLog_Othms @ SV10 @ SV15 ) @ ( tc_PropLog_Opl @ SV15 ) ) )
= $true )
| ( ( ! [SY49: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SY49 @ SV5 @ SV15 ) @ ( c_PropLog_Othms @ SV10 @ SV15 ) @ ( tc_PropLog_Opl @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(85,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ c_PropLog_Opl_Ofalse @ SV6 ) @ ( c_PropLog_Othms @ SV11 @ SV6 ) @ ( tc_PropLog_Opl @ SV6 ) )
= $false )
| ( ( ! [SY45: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ SY45 @ SV6 ) @ ( c_PropLog_Othms @ SV11 @ SV6 ) @ ( tc_PropLog_Opl @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(86,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ( c_in @ SV2 @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) )
= $false )
| ( ( ! [SY46: $i] :
( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SY46 @ c_PropLog_Opl_Ofalse @ SV12 ) @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ SV2 @ SY46 @ SV12 ) @ c_PropLog_Opl_Ofalse @ SV12 ) @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(87,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( c_in @ SV3 @ ( c_PropLog_Othms @ SV8 @ SV13 ) @ ( tc_PropLog_Opl @ SV13 ) )
= $false )
| ( ( ! [SY47: $i] : ( c_in @ SV3 @ ( c_PropLog_Othms @ ( c_union @ SV8 @ SY47 @ ( tc_PropLog_Opl @ SV13 ) ) @ SV13 ) @ ( tc_PropLog_Opl @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(88,plain,
! [SV14: $i,SV9: $i,SV4: $i] :
( ( ( c_in @ SV4 @ ( c_PropLog_Othms @ SV9 @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) )
= $false )
| ( ( ! [SY48: $i] : ( c_in @ SV4 @ ( c_PropLog_Othms @ ( c_union @ SY48 @ SV9 @ ( tc_PropLog_Opl @ SV14 ) ) @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(89,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( c_in @ SV5 @ ( c_PropLog_Othms @ SV10 @ SV15 ) @ ( tc_PropLog_Opl @ SV15 ) )
= $false )
| ( ( ! [SY49: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SY49 @ SV5 @ SV15 ) @ ( c_PropLog_Othms @ SV10 @ SV15 ) @ ( tc_PropLog_Opl @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(90,plain,
! [SV11: $i,SV6: $i,SV16: $i,SV1: $i] :
( ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ SV16 @ SV6 ) @ ( c_PropLog_Othms @ SV11 @ SV6 ) @ ( tc_PropLog_Opl @ SV6 ) )
= $true )
| ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ c_PropLog_Opl_Ofalse @ SV6 ) @ ( c_PropLog_Othms @ SV11 @ SV6 ) @ ( tc_PropLog_Opl @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(91,plain,
! [SV2: $i,SV7: $i,SV12: $i,SV17: $i] :
( ( ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV17 @ c_PropLog_Opl_Ofalse @ SV12 ) @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ SV2 @ SV17 @ SV12 ) @ c_PropLog_Opl_Ofalse @ SV12 ) @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) ) )
= $true )
| ( ( c_in @ SV2 @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(92,plain,
! [SV13: $i,SV18: $i,SV8: $i,SV3: $i] :
( ( ( c_in @ SV3 @ ( c_PropLog_Othms @ ( c_union @ SV8 @ SV18 @ ( tc_PropLog_Opl @ SV13 ) ) @ SV13 ) @ ( tc_PropLog_Opl @ SV13 ) )
= $true )
| ( ( c_in @ SV3 @ ( c_PropLog_Othms @ SV8 @ SV13 ) @ ( tc_PropLog_Opl @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(93,plain,
! [SV14: $i,SV9: $i,SV19: $i,SV4: $i] :
( ( ( c_in @ SV4 @ ( c_PropLog_Othms @ ( c_union @ SV19 @ SV9 @ ( tc_PropLog_Opl @ SV14 ) ) @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) )
= $true )
| ( ( c_in @ SV4 @ ( c_PropLog_Othms @ SV9 @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(94,plain,
! [SV10: $i,SV15: $i,SV5: $i,SV20: $i] :
( ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV20 @ SV5 @ SV15 ) @ ( c_PropLog_Othms @ SV10 @ SV15 ) @ ( tc_PropLog_Opl @ SV15 ) )
= $true )
| ( ( c_in @ SV5 @ ( c_PropLog_Othms @ SV10 @ SV15 ) @ ( tc_PropLog_Opl @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(95,plain,
! [SV2: $i,SV7: $i,SV12: $i,SV17: $i] :
( ( ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV17 @ c_PropLog_Opl_Ofalse @ SV12 ) @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) ) )
= $true )
| ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ SV2 @ SV17 @ SV12 ) @ c_PropLog_Opl_Ofalse @ SV12 ) @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) )
= $true )
| ( ( c_in @ SV2 @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(96,plain,
! [SV2: $i,SV7: $i,SV12: $i,SV17: $i] :
( ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV17 @ c_PropLog_Opl_Ofalse @ SV12 ) @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) )
= $false )
| ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ SV2 @ SV17 @ SV12 ) @ c_PropLog_Opl_Ofalse @ SV12 ) @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) )
= $true )
| ( ( c_in @ SV2 @ ( c_PropLog_Othms @ SV7 @ SV12 ) @ ( tc_PropLog_Opl @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(97,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[50,96,94,93,92,90,79,72,64,63,62,61,52]) ).
thf(98,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL442-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 10:17:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.36
% 0.20/0.36 No.of.Axioms: 12
% 0.20/0.36
% 0.20/0.36 Length.of.Defs: 0
% 0.20/0.36
% 0.20/0.36 Contains.Choice.Funs: false
% 0.20/0.37 (rf:0,axioms:12,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:14,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.20/0.47
% 0.20/0.47 ********************************
% 0.20/0.47 * All subproblems solved! *
% 0.20/0.47 ********************************
% 0.20/0.47 % SZS status Unsatisfiable for /export/starexec/sandbox/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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:97,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.48
% 0.20/0.48 %**** Beginning of derivation protocol ****
% 0.20/0.48 % SZS output start CNFRefutation
% See solution above
% 0.20/0.48
% 0.20/0.48 %**** End of derivation protocol ****
% 0.20/0.48 %**** no. of clauses in derivation: 98 ****
% 0.20/0.48 %**** clause counter: 97 ****
% 0.20/0.48
% 0.20/0.48 % SZS status Unsatisfiable for /export/starexec/sandbox/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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:97,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------