TSTP Solution File: LCL429-2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL429-2 : 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 : n027.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 12:23:10 EDT 2022
% Result : Unsatisfiable 0.18s 0.51s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 26
% Syntax : Number of formulae : 91 ( 57 unt; 17 typ; 0 def)
% Number of atoms : 314 ( 84 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1761 ( 63 ~; 72 |; 0 &;1626 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 9 con; 0-3 aty)
% Number of variables : 257 ( 0 ^ 257 !; 0 ?; 257 :)
% Comments :
%------------------------------------------------------------------------------
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_Opl_Ovar,type,
c_PropLog_Opl_Ovar: $i > $i > $i ).
thf(tp_c_PropLog_Othms,type,
c_PropLog_Othms: $i > $i > $i ).
thf(tp_c_emptyset,type,
c_emptyset: $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_insert,type,
c_insert: $i > $i > $i > $i ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_c_minus,type,
c_minus: $i > $i > $i > $i ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_PropLog_Opl,type,
tc_PropLog_Opl: $i > $i ).
thf(tp_tc_set,type,
tc_set: $i > $i ).
thf(tp_v_F,type,
v_F: $i ).
thf(tp_v_p,type,
v_p: $i ).
thf(tp_v_t,type,
v_t: $i ).
thf(tp_v_v,type,
v_v: $i ).
thf(1,axiom,
! [V_p: $i,V_G: $i,T_a: $i,V_H: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_G @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ~ ( c_lessequals @ V_G @ V_H @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) )
| ( c_in @ V_p @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left_0) ).
thf(2,axiom,
! [V_q: $i,V_p: $i,V_H: $i,T_a: $i] :
( ~ ( c_in @ V_q @ ( c_PropLog_Othms @ ( c_insert @ V_p @ V_H @ ( tc_PropLog_Opl @ T_a ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ~ ( c_in @ V_q @ ( c_PropLog_Othms @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ c_PropLog_Opl_Ofalse @ T_a ) @ V_H @ ( tc_PropLog_Opl @ T_a ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ V_q @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms__excluded__middle__rule_0) ).
thf(3,axiom,
! [V_a: $i,V_B: $i,V_c: $i,T_a: $i,V_D: $i] : ( c_lessequals @ ( c_minus @ ( c_insert @ V_a @ ( c_minus @ V_B @ ( c_insert @ V_c @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) ) @ T_a ) @ V_D @ ( tc_set @ T_a ) ) @ ( c_insert @ V_a @ ( c_minus @ V_B @ ( c_insert @ V_c @ V_D @ T_a ) @ ( tc_set @ T_a ) ) @ T_a ) @ ( tc_set @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oinsert__Diff__subset2_0) ).
thf(4,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_a: $i] : ( c_lessequals @ ( c_minus @ V_B @ V_C @ ( tc_set @ T_a ) ) @ ( c_insert @ V_a @ ( c_minus @ V_B @ ( c_insert @ V_a @ V_C @ T_a ) @ ( tc_set @ T_a ) ) @ T_a ) @ ( tc_set @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oinsert__Diff__same_0) ).
thf(5,axiom,
! [V_p: $i,V_t: $i,V_v: $i,T_a: $i] : ( c_lessequals @ ( c_PropLog_Ohyps @ V_p @ ( c_minus @ V_t @ ( c_insert @ V_v @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) ) @ T_a ) @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Ovar @ V_v @ T_a ) @ c_PropLog_Opl_Ofalse @ T_a ) @ ( c_minus @ ( c_PropLog_Ohyps @ V_p @ V_t @ T_a ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ V_v @ T_a ) @ c_emptyset @ ( tc_PropLog_Opl @ T_a ) ) @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) @ ( tc_PropLog_Opl @ T_a ) ) @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Ohyps__Diff_0) ).
thf(6,axiom,
! [V_p: $i,V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_minus @ V_A @ V_B @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) )
| ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_minus @ V_C @ V_B @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_ODiff__weaken__left_0) ).
thf(7,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(8,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,negated_conjecture,
~ ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ v_t @ t_a ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ v_v @ t_a ) @ v_F @ ( tc_PropLog_Opl @ t_a ) ) @ ( tc_set @ ( 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,
! [V_U: $i] : ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ V_U @ t_a ) @ v_F @ ( tc_set @ ( tc_PropLog_Opl @ t_a ) ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(11,plain,
$false = $false,
inference(unfold_def,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [V_p: $i,V_G: $i,T_a: $i,V_H: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_G @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ~ ( c_lessequals @ V_G @ V_H @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) )
| ( c_in @ V_p @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [V_q: $i,V_p: $i,V_H: $i,T_a: $i] :
( ~ ( c_in @ V_q @ ( c_PropLog_Othms @ ( c_insert @ V_p @ V_H @ ( tc_PropLog_Opl @ T_a ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ~ ( c_in @ V_q @ ( c_PropLog_Othms @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ c_PropLog_Opl_Ofalse @ T_a ) @ V_H @ ( tc_PropLog_Opl @ T_a ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ V_q @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ! [V_a: $i,V_B: $i,V_c: $i,T_a: $i,V_D: $i] : ( c_lessequals @ ( c_minus @ ( c_insert @ V_a @ ( c_minus @ V_B @ ( c_insert @ V_c @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) ) @ T_a ) @ V_D @ ( tc_set @ T_a ) ) @ ( c_insert @ V_a @ ( c_minus @ V_B @ ( c_insert @ V_c @ V_D @ T_a ) @ ( tc_set @ T_a ) ) @ T_a ) @ ( tc_set @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_a: $i] : ( c_lessequals @ ( c_minus @ V_B @ V_C @ ( tc_set @ T_a ) ) @ ( c_insert @ V_a @ ( c_minus @ V_B @ ( c_insert @ V_a @ V_C @ T_a ) @ ( tc_set @ T_a ) ) @ T_a ) @ ( tc_set @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [V_p: $i,V_t: $i,V_v: $i,T_a: $i] : ( c_lessequals @ ( c_PropLog_Ohyps @ V_p @ ( c_minus @ V_t @ ( c_insert @ V_v @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) ) @ T_a ) @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Ovar @ V_v @ T_a ) @ c_PropLog_Opl_Ofalse @ T_a ) @ ( c_minus @ ( c_PropLog_Ohyps @ V_p @ V_t @ T_a ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ V_v @ T_a ) @ c_emptyset @ ( tc_PropLog_Opl @ T_a ) ) @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) @ ( tc_PropLog_Opl @ T_a ) ) @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ! [V_p: $i,V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_minus @ V_A @ V_B @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) )
| ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_minus @ V_C @ V_B @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ~ ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ v_t @ t_a ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ v_v @ t_a ) @ v_F @ ( tc_PropLog_Opl @ t_a ) ) @ ( tc_set @ ( tc_PropLog_Opl @ t_a ) ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(19,plain,
( ( ! [V_U: $i] : ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ V_U @ t_a ) @ v_F @ ( tc_set @ ( tc_PropLog_Opl @ t_a ) ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(20,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(21,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_H: $i] :
( ~ ( c_lessequals @ V_G @ V_H @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) )
| ( c_in @ V_p @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(22,plain,
( ( ! [V_p: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_minus @ V_A @ V_B @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ! [V_C: $i] :
( ~ ( c_lessequals @ V_A @ V_C @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) )
| ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_minus @ V_C @ V_B @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(23,plain,
( ( ! [V_U: $i] : ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ V_U @ t_a ) @ v_F @ ( tc_set @ ( tc_PropLog_Opl @ t_a ) ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ v_t @ t_a ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ v_v @ t_a ) @ v_F @ ( tc_PropLog_Opl @ t_a ) ) @ ( tc_set @ ( tc_PropLog_Opl @ t_a ) ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(25,plain,
( ( ! [V_p: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_minus @ V_A @ V_B @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ! [V_C: $i] :
( ~ ( c_lessequals @ V_A @ V_C @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) )
| ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_minus @ V_C @ V_B @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(26,plain,
( ( ! [V_p: $i,V_t: $i,V_v: $i,T_a: $i] : ( c_lessequals @ ( c_PropLog_Ohyps @ V_p @ ( c_minus @ V_t @ ( c_insert @ V_v @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) ) @ T_a ) @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Ovar @ V_v @ T_a ) @ c_PropLog_Opl_Ofalse @ T_a ) @ ( c_minus @ ( c_PropLog_Ohyps @ V_p @ V_t @ T_a ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ V_v @ T_a ) @ c_emptyset @ ( tc_PropLog_Opl @ T_a ) ) @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) @ ( tc_PropLog_Opl @ T_a ) ) @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(27,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_a: $i] : ( c_lessequals @ ( c_minus @ V_B @ V_C @ ( tc_set @ T_a ) ) @ ( c_insert @ V_a @ ( c_minus @ V_B @ ( c_insert @ V_a @ V_C @ T_a ) @ ( tc_set @ T_a ) ) @ T_a ) @ ( tc_set @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(28,plain,
( ( ! [V_a: $i,V_B: $i,V_c: $i,T_a: $i,V_D: $i] : ( c_lessequals @ ( c_minus @ ( c_insert @ V_a @ ( c_minus @ V_B @ ( c_insert @ V_c @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) ) @ T_a ) @ V_D @ ( tc_set @ T_a ) ) @ ( c_insert @ V_a @ ( c_minus @ V_B @ ( c_insert @ V_c @ V_D @ T_a ) @ ( tc_set @ T_a ) ) @ T_a ) @ ( tc_set @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(29,plain,
( ( ! [V_q: $i,V_p: $i,V_H: $i,T_a: $i] :
( ~ ( c_in @ V_q @ ( c_PropLog_Othms @ ( c_insert @ V_p @ V_H @ ( tc_PropLog_Opl @ T_a ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ~ ( c_in @ V_q @ ( c_PropLog_Othms @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ V_p @ c_PropLog_Opl_Ofalse @ T_a ) @ V_H @ ( tc_PropLog_Opl @ T_a ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ V_q @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
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_H: $i] :
( ~ ( c_lessequals @ V_G @ V_H @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) )
| ( c_in @ V_p @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(31,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(32,plain,
! [SV1: $i] :
( ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ SV1 @ t_a ) @ v_F @ ( tc_set @ ( tc_PropLog_Opl @ t_a ) ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(33,plain,
( ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ v_t @ t_a ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ v_v @ t_a ) @ v_F @ ( tc_PropLog_Opl @ t_a ) ) @ ( tc_set @ ( tc_PropLog_Opl @ t_a ) ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(34,plain,
! [SV2: $i] :
( ( ! [SY27: $i,SY28: $i,SY29: $i] :
( ~ ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SY27 @ SY28 @ ( tc_set @ ( tc_PropLog_Opl @ SY29 ) ) ) @ SY29 ) @ ( tc_PropLog_Opl @ SY29 ) )
| ! [SY30: $i] :
( ~ ( c_lessequals @ SY27 @ SY30 @ ( tc_set @ ( tc_PropLog_Opl @ SY29 ) ) )
| ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SY30 @ SY28 @ ( tc_set @ ( tc_PropLog_Opl @ SY29 ) ) ) @ SY29 ) @ ( tc_PropLog_Opl @ SY29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(35,plain,
! [SV3: $i] :
( ( ! [SY31: $i,SY32: $i,SY33: $i] : ( c_lessequals @ ( c_PropLog_Ohyps @ SV3 @ ( c_minus @ SY31 @ ( c_insert @ SY32 @ c_emptyset @ SY33 ) @ ( tc_set @ SY33 ) ) @ SY33 ) @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Ovar @ SY32 @ SY33 ) @ c_PropLog_Opl_Ofalse @ SY33 ) @ ( c_minus @ ( c_PropLog_Ohyps @ SV3 @ SY31 @ SY33 ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ SY32 @ SY33 ) @ c_emptyset @ ( tc_PropLog_Opl @ SY33 ) ) @ ( tc_set @ ( tc_PropLog_Opl @ SY33 ) ) ) @ ( tc_PropLog_Opl @ SY33 ) ) @ ( tc_set @ ( tc_PropLog_Opl @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(36,plain,
! [SV4: $i] :
( ( ! [SY34: $i,SY35: $i,SY36: $i] : ( c_lessequals @ ( c_minus @ SV4 @ SY34 @ ( tc_set @ SY35 ) ) @ ( c_insert @ SY36 @ ( c_minus @ SV4 @ ( c_insert @ SY36 @ SY34 @ SY35 ) @ ( tc_set @ SY35 ) ) @ SY35 ) @ ( tc_set @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(37,plain,
! [SV5: $i] :
( ( ! [SY37: $i,SY38: $i,SY39: $i,SY40: $i] : ( c_lessequals @ ( c_minus @ ( c_insert @ SV5 @ ( c_minus @ SY37 @ ( c_insert @ SY38 @ c_emptyset @ SY39 ) @ ( tc_set @ SY39 ) ) @ SY39 ) @ SY40 @ ( tc_set @ SY39 ) ) @ ( c_insert @ SV5 @ ( c_minus @ SY37 @ ( c_insert @ SY38 @ SY40 @ SY39 ) @ ( tc_set @ SY39 ) ) @ SY39 ) @ ( tc_set @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(38,plain,
! [SV6: $i] :
( ( ! [SY41: $i,SY42: $i,SY43: $i] :
( ~ ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ SY41 @ SY42 @ ( tc_PropLog_Opl @ SY43 ) ) @ SY43 ) @ ( tc_PropLog_Opl @ SY43 ) )
| ~ ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ SY41 @ c_PropLog_Opl_Ofalse @ SY43 ) @ SY42 @ ( tc_PropLog_Opl @ SY43 ) ) @ SY43 ) @ ( tc_PropLog_Opl @ SY43 ) )
| ( c_in @ SV6 @ ( c_PropLog_Othms @ SY42 @ SY43 ) @ ( tc_PropLog_Opl @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(39,plain,
! [SV7: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ( c_in @ SV7 @ ( c_PropLog_Othms @ SY44 @ SY45 ) @ ( tc_PropLog_Opl @ SY45 ) )
| ! [SY46: $i] :
( ~ ( c_lessequals @ SY44 @ SY46 @ ( tc_set @ ( tc_PropLog_Opl @ SY45 ) ) )
| ( c_in @ SV7 @ ( c_PropLog_Othms @ SY46 @ SY45 ) @ ( tc_PropLog_Opl @ SY45 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(40,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(41,plain,
! [SV8: $i,SV2: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ~ ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SV8 @ SY47 @ ( tc_set @ ( tc_PropLog_Opl @ SY48 ) ) ) @ SY48 ) @ ( tc_PropLog_Opl @ SY48 ) )
| ! [SY49: $i] :
( ~ ( c_lessequals @ SV8 @ SY49 @ ( tc_set @ ( tc_PropLog_Opl @ SY48 ) ) )
| ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SY49 @ SY47 @ ( tc_set @ ( tc_PropLog_Opl @ SY48 ) ) ) @ SY48 ) @ ( tc_PropLog_Opl @ SY48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV9: $i,SV3: $i] :
( ( ! [SY50: $i,SY51: $i] : ( c_lessequals @ ( c_PropLog_Ohyps @ SV3 @ ( c_minus @ SV9 @ ( c_insert @ SY50 @ c_emptyset @ SY51 ) @ ( tc_set @ SY51 ) ) @ SY51 ) @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Ovar @ SY50 @ SY51 ) @ c_PropLog_Opl_Ofalse @ SY51 ) @ ( c_minus @ ( c_PropLog_Ohyps @ SV3 @ SV9 @ SY51 ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ SY50 @ SY51 ) @ c_emptyset @ ( tc_PropLog_Opl @ SY51 ) ) @ ( tc_set @ ( tc_PropLog_Opl @ SY51 ) ) ) @ ( tc_PropLog_Opl @ SY51 ) ) @ ( tc_set @ ( tc_PropLog_Opl @ SY51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV10: $i,SV4: $i] :
( ( ! [SY52: $i,SY53: $i] : ( c_lessequals @ ( c_minus @ SV4 @ SV10 @ ( tc_set @ SY52 ) ) @ ( c_insert @ SY53 @ ( c_minus @ SV4 @ ( c_insert @ SY53 @ SV10 @ SY52 ) @ ( tc_set @ SY52 ) ) @ SY52 ) @ ( tc_set @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV11: $i,SV5: $i] :
( ( ! [SY54: $i,SY55: $i,SY56: $i] : ( c_lessequals @ ( c_minus @ ( c_insert @ SV5 @ ( c_minus @ SV11 @ ( c_insert @ SY54 @ c_emptyset @ SY55 ) @ ( tc_set @ SY55 ) ) @ SY55 ) @ SY56 @ ( tc_set @ SY55 ) ) @ ( c_insert @ SV5 @ ( c_minus @ SV11 @ ( c_insert @ SY54 @ SY56 @ SY55 ) @ ( tc_set @ SY55 ) ) @ SY55 ) @ ( tc_set @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV12: $i,SV6: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ SV12 @ SY57 @ ( tc_PropLog_Opl @ SY58 ) ) @ SY58 ) @ ( tc_PropLog_Opl @ SY58 ) )
| ~ ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ SV12 @ c_PropLog_Opl_Ofalse @ SY58 ) @ SY57 @ ( tc_PropLog_Opl @ SY58 ) ) @ SY58 ) @ ( tc_PropLog_Opl @ SY58 ) )
| ( c_in @ SV6 @ ( c_PropLog_Othms @ SY57 @ SY58 ) @ ( tc_PropLog_Opl @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV13: $i,SV7: $i] :
( ( ! [SY59: $i] :
( ~ ( c_in @ SV7 @ ( c_PropLog_Othms @ SV13 @ SY59 ) @ ( tc_PropLog_Opl @ SY59 ) )
| ! [SY60: $i] :
( ~ ( c_lessequals @ SV13 @ SY60 @ ( tc_set @ ( tc_PropLog_Opl @ SY59 ) ) )
| ( c_in @ SV7 @ ( c_PropLog_Othms @ SY60 @ SY59 ) @ ( tc_PropLog_Opl @ SY59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ! [SY61: $i] :
( ~ ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SV8 @ SV14 @ ( tc_set @ ( tc_PropLog_Opl @ SY61 ) ) ) @ SY61 ) @ ( tc_PropLog_Opl @ SY61 ) )
| ! [SY62: $i] :
( ~ ( c_lessequals @ SV8 @ SY62 @ ( tc_set @ ( tc_PropLog_Opl @ SY61 ) ) )
| ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SY62 @ SV14 @ ( tc_set @ ( tc_PropLog_Opl @ SY61 ) ) ) @ SY61 ) @ ( tc_PropLog_Opl @ SY61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV15: $i,SV9: $i,SV3: $i] :
( ( ! [SY63: $i] : ( c_lessequals @ ( c_PropLog_Ohyps @ SV3 @ ( c_minus @ SV9 @ ( c_insert @ SV15 @ c_emptyset @ SY63 ) @ ( tc_set @ SY63 ) ) @ SY63 ) @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Ovar @ SV15 @ SY63 ) @ c_PropLog_Opl_Ofalse @ SY63 ) @ ( c_minus @ ( c_PropLog_Ohyps @ SV3 @ SV9 @ SY63 ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ SV15 @ SY63 ) @ c_emptyset @ ( tc_PropLog_Opl @ SY63 ) ) @ ( tc_set @ ( tc_PropLog_Opl @ SY63 ) ) ) @ ( tc_PropLog_Opl @ SY63 ) ) @ ( tc_set @ ( tc_PropLog_Opl @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV16: $i,SV10: $i,SV4: $i] :
( ( ! [SY64: $i] : ( c_lessequals @ ( c_minus @ SV4 @ SV10 @ ( tc_set @ SV16 ) ) @ ( c_insert @ SY64 @ ( c_minus @ SV4 @ ( c_insert @ SY64 @ SV10 @ SV16 ) @ ( tc_set @ SV16 ) ) @ SV16 ) @ ( tc_set @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV17: $i,SV11: $i,SV5: $i] :
( ( ! [SY65: $i,SY66: $i] : ( c_lessequals @ ( c_minus @ ( c_insert @ SV5 @ ( c_minus @ SV11 @ ( c_insert @ SV17 @ c_emptyset @ SY65 ) @ ( tc_set @ SY65 ) ) @ SY65 ) @ SY66 @ ( tc_set @ SY65 ) ) @ ( c_insert @ SV5 @ ( c_minus @ SV11 @ ( c_insert @ SV17 @ SY66 @ SY65 ) @ ( tc_set @ SY65 ) ) @ SY65 ) @ ( tc_set @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ! [SY67: $i] :
( ~ ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ SV12 @ SV18 @ ( tc_PropLog_Opl @ SY67 ) ) @ SY67 ) @ ( tc_PropLog_Opl @ SY67 ) )
| ~ ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ SV12 @ c_PropLog_Opl_Ofalse @ SY67 ) @ SV18 @ ( tc_PropLog_Opl @ SY67 ) ) @ SY67 ) @ ( tc_PropLog_Opl @ SY67 ) )
| ( c_in @ SV6 @ ( c_PropLog_Othms @ SV18 @ SY67 ) @ ( tc_PropLog_Opl @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV19: $i,SV13: $i,SV7: $i] :
( ( ~ ( c_in @ SV7 @ ( c_PropLog_Othms @ SV13 @ SV19 ) @ ( tc_PropLog_Opl @ SV19 ) )
| ! [SY68: $i] :
( ~ ( c_lessequals @ SV13 @ SY68 @ ( tc_set @ ( tc_PropLog_Opl @ SV19 ) ) )
| ( c_in @ SV7 @ ( c_PropLog_Othms @ SY68 @ SV19 ) @ ( tc_PropLog_Opl @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV20: $i,SV14: $i,SV8: $i,SV2: $i] :
( ( ~ ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SV8 @ SV14 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) ) @ SV20 ) @ ( tc_PropLog_Opl @ SV20 ) )
| ! [SY69: $i] :
( ~ ( c_lessequals @ SV8 @ SY69 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) )
| ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SY69 @ SV14 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) ) @ SV20 ) @ ( tc_PropLog_Opl @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV21: $i,SV15: $i,SV9: $i,SV3: $i] :
( ( c_lessequals @ ( c_PropLog_Ohyps @ SV3 @ ( c_minus @ SV9 @ ( c_insert @ SV15 @ c_emptyset @ SV21 ) @ ( tc_set @ SV21 ) ) @ SV21 ) @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Ovar @ SV15 @ SV21 ) @ c_PropLog_Opl_Ofalse @ SV21 ) @ ( c_minus @ ( c_PropLog_Ohyps @ SV3 @ SV9 @ SV21 ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ SV15 @ SV21 ) @ c_emptyset @ ( tc_PropLog_Opl @ SV21 ) ) @ ( tc_set @ ( tc_PropLog_Opl @ SV21 ) ) ) @ ( tc_PropLog_Opl @ SV21 ) ) @ ( tc_set @ ( tc_PropLog_Opl @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV22: $i,SV16: $i,SV10: $i,SV4: $i] :
( ( c_lessequals @ ( c_minus @ SV4 @ SV10 @ ( tc_set @ SV16 ) ) @ ( c_insert @ SV22 @ ( c_minus @ SV4 @ ( c_insert @ SV22 @ SV10 @ SV16 ) @ ( tc_set @ SV16 ) ) @ SV16 ) @ ( tc_set @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV23: $i,SV17: $i,SV11: $i,SV5: $i] :
( ( ! [SY70: $i] : ( c_lessequals @ ( c_minus @ ( c_insert @ SV5 @ ( c_minus @ SV11 @ ( c_insert @ SV17 @ c_emptyset @ SV23 ) @ ( tc_set @ SV23 ) ) @ SV23 ) @ SY70 @ ( tc_set @ SV23 ) ) @ ( c_insert @ SV5 @ ( c_minus @ SV11 @ ( c_insert @ SV17 @ SY70 @ SV23 ) @ ( tc_set @ SV23 ) ) @ SV23 ) @ ( tc_set @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV24: $i,SV18: $i,SV12: $i,SV6: $i] :
( ( ~ ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ SV12 @ SV18 @ ( tc_PropLog_Opl @ SV24 ) ) @ SV24 ) @ ( tc_PropLog_Opl @ SV24 ) )
| ~ ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ SV12 @ c_PropLog_Opl_Ofalse @ SV24 ) @ SV18 @ ( tc_PropLog_Opl @ SV24 ) ) @ SV24 ) @ ( tc_PropLog_Opl @ SV24 ) )
| ( c_in @ SV6 @ ( c_PropLog_Othms @ SV18 @ SV24 ) @ ( tc_PropLog_Opl @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV19: $i,SV13: $i,SV7: $i] :
( ( ( ~ ( c_in @ SV7 @ ( c_PropLog_Othms @ SV13 @ SV19 ) @ ( tc_PropLog_Opl @ SV19 ) ) )
= $true )
| ( ( ! [SY68: $i] :
( ~ ( c_lessequals @ SV13 @ SY68 @ ( tc_set @ ( tc_PropLog_Opl @ SV19 ) ) )
| ( c_in @ SV7 @ ( c_PropLog_Othms @ SY68 @ SV19 ) @ ( tc_PropLog_Opl @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV20: $i,SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SV8 @ SV14 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) ) @ SV20 ) @ ( tc_PropLog_Opl @ SV20 ) ) )
= $true )
| ( ( ! [SY69: $i] :
( ~ ( c_lessequals @ SV8 @ SY69 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) )
| ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SY69 @ SV14 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) ) @ SV20 ) @ ( tc_PropLog_Opl @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(60,plain,
! [SV25: $i,SV23: $i,SV17: $i,SV11: $i,SV5: $i] :
( ( c_lessequals @ ( c_minus @ ( c_insert @ SV5 @ ( c_minus @ SV11 @ ( c_insert @ SV17 @ c_emptyset @ SV23 ) @ ( tc_set @ SV23 ) ) @ SV23 ) @ SV25 @ ( tc_set @ SV23 ) ) @ ( c_insert @ SV5 @ ( c_minus @ SV11 @ ( c_insert @ SV17 @ SV25 @ SV23 ) @ ( tc_set @ SV23 ) ) @ SV23 ) @ ( tc_set @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV24: $i,SV18: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ SV12 @ SV18 @ ( tc_PropLog_Opl @ SV24 ) ) @ SV24 ) @ ( tc_PropLog_Opl @ SV24 ) ) )
= $true )
| ( ( ~ ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ SV12 @ c_PropLog_Opl_Ofalse @ SV24 ) @ SV18 @ ( tc_PropLog_Opl @ SV24 ) ) @ SV24 ) @ ( tc_PropLog_Opl @ SV24 ) )
| ( c_in @ SV6 @ ( c_PropLog_Othms @ SV18 @ SV24 ) @ ( tc_PropLog_Opl @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV19: $i,SV13: $i,SV7: $i] :
( ( ( c_in @ SV7 @ ( c_PropLog_Othms @ SV13 @ SV19 ) @ ( tc_PropLog_Opl @ SV19 ) )
= $false )
| ( ( ! [SY68: $i] :
( ~ ( c_lessequals @ SV13 @ SY68 @ ( tc_set @ ( tc_PropLog_Opl @ SV19 ) ) )
| ( c_in @ SV7 @ ( c_PropLog_Othms @ SY68 @ SV19 ) @ ( tc_PropLog_Opl @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV20: $i,SV14: $i,SV8: $i,SV2: $i] :
( ( ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SV8 @ SV14 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) ) @ SV20 ) @ ( tc_PropLog_Opl @ SV20 ) )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( c_lessequals @ SV8 @ SY69 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) )
| ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SY69 @ SV14 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) ) @ SV20 ) @ ( tc_PropLog_Opl @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV24: $i,SV18: $i,SV12: $i,SV6: $i] :
( ( ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ SV12 @ SV18 @ ( tc_PropLog_Opl @ SV24 ) ) @ SV24 ) @ ( tc_PropLog_Opl @ SV24 ) )
= $false )
| ( ( ~ ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ SV12 @ c_PropLog_Opl_Ofalse @ SV24 ) @ SV18 @ ( tc_PropLog_Opl @ SV24 ) ) @ SV24 ) @ ( tc_PropLog_Opl @ SV24 ) )
| ( c_in @ SV6 @ ( c_PropLog_Othms @ SV18 @ SV24 ) @ ( tc_PropLog_Opl @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV7: $i,SV19: $i,SV26: $i,SV13: $i] :
( ( ( ~ ( c_lessequals @ SV13 @ SV26 @ ( tc_set @ ( tc_PropLog_Opl @ SV19 ) ) )
| ( c_in @ SV7 @ ( c_PropLog_Othms @ SV26 @ SV19 ) @ ( tc_PropLog_Opl @ SV19 ) ) )
= $true )
| ( ( c_in @ SV7 @ ( c_PropLog_Othms @ SV13 @ SV19 ) @ ( tc_PropLog_Opl @ SV19 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV14: $i,SV2: $i,SV20: $i,SV27: $i,SV8: $i] :
( ( ( ~ ( c_lessequals @ SV8 @ SV27 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) )
| ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SV27 @ SV14 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) ) @ SV20 ) @ ( tc_PropLog_Opl @ SV20 ) ) )
= $true )
| ( ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SV8 @ SV14 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) ) @ SV20 ) @ ( tc_PropLog_Opl @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV18: $i,SV24: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ SV12 @ c_PropLog_Opl_Ofalse @ SV24 ) @ SV18 @ ( tc_PropLog_Opl @ SV24 ) ) @ SV24 ) @ ( tc_PropLog_Opl @ SV24 ) ) )
= $true )
| ( ( c_in @ SV6 @ ( c_PropLog_Othms @ SV18 @ SV24 ) @ ( tc_PropLog_Opl @ SV24 ) )
= $true )
| ( ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ SV12 @ SV18 @ ( tc_PropLog_Opl @ SV24 ) ) @ SV24 ) @ ( tc_PropLog_Opl @ SV24 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(68,plain,
! [SV7: $i,SV19: $i,SV26: $i,SV13: $i] :
( ( ( ~ ( c_lessequals @ SV13 @ SV26 @ ( tc_set @ ( tc_PropLog_Opl @ SV19 ) ) ) )
= $true )
| ( ( c_in @ SV7 @ ( c_PropLog_Othms @ SV26 @ SV19 ) @ ( tc_PropLog_Opl @ SV19 ) )
= $true )
| ( ( c_in @ SV7 @ ( c_PropLog_Othms @ SV13 @ SV19 ) @ ( tc_PropLog_Opl @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(69,plain,
! [SV14: $i,SV2: $i,SV20: $i,SV27: $i,SV8: $i] :
( ( ( ~ ( c_lessequals @ SV8 @ SV27 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) ) )
= $true )
| ( ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SV27 @ SV14 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) ) @ SV20 ) @ ( tc_PropLog_Opl @ SV20 ) )
= $true )
| ( ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SV8 @ SV14 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) ) @ SV20 ) @ ( tc_PropLog_Opl @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(70,plain,
! [SV18: $i,SV24: $i,SV12: $i,SV6: $i] :
( ( ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ SV12 @ c_PropLog_Opl_Ofalse @ SV24 ) @ SV18 @ ( tc_PropLog_Opl @ SV24 ) ) @ SV24 ) @ ( tc_PropLog_Opl @ SV24 ) )
= $false )
| ( ( c_in @ SV6 @ ( c_PropLog_Othms @ SV18 @ SV24 ) @ ( tc_PropLog_Opl @ SV24 ) )
= $true )
| ( ( c_in @ SV6 @ ( c_PropLog_Othms @ ( c_insert @ SV12 @ SV18 @ ( tc_PropLog_Opl @ SV24 ) ) @ SV24 ) @ ( tc_PropLog_Opl @ SV24 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(71,plain,
! [SV7: $i,SV19: $i,SV26: $i,SV13: $i] :
( ( ( c_lessequals @ SV13 @ SV26 @ ( tc_set @ ( tc_PropLog_Opl @ SV19 ) ) )
= $false )
| ( ( c_in @ SV7 @ ( c_PropLog_Othms @ SV26 @ SV19 ) @ ( tc_PropLog_Opl @ SV19 ) )
= $true )
| ( ( c_in @ SV7 @ ( c_PropLog_Othms @ SV13 @ SV19 ) @ ( tc_PropLog_Opl @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV14: $i,SV2: $i,SV20: $i,SV27: $i,SV8: $i] :
( ( ( c_lessequals @ SV8 @ SV27 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) )
= $false )
| ( ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SV27 @ SV14 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) ) @ SV20 ) @ ( tc_PropLog_Opl @ SV20 ) )
= $true )
| ( ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_minus @ SV8 @ SV14 @ ( tc_set @ ( tc_PropLog_Opl @ SV20 ) ) ) @ SV20 ) @ ( tc_PropLog_Opl @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(73,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[32,72,71,70,60,55,54,40,33]) ).
thf(74,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LCL429-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n027.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 : Sat Jul 2 11:49:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 8
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.12/0.37 (rf:0,axioms:8,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:10,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.18/0.51
% 0.18/0.51 ********************************
% 0.18/0.51 * All subproblems solved! *
% 0.18/0.51 ********************************
% 0.18/0.51 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,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:73,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.51
% 0.18/0.51 %**** Beginning of derivation protocol ****
% 0.18/0.51 % SZS output start CNFRefutation
% See solution above
% 0.18/0.51
% 0.18/0.51 %**** End of derivation protocol ****
% 0.18/0.51 %**** no. of clauses in derivation: 74 ****
% 0.18/0.51 %**** clause counter: 73 ****
% 0.18/0.51
% 0.18/0.51 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,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:73,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------