TSTP Solution File: LCL433-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL433-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 : 300s
% DateTime : Sun Sep 18 04:56:14 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 45
% Syntax : Number of formulae : 86 ( 22 unt; 10 typ; 0 def)
% Number of atoms : 276 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 346 ( 160 ~; 154 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 6 >; 9 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 258 ( 234 !; 0 ?; 258 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_PropLog_Opl_type,type,
tc_PropLog_Opl: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_PropLog_Othms_type,type,
c_PropLog_Othms: ( $i * $i ) > $i ).
tff(c_insert_type,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(v_F_type,type,
v_F: $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_PropLog_Opl_Oop_A_N_62_type,type,
c_PropLog_Opl_Oop_A_N_62: ( $i * $i * $i ) > $i ).
tff(v_xa_type,type,
v_xa: $i ).
tff(c_PropLog_Osat_type,type,
c_PropLog_Osat: ( $i * $i * $i ) > $o ).
tff(1,plain,
^ [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
refl(
( ( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
| c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) )
<=> ( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
| c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
| c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) )
<=> ! [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
| c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
| c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) )
<=> ! [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
| c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
| c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Osat__imp_0) ).
tff(5,plain,
! [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
| c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
| c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
| c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a)
<=> c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(10,plain,
c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
| c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) )
| ~ c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a)
| c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),t_a) )
<=> ( ~ ! [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
| c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) )
| ~ c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a)
| c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
| c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) )
| ~ c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a)
| c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
| c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) )
| ~ c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a)
| c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),t_a) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),t_a),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
^ [V_U: $i] :
refl(
( ( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) )
<=> ( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [V_U: $i] :
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) )
<=> ! [V_U: $i] :
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V_U: $i] :
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) )
<=> ! [V_U: $i] :
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
^ [V_U: $i] :
rewrite(
( ( c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a))
| ~ c_PropLog_Osat(v_F,V_U,t_a) )
<=> ( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [V_U: $i] :
( c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a))
| ~ c_PropLog_Osat(v_F,V_U,t_a) )
<=> ! [V_U: $i] :
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [V_U: $i] :
( c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a))
| ~ c_PropLog_Osat(v_F,V_U,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(21,plain,
! [V_U: $i] :
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [V_U: $i] :
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [V_U: $i] :
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_U: $i] :
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ( ~ ! [V_U: $i] :
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) )
| ~ c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),t_a)
| c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) )
<=> ( ~ ! [V_U: $i] :
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) )
| ~ c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),t_a)
| c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [V_U: $i] :
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) )
| ~ c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),t_a)
| c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [V_U: $i] :
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) )
| ~ c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),t_a)
| c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)),
inference(unit_resolution,[status(thm)],[27,24,14]) ).
tff(29,plain,
^ [V_a: $i,T_a: $i,V_p: $i,V_G: $i] :
refl(
( ( ~ c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(c_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) )
<=> ( ~ c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(c_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [V_a: $i,T_a: $i,V_p: $i,V_G: $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_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) )
<=> ! [V_a: $i,T_a: $i,V_p: $i,V_G: $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_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [V_a: $i,T_a: $i,V_p: $i,V_G: $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_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) )
<=> ! [V_a: $i,T_a: $i,V_p: $i,V_G: $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_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
! [V_a: $i,T_a: $i,V_p: $i,V_G: $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_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left__insert_0) ).
tff(33,plain,
! [V_a: $i,T_a: $i,V_p: $i,V_G: $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_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [V_a: $i,T_a: $i,V_p: $i,V_G: $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_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [V_a: $i,T_a: $i,V_p: $i,V_G: $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_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_p: $i,V_G: $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_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) )
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_p: $i,V_G: $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_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) )
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i,V_G: $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_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) )
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i,V_G: $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_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) )
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(unit_resolution,[status(thm)],[38,35,28]) ).
tff(40,plain,
^ [V_x: $i,T_a: $i,V_B: $i] :
refl(
( c_in(V_x,c_insert(V_x,V_B,T_a),T_a)
<=> c_in(V_x,c_insert(V_x,V_B,T_a),T_a) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a)
<=> ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a)
<=> ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
tff(44,plain,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a)
| c_in(v_x,c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
c_in(v_x,c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
^ [V_H: $i,T_a: $i,V_p: $i] :
refl(
( ( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
<=> ( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [V_H: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
<=> ! [V_H: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [V_H: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
<=> ! [V_H: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,axiom,
! [V_H: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
tff(53,plain,
! [V_H: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [V_H: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [V_H: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ( ~ ! [V_H: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
| ~ c_in(v_x,c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a))
| c_in(v_x,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) )
<=> ( ~ ! [V_H: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
| ~ c_in(v_x,c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a))
| c_in(v_x,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ~ ! [V_H: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
| ~ c_in(v_x,c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a))
| c_in(v_x,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [V_H: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
| ~ c_in(v_x,c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a))
| c_in(v_x,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
c_in(v_x,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(unit_resolution,[status(thm)],[58,55,48]) ).
tff(60,plain,
^ [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
refl(
( ( 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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
<=> ( 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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(61,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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
<=> ! [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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
<=> ! [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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
^ [V_q: $i,V_H: $i,T_a: $i,V_p: $i] :
trans(
monotonicity(
rewrite(
( ( ~ 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_p,V_q,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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) )),
( ( ~ 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_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| 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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) )),
rewrite(
( ( ~ 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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
<=> ( 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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) )),
( ( ~ 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_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
<=> ( 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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [V_q: $i,V_H: $i,T_a: $i,V_p: $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_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
<=> ! [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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,axiom,
! [V_q: $i,V_H: $i,T_a: $i,V_p: $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_p,V_q,T_a),c_PropLog_Othms(V_H,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/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
tff(66,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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
( ~ c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
<=> ~ c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(71,axiom,
~ c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(72,plain,
~ c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
| c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(v_x,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) )
<=> ( ~ ! [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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
| c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(v_x,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
| c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(v_x,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,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))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )
| c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(v_x,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
$false,
inference(unit_resolution,[status(thm)],[75,72,69,59,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL433-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n003.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 : 300
% 0.12/0.34 % DateTime : Thu Sep 1 21:25:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------