%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL434-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:01 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of formulae : 59 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 182 ( 27 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 199 ( 81 ~; 96 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 189 ( 171 !; 0 ?; 189 :)
% 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(v_H_type,type,
v_H: $i ).
tff(c_PropLog_Opl_Oop_A_N_62_type,type,
c_PropLog_Opl_Oop_A_N_62: ( $i * $i * $i ) > $i ).
tff(v_p_type,type,
v_p: $i ).
tff(v_pa_type,type,
v_pa: $i ).
tff(c_insert_type,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(1,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_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)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,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)) )
<=> ! [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)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,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)) )
<=> ! [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)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,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/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oweaken__right_0) ).
tff(5,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)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,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)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,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)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,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_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(10,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(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_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_pa,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),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_pa,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,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_pa,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,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_pa,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ c_in(v_pa,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,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(16,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)],[15]) ).
tff(17,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(18,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(19,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)],[18,17]) ).
tff(20,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)],[19]) ).
tff(21,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)],[20,16]) ).
tff(22,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_pa,v_H,tc_PropLog_Opl(t_a))
| c_in(v_pa,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)) )
| ~ c_in(v_pa,v_H,tc_PropLog_Opl(t_a))
| c_in(v_pa,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,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_pa,v_H,tc_PropLog_Opl(t_a))
| c_in(v_pa,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,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_pa,v_H,tc_PropLog_Opl(t_a))
| c_in(v_pa,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
~ c_in(v_pa,v_H,tc_PropLog_Opl(t_a)),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,plain,
^ [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
refl(( ( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
<=> ( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
^ [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
rewrite(( ( ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
| c_in(V_a,V_A,T_a)
| ( V_a = V_b ) )
<=> ( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
| c_in(V_a,V_A,T_a)
| ( V_a = V_b ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,axiom,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
| c_in(V_a,V_A,T_a)
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
tff(32,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
( c_in(v_pa,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a))
<=> c_in(v_pa,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
c_in(v_pa,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(38,plain,
c_in(v_pa,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| ( v_pa = v_p )
| c_in(v_pa,v_H,tc_PropLog_Opl(t_a))
| ~ c_in(v_pa,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| ( v_pa = v_p )
| c_in(v_pa,v_H,tc_PropLog_Opl(t_a))
| ~ c_in(v_pa,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| ( v_pa = v_p )
| c_in(v_pa,v_H,tc_PropLog_Opl(t_a))
| ~ c_in(v_pa,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ( V_a = V_b )
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| ( v_pa = v_p )
| c_in(v_pa,v_H,tc_PropLog_Opl(t_a))
| ~ c_in(v_pa,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ( v_pa = v_p )
| c_in(v_pa,v_H,tc_PropLog_Opl(t_a)) ),
inference(unit_resolution,[status(thm)],[41,38,35]) ).
tff(43,plain,
v_pa = v_p,
inference(unit_resolution,[status(thm)],[42,25]) ).
tff(44,plain,
v_p = v_pa,
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
c_PropLog_Opl_Oop_A_N_62(v_p,v_p,t_a) = c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_p,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_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,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_p,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,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_p,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_p,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(modus_ponens,[status(thm)],[10,48]) ).
tff(50,plain,
^ [V_H: $i,T_a: $i,V_p: $i] :
refl(( c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_p,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_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [V_H: $i,T_a: $i,V_p: $i] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
<=> ! [V_H: $i,T_a: $i,V_p: $i] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [V_H: $i,T_a: $i,V_p: $i] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
<=> ! [V_H: $i,T_a: $i,V_p: $i] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
! [V_H: $i,T_a: $i,V_p: $i] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms__I_0) ).
tff(54,plain,
! [V_H: $i,T_a: $i,V_p: $i] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [V_H: $i,T_a: $i,V_p: $i] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [V_H: $i,T_a: $i,V_p: $i] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [V_H: $i,T_a: $i,V_p: $i] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_p,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_p,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_p,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
$false,
inference(unit_resolution,[status(thm)],[58,49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL434-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n010.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 6 01:31:26 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% See solution above
% 0.12/0.41 % E exiting
%------------------------------------------------------------------------------