TSTP Solution File: LCL440-1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL440-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 04:56:17 EDT 2022
% Result : Unsatisfiable 0.54s 0.70s
% Output : Proof 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 13
% Syntax : Number of formulae : 19 ( 8 unt; 7 typ; 0 def)
% Number of atoms : 18 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 1 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 4 >; 5 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 30 ( 27 !; 0 ?; 30 :)
% 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_emptyset_type,type,
c_emptyset: $i ).
tff(c_PropLog_Opl_Oop_A_N_62_type,type,
c_PropLog_Opl_Oop_A_N_62: ( $i * $i * $i ) > $i ).
tff(c_PropLog_Opl_Ofalse_type,type,
c_PropLog_Opl_Ofalse: $i ).
tff(1,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ofalse,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a))
<=> ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ofalse,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ofalse,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ofalse,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(5,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)],[4]) ).
tff(6,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(7,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/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms__I_0) ).
tff(8,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)],[7,6]) ).
tff(9,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)],[8]) ).
tff(10,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)],[9,5]) ).
tff(11,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(c_PropLog_Opl_Ofalse,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
$false,
inference(unit_resolution,[status(thm)],[11,10,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL440-1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Sep 1 21:24:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.54/0.70 % SZS status Unsatisfiable
% 0.54/0.70 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------