TSTP Solution File: LAT279-2 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT279-2 : 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 : Sat Sep 17 18:32:38 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 19
% Syntax : Number of formulae : 28 ( 7 unt; 9 typ; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 58 ( 29 ~; 22 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 10 ( 4 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 26 ( 24 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Tarski_Opotype_Opotype__ext__type_type,type,
tc_Tarski_Opotype_Opotype__ext__type: ( $i * $i ) > $i ).
tff(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Tarski_OPartialOrder_type,type,
c_Tarski_OPartialOrder: $i ).
tff(v_cl_type,type,
v_cl: $i ).
tff(c_Relation_Oantisym_type,type,
c_Relation_Oantisym: ( $i * $i ) > $o ).
tff(c_Tarski_Opotype_Oorder_type,type,
c_Tarski_Opotype_Oorder: ( $i * $i * $i ) > $i ).
tff(v_r_type,type,
v_r: $i ).
tff(1,plain,
( c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
<=> c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).
tff(3,plain,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T_a: $i,V_P: $i] :
refl(
( ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
<=> ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
<=> ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
<=> ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_1) ).
tff(8,plain,
! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ c_Relation_Oantisym(v_r,t_a)
<=> ~ c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ c_Relation_Oantisym(v_r,t_a)
<=> ~ c_Relation_Oantisym(v_r,t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
~ c_Relation_Oantisym(v_r,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(14,plain,
~ c_Relation_Oantisym(v_r,t_a),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
~ c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
( ( ~ ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
| ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) )
<=> ( ~ ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
| ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( ~ ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
| ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
( ~ ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
| ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
$false,
inference(unit_resolution,[status(thm)],[18,15,10,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LAT279-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 12:59:39 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.
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------