TSTP Solution File: SWB054+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB054+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 : Tue Sep 20 08:32:08 EDT 2022
% Result : Theorem 0.78s 0.81s
% Output : Proof 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 69
% Syntax : Number of formulae : 142 ( 31 unt; 13 typ; 0 def)
% Number of atoms : 883 ( 0 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 1433 ( 711 ~; 520 |; 69 &)
% ( 115 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 32 ( 32 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 327 ( 299 !; 0 ?; 327 :)
% Comments :
%------------------------------------------------------------------------------
tff(ir_type,type,
ir: $i > $o ).
tff(tptp_fun_X_61_type,type,
tptp_fun_X_61: ( $i * $i ) > $i ).
tff(uri_ex_c_type,type,
uri_ex_c: $i ).
tff(uri_owl_Thing_type,type,
uri_owl_Thing: $i ).
tff(icext_type,type,
icext: ( $i * $i ) > $o ).
tff(ic_type,type,
ic: $i > $o ).
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(uri_rdfs_subClassOf_type,type,
uri_rdfs_subClassOf: $i ).
tff(uri_owl_Class_type,type,
uri_owl_Class: $i ).
tff(uri_rdf_type_type,type,
uri_rdf_type: $i ).
tff(ip_type,type,
ip: $i > $o ).
tff(uri_rdf_Property_type,type,
uri_rdf_Property: $i ).
tff(uri_rdf_first_type,type,
uri_rdf_first: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( icext(uri_owl_Thing,X)
<=> ir(X) )
<=> ( icext(uri_owl_Thing,X)
<=> ir(X) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
( icext(uri_owl_Thing,X)
<=> ir(X) )
<=> ! [X: $i] :
( icext(uri_owl_Thing,X)
<=> ir(X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] :
( icext(uri_owl_Thing,X)
<=> ir(X) )
<=> ! [X: $i] :
( icext(uri_owl_Thing,X)
<=> ir(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] :
( icext(uri_owl_Thing,X)
<=> ir(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_class_thing_ext) ).
tff(5,plain,
! [X: $i] :
( icext(uri_owl_Thing,X)
<=> ir(X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] :
( icext(uri_owl_Thing,X)
<=> ir(X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] :
( icext(uri_owl_Thing,X)
<=> ir(X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] :
( icext(uri_owl_Thing,X)
<=> ir(X) )
| ( icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
<=> ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
( icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
<=> ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [C1: $i,C2: $i] :
rewrite(
( ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [C1: $i,C2: $i] :
refl(
( ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [C1: $i,C2: $i] :
rewrite(
( ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(transitivity,[status(thm)],[15,13]) ).
tff(17,plain,
^ [C1: $i,C2: $i] :
trans(
monotonicity(
rewrite(
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
<=> ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )),
rewrite(
( ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
<=> ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )),
( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
rewrite(
( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
^ [C1: $i,C2: $i] :
rewrite(
( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C1)
| ~ ic(C2)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C1)
| ~ ic(C2)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
<=> ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [C1: $i,C2: $i] :
rewrite(
( ( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
=> icext(C2,X) ) ) )
<=> ( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
=> icext(C2,X) ) ) )
<=> ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
=> icext(C2,X) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_rdfsext_subclassof) ).
tff(25,plain,
! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C1)
| ~ ic(C2)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(modus_ponens,[status(thm)],[28,18]) ).
tff(30,plain,
! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(modus_ponens,[status(thm)],[29,16]) ).
tff(31,plain,
! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ),
inference(modus_ponens,[status(thm)],[30,11]) ).
tff(32,plain,
( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_c,uri_owl_Thing)
| ~ ic(uri_owl_Thing)
| ~ ic(uri_ex_c)
| ~ ( ~ icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_c,uri_owl_Thing)
| ~ ( ~ ic(uri_owl_Thing)
| ~ ic(uri_ex_c)
| ~ ! [X: $i] :
( ~ icext(uri_ex_c,X)
| icext(uri_owl_Thing,X) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_c,uri_owl_Thing)
| ~ ic(uri_owl_Thing)
| ~ ic(uri_ex_c)
| ~ ( ~ icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_c,uri_owl_Thing)
| ~ ( ~ ic(uri_owl_Thing)
| ~ ic(uri_ex_c)
| ~ ! [X: $i] :
( ~ icext(uri_ex_c,X)
| icext(uri_owl_Thing,X) ) ) ) ),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_c,uri_owl_Thing)
| ~ ic(uri_owl_Thing)
| ~ ic(uri_ex_c)
| ~ ( ~ icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_c,uri_owl_Thing)
| ~ ( ~ ic(uri_owl_Thing)
| ~ ic(uri_ex_c)
| ~ ! [X: $i] :
( ~ icext(uri_ex_c,X)
| icext(uri_owl_Thing,X) ) ) )
| iext(uri_rdfs_subClassOf,uri_ex_c,uri_owl_Thing)
| ~ ic(uri_owl_Thing)
| ~ ic(uri_ex_c)
| ~ ( ~ icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) ),
inference(tautology,[status(thm)],]) ).
tff(35,plain,
( iext(uri_rdfs_subClassOf,uri_ex_c,uri_owl_Thing)
| ~ ic(uri_owl_Thing)
| ~ ic(uri_ex_c)
| ~ ( ~ icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) ),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
^ [X: $i] :
refl(
( ( icext(uri_owl_Class,X)
<=> ic(X) )
<=> ( icext(uri_owl_Class,X)
<=> ic(X) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X: $i] :
( icext(uri_owl_Class,X)
<=> ic(X) )
<=> ! [X: $i] :
( icext(uri_owl_Class,X)
<=> ic(X) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X: $i] :
( icext(uri_owl_Class,X)
<=> ic(X) )
<=> ! [X: $i] :
( icext(uri_owl_Class,X)
<=> ic(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
! [X: $i] :
( icext(uri_owl_Class,X)
<=> ic(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_class_classowl_ext) ).
tff(40,plain,
! [X: $i] :
( icext(uri_owl_Class,X)
<=> ic(X) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [X: $i] :
( icext(uri_owl_Class,X)
<=> ic(X) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [X: $i] :
( icext(uri_owl_Class,X)
<=> ic(X) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [X: $i] :
( icext(uri_owl_Class,X)
<=> ic(X) )
| ( icext(uri_owl_Class,uri_ex_c)
<=> ic(uri_ex_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( icext(uri_owl_Class,uri_ex_c)
<=> ic(uri_ex_c) ),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
^ [X: $i,C: $i] :
refl(
( ( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',rdfs_cext_def) ).
tff(49,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
| ( iext(uri_rdf_type,uri_ex_c,uri_owl_Class)
<=> icext(uri_owl_Class,uri_ex_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
( iext(uri_rdf_type,uri_ex_c,uri_owl_Class)
<=> icext(uri_owl_Class,uri_ex_c) ),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
( iext(uri_rdf_type,uri_ex_c,uri_owl_Class)
<=> iext(uri_rdf_type,uri_ex_c,uri_owl_Class) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
iext(uri_rdf_type,uri_ex_c,uri_owl_Class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_rdfbased_sem_class_thing_term) ).
tff(56,plain,
iext(uri_rdf_type,uri_ex_c,uri_owl_Class),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ~ ( iext(uri_rdf_type,uri_ex_c,uri_owl_Class)
<=> icext(uri_owl_Class,uri_ex_c) )
| ~ iext(uri_rdf_type,uri_ex_c,uri_owl_Class)
| icext(uri_owl_Class,uri_ex_c) ),
inference(tautology,[status(thm)],]) ).
tff(58,plain,
( ~ ( iext(uri_rdf_type,uri_ex_c,uri_owl_Class)
<=> icext(uri_owl_Class,uri_ex_c) )
| icext(uri_owl_Class,uri_ex_c) ),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
icext(uri_owl_Class,uri_ex_c),
inference(unit_resolution,[status(thm)],[58,53]) ).
tff(60,plain,
( ~ ( icext(uri_owl_Class,uri_ex_c)
<=> ic(uri_ex_c) )
| ~ icext(uri_owl_Class,uri_ex_c)
| ic(uri_ex_c) ),
inference(tautology,[status(thm)],]) ).
tff(61,plain,
( ~ ( icext(uri_owl_Class,uri_ex_c)
<=> ic(uri_ex_c) )
| ic(uri_ex_c) ),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
ic(uri_ex_c),
inference(unit_resolution,[status(thm)],[61,44]) ).
tff(63,plain,
( ~ iext(uri_rdfs_subClassOf,uri_ex_c,uri_owl_Thing)
<=> ~ iext(uri_rdfs_subClassOf,uri_ex_c,uri_owl_Thing) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
~ iext(uri_rdfs_subClassOf,uri_ex_c,uri_owl_Thing),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion_rdfbased_sem_class_thing_term) ).
tff(65,plain,
~ iext(uri_rdfs_subClassOf,uri_ex_c,uri_owl_Thing),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
( ic(uri_owl_Thing)
<=> ic(uri_owl_Thing) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
ic(uri_owl_Thing),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_class_thing_type) ).
tff(68,plain,
ic(uri_owl_Thing),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_c,uri_owl_Thing)
| ~ ic(uri_owl_Thing)
| ~ ic(uri_ex_c)
| ~ ( ~ icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) )
| iext(uri_rdfs_subClassOf,uri_ex_c,uri_owl_Thing)
| ~ ic(uri_owl_Thing)
| ~ ic(uri_ex_c)
| ~ ( ~ icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) ),
inference(tautology,[status(thm)],]) ).
tff(70,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_c,uri_owl_Thing)
| ~ ic(uri_owl_Thing)
| ~ ic(uri_ex_c)
| ~ ( ~ icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) )
| ~ ic(uri_ex_c)
| ~ ( ~ icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) ),
inference(unit_resolution,[status(thm)],[69,68,65]) ).
tff(71,plain,
~ ( ~ icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ),
inference(unit_resolution,[status(thm)],[70,62,35]) ).
tff(72,plain,
( ~ icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| ~ icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ),
inference(tautology,[status(thm)],]) ).
tff(73,plain,
~ icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
( ~ ( icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
<=> ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) )
| icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| ~ ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ),
inference(tautology,[status(thm)],]) ).
tff(75,plain,
( ~ ( icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
<=> ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) )
| ~ ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
~ ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c)),
inference(unit_resolution,[status(thm)],[75,9]) ).
tff(77,plain,
( ~ ir(uri_ex_c)
| ~ ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ),
inference(tautology,[status(thm)],]) ).
tff(78,plain,
( ~ ir(uri_ex_c)
| ~ ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
( ~ ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
| ( iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c)
<=> icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
( iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c)
<=> icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ),
inference(unit_resolution,[status(thm)],[79,51]) ).
tff(81,plain,
( ~ icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| icext(uri_owl_Thing,tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ),
inference(tautology,[status(thm)],]) ).
tff(82,plain,
icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)),
inference(unit_resolution,[status(thm)],[81,71]) ).
tff(83,plain,
( ~ ( iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c)
<=> icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) )
| iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c)
| ~ icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ),
inference(tautology,[status(thm)],]) ).
tff(84,plain,
( ~ ( iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c)
<=> icext(uri_ex_c,tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) )
| iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c) ),
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c),
inference(unit_resolution,[status(thm)],[84,80]) ).
tff(86,plain,
( iext(uri_rdf_type,uri_rdf_first,uri_rdf_Property)
<=> iext(uri_rdf_type,uri_rdf_first,uri_rdf_Property) ),
inference(rewrite,[status(thm)],]) ).
tff(87,axiom,
iext(uri_rdf_type,uri_rdf_first,uri_rdf_Property),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',rdf_collection_first_type) ).
tff(88,plain,
iext(uri_rdf_type,uri_rdf_first,uri_rdf_Property),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
^ [S: $i,P: $i,O: $i] :
refl(
( ( ip(P)
| ~ iext(P,S,O) )
<=> ( ip(P)
| ~ iext(P,S,O) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) )
<=> ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) )
<=> ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [S: $i,P: $i,O: $i] :
rewrite(
( ( iext(P,S,O)
=> ip(P) )
<=> ( ip(P)
| ~ iext(P,S,O) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [S: $i,P: $i,O: $i] :
( iext(P,S,O)
=> ip(P) )
<=> ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [S: $i,P: $i,O: $i] :
( iext(P,S,O)
=> ip(P) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',simple_iext_property) ).
tff(95,plain,
! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) )
| ip(uri_rdf_type)
| ~ iext(uri_rdf_type,uri_rdf_first,uri_rdf_Property) )
<=> ( ~ ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) )
| ip(uri_rdf_type)
| ~ iext(uri_rdf_type,uri_rdf_first,uri_rdf_Property) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) )
| ip(uri_rdf_type)
| ~ iext(uri_rdf_type,uri_rdf_first,uri_rdf_Property) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) )
| ip(uri_rdf_type)
| ~ iext(uri_rdf_type,uri_rdf_first,uri_rdf_Property) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
ip(uri_rdf_type),
inference(unit_resolution,[status(thm)],[101,98,88]) ).
tff(103,plain,
^ [X: $i] :
refl(
( ( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) )
<=> ( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(104,plain,
( ! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) )
<=> ! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
^ [X: $i] :
rewrite(
( ( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) )
<=> ( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) )
<=> ! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) )
<=> ! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) ) ),
inference(transitivity,[status(thm)],[106,104]) ).
tff(108,plain,
^ [X: $i] :
rewrite(
( ( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& ir(Z) ) ) )
<=> ( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(109,plain,
( ! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& ir(Z) ) ) )
<=> ! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,plain,
( ! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& ir(Z) ) ) )
<=> ! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& ir(Z) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
^ [X: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [Y: $i,Z: $i] :
rewrite(
( ( iext(X,Y,Z)
=> ( ir(Y)
& ir(Z) ) )
<=> ( ~ iext(X,Y,Z)
| ( ir(Y)
& ir(Z) ) ) ))),
( ! [Y: $i,Z: $i] :
( iext(X,Y,Z)
=> ( ir(Y)
& ir(Z) ) )
<=> ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& ir(Z) ) ) )),
( ( ip(X)
=> ! [Y: $i,Z: $i] :
( iext(X,Y,Z)
=> ( ir(Y)
& ir(Z) ) ) )
<=> ( ip(X)
=> ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& ir(Z) ) ) ) )),
rewrite(
( ( ip(X)
=> ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& ir(Z) ) ) )
<=> ( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& ir(Z) ) ) ) )),
( ( ip(X)
=> ! [Y: $i,Z: $i] :
( iext(X,Y,Z)
=> ( ir(Y)
& ir(Z) ) ) )
<=> ( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& ir(Z) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(112,plain,
( ! [X: $i] :
( ip(X)
=> ! [Y: $i,Z: $i] :
( iext(X,Y,Z)
=> ( ir(Y)
& ir(Z) ) ) )
<=> ! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& ir(Z) ) ) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,axiom,
! [X: $i] :
( ip(X)
=> ! [Y: $i,Z: $i] :
( iext(X,Y,Z)
=> ( ir(Y)
& ir(Z) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_parts_ip_cond_inst) ).
tff(114,plain,
! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& ir(Z) ) ) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& ir(Z) ) ) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& ir(Z) ) ) ),
inference(skolemize,[status(sab)],[115]) ).
tff(117,plain,
! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) ),
inference(modus_ponens,[status(thm)],[116,109]) ).
tff(118,plain,
! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) ),
inference(modus_ponens,[status(thm)],[117,107]) ).
tff(119,plain,
( ( ~ ! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) )
| ~ ip(uri_rdf_type)
| ! [Y: $i,Z: $i] :
( ~ iext(uri_rdf_type,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) )
<=> ( ~ ! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) )
| ~ ip(uri_rdf_type)
| ! [Y: $i,Z: $i] :
( ~ iext(uri_rdf_type,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,plain,
( ~ ! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) )
| ~ ip(uri_rdf_type)
| ! [Y: $i,Z: $i] :
( ~ iext(uri_rdf_type,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
( ~ ! [X: $i] :
( ~ ip(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) )
| ~ ip(uri_rdf_type)
| ! [Y: $i,Z: $i] :
( ~ iext(uri_rdf_type,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [Y: $i,Z: $i] :
( ~ iext(uri_rdf_type,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) ),
inference(unit_resolution,[status(thm)],[121,118,102]) ).
tff(123,plain,
( ( ~ ! [Y: $i,Z: $i] :
( ~ iext(uri_rdf_type,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) )
| ~ iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c)
| ~ ( ~ ir(uri_ex_c)
| ~ ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) )
<=> ( ~ ! [Y: $i,Z: $i] :
( ~ iext(uri_rdf_type,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) )
| ~ iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c)
| ~ ( ~ ir(uri_ex_c)
| ~ ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ( ~ iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c)
| ~ ( ~ ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| ~ ir(uri_ex_c) ) )
<=> ( ~ iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c)
| ~ ( ~ ir(uri_ex_c)
| ~ ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
( ( ~ ! [Y: $i,Z: $i] :
( ~ iext(uri_rdf_type,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) )
| ~ iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c)
| ~ ( ~ ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| ~ ir(uri_ex_c) ) )
<=> ( ~ ! [Y: $i,Z: $i] :
( ~ iext(uri_rdf_type,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) )
| ~ iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c)
| ~ ( ~ ir(uri_ex_c)
| ~ ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) ) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( ( ~ ! [Y: $i,Z: $i] :
( ~ iext(uri_rdf_type,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) )
| ~ iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c)
| ~ ( ~ ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| ~ ir(uri_ex_c) ) )
<=> ( ~ ! [Y: $i,Z: $i] :
( ~ iext(uri_rdf_type,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) )
| ~ iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c)
| ~ ( ~ ir(uri_ex_c)
| ~ ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) ) ),
inference(transitivity,[status(thm)],[125,123]) ).
tff(127,plain,
( ~ ! [Y: $i,Z: $i] :
( ~ iext(uri_rdf_type,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) )
| ~ iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c)
| ~ ( ~ ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c))
| ~ ir(uri_ex_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
( ~ ! [Y: $i,Z: $i] :
( ~ iext(uri_rdf_type,Y,Z)
| ~ ( ~ ir(Y)
| ~ ir(Z) ) )
| ~ iext(uri_rdf_type,tptp_fun_X_61(uri_owl_Thing,uri_ex_c),uri_ex_c)
| ~ ( ~ ir(uri_ex_c)
| ~ ir(tptp_fun_X_61(uri_owl_Thing,uri_ex_c)) ) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
$false,
inference(unit_resolution,[status(thm)],[128,122,85,78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWB054+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Sep 3 20:12:20 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 0.78/0.81 % SZS status Theorem
% 0.78/0.81 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------