%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB040+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 Jun 21 05:29:44 AM UTC 2025
% Result : Theorem 0.60s 0.77s
% Output : Proof 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 59
% Syntax : Number of formulae : 141 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 1367 ( 0 equ)
% Maximal formula atoms : 40 ( 9 avg)
% Number of connectives : 2398 (1231 ~; 827 |; 152 &)
% ( 162 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 59 ( 59 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 420 ( 384 !; 0 ?; 420 :)
% Comments :
%------------------------------------------------------------------------------
tff(icext_type,type,
icext: ( $i * $i ) > $o ).
tff(tptp_fun_X_61_type,type,
tptp_fun_X_61: ( $i * $i ) > $i ).
tff(uri_ex_n2_type,type,
uri_ex_n2: $i ).
tff(uri_ex_n1_type,type,
uri_ex_n1: $i ).
tff(uri_ex_c2_type,type,
uri_ex_c2: $i ).
tff(ic_type,type,
ic: $i > $o ).
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(uri_owl_complementOf_type,type,
uri_owl_complementOf: $i ).
tff(uri_ex_c1_type,type,
uri_ex_c1: $i ).
tff(uri_rdfs_subClassOf_type,type,
uri_rdfs_subClassOf: $i ).
tff(1,plain,
( iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
<=> iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
& iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
& iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_rdfbased_sem_bool_tollens) ).
tff(3,plain,
( iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
& iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [Z: $i,C: $i] :
refl(( ( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
<=> ( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
<=> ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [Z: $i,C: $i] :
rewrite(( ( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
<=> ( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
<=> ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
<=> ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ) ),
inference(transitivity,[status(thm)],[9,7]) ).
tff(11,plain,
^ [Z: $i,C: $i] :
rewrite(( ( ~ iext(uri_owl_complementOf,Z,C)
| ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
<=> ( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
<=> ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
<=> ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
^ [Z: $i,C: $i] :
trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [X: $i] :
trans(rewrite(( ( icext(Z,X)
<=> ~ icext(C,X) )
<=> ~ ( icext(C,X)
<=> icext(Z,X) ) )),
rewrite(( ~ ( icext(C,X)
<=> icext(Z,X) )
<=> ~ ( icext(C,X)
<=> icext(Z,X) ) )),
( ( icext(Z,X)
<=> ~ icext(C,X) )
<=> ~ ( icext(C,X)
<=> icext(Z,X) ) ))),
( ! [X: $i] :
( icext(Z,X)
<=> ~ icext(C,X) )
<=> ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) )),
( ( ic(Z)
& ic(C)
& ! [X: $i] :
( icext(Z,X)
<=> ~ icext(C,X) ) )
<=> ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )),
rewrite(( ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) )
<=> ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )),
( ( ic(Z)
& ic(C)
& ! [X: $i] :
( icext(Z,X)
<=> ~ icext(C,X) ) )
<=> ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )),
( ( iext(uri_owl_complementOf,Z,C)
=> ( ic(Z)
& ic(C)
& ! [X: $i] :
( icext(Z,X)
<=> ~ icext(C,X) ) ) )
<=> ( iext(uri_owl_complementOf,Z,C)
=> ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ) )),
rewrite(( ( iext(uri_owl_complementOf,Z,C)
=> ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
<=> ( ~ iext(uri_owl_complementOf,Z,C)
| ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ) )),
( ( iext(uri_owl_complementOf,Z,C)
=> ( ic(Z)
& ic(C)
& ! [X: $i] :
( icext(Z,X)
<=> ~ icext(C,X) ) ) )
<=> ( ~ iext(uri_owl_complementOf,Z,C)
| ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [Z: $i,C: $i] :
( iext(uri_owl_complementOf,Z,C)
=> ( ic(Z)
& ic(C)
& ! [X: $i] :
( icext(Z,X)
<=> ~ icext(C,X) ) ) )
<=> ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,axiom,
! [Z: $i,C: $i] :
( iext(uri_owl_complementOf,Z,C)
=> ( ic(Z)
& ic(C)
& ! [X: $i] :
( icext(Z,X)
<=> ~ icext(C,X) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_bool_complementof_class) ).
tff(17,plain,
! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ( ic(Z)
& ic(C)
& ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) ),
inference(modus_ponens,[status(thm)],[20,10]) ).
tff(22,plain,
( ( ~ ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
~ ( icext(uri_ex_c2,X)
<=> icext(uri_ex_n2,X) ) ) )
<=> ( ~ ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
~ ( icext(uri_ex_c2,X)
<=> icext(uri_ex_n2,X) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
~ ( icext(uri_ex_c2,X)
<=> icext(uri_ex_n2,X) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
~ ( icext(uri_ex_c2,X)
<=> icext(uri_ex_n2,X) ) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
~ ( icext(uri_ex_c2,X)
<=> icext(uri_ex_n2,X) ) ),
inference(unit_resolution,[status(thm)],[24,21,5]) ).
tff(26,plain,
( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
~ ( icext(uri_ex_c2,X)
<=> icext(uri_ex_n2,X) )
| ! [X: $i] :
~ ( icext(uri_ex_c2,X)
<=> icext(uri_ex_n2,X) ) ),
inference(tautology,[status(thm)],[]) ).
tff(27,plain,
! [X: $i] :
~ ( icext(uri_ex_c2,X)
<=> icext(uri_ex_n2,X) ),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ ! [X: $i] :
~ ( icext(uri_ex_c2,X)
<=> icext(uri_ex_n2,X) )
| ~ ( icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
<=> icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
~ ( icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
<=> icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,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(31,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)],[30]) ).
tff(32,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(33,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)],[32]) ).
tff(34,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(35,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)],[34]) ).
tff(36,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)],[35,33]) ).
tff(37,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(38,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)],[37]) ).
tff(39,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(40,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)],[39]) ).
tff(41,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(42,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(43,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)],[42]) ).
tff(44,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(45,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)],[44,43]) ).
tff(46,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)],[45,41]) ).
tff(47,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)],[46]) ).
tff(48,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)],[47,40]) ).
tff(49,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)],[48,38]) ).
tff(50,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)],[49,36]) ).
tff(51,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)],[50,31]) ).
tff(52,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_n2,uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ic(uri_ex_n1)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ( ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
( ~ icext(uri_ex_n2,X)
| icext(uri_ex_n1,X) ) ) ) ) )
<=> ( ~ ! [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_n2,uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ic(uri_ex_n1)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ( ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
( ~ icext(uri_ex_n2,X)
| icext(uri_ex_n1,X) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ( ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
( ~ icext(uri_ex_n2,X)
| icext(uri_ex_n1,X) ) ) ) )
<=> ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ic(uri_ex_n1)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ( ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
( ~ icext(uri_ex_n2,X)
| icext(uri_ex_n1,X) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,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_n2,uri_ex_n1)
| ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ( ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
( ~ icext(uri_ex_n2,X)
| icext(uri_ex_n1,X) ) ) ) ) )
<=> ( ~ ! [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_n2,uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ic(uri_ex_n1)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ( ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
( ~ icext(uri_ex_n2,X)
| icext(uri_ex_n1,X) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,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_n2,uri_ex_n1)
| ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ( ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
( ~ icext(uri_ex_n2,X)
| icext(uri_ex_n1,X) ) ) ) ) )
<=> ( ~ ! [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_n2,uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ic(uri_ex_n1)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ( ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
( ~ icext(uri_ex_n2,X)
| icext(uri_ex_n1,X) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,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_n2,uri_ex_n1)
| ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ( ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
( ~ icext(uri_ex_n2,X)
| icext(uri_ex_n1,X) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,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_n2,uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ic(uri_ex_n1)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ( ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
( ~ icext(uri_ex_n2,X)
| icext(uri_ex_n1,X) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ic(uri_ex_n1)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ( ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
( ~ icext(uri_ex_n2,X)
| icext(uri_ex_n1,X) ) ) ) ),
inference(unit_resolution,[status(thm)],[57,51]) ).
tff(59,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ic(uri_ex_n1)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ( ~ ic(uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ! [X: $i] :
( ~ icext(uri_ex_n2,X)
| icext(uri_ex_n1,X) ) ) )
| iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ic(uri_ex_n1)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(60,plain,
( iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ic(uri_ex_n1)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) ),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
<=> ( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
^ [X: $i,Y: $i] :
rewrite(( ( ~ iext(uri_owl_complementOf,X,Y)
| ( ic(X)
& ic(Y) ) )
<=> ( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ( ic(X)
& ic(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ( ic(X)
& ic(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ( ic(X)
& ic(Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
^ [X: $i,Y: $i] :
rewrite(( ( iext(uri_owl_complementOf,X,Y)
=> ( ic(X)
& ic(Y) ) )
<=> ( ~ iext(uri_owl_complementOf,X,Y)
| ( ic(X)
& ic(Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_complementOf,X,Y)
=> ( ic(X)
& ic(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ( ic(X)
& ic(Y) ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,axiom,
! [X: $i,Y: $i] :
( iext(uri_owl_complementOf,X,Y)
=> ( ic(X)
& ic(Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_prop_complementof_ext) ).
tff(69,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ( ic(X)
& ic(Y) ) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ( ic(X)
& ic(Y) ) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ( ic(X)
& ic(Y) ) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) ),
inference(modus_ponens,[status(thm)],[71,64]) ).
tff(73,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) ),
inference(modus_ponens,[status(thm)],[72,62]) ).
tff(74,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_n2) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_n2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_n2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_n2) ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_n2) ),
inference(unit_resolution,[status(thm)],[76,73,5]) ).
tff(78,plain,
( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_n2)
| ic(uri_ex_n2) ),
inference(tautology,[status(thm)],[]) ).
tff(79,plain,
ic(uri_ex_n2),
inference(unit_resolution,[status(thm)],[78,77]) ).
tff(80,plain,
( iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
<=> iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1),
inference(and_elim,[status(thm)],[3]) ).
tff(82,plain,
iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
| ~ ( ~ ic(uri_ex_c1)
| ~ ic(uri_ex_n1) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
| ~ ( ~ ic(uri_ex_c1)
| ~ ic(uri_ex_n1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
| ~ ( ~ ic(uri_ex_c1)
| ~ ic(uri_ex_n1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_complementOf,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
| ~ ( ~ ic(uri_ex_c1)
| ~ ic(uri_ex_n1) ) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
~ ( ~ ic(uri_ex_c1)
| ~ ic(uri_ex_n1) ),
inference(unit_resolution,[status(thm)],[85,73,82]) ).
tff(87,plain,
( ~ ic(uri_ex_c1)
| ~ ic(uri_ex_n1)
| ic(uri_ex_n1) ),
inference(tautology,[status(thm)],[]) ).
tff(88,plain,
ic(uri_ex_n1),
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
<=> ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion_rdfbased_sem_bool_tollens) ).
tff(91,plain,
~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ic(uri_ex_n1)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
| iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ic(uri_ex_n1)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(93,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
| ~ ic(uri_ex_n2)
| ~ ic(uri_ex_n1)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
| ~ ic(uri_ex_n2)
| ~ ic(uri_ex_n1)
| ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) ),
inference(unit_resolution,[status(thm)],[92,91]) ).
tff(94,plain,
~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
inference(unit_resolution,[status(thm)],[93,88,79,60]) ).
tff(95,plain,
( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
inference(tautology,[status(thm)],[]) ).
tff(96,plain,
icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)),
inference(unit_resolution,[status(thm)],[95,94]) ).
tff(97,plain,
( ( icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
<=> icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) )
| ~ icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
inference(tautology,[status(thm)],[]) ).
tff(98,plain,
( ( icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
<=> icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) )
| ~ icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
inference(unit_resolution,[status(thm)],[97,96]) ).
tff(99,plain,
~ icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)),
inference(unit_resolution,[status(thm)],[98,29]) ).
tff(100,plain,
( ( ~ ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
| ~ ( ~ ic(uri_ex_c1)
| ~ ic(uri_ex_n1)
| ~ ! [X: $i] :
~ ( icext(uri_ex_c1,X)
<=> icext(uri_ex_n1,X) ) ) )
<=> ( ~ ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
| ~ ( ~ ic(uri_ex_c1)
| ~ ic(uri_ex_n1)
| ~ ! [X: $i] :
~ ( icext(uri_ex_c1,X)
<=> icext(uri_ex_n1,X) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ~ ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
| ~ ( ~ ic(uri_ex_c1)
| ~ ic(uri_ex_n1)
| ~ ! [X: $i] :
~ ( icext(uri_ex_c1,X)
<=> icext(uri_ex_n1,X) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
( ~ ! [Z: $i,C: $i] :
( ~ iext(uri_owl_complementOf,Z,C)
| ~ ( ~ ic(C)
| ~ ic(Z)
| ~ ! [X: $i] :
~ ( icext(C,X)
<=> icext(Z,X) ) ) )
| ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
| ~ ( ~ ic(uri_ex_c1)
| ~ ic(uri_ex_n1)
| ~ ! [X: $i] :
~ ( icext(uri_ex_c1,X)
<=> icext(uri_ex_n1,X) ) ) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
~ ( ~ ic(uri_ex_c1)
| ~ ic(uri_ex_n1)
| ~ ! [X: $i] :
~ ( icext(uri_ex_c1,X)
<=> icext(uri_ex_n1,X) ) ),
inference(unit_resolution,[status(thm)],[102,21,82]) ).
tff(104,plain,
( ~ ic(uri_ex_c1)
| ~ ic(uri_ex_n1)
| ~ ! [X: $i] :
~ ( icext(uri_ex_c1,X)
<=> icext(uri_ex_n1,X) )
| ! [X: $i] :
~ ( icext(uri_ex_c1,X)
<=> icext(uri_ex_n1,X) ) ),
inference(tautology,[status(thm)],[]) ).
tff(105,plain,
! [X: $i] :
~ ( icext(uri_ex_c1,X)
<=> icext(uri_ex_n1,X) ),
inference(unit_resolution,[status(thm)],[104,103]) ).
tff(106,plain,
( ~ ! [X: $i] :
~ ( icext(uri_ex_c1,X)
<=> icext(uri_ex_n1,X) )
| ~ ( icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
<=> icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
~ ( icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
<=> icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
inference(unit_resolution,[status(thm)],[106,105]) ).
tff(108,plain,
( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| ~ icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
inference(tautology,[status(thm)],[]) ).
tff(109,plain,
~ icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)),
inference(unit_resolution,[status(thm)],[108,94]) ).
tff(110,plain,
( ( icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
<=> icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) )
| icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
inference(tautology,[status(thm)],[]) ).
tff(111,plain,
( ( icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
<=> icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) )
| icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
inference(unit_resolution,[status(thm)],[110,109]) ).
tff(112,plain,
icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)),
inference(unit_resolution,[status(thm)],[111,107]) ).
tff(113,plain,
( iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2)
<=> iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2),
inference(and_elim,[status(thm)],[2]) ).
tff(115,plain,
iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
^ [C: $i,D: $i] :
refl(( ( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(117,plain,
( ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,plain,
^ [C: $i,D: $i] :
rewrite(( ( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(119,plain,
( ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
( ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) ),
inference(transitivity,[status(thm)],[119,117]) ).
tff(121,plain,
^ [C: $i,D: $i] :
rewrite(( ( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(122,plain,
( ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,plain,
^ [C: $i,D: $i] :
trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [X: $i] :
rewrite(( ( icext(C,X)
=> icext(D,X) )
<=> ( ~ icext(C,X)
| icext(D,X) ) ))),
( ! [X: $i] :
( icext(C,X)
=> icext(D,X) )
<=> ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) )),
( ( ic(C)
& ic(D)
& ! [X: $i] :
( icext(C,X)
=> icext(D,X) ) )
<=> ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )),
rewrite(( ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) )
<=> ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )),
( ( ic(C)
& ic(D)
& ! [X: $i] :
( icext(C,X)
=> icext(D,X) ) )
<=> ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )),
( ( iext(uri_rdfs_subClassOf,C,D)
=> ( ic(C)
& ic(D)
& ! [X: $i] :
( icext(C,X)
=> icext(D,X) ) ) )
<=> ( iext(uri_rdfs_subClassOf,C,D)
=> ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) )),
rewrite(( ( iext(uri_rdfs_subClassOf,C,D)
=> ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) )),
( ( iext(uri_rdfs_subClassOf,C,D)
=> ( ic(C)
& ic(D)
& ! [X: $i] :
( icext(C,X)
=> icext(D,X) ) ) )
<=> ( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(125,plain,
( ! [C: $i,D: $i] :
( iext(uri_rdfs_subClassOf,C,D)
=> ( ic(C)
& ic(D)
& ! [X: $i] :
( icext(C,X)
=> icext(D,X) ) ) )
<=> ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,axiom,
! [C: $i,D: $i] :
( iext(uri_rdfs_subClassOf,C,D)
=> ( ic(C)
& ic(D)
& ! [X: $i] :
( icext(C,X)
=> icext(D,X) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',rdfs_subclassof_main) ).
tff(127,plain,
! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ),
inference(skolemize,[status(sab)],[128]) ).
tff(130,plain,
! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ),
inference(modus_ponens,[status(thm)],[129,122]) ).
tff(131,plain,
! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ),
inference(modus_ponens,[status(thm)],[130,120]) ).
tff(132,plain,
( ( ~ ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
| ~ iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_c1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) ) ) )
<=> ( ~ ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
| ~ iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_c1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,plain,
( ~ ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
| ~ iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_c1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
( ~ ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
| ~ iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_c1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) ) ) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_c1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) ) ),
inference(unit_resolution,[status(thm)],[134,131,115]) ).
tff(136,plain,
( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_c1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) )
| ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) ) ),
inference(tautology,[status(thm)],[]) ).
tff(137,plain,
! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) ),
inference(unit_resolution,[status(thm)],[136,135]) ).
tff(138,plain,
( ( ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) )
| ~ icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) )
<=> ( ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) )
| ~ icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,plain,
( ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) )
| ~ icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(140,plain,
( ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) )
| ~ icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
| icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
$false,
inference(unit_resolution,[status(thm)],[140,137,112,99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWB040+1 : TPTP v9.0.0. Released v5.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 07:53:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.60/0.77 % SZS status Theorem
% 0.60/0.77 % SZS output start Proof
% See solution above
% 0.60/0.81 % E exiting
%------------------------------------------------------------------------------