%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB077+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:29:48 AM UTC 2025
% Result : Theorem 0.61s 0.80s
% Output : Proof 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 40
% Syntax : Number of formulae : 94 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 1061 ( 0 equ)
% Maximal formula atoms : 40 ( 11 avg)
% Number of connectives : 1964 (1030 ~; 766 |; 94 &)
% ( 57 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 33 ( 33 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; 5 con; 0-2 aty)
% Number of variables : 432 ( 410 !; 0 ?; 432 :)
% Comments :
%------------------------------------------------------------------------------
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(tptp_fun_Y_59_type,type,
tptp_fun_Y_59: ( $i * $i ) > $i ).
tff(uri_ex_p1_type,type,
uri_ex_p1: $i ).
tff(uri_ex_c_type,type,
uri_ex_c: $i ).
tff(tptp_fun_X_60_type,type,
tptp_fun_X_60: ( $i * $i ) > $i ).
tff(uri_ex_p2_type,type,
uri_ex_p2: $i ).
tff(ip_type,type,
ip: $i > $o ).
tff(uri_rdfs_subPropertyOf_type,type,
uri_rdfs_subPropertyOf: $i ).
tff(uri_rdfs_range_type,type,
uri_rdfs_range: $i ).
tff(icext_type,type,
icext: ( $i * $i ) > $o ).
tff(1,plain,
( iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
<=> iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( iext(uri_rdfs_range,uri_ex_p2,uri_ex_c)
& iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_rdfbased_sem_rdfsext_range_subprop) ).
tff(3,plain,
iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
^ [P: $i,Q: $i] :
refl(( ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
^ [P: $i,Q: $i] :
rewrite(( ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(transitivity,[status(thm)],[8,6]) ).
tff(10,plain,
^ [P: $i,Q: $i] :
rewrite(( ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [P: $i,Q: $i] :
trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [X: $i,Y: $i] :
rewrite(( ( iext(P,X,Y)
=> iext(Q,X,Y) )
<=> ( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ))),
( ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) )),
( ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) )
<=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )),
rewrite(( ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) )
<=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )),
( ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) )
<=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )),
( ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) )
<=> ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
rewrite(( ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
( ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [P: $i,Q: $i] :
( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [P: $i,Q: $i] :
( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',rdfs_subpropertyof_main) ).
tff(16,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
( ( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) )
<=> ( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) )
<=> ( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) ) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) )
<=> ( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) ) ),
inference(transitivity,[status(thm)],[23,21]) ).
tff(25,plain,
( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ),
inference(unit_resolution,[status(thm)],[26,20,4]) ).
tff(28,plain,
( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(29,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
^ [P: $i,C: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) )
<=> ~ ( ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) )
| ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [P: $i,C: $i] :
~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) )
<=> ! [P: $i,C: $i] :
~ ( ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) )
| ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
^ [P: $i,C: $i] :
refl(( ~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [P: $i,C: $i] :
~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) )
<=> ! [P: $i,C: $i] :
~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
^ [P: $i,C: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [P: $i,C: $i] :
~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) )
<=> ! [P: $i,C: $i] :
~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [P: $i,C: $i] :
~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) )
<=> ! [P: $i,C: $i] :
~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) ) ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,plain,
^ [P: $i,C: $i] :
trans(monotonicity(rewrite(( ( ~ iext(uri_rdfs_range,P,C)
| ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
<=> ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) )),
rewrite(( ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) )
<=> ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) )),
( ( ( ~ iext(uri_rdfs_range,P,C)
| ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
& ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) )
<=> ( ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
& ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) ) )),
rewrite(( ( ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
& ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) ) )),
( ( ( ~ iext(uri_rdfs_range,P,C)
| ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
& ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [P: $i,C: $i] :
( ( ~ iext(uri_rdfs_range,P,C)
| ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
& ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) )
<=> ! [P: $i,C: $i] :
~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
^ [P: $i,C: $i] :
rewrite(( ( ( ~ iext(uri_rdfs_range,P,C)
| ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
& ( iext(uri_rdfs_range,P,C)
| ~ ip(P)
| ~ ip(C)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) )
<=> ( ( ~ iext(uri_rdfs_range,P,C)
| ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
& ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [P: $i,C: $i] :
( ( ~ iext(uri_rdfs_range,P,C)
| ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
& ( iext(uri_rdfs_range,P,C)
| ~ ip(P)
| ~ ip(C)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) )
<=> ! [P: $i,C: $i] :
( ( ~ iext(uri_rdfs_range,P,C)
| ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
& ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [P: $i,C: $i] :
( iext(uri_rdfs_range,P,C)
<=> ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
<=> ! [P: $i,C: $i] :
( iext(uri_rdfs_range,P,C)
<=> ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
^ [P: $i,C: $i] :
rewrite(( ( iext(uri_rdfs_range,P,C)
<=> ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> icext(C,Y) ) ) )
<=> ( iext(uri_rdfs_range,P,C)
<=> ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [P: $i,C: $i] :
( iext(uri_rdfs_range,P,C)
<=> ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> icext(C,Y) ) ) )
<=> ! [P: $i,C: $i] :
( iext(uri_rdfs_range,P,C)
<=> ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [P: $i,C: $i] :
( iext(uri_rdfs_range,P,C)
<=> ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> icext(C,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_rdfsext_range) ).
tff(45,plain,
! [P: $i,C: $i] :
( iext(uri_rdfs_range,P,C)
<=> ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [P: $i,C: $i] :
( iext(uri_rdfs_range,P,C)
<=> ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [P: $i,C: $i] :
( ( ~ iext(uri_rdfs_range,P,C)
| ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
& ( iext(uri_rdfs_range,P,C)
| ~ ip(P)
| ~ ip(C)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [P: $i,C: $i] :
( ( ~ iext(uri_rdfs_range,P,C)
| ( ip(P)
& ip(C)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
& ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
! [P: $i,C: $i] :
~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) ),
inference(modus_ponens,[status(thm)],[48,38]) ).
tff(50,plain,
! [P: $i,C: $i] :
~ ( ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) )
| ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) ) ),
inference(modus_ponens,[status(thm)],[49,36]) ).
tff(51,plain,
! [P: $i,C: $i] :
~ ( ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) )
| ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[50,31]) ).
tff(52,plain,
( ( ~ ! [P: $i,C: $i] :
~ ( ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) )
| ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_c)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) )
| ~ ( ~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| icext(uri_ex_c,Y) ) ) ) ) )
<=> ( ~ ! [P: $i,C: $i] :
~ ( ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) )
| ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_c)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) )
| ~ ( ~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| icext(uri_ex_c,Y) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ~ ( ~ ( iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) )
| ~ ( ~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| icext(uri_ex_c,Y) ) ) ) )
<=> ~ ( ~ ( iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_c)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) )
| ~ ( ~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| icext(uri_ex_c,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ( ~ ! [P: $i,C: $i] :
~ ( ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) )
| ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) )
| ~ ( ~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| icext(uri_ex_c,Y) ) ) ) ) )
<=> ( ~ ! [P: $i,C: $i] :
~ ( ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) )
| ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_c)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) )
| ~ ( ~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| icext(uri_ex_c,Y) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ( ~ ! [P: $i,C: $i] :
~ ( ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) )
| ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) )
| ~ ( ~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| icext(uri_ex_c,Y) ) ) ) ) )
<=> ( ~ ! [P: $i,C: $i] :
~ ( ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) )
| ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_c)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) )
| ~ ( ~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| icext(uri_ex_c,Y) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,plain,
( ~ ! [P: $i,C: $i] :
~ ( ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) )
| ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) )
| ~ ( ~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| icext(uri_ex_c,Y) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [P: $i,C: $i] :
~ ( ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) )
| ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_c)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) )
| ~ ( ~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| icext(uri_ex_c,Y) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
~ ( ~ ( iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_c)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) )
| ~ ( ~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| icext(uri_ex_c,Y) ) ) ) ),
inference(unit_resolution,[status(thm)],[57,51]) ).
tff(59,plain,
( ~ ( iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_c)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) )
| ~ ( ~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| icext(uri_ex_c,Y) ) ) )
| iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_c)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(60,plain,
( iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_c)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) ),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ip(uri_ex_p1) ),
inference(tautology,[status(thm)],[]) ).
tff(62,plain,
ip(uri_ex_p1),
inference(unit_resolution,[status(thm)],[61,27]) ).
tff(63,plain,
( ~ ! [P: $i,C: $i] :
~ ( ~ ( iext(uri_rdfs_range,P,C)
| ~ ip(C)
| ~ ip(P)
| ~ ( ~ iext(P,tptp_fun_X_60(C,P),tptp_fun_Y_59(C,P))
| icext(C,tptp_fun_Y_59(C,P)) ) )
| ~ ( ~ iext(uri_rdfs_range,P,C)
| ~ ( ~ ip(C)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| icext(C,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_range,uri_ex_p2,uri_ex_c)
| ~ ip(uri_ex_c)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X_60(uri_ex_c,uri_ex_p2),tptp_fun_Y_59(uri_ex_c,uri_ex_p2))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p2)) ) )
| ~ ( ~ iext(uri_rdfs_range,uri_ex_p2,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
~ ( ~ ( iext(uri_rdfs_range,uri_ex_p2,uri_ex_c)
| ~ ip(uri_ex_c)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X_60(uri_ex_c,uri_ex_p2),tptp_fun_Y_59(uri_ex_c,uri_ex_p2))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p2)) ) )
| ~ ( ~ iext(uri_rdfs_range,uri_ex_p2,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) ) ) ) ),
inference(unit_resolution,[status(thm)],[63,51]) ).
tff(65,plain,
( ~ ( iext(uri_rdfs_range,uri_ex_p2,uri_ex_c)
| ~ ip(uri_ex_c)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X_60(uri_ex_c,uri_ex_p2),tptp_fun_Y_59(uri_ex_c,uri_ex_p2))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p2)) ) )
| ~ ( ~ iext(uri_rdfs_range,uri_ex_p2,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) ) ) )
| ~ iext(uri_rdfs_range,uri_ex_p2,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(66,plain,
( ~ iext(uri_rdfs_range,uri_ex_p2,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) ) ) ),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
( iext(uri_rdfs_range,uri_ex_p2,uri_ex_c)
<=> iext(uri_rdfs_range,uri_ex_p2,uri_ex_c) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
iext(uri_rdfs_range,uri_ex_p2,uri_ex_c),
inference(and_elim,[status(thm)],[2]) ).
tff(69,plain,
iext(uri_rdfs_range,uri_ex_p2,uri_ex_c),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( ~ ( ~ iext(uri_rdfs_range,uri_ex_p2,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) ) ) )
| ~ iext(uri_rdfs_range,uri_ex_p2,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(71,plain,
( ~ ( ~ iext(uri_rdfs_range,uri_ex_p2,uri_ex_c)
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) ) ) )
| ~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) ) ) ),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
~ ( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) ) ),
inference(unit_resolution,[status(thm)],[71,66]) ).
tff(73,plain,
( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) )
| ip(uri_ex_c) ),
inference(tautology,[status(thm)],[]) ).
tff(74,plain,
ip(uri_ex_c),
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
( ~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
<=> ~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,axiom,
~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion_rdfbased_sem_rdfsext_range_subprop) ).
tff(77,plain,
~ iext(uri_rdfs_range,uri_ex_p1,uri_ex_c),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( ~ ( iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_c)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) )
| iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_c)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(79,plain,
( ~ ( iext(uri_rdfs_range,uri_ex_p1,uri_ex_c)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_c)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) )
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_c)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) ),
inference(unit_resolution,[status(thm)],[78,77]) ).
tff(80,plain,
~ ( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ),
inference(unit_resolution,[status(thm)],[79,74,62,60]) ).
tff(81,plain,
( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ),
inference(tautology,[status(thm)],[]) ).
tff(82,plain,
iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1)),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| iext(uri_ex_p2,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| iext(uri_ex_p2,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| iext(uri_ex_p2,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| iext(uri_ex_p2,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
iext(uri_ex_p2,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1)),
inference(unit_resolution,[status(thm)],[85,82,29]) ).
tff(87,plain,
( ~ ip(uri_ex_c)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) )
| ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(88,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) ),
inference(unit_resolution,[status(thm)],[87,72]) ).
tff(89,plain,
( ~ iext(uri_ex_p1,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ),
inference(tautology,[status(thm)],[]) ).
tff(90,plain,
~ icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)),
inference(unit_resolution,[status(thm)],[89,80]) ).
tff(91,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) )
| ~ iext(uri_ex_p2,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) )
| ~ iext(uri_ex_p2,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) )
| ~ iext(uri_ex_p2,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| icext(uri_ex_c,Y) )
| ~ iext(uri_ex_p2,tptp_fun_X_60(uri_ex_c,uri_ex_p1),tptp_fun_Y_59(uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_59(uri_ex_c,uri_ex_p1)) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
$false,
inference(unit_resolution,[status(thm)],[93,90,88,86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWB077+1 : TPTP v9.0.0. Released v5.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 07:58:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.61/0.80 % SZS status Theorem
% 0.61/0.80 % SZS output start Proof
% See solution above
% 0.61/0.84 % E exiting
%------------------------------------------------------------------------------