TSTP Solution File: NUM618+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM618+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:10:56 EDT 2022
% Result : Theorem 0.19s 0.54s
% Output : Proof 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 35
% Syntax : Number of formulae : 68 ( 14 unt; 13 typ; 0 def)
% Number of atoms : 284 ( 89 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 384 ( 179 ~; 99 |; 73 &)
% ( 27 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 75 ( 32 !; 35 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(tptp_fun_W1_24_type,type,
tptp_fun_W1_24: $i > $i ).
tff(xx_type,type,
xx: $i ).
tff(xe_type,type,
xe: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(xN_type,type,
xN: $i ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(xO_type,type,
xO: $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(1,plain,
( aElementOf0(xx,xO)
<=> aElementOf0(xx,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aElementOf0(xx,xO)
<=> aElementOf0(xx,xO) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( aElementOf0(xx,szNzAzT0)
& aElementOf0(xx,xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5365) ).
tff(4,plain,
aElementOf0(xx,xO),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aElementOf0(xx,xO),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
aElementOf0(xx,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
<=> ( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
& aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) = W0 ) ) )
<=> ( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
& aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )
<=> ( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xN))
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xN))
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) )
<=> ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ))),
( ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) )
<=> ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )),
( ( aElementOf0(W0,xO)
=> ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )
<=> ( aElementOf0(W0,xO)
=> ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ) )),
rewrite(
( ( aElementOf0(W0,xO)
=> ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )
<=> ( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ) )),
( ( aElementOf0(W0,xO)
=> ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )
<=> ( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [W0: $i] :
( aElementOf0(W0,xO)
=> ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,axiom,
! [W0: $i] :
( aElementOf0(W0,xO)
=> ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4982) ).
tff(17,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xN))
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[18,12]) ).
tff(20,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ( aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
& aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) = W0 ) ) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ),
inference(modus_ponens,[status(thm)],[20,10]) ).
tff(22,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ),
inference(modus_ponens,[status(thm)],[21,8]) ).
tff(23,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
| ~ aElementOf0(xx,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(xx),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(xx),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(xx)) != xx ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
| ~ aElementOf0(xx,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(xx),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(xx),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(xx)) != xx ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
| ~ aElementOf0(xx,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(xx),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(xx),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(xx)) != xx ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
| ~ aElementOf0(xx,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W1_24(xx),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(xx),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(xx)) != xx ) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ ( ~ aElementOf0(tptp_fun_W1_24(xx),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(xx),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(xx)) != xx ) ),
inference(unit_resolution,[status(thm)],[25,22,6]) ).
tff(27,plain,
( ~ aElementOf0(tptp_fun_W1_24(xx),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(xx),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(xx)) != xx )
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(xx)) = xx ) ),
inference(tautology,[status(thm)],]) ).
tff(28,plain,
sdtlpdtrp0(xe,tptp_fun_W1_24(xx)) = xx,
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
xx = sdtlpdtrp0(xe,tptp_fun_W1_24(xx)),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ~ aElementOf0(tptp_fun_W1_24(xx),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W1_24(xx),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(xx)) != xx )
| aElementOf0(tptp_fun_W1_24(xx),szDzozmdt0(xN)) ),
inference(tautology,[status(thm)],]) ).
tff(31,plain,
aElementOf0(tptp_fun_W1_24(xx),szDzozmdt0(xN)),
inference(unit_resolution,[status(thm)],[30,26]) ).
tff(32,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( aElementOf0(W0,szDzozmdt0(xN))
& ( xx = sdtlpdtrp0(xe,W0) ) )
<=> ~ ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& ( xx = sdtlpdtrp0(xe,W0) ) )
<=> ~ ~ ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) ) )),
rewrite(
( ~ ~ ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& ( xx = sdtlpdtrp0(xe,W0) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [W0: $i] :
~ ( aElementOf0(W0,szDzozmdt0(xN))
& ( xx = sdtlpdtrp0(xe,W0) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xN))
& ( xx = sdtlpdtrp0(xe,W0) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xN))
& ( xx = sdtlpdtrp0(xe,W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( xx = sdtlpdtrp0(xe,W0) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xN))
& ( xx = sdtlpdtrp0(xe,W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( xx = sdtlpdtrp0(xe,W0) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( xx = sdtlpdtrp0(xe,W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( xx = sdtlpdtrp0(xe,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(40,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( xx = sdtlpdtrp0(xe,W0) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( xx = sdtlpdtrp0(xe,W0) ) ),
inference(modus_ponens,[status(thm)],[40,38]) ).
tff(42,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( xx = sdtlpdtrp0(xe,W0) ) ),
inference(modus_ponens,[status(thm)],[41,38]) ).
tff(43,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szNzAzT0)
& ( xx = sdtlpdtrp0(xe,W0) ) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xN))
& ( xx = sdtlpdtrp0(xe,W0) ) ),
inference(modus_ponens,[status(thm)],[43,37]) ).
tff(45,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xN))
& ( xx = sdtlpdtrp0(xe,W0) ) ),
inference(modus_ponens,[status(thm)],[44,36]) ).
tff(46,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xN))
& ( xx = sdtlpdtrp0(xe,W0) ) ),
inference(modus_ponens,[status(thm)],[45,36]) ).
tff(47,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xN))
& ( xx = sdtlpdtrp0(xe,W0) ) ),
inference(modus_ponens,[status(thm)],[46,36]) ).
tff(48,plain,
^ [W0: $i] :
refl(
$oeq(
~ ( aElementOf0(W0,szDzozmdt0(xN))
& ( xx = sdtlpdtrp0(xe,W0) ) ),
~ ( aElementOf0(W0,szDzozmdt0(xN))
& ( xx = sdtlpdtrp0(xe,W0) ) ))),
inference(bind,[status(th)],]) ).
tff(49,plain,
! [W0: $i] :
~ ( aElementOf0(W0,szDzozmdt0(xN))
& ( xx = sdtlpdtrp0(xe,W0) ) ),
inference(nnf-neg,[status(sab)],[47,48]) ).
tff(50,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) ),
inference(modus_ponens,[status(thm)],[49,35]) ).
tff(51,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) ),
inference(modus_ponens,[status(thm)],[50,33]) ).
tff(52,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) )
| ~ aElementOf0(tptp_fun_W1_24(xx),szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,tptp_fun_W1_24(xx)) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) )
| ~ aElementOf0(tptp_fun_W1_24(xx),szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,tptp_fun_W1_24(xx)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) )
| ~ aElementOf0(tptp_fun_W1_24(xx),szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,tptp_fun_W1_24(xx)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,W0) ) )
| ~ aElementOf0(tptp_fun_W1_24(xx),szDzozmdt0(xN))
| ( xx != sdtlpdtrp0(xe,tptp_fun_W1_24(xx)) ) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
$false,
inference(unit_resolution,[status(thm)],[54,51,31,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM618+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 12:32:47 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.54 % SZS status Theorem
% 0.19/0.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------