%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM615+1 : TPTP v9.0.0. Released v4.0.0.
% 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 05:21:36 AM UTC 2025
% Result : Theorem 0.41s 0.62s
% Output : Proof 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 51 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 256 ( 82 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 353 ( 171 ~; 97 |; 54 &)
% ( 25 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 23 ( 23 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 58 ( 29 !; 22 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
tff(xp_type,type,
xp: $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(tptp_fun_W1_24_type,type,
tptp_fun_W1_24: $i > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xQ_type,type,
xQ: $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(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(xO_type,type,
xO: $i ).
tff(1,plain,
( ( xp = szmzizndt0(xQ) )
<=> ( xp = szmzizndt0(xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
tff(3,plain,
xp = szmzizndt0(xQ),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
szmzizndt0(xQ) = xp,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( aElementOf0(szmzizndt0(xQ),xO)
<=> aElementOf0(xp,xO) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( aElementOf0(xp,xO)
<=> aElementOf0(szmzizndt0(xQ),xO) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( aElementOf0(xp,xO)
<=> aElementOf0(xp,xO) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
aElementOf0(xp,xO),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5182) ).
tff(9,plain,
aElementOf0(xp,xO),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
aElementOf0(szmzizndt0(xQ),xO),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
<=> ( ~ aElementOf0(W0,xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xO)
| ( aElementOf0(tptp_fun_W1_24(W0),szNzAzT0)
& aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) = W0 ) ) )
<=> ( ~ aElementOf0(W0,xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ( aElementOf0(tptp_fun_W1_24(W0),szNzAzT0)
& aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
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(rewrite,[status(thm)],[]) ).
tff(16,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(17,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)],[16]) ).
tff(18,axiom,
! [W0: $i] :
( aElementOf0(W0,xO)
=> ? [W1: $i] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W1) = W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4982) ).
tff(19,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)],[18,17]) ).
tff(20,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)],[19,15]) ).
tff(21,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ( aElementOf0(tptp_fun_W1_24(W0),szNzAzT0)
& aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) = W0 ) ) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) ),
inference(modus_ponens,[status(thm)],[22,12]) ).
tff(24,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
| ~ aElementOf0(szmzizndt0(xQ),xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(szmzizndt0(xQ))) != szmzizndt0(xQ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
| ~ aElementOf0(szmzizndt0(xQ),xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(szmzizndt0(xQ))) != szmzizndt0(xQ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
| ~ aElementOf0(szmzizndt0(xQ),xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(szmzizndt0(xQ))) != szmzizndt0(xQ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(W0),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(W0)) != W0 ) ) )
| ~ aElementOf0(szmzizndt0(xQ),xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(szmzizndt0(xQ))) != szmzizndt0(xQ) ) ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
( ~ aElementOf0(szmzizndt0(xQ),xO)
| ~ ( ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(szmzizndt0(xQ))) != szmzizndt0(xQ) ) ) ),
inference(unit_resolution,[status(thm)],[26,23]) ).
tff(28,plain,
~ ( ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(szmzizndt0(xQ))) != szmzizndt0(xQ) ) ),
inference(unit_resolution,[status(thm)],[27,10]) ).
tff(29,plain,
( ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(szmzizndt0(xQ))) != szmzizndt0(xQ) )
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(szmzizndt0(xQ))) = szmzizndt0(xQ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(30,plain,
sdtlpdtrp0(xe,tptp_fun_W1_24(szmzizndt0(xQ))) = szmzizndt0(xQ),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
sdtlpdtrp0(xe,tptp_fun_W1_24(szmzizndt0(xQ))) = xp,
inference(transitivity,[status(thm)],[30,4]) ).
tff(32,plain,
( ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),szNzAzT0)
| ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(szmzizndt0(xQ))) != szmzizndt0(xQ) )
| aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(tautology,[status(thm)],[]) ).
tff(33,plain,
aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(unit_resolution,[status(thm)],[32,28]) ).
tff(34,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) )
<=> ( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xp ) )
<=> ~ ( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) ) )),
( ~ ( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xp ) )
<=> ~ ~ ( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) ) )),
rewrite(( ~ ~ ( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) )
<=> ( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) ) )),
( ~ ( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xp ) )
<=> ( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [W0: $i] :
~ ( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xp ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xp ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xp ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
~ ? [W0: $i] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(40,plain,
~ ? [W0: $i] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xp ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
~ ? [W0: $i] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xp ) ),
inference(modus_ponens,[status(thm)],[40,38]) ).
tff(42,plain,
~ ? [W0: $i] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xp ) ),
inference(modus_ponens,[status(thm)],[41,38]) ).
tff(43,plain,
~ ? [W0: $i] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xp ) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
^ [W0: $i] :
refl($oeq(~ ( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xp ) ),
~ ( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xp ) ))),
inference(bind,[status(th)],[]) ).
tff(45,plain,
! [W0: $i] :
~ ( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xp ) ),
inference(nnf-neg,[status(sab)],[43,44]) ).
tff(46,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) ),
inference(modus_ponens,[status(thm)],[45,37]) ).
tff(47,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) ),
inference(modus_ponens,[status(thm)],[46,35]) ).
tff(48,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) )
| ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(szmzizndt0(xQ))) != xp ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) )
| ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(szmzizndt0(xQ))) != xp ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) )
| ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(szmzizndt0(xQ))) != xp ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,W0) != xp ) )
| ~ aElementOf0(tptp_fun_W1_24(szmzizndt0(xQ)),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xe,tptp_fun_W1_24(szmzizndt0(xQ))) != xp ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
$false,
inference(unit_resolution,[status(thm)],[50,47,33,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM615+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:35:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.41/0.62 % SZS status Theorem
% 0.41/0.62 % SZS output start Proof
% See solution above
% 0.47/0.63 % E exiting
%------------------------------------------------------------------------------