%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG099+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:24:12 AM UTC 2025
% Result : Theorem 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 54
% Syntax : Number of formulae : 138 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 760 ( 8 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 929 ( 360 ~; 372 |; 90 &)
% ( 68 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 53 ( 53 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 216 ( 188 !; 9 ?; 216 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xb_type,type,
xb: $i ).
tff(xx_type,type,
xx: $i ).
tff(xa_type,type,
xa: $i ).
tff(xy_type,type,
xy: $i ).
tff(sdteqdtlpzmzozddtrp0_type,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(xJ_type,type,
xJ: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(xw_type,type,
xw: $i ).
tff(xI_type,type,
xI: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aIdeal0_type,type,
aIdeal0: $i > $o ).
tff(sz10_type,type,
sz10: $i ).
tff(1,plain,
( ( xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)) )
<=> ( xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1319) ).
tff(3,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)) = xw,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)) = sdtpldt0(xw,smndt0(xy)),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ)
<=> aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ)
<=> aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1409) ).
tff(10,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ),
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ)
| ~ aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) ),
inference(tautology,[status(thm)],[]) ).
tff(13,plain,
( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ) ),
inference(unit_resolution,[status(thm)],[12,11]) ).
tff(14,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)) = sdtpldt0(xw,smndt0(xx)),
inference(monotonicity,[status(thm)],[4]) ).
tff(15,plain,
( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI)
<=> aElementOf0(sdtpldt0(xw,smndt0(xx)),xI) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( aElementOf0(sdtpldt0(xw,smndt0(xx)),xI)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) ),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
( aElementOf0(sdtpldt0(xw,smndt0(xx)),xI)
<=> aElementOf0(sdtpldt0(xw,smndt0(xx)),xI) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1332) ).
tff(19,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
| ~ aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) ),
inference(tautology,[status(thm)],[]) ).
tff(22,plain,
( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI) ),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
^ [W0: $i] :
refl(( ( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )
<=> ( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )
<=> ~ ( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ) )),
( ~ ( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )
<=> ~ ~ ( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ) )),
rewrite(( ~ ~ ( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )
<=> ( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ) )),
( ~ ( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )
<=> ( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [W0: $i] :
~ ( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ~ ? [W0: $i] :
( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )
<=> ~ ? [W0: $i] :
( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ~ ? [W0: $i] :
( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )
<=> ~ ? [W0: $i] :
( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
~ ? [W0: $i] :
( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(30,plain,
~ ? [W0: $i] :
( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
~ ? [W0: $i] :
( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
inference(modus_ponens,[status(thm)],[30,27]) ).
tff(32,plain,
~ ? [W0: $i] :
( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
~ ? [W0: $i] :
( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
inference(modus_ponens,[status(thm)],[32,27]) ).
tff(34,plain,
^ [W0: $i] :
refl($oeq(~ ( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
~ ( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ))),
inference(bind,[status(th)],[]) ).
tff(35,plain,
! [W0: $i] :
~ ( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
inference(nnf-neg,[status(sab)],[33,34]) ).
tff(36,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
inference(modus_ponens,[status(thm)],[35,26]) ).
tff(37,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
inference(modus_ponens,[status(thm)],[36,24]) ).
tff(38,plain,
( ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ ( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI) )
| ~ ( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ ( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI) )
| ~ ( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ ( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI) )
| ~ ( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ~ ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ ( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI) )
| ~ ( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ ( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI) )
| ~ ( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ) ) ),
inference(unit_resolution,[status(thm)],[40,37]) ).
tff(42,plain,
~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))),
inference(unit_resolution,[status(thm)],[41,22,13]) ).
tff(43,plain,
( aSet0(xI)
<=> aSet0(xI) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [W0: $i] :
( aElementOf0(W0,xJ)
=> ( ! [W1: $i] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) ) ) )
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205) ).
tff(45,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [W0: $i] :
( aElementOf0(W0,xJ)
=> ( ! [W1: $i] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) ) ) ) ),
inference(and_elim,[status(thm)],[44]) ).
tff(46,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ) ),
inference(and_elim,[status(thm)],[45]) ).
tff(47,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI) ),
inference(and_elim,[status(thm)],[46]) ).
tff(48,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) ),
inference(and_elim,[status(thm)],[47]) ).
tff(49,plain,
aSet0(xI),
inference(and_elim,[status(thm)],[48]) ).
tff(50,plain,
aSet0(xI),
inference(modus_ponens,[status(thm)],[49,43]) ).
tff(51,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
rewrite(( ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
tff(60,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[62,55]) ).
tff(64,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ),
inference(unit_resolution,[status(thm)],[66,63,50]) ).
tff(68,plain,
( aElementOf0(xa,xI)
<=> aElementOf0(xa,xI) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& ( sdtpldt0(xa,xb) = sz10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1294) ).
tff(70,plain,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ) ),
inference(and_elim,[status(thm)],[69]) ).
tff(71,plain,
aElementOf0(xa,xI),
inference(and_elim,[status(thm)],[70]) ).
tff(72,plain,
aElementOf0(xa,xI),
inference(modus_ponens,[status(thm)],[71,68]) ).
tff(73,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xa)
| ~ aElementOf0(xa,xI) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xa)
| ~ aElementOf0(xa,xI) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xa)
| ~ aElementOf0(xa,xI) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xa)
| ~ aElementOf0(xa,xI) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
aElement0(xa),
inference(unit_resolution,[status(thm)],[75,72,67]) ).
tff(77,plain,
( aElement0(xy)
<=> aElement0(xy) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
( aElement0(xx)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1217) ).
tff(79,plain,
aElement0(xy),
inference(and_elim,[status(thm)],[78]) ).
tff(80,plain,
aElement0(xy),
inference(modus_ponens,[status(thm)],[79,77]) ).
tff(81,plain,
^ [W0: $i,W1: $i] :
refl(( ( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElement0(W0)
& aElement0(W1) )
<=> ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(( ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(( ( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtasdt0(W0,W1)) )
<=> ( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(87,plain,
( ! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtasdt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,axiom,
! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
tff(89,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[92,82]) ).
tff(94,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xy,xa))
| ~ aElement0(xa)
| ~ aElement0(xy) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xy,xa))
| ~ aElement0(xa)
| ~ aElement0(xy) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xy,xa))
| ~ aElement0(xa)
| ~ aElement0(xy) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xy,xa))
| ~ aElement0(xa)
| ~ aElement0(xy) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
( aElement0(sdtasdt0(xy,xa))
| ~ aElement0(xa) ),
inference(unit_resolution,[status(thm)],[96,93,80]) ).
tff(98,plain,
aElement0(sdtasdt0(xy,xa)),
inference(unit_resolution,[status(thm)],[97,76]) ).
tff(99,plain,
( aSet0(xJ)
<=> aSet0(xJ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
aSet0(xJ),
inference(and_elim,[status(thm)],[46]) ).
tff(101,plain,
aSet0(xJ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ),
inference(unit_resolution,[status(thm)],[104,63,101]) ).
tff(106,plain,
( aElementOf0(xb,xJ)
<=> aElementOf0(xb,xJ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
aElementOf0(xb,xJ),
inference(and_elim,[status(thm)],[70]) ).
tff(108,plain,
aElementOf0(xb,xJ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xb)
| ~ aElementOf0(xb,xJ) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xb)
| ~ aElementOf0(xb,xJ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xb)
| ~ aElementOf0(xb,xJ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xb)
| ~ aElementOf0(xb,xJ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
aElement0(xb),
inference(unit_resolution,[status(thm)],[111,108,105]) ).
tff(113,plain,
( aElement0(xx)
<=> aElement0(xx) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
aElement0(xx),
inference(and_elim,[status(thm)],[78]) ).
tff(115,plain,
aElement0(xx),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xx,xb))
| ~ aElement0(xb)
| ~ aElement0(xx) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xx,xb))
| ~ aElement0(xb)
| ~ aElement0(xx) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xx,xb))
| ~ aElement0(xb)
| ~ aElement0(xx) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xx,xb))
| ~ aElement0(xb)
| ~ aElement0(xx) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
( aElement0(sdtasdt0(xx,xb))
| ~ aElement0(xb) ),
inference(unit_resolution,[status(thm)],[118,93,115]) ).
tff(120,plain,
aElement0(sdtasdt0(xx,xb)),
inference(unit_resolution,[status(thm)],[119,112]) ).
tff(121,plain,
^ [W0: $i,W1: $i] :
refl(( ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(122,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElement0(W0)
& aElement0(W1) )
<=> ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(( ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(( ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(124,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[123]) ).
tff(125,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,axiom,
! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(129,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[129,125]) ).
tff(131,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(skolemize,[status(sab)],[130]) ).
tff(132,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[131,124]) ).
tff(133,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[132,122]) ).
tff(134,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
( aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(unit_resolution,[status(thm)],[136,133]) ).
tff(138,plain,
$false,
inference(unit_resolution,[status(thm)],[137,120,98,42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : RNG099+2 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n016.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Fri Jun 20 03:21:02 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.22/0.43 % SZS status Theorem
% 0.22/0.43 % SZS output start Proof
% See solution above
% 0.22/0.45 % E exiting
%------------------------------------------------------------------------------