%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG121+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:24:15 AM UTC 2025
% Result : Theorem 3.04s 3.30s
% Output : Proof 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 29
% Syntax : Number of formulae : 78 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 677 ( 211 equ)
% Maximal formula atoms : 32 ( 8 avg)
% Number of connectives : 1182 ( 598 ~; 397 |; 129 &)
% ( 49 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 228 ( 172 !; 49 ?; 228 :)
% Comments :
%------------------------------------------------------------------------------
tff(xb_type,type,
xb: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(xa_type,type,
xa: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slsdtgt0_type,type,
slsdtgt0: $i > $i ).
tff(xI_type,type,
xI: $i ).
tff(tptp_fun_W2_25_type,type,
tptp_fun_W2_25: $i > $i ).
tff(tptp_fun_W1_26_type,type,
tptp_fun_W1_26: $i > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(aIdeal0_type,type,
aIdeal0: $i > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(sdtpldt1_type,type,
sdtpldt1: ( $i * $i ) > $i ).
tff(1,plain,
( aElement0(xb)
<=> aElement0(xb) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
tff(3,plain,
aElement0(xb),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aElement0(xb),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
^ [W0: $i] :
refl(( ( ~ aElement0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
<=> ( ~ aElement0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
^ [W0: $i] :
rewrite(( ( ~ aElement0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ( ~ aElement0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(( ( aElement0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ( ~ aElement0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( aElement0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [W0: $i] :
( aElement0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
tff(13,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[16,6]) ).
tff(18,plain,
( ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aElement0(xb)
| ~ ( ( sdtpldt0(xb,sz00) != xb )
| ( xb != sdtpldt0(sz00,xb) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aElement0(xb)
| ~ ( ( sdtpldt0(xb,sz00) != xb )
| ( xb != sdtpldt0(sz00,xb) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aElement0(xb)
| ~ ( ( sdtpldt0(xb,sz00) != xb )
| ( xb != sdtpldt0(sz00,xb) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aElement0(xb)
| ~ ( ( sdtpldt0(xb,sz00) != xb )
| ( xb != sdtpldt0(sz00,xb) ) ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
~ ( ( sdtpldt0(xb,sz00) != xb )
| ( xb != sdtpldt0(sz00,xb) ) ),
inference(unit_resolution,[status(thm)],[20,17,4]) ).
tff(22,plain,
( ( sdtpldt0(xb,sz00) != xb )
| ( xb != sdtpldt0(sz00,xb) )
| ( xb = sdtpldt0(sz00,xb) ) ),
inference(tautology,[status(thm)],[]) ).
tff(23,plain,
xb = sdtpldt0(sz00,xb),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
sdtpldt0(sz00,xb) = xb,
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
^ [W0: $i] :
refl(( ~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ~ aElementOf0(W0,xI)
| ( aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
& aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
& ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) = W0 ) ) )
<=> ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) ) )),
rewrite(( ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
<=> ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )),
( ( ( ~ aElementOf0(W0,xI)
| ( aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
& aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
& ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) = W0 ) ) )
& ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) )
<=> ( ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
& ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) )),
rewrite(( ( ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
& ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) )),
( ( ( ~ aElementOf0(W0,xI)
| ( aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
& aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
& ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) = W0 ) ) )
& ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,xI)
| ( aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
& aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
& ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) = W0 ) ) )
& ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [W0: $i] :
( aElementOf0(W0,xI)
<=> ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
<=> ! [W0: $i] :
( aElementOf0(W0,xI)
<=> ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,xI)
<=> ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
<=> ( aElementOf0(W0,xI)
<=> ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [W0: $i] :
( aElementOf0(W0,xI)
<=> ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
<=> ! [W0: $i] :
( aElementOf0(W0,xI)
<=> ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,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)
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xa,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xb,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,xI)
<=> ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
tff(36,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)
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xa,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xb,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,xI)
<=> ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) ),
inference(and_elim,[status(thm)],[35]) ).
tff(37,plain,
! [W0: $i] :
( aElementOf0(W0,xI)
<=> ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ),
inference(and_elim,[status(thm)],[36]) ).
tff(38,plain,
! [W0: $i] :
( aElementOf0(W0,xI)
<=> ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[37,34]) ).
tff(39,plain,
! [W0: $i] :
( aElementOf0(W0,xI)
<=> ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[38,32]) ).
tff(40,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,xI)
| ( aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
& aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
& ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) = W0 ) ) )
& ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ),
inference(modus_ponens,[status(thm)],[40,31]) ).
tff(42,plain,
! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ),
inference(modus_ponens,[status(thm)],[41,29]) ).
tff(43,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(xb),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(xb),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(xb),tptp_fun_W2_25(xb)) != xb ) ) )
| ~ ( aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(xb),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(xb),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(xb),tptp_fun_W2_25(xb)) != xb ) ) )
| ~ ( aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ~ ( ~ ( ~ aElementOf0(xb,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(xb),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(xb),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(xb),tptp_fun_W2_25(xb)) != xb ) ) )
| ~ ( aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != xb )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(xb,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(xb),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(xb),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(xb),tptp_fun_W2_25(xb)) != xb ) ) )
| ~ ( aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(xb),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(xb),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(xb),tptp_fun_W2_25(xb)) != xb ) ) )
| ~ ( aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != xb )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(xb),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(xb),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(xb),tptp_fun_W2_25(xb)) != xb ) ) )
| ~ ( aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(xb),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(xb),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(xb),tptp_fun_W2_25(xb)) != xb ) ) )
| ~ ( aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != xb )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(xb),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(xb),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(xb),tptp_fun_W2_25(xb)) != xb ) ) )
| ~ ( aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) ) ) ) ) ),
inference(transitivity,[status(thm)],[45,43]) ).
tff(47,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(xb),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(xb),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(xb),tptp_fun_W2_25(xb)) != xb ) ) )
| ~ ( aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != xb )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(W0),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(W0),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(W0),tptp_fun_W2_25(W0)) != W0 ) ) )
| ~ ( aElementOf0(W0,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(xb),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(xb),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(xb),tptp_fun_W2_25(xb)) != xb ) ) )
| ~ ( aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) ) ) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
~ ( ~ ( ~ aElementOf0(xb,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(xb),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(xb),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(xb),tptp_fun_W2_25(xb)) != xb ) ) )
| ~ ( aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) ) ) ),
inference(unit_resolution,[status(thm)],[48,42]) ).
tff(50,plain,
( ~ ( ~ aElementOf0(xb,xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_26(xb),slsdtgt0(xa))
| ~ aElementOf0(tptp_fun_W2_25(xb),slsdtgt0(xb))
| ( sdtpldt0(tptp_fun_W1_26(xb),tptp_fun_W2_25(xb)) != xb ) ) )
| ~ ( aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) ) )
| aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(51,plain,
( aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) ) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( ~ aElementOf0(xb,xI)
<=> ~ aElementOf0(xb,xI) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
~ ( ? [W0: $i,W1: $i] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& ( sdtpldt0(W0,W1) = xb ) )
| ? [W0: $i,W1: $i] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& ( sdtpldt0(W0,W1) = xb ) )
| aElementOf0(xb,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(54,plain,
~ aElementOf0(xb,xI),
inference(or_elim,[status(thm)],[53]) ).
tff(55,plain,
~ aElementOf0(xb,xI),
inference(modus_ponens,[status(thm)],[54,52]) ).
tff(56,plain,
( ~ ( aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) ) )
| aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(57,plain,
( ~ ( aElementOf0(xb,xI)
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) ) )
| ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) ) ),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) ),
inference(unit_resolution,[status(thm)],[57,51]) ).
tff(59,plain,
( aElementOf0(xb,slsdtgt0(xb))
<=> aElementOf0(xb,slsdtgt0(xb)) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xa,W0) = sz00 ) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xa,W0) = xa ) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xb,W0) = sz00 ) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xb,W0) = xb ) )
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2203) ).
tff(61,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(and_elim,[status(thm)],[60]) ).
tff(62,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(modus_ponens,[status(thm)],[61,59]) ).
tff(63,plain,
( aElementOf0(sz00,slsdtgt0(xa))
<=> aElementOf0(sz00,slsdtgt0(xa)) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xa,W0) = sz00 ) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xa,W0) = xa ) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xb,W0) = sz00 ) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xb,W0) = xb ) ) ),
inference(and_elim,[status(thm)],[60]) ).
tff(65,plain,
( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xa,W0) = sz00 ) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xa,W0) = xa ) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xb,W0) = sz00 ) )
& aElementOf0(sz00,slsdtgt0(xb)) ),
inference(and_elim,[status(thm)],[64]) ).
tff(66,plain,
( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xa,W0) = sz00 ) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xa,W0) = xa ) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xb,W0) = sz00 ) ) ),
inference(and_elim,[status(thm)],[65]) ).
tff(67,plain,
( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xa,W0) = sz00 ) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xa,W0) = xa ) )
& aElementOf0(xa,slsdtgt0(xa)) ),
inference(and_elim,[status(thm)],[66]) ).
tff(68,plain,
( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xa,W0) = sz00 ) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xa,W0) = xa ) ) ),
inference(and_elim,[status(thm)],[67]) ).
tff(69,plain,
( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xa,W0) = sz00 ) )
& aElementOf0(sz00,slsdtgt0(xa)) ),
inference(and_elim,[status(thm)],[68]) ).
tff(70,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(and_elim,[status(thm)],[69]) ).
tff(71,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,plain,
( ( ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) )
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xb,slsdtgt0(xb))
| ( sdtpldt0(sz00,xb) != xb ) )
<=> ( ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) )
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xb,slsdtgt0(xb))
| ( sdtpldt0(sz00,xb) != xb ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ( sdtpldt0(sz00,xb) != xb ) )
<=> ( ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xb,slsdtgt0(xb))
| ( sdtpldt0(sz00,xb) != xb ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) )
| ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ( sdtpldt0(sz00,xb) != xb ) )
<=> ( ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) )
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xb,slsdtgt0(xb))
| ( sdtpldt0(sz00,xb) != xb ) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) )
| ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ( sdtpldt0(sz00,xb) != xb ) )
<=> ( ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) )
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xb,slsdtgt0(xb))
| ( sdtpldt0(sz00,xb) != xb ) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
( ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) )
| ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ( sdtpldt0(sz00,xb) != xb ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != xb ) )
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xb,slsdtgt0(xb))
| ( sdtpldt0(sz00,xb) != xb ) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
$false,
inference(unit_resolution,[status(thm)],[77,71,62,58,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.14 % Problem : RNG121+4 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.14 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n002.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 03:26:46 EDT 2025
% 0.15/0.36 % CPUTime :
% 3.04/3.30 % SZS status Theorem
% 3.04/3.30 % SZS output start Proof
% See solution above
% 3.14/3.33 % E exiting
%------------------------------------------------------------------------------