%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG095+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:24:10 AM UTC 2025
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 51 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 372 ( 91 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 550 ( 250 ~; 166 |; 101 &)
% ( 27 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 21 ( 21 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 109 ( 51 !; 48 ?; 109 :)
% Comments :
%------------------------------------------------------------------------------
tff(sz10_type,type,
sz10: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(tptp_fun_W2_11_type,type,
tptp_fun_W2_11: $i > $i ).
tff(tptp_fun_W1_12_type,type,
tptp_fun_W1_12: $i > $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtpldt1_type,type,
sdtpldt1: ( $i * $i ) > $i ).
tff(xJ_type,type,
xJ: $i ).
tff(xI_type,type,
xI: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(1,plain,
^ [W0: $i] :
refl(( ( ~ aElement0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),xI)
| ~ aElementOf0(tptp_fun_W2_11(W0),xJ)
| ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) != W0 )
| ~ aElementOf0(W0,sdtpldt1(xI,xJ)) ) )
<=> ( ~ aElement0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),xI)
| ~ aElementOf0(tptp_fun_W2_11(W0),xJ)
| ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) != W0 )
| ~ aElementOf0(W0,sdtpldt1(xI,xJ)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),xI)
| ~ aElementOf0(tptp_fun_W2_11(W0),xJ)
| ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) != W0 )
| ~ aElementOf0(W0,sdtpldt1(xI,xJ)) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),xI)
| ~ aElementOf0(tptp_fun_W2_11(W0),xJ)
| ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) != W0 )
| ~ aElementOf0(W0,sdtpldt1(xI,xJ)) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [W0: $i] :
rewrite(( ( ~ aElement0(W0)
| ( aElementOf0(tptp_fun_W1_12(W0),xI)
& aElementOf0(tptp_fun_W2_11(W0),xJ)
& ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) = W0 )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) )
<=> ( ~ aElement0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),xI)
| ~ aElementOf0(tptp_fun_W2_11(W0),xJ)
| ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) != W0 )
| ~ aElementOf0(W0,sdtpldt1(xI,xJ)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ( aElementOf0(tptp_fun_W1_12(W0),xI)
& aElementOf0(tptp_fun_W2_11(W0),xJ)
& ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) = W0 )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),xI)
| ~ aElementOf0(tptp_fun_W2_11(W0),xJ)
| ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) != W0 )
| ~ aElementOf0(W0,sdtpldt1(xI,xJ)) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [W0: $i] :
rewrite(( ( ~ aElement0(W0)
| ( aElementOf0(tptp_fun_W1_12(W0),xI)
& aElementOf0(tptp_fun_W2_11(W0),xJ)
& ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) = W0 )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) )
<=> ( ~ aElement0(W0)
| ( aElementOf0(tptp_fun_W1_12(W0),xI)
& aElementOf0(tptp_fun_W2_11(W0),xJ)
& ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) = W0 )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ( aElementOf0(tptp_fun_W1_12(W0),xI)
& aElementOf0(tptp_fun_W2_11(W0),xJ)
& ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) = W0 )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ( aElementOf0(tptp_fun_W1_12(W0),xI)
& aElementOf0(tptp_fun_W2_11(W0),xJ)
& ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) = W0 )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& ( sdtpldt0(W1,W2) = W0 ) )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& ( sdtpldt0(W1,W2) = W0 ) )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& ( sdtpldt0(W1,W2) = W0 ) )
& aElementOf0(W0,sdtpldt1(xI,xJ)) )
<=> ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& ( sdtpldt0(W1,W2) = W0 ) )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) )),
( ( aElement0(W0)
=> ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& ( sdtpldt0(W1,W2) = W0 ) )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) )
<=> ( aElement0(W0)
=> ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& ( sdtpldt0(W1,W2) = W0 ) )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) ) )),
rewrite(( ( aElement0(W0)
=> ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& ( sdtpldt0(W1,W2) = W0 ) )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) )
<=> ( ~ aElement0(W0)
| ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& ( sdtpldt0(W1,W2) = W0 ) )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) ) )),
( ( aElement0(W0)
=> ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& ( sdtpldt0(W1,W2) = W0 ) )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) )
<=> ( ~ aElement0(W0)
| ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& ( sdtpldt0(W1,W2) = W0 ) )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W0: $i] :
( aElement0(W0)
=> ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& ( sdtpldt0(W1,W2) = W0 ) )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& ( sdtpldt0(W1,W2) = W0 ) )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,axiom,
! [W0: $i] :
( aElement0(W0)
=> ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& ( sdtpldt0(W1,W2) = W0 ) )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205_03) ).
tff(11,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& ( sdtpldt0(W1,W2) = W0 ) )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& ( sdtpldt0(W1,W2) = W0 ) )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ( aElementOf0(tptp_fun_W1_12(W0),xI)
& aElementOf0(tptp_fun_W2_11(W0),xJ)
& ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) = W0 )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ( aElementOf0(tptp_fun_W1_12(W0),xI)
& aElementOf0(tptp_fun_W2_11(W0),xJ)
& ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) = W0 )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) ),
inference(modus_ponens,[status(thm)],[13,6]) ).
tff(15,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),xI)
| ~ aElementOf0(tptp_fun_W2_11(W0),xJ)
| ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) != W0 )
| ~ aElementOf0(W0,sdtpldt1(xI,xJ)) ) ),
inference(modus_ponens,[status(thm)],[14,4]) ).
tff(16,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),xI)
| ~ aElementOf0(tptp_fun_W2_11(W0),xJ)
| ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) != W0 )
| ~ aElementOf0(W0,sdtpldt1(xI,xJ)) ) ),
inference(modus_ponens,[status(thm)],[15,2]) ).
tff(17,plain,
( aElement0(sz10)
<=> aElement0(sz10) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
tff(19,plain,
aElement0(sz10),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),xI)
| ~ aElementOf0(tptp_fun_W2_11(W0),xJ)
| ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) != W0 )
| ~ aElementOf0(W0,sdtpldt1(xI,xJ)) ) )
| ~ aElement0(sz10)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 )
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ)) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),xI)
| ~ aElementOf0(tptp_fun_W2_11(W0),xJ)
| ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) != W0 )
| ~ aElementOf0(W0,sdtpldt1(xI,xJ)) ) )
| ~ aElement0(sz10)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 )
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),xI)
| ~ aElementOf0(tptp_fun_W2_11(W0),xJ)
| ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) != W0 )
| ~ aElementOf0(W0,sdtpldt1(xI,xJ)) ) )
| ~ aElement0(sz10)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 )
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),xI)
| ~ aElementOf0(tptp_fun_W2_11(W0),xJ)
| ( sdtpldt0(tptp_fun_W1_12(W0),tptp_fun_W2_11(W0)) != W0 )
| ~ aElementOf0(W0,sdtpldt1(xI,xJ)) ) )
| ~ aElement0(sz10)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 )
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ)) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ ( ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 )
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ)) ),
inference(unit_resolution,[status(thm)],[22,19,16]) ).
tff(24,plain,
( ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 )
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) = sz10 ) ),
inference(tautology,[status(thm)],[]) ).
tff(25,plain,
sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) = sz10,
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
( ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 )
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
| aElementOf0(tptp_fun_W2_11(sz10),xJ) ),
inference(tautology,[status(thm)],[]) ).
tff(27,plain,
aElementOf0(tptp_fun_W2_11(sz10),xJ),
inference(unit_resolution,[status(thm)],[26,23]) ).
tff(28,plain,
( ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 )
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
| aElementOf0(tptp_fun_W1_12(sz10),xI) ),
inference(tautology,[status(thm)],[]) ).
tff(29,plain,
aElementOf0(tptp_fun_W1_12(sz10),xI),
inference(unit_resolution,[status(thm)],[28,23]) ).
tff(30,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) )
<=> ( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) )
<=> ~ ( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) ) )),
( ~ ( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) )
<=> ~ ~ ( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) ) )),
rewrite(( ~ ~ ( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) )
<=> ( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) ) )),
( ~ ( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) )
<=> ( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [W0: $i,W1: $i] :
~ ( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) )
<=> ~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) )
<=> ~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(37,plain,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) ),
inference(modus_ponens,[status(thm)],[37,34]) ).
tff(39,plain,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) ),
inference(modus_ponens,[status(thm)],[39,34]) ).
tff(41,plain,
^ [W0: $i,W1: $i] :
refl($oeq(~ ( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) ),
~ ( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) ))),
inference(bind,[status(th)],[]) ).
tff(42,plain,
! [W0: $i,W1: $i] :
~ ( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) ),
inference(nnf-neg,[status(sab)],[40,41]) ).
tff(43,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) ),
inference(modus_ponens,[status(thm)],[42,33]) ).
tff(44,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) ),
inference(modus_ponens,[status(thm)],[43,31]) ).
tff(45,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) )
| ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) )
| ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 ) )
<=> ( ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) )
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) )
| ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 ) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) )
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) )
| ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 ) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) )
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) )
| ~ aElementOf0(tptp_fun_W1_12(sz10),xI)
| ~ aElementOf0(tptp_fun_W2_11(sz10),xJ)
| ( sdtpldt0(tptp_fun_W1_12(sz10),tptp_fun_W2_11(sz10)) != sz10 ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
$false,
inference(unit_resolution,[status(thm)],[50,44,29,27,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG095+2 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 03:21:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% See solution above
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------