TSTP Solution File: RNG095+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG095+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 : Tue Sep 20 03:18:22 EDT 2022
% Result : Theorem 0.36s 0.58s
% Output : Proof 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 31
% Syntax : Number of formulae : 63 ( 13 unt; 9 typ; 0 def)
% Number of atoms : 381 ( 94 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 559 ( 253 ~; 166 |; 107 &)
% ( 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 : 9 ( 6 >; 3 *; 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 : 115 ( 51 !; 54 ?; 115 :)
% 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/sandbox2/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/sandbox2/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/sandbox2/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] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) ),
inference(modus_ponens,[status(thm)],[40,34]) ).
tff(42,plain,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
~ ? [W0: $i,W1: $i] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) ),
inference(modus_ponens,[status(thm)],[42,34]) ).
tff(44,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(45,plain,
! [W0: $i,W1: $i] :
~ ( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sz10 ) ),
inference(nnf-neg,[status(sab)],[43,44]) ).
tff(46,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) ),
inference(modus_ponens,[status(thm)],[45,33]) ).
tff(47,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI)
| ( sdtpldt0(W0,W1) != sz10 ) ),
inference(modus_ponens,[status(thm)],[46,31]) ).
tff(48,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(49,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(50,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)],[49]) ).
tff(51,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)],[50,48]) ).
tff(52,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(53,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)],[52,51]) ).
tff(54,plain,
$false,
inference(unit_resolution,[status(thm)],[53,47,29,27,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : RNG095+2 : TPTP v8.1.0. Released v4.0.0.
% 0.05/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Sep 2 22:27:40 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.36/0.58 % SZS status Theorem
% 0.36/0.58 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------