TSTP Solution File: RNG124+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG124+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 03:18:33 EDT 2022
% Result : Theorem 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 34
% Syntax : Number of formulae : 58 ( 14 unt; 16 typ; 0 def)
% Number of atoms : 183 ( 60 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 243 ( 118 ~; 68 |; 27 &)
% ( 26 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 9 >; 5 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 26 ( 22 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtpldt1_type,type,
sdtpldt1: ( $i * $i ) > $i ).
tff(slsdtgt0_type,type,
slsdtgt0: $i > $i ).
tff(xb_type,type,
xb: $i ).
tff(xa_type,type,
xa: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xu_type,type,
xu: $i ).
tff(xq_type,type,
xq: $i ).
tff(xI_type,type,
xI: $i ).
tff(xr_type,type,
xr: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(iLess0_type,type,
iLess0: ( $i * $i ) > $o ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(1,plain,
( aElementOf0(xr,xI)
<=> aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aElementOf0(xr,xI)
<=> aElementOf0(xr,xI) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
aElementOf0(xr,xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2729) ).
tff(4,plain,
aElementOf0(xr,xI),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( ( xr != sz00 )
<=> ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
( ( xr != sz00 )
<=> ( xr != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
xr != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2673) ).
tff(9,plain,
xr != sz00,
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) != sz00,
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
<=> iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu)) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
<=> iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ( $false
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) )
<=> iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ( xr = sz00 )
<=> $false ),
inference(iff_false,[status(thm)],[8]) ).
tff(15,plain,
( ( ( xr = sz00 )
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) )
<=> ( $false
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ( ( xr = sz00 )
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) )
<=> iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
inference(transitivity,[status(thm)],[15,13]) ).
tff(17,axiom,
( aElement0(xq)
& aElement0(xr)
& ( xb = sdtpldt0(sdtasdt0(xq,xu),xr) )
& ( ( xr = sz00 )
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2666) ).
tff(18,plain,
( ( xr = sz00 )
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
inference(and_elim,[status(thm)],[17]) ).
tff(19,plain,
iLess0(sbrdtbr0(xr),sbrdtbr0(xu)),
inference(modus_ponens,[status(thm)],[18,16]) ).
tff(20,plain,
iLess0(sbrdtbr0(xr),sbrdtbr0(xu)),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu)),
inference(modus_ponens,[status(thm)],[20,11]) ).
tff(22,plain,
^ [W0: $i] :
refl(
( ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
<=> ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
^ [W0: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ( W0 != sz00 ) )
<=> ~ ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ( W0 = sz00 ) ) )),
( ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ( W0 != sz00 ) )
<=> ~ ~ ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ( W0 = sz00 ) ) )),
rewrite(
( ~ ~ ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ( W0 = sz00 ) )
<=> ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ( W0 = sz00 ) ) )),
( ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ( W0 != sz00 ) )
<=> ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ( W0 = sz00 ) ) )),
( ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ( W0 != sz00 ) ) )
<=> ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ( W0 = sz00 ) ) )),
rewrite(
( ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ( W0 = sz00 ) )
<=> ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) )),
( ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ( W0 != sz00 ) ) )
<=> ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ( W0 != sz00 ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
^ [W0: $i] :
rewrite(
( ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,xI)
& ( W0 != sz00 ) ) )
<=> ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ( W0 != sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,xI)
& ( W0 != sz00 ) ) )
<=> ! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ( W0 != sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,xI)
& ( W0 != sz00 ) ) )
<=> ! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,xI)
& ( W0 != sz00 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
^ [W0: $i] :
rewrite(
( ( ( aElementOf0(W0,xI)
& ( W0 != sz00 ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
<=> ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,xI)
& ( W0 != sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [W0: $i] :
( ( aElementOf0(W0,xI)
& ( W0 != sz00 ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
<=> ! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,xI)
& ( W0 != sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,axiom,
( aElementOf0(xu,xI)
& ( xu != sz00 )
& ! [W0: $i] :
( ( aElementOf0(W0,xI)
& ( W0 != sz00 ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
tff(32,plain,
! [W0: $i] :
( ( aElementOf0(W0,xI)
& ( W0 != sz00 ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ),
inference(and_elim,[status(thm)],[31]) ).
tff(33,plain,
! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,xI)
& ( W0 != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[32,30]) ).
tff(34,plain,
! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,xI)
& ( W0 != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[33,28]) ).
tff(35,plain,
! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ( W0 != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ( W0 != sz00 ) ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(modus_ponens,[status(thm)],[36,25]) ).
tff(38,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(modus_ponens,[status(thm)],[37,23]) ).
tff(39,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
$false,
inference(unit_resolution,[status(thm)],[41,38,21,10,5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : RNG124+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Sep 2 22:49:48 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.46 % SZS status Theorem
% 0.21/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------