TSTP Solution File: SYN986+1.001 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN986+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 : Fri Sep 30 00:01:30 EDT 2022
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 52 ( 14 unt; 3 typ; 0 def)
% Number of atoms : 220 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 291 ( 140 ~; 99 |; 17 &)
% ( 24 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 143 ( 108 !; 20 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
tff(r_type,type,
r: ( $i * $i * $i ) > $o ).
tff(succ_type,type,
succ: $i > $i ).
tff(zero_type,type,
zero: $i ).
tff(1,plain,
^ [Y: $i] :
refl(
( r(Y,zero,succ(Y))
<=> r(Y,zero,succ(Y)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i] : r(Y,zero,succ(Y))
<=> ! [Y: $i] : r(Y,zero,succ(Y)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i] : r(Y,zero,succ(Y))
<=> ! [Y: $i] : r(Y,zero,succ(Y)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i] : r(Y,zero,succ(Y)),
file('/export/starexec/sandbox/benchmark/Axioms/SYN002+0.ax',hyp1) ).
tff(5,plain,
! [Y: $i] : r(Y,zero,succ(Y)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i] : r(Y,zero,succ(Y)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i] : r(Y,zero,succ(Y)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i] : r(Y,zero,succ(Y))
| r(succ(zero),zero,succ(succ(zero))) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
r(succ(zero),zero,succ(succ(zero))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [Y: $i] : r(Y,zero,succ(Y))
| r(zero,zero,succ(zero)) ),
inference(quant_inst,[status(thm)],]) ).
tff(11,plain,
r(zero,zero,succ(zero)),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
^ [Y: $i,X: $i,Z: $i,Z1: $i] :
refl(
( ( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) )
<=> ( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) )
<=> ! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) )
<=> ! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
^ [Y: $i,X: $i,Z: $i,Z1: $i] :
trans(
monotonicity(
rewrite(
( ( r(Z,X,Z1)
=> r(Y,succ(X),Z1) )
<=> ( ~ r(Z,X,Z1)
| r(Y,succ(X),Z1) ) )),
( ( r(Y,X,Z)
=> ( r(Z,X,Z1)
=> r(Y,succ(X),Z1) ) )
<=> ( r(Y,X,Z)
=> ( ~ r(Z,X,Z1)
| r(Y,succ(X),Z1) ) ) )),
rewrite(
( ( r(Y,X,Z)
=> ( ~ r(Z,X,Z1)
| r(Y,succ(X),Z1) ) )
<=> ( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) ) )),
( ( r(Y,X,Z)
=> ( r(Z,X,Z1)
=> r(Y,succ(X),Z1) ) )
<=> ( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,X,Z)
=> ( r(Z,X,Z1)
=> r(Y,succ(X),Z1) ) )
<=> ! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,axiom,
! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,X,Z)
=> ( r(Z,X,Z1)
=> r(Y,succ(X),Z1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN002+0.ax',hyp2) ).
tff(18,plain,
! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[20,13]) ).
tff(22,plain,
( ( ~ ! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) )
| ~ r(zero,zero,succ(zero))
| r(zero,succ(zero),succ(succ(zero)))
| ~ r(succ(zero),zero,succ(succ(zero))) )
<=> ( ~ ! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) )
| ~ r(zero,zero,succ(zero))
| r(zero,succ(zero),succ(succ(zero)))
| ~ r(succ(zero),zero,succ(succ(zero))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( r(zero,succ(zero),succ(succ(zero)))
| ~ r(succ(zero),zero,succ(succ(zero)))
| ~ r(zero,zero,succ(zero)) )
<=> ( ~ r(zero,zero,succ(zero))
| r(zero,succ(zero),succ(succ(zero)))
| ~ r(succ(zero),zero,succ(succ(zero))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ ! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) )
| r(zero,succ(zero),succ(succ(zero)))
| ~ r(succ(zero),zero,succ(succ(zero)))
| ~ r(zero,zero,succ(zero)) )
<=> ( ~ ! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) )
| ~ r(zero,zero,succ(zero))
| r(zero,succ(zero),succ(succ(zero)))
| ~ r(succ(zero),zero,succ(succ(zero))) ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( ~ ! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) )
| r(zero,succ(zero),succ(succ(zero)))
| ~ r(succ(zero),zero,succ(succ(zero)))
| ~ r(zero,zero,succ(zero)) )
<=> ( ~ ! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) )
| ~ r(zero,zero,succ(zero))
| r(zero,succ(zero),succ(succ(zero)))
| ~ r(succ(zero),zero,succ(succ(zero))) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) )
| r(zero,succ(zero),succ(succ(zero)))
| ~ r(succ(zero),zero,succ(succ(zero)))
| ~ r(zero,zero,succ(zero)) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i,Z: $i,Z1: $i] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) )
| ~ r(zero,zero,succ(zero))
| r(zero,succ(zero),succ(succ(zero)))
| ~ r(succ(zero),zero,succ(succ(zero))) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
r(zero,succ(zero),succ(succ(zero))),
inference(unit_resolution,[status(thm)],[27,21,11,9]) ).
tff(29,plain,
^ [Z1: $i,Z0: $i] :
refl(
( ( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) )
<=> ( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [Z1: $i,Z0: $i] :
( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) )
<=> ! [Z1: $i,Z0: $i] :
( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
^ [Z1: $i,Z0: $i] :
trans(
monotonicity(
rewrite(
( ( r(zero,zero,Z1)
& r(zero,Z1,Z0) )
<=> ~ ( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) ) )),
( ~ ( r(zero,zero,Z1)
& r(zero,Z1,Z0) )
<=> ~ ~ ( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) ) )),
rewrite(
( ~ ~ ( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) )
<=> ( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) ) )),
( ~ ( r(zero,zero,Z1)
& r(zero,Z1,Z0) )
<=> ( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [Z1: $i,Z0: $i] :
~ ( r(zero,zero,Z1)
& r(zero,Z1,Z0) )
<=> ! [Z1: $i,Z0: $i] :
( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ~ ? [Z1: $i,Z0: $i] :
( r(zero,zero,Z1)
& r(zero,Z1,Z0) )
<=> ~ ? [Z1: $i,Z0: $i] :
( r(zero,zero,Z1)
& r(zero,Z1,Z0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
~ ? [Z1: $i,Z0: $i] :
( r(zero,zero,Z1)
& r(zero,Z1,Z0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ck) ).
tff(35,plain,
~ ? [Z1: $i,Z0: $i] :
( r(zero,zero,Z1)
& r(zero,Z1,Z0) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
~ ? [Z1: $i,Z0: $i] :
( r(zero,zero,Z1)
& r(zero,Z1,Z0) ),
inference(modus_ponens,[status(thm)],[35,33]) ).
tff(37,plain,
~ ? [Z1: $i,Z0: $i] :
( r(zero,zero,Z1)
& r(zero,Z1,Z0) ),
inference(modus_ponens,[status(thm)],[36,33]) ).
tff(38,plain,
~ ? [Z1: $i,Z0: $i] :
( r(zero,zero,Z1)
& r(zero,Z1,Z0) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
~ ? [Z1: $i,Z0: $i] :
( r(zero,zero,Z1)
& r(zero,Z1,Z0) ),
inference(modus_ponens,[status(thm)],[38,33]) ).
tff(40,plain,
~ ? [Z1: $i,Z0: $i] :
( r(zero,zero,Z1)
& r(zero,Z1,Z0) ),
inference(modus_ponens,[status(thm)],[39,33]) ).
tff(41,plain,
~ ? [Z1: $i,Z0: $i] :
( r(zero,zero,Z1)
& r(zero,Z1,Z0) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
^ [Z1: $i,Z0: $i] :
refl(
$oeq(
~ ( r(zero,zero,Z1)
& r(zero,Z1,Z0) ),
~ ( r(zero,zero,Z1)
& r(zero,Z1,Z0) ))),
inference(bind,[status(th)],]) ).
tff(43,plain,
! [Z1: $i,Z0: $i] :
~ ( r(zero,zero,Z1)
& r(zero,Z1,Z0) ),
inference(nnf-neg,[status(sab)],[41,42]) ).
tff(44,plain,
! [Z1: $i,Z0: $i] :
( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) ),
inference(modus_ponens,[status(thm)],[43,32]) ).
tff(45,plain,
! [Z1: $i,Z0: $i] :
( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) ),
inference(modus_ponens,[status(thm)],[44,30]) ).
tff(46,plain,
( ( ~ ! [Z1: $i,Z0: $i] :
( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) )
| ~ r(zero,zero,succ(zero))
| ~ r(zero,succ(zero),succ(succ(zero))) )
<=> ( ~ ! [Z1: $i,Z0: $i] :
( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) )
| ~ r(zero,zero,succ(zero))
| ~ r(zero,succ(zero),succ(succ(zero))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ! [Z1: $i,Z0: $i] :
( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) )
| ~ r(zero,zero,succ(zero))
| ~ r(zero,succ(zero),succ(succ(zero))) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [Z1: $i,Z0: $i] :
( ~ r(zero,zero,Z1)
| ~ r(zero,Z1,Z0) )
| ~ r(zero,zero,succ(zero))
| ~ r(zero,succ(zero),succ(succ(zero))) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,45,11,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN986+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n017.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 : Mon Sep 5 09:15:25 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.
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------