TSTP Solution File: DAT019_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT019_1 : TPTP v8.1.0. Released v5.0.0.
% 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 16 14:36:24 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 41 ( 13 unt; 3 typ; 0 def)
% Number of atoms : 155 ( 37 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 129 ( 17 ~; 49 |; 0 &)
% ( 63 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number arithmetic : 303 ( 0 atm; 52 fun; 183 num; 68 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 2 usr; 6 con; 0-2 aty)
% Number of variables : 107 ( 93 !; 0 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
tff(in_type,type,
in: ( $int * collection ) > $o ).
tff(add_type,type,
add: ( $int * collection ) > collection ).
tff(empty_type,type,
empty: collection ).
tff(1,plain,
^ [Z: $int,X1: collection,X2: $int] :
refl(
( ( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
<=> ( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
<=> ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [Z: $int,X1: collection,X2: $int] :
rewrite(
( ( ( in(Z,X1)
| ( $sum(Z,$product(-1,X2)) = 0 ) )
<=> in(Z,add(X2,X1)) )
<=> ( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(Z,$product(-1,X2)) = 0 ) )
<=> in(Z,add(X2,X1)) )
<=> ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [Z: $int,X1: collection,X2: $int] :
rewrite(
( ( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) )
<=> ( ( in(Z,X1)
| ( $sum(Z,$product(-1,X2)) = 0 ) )
<=> in(Z,add(X2,X1)) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [Z: $int,X1: collection,X2: $int] :
( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) )
<=> ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(Z,$product(-1,X2)) = 0 ) )
<=> in(Z,add(X2,X1)) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [Z: $int,X1: collection,X2: $int] :
( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) )
<=> ! [Z: $int,X1: collection,X2: $int] :
( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
^ [Z: $int,X1: collection,X2: $int] :
rewrite(
( ( ( in(Z,X1)
| ( Z = X2 ) )
<=> in(Z,add(X2,X1)) )
<=> ( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( Z = X2 ) )
<=> in(Z,add(X2,X1)) )
<=> ! [Z: $int,X1: collection,X2: $int] :
( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,axiom,
! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( Z = X2 ) )
<=> in(Z,add(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=0.ax',ax4) ).
tff(11,plain,
! [Z: $int,X1: collection,X2: $int] :
( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [Z: $int,X1: collection,X2: $int] :
( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(Z,$product(-1,X2)) = 0 ) )
<=> in(Z,add(X2,X1)) ),
inference(modus_ponens,[status(thm)],[12,6]) ).
tff(14,plain,
! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) ),
inference(modus_ponens,[status(thm)],[13,4]) ).
tff(15,plain,
! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) ),
inference(modus_ponens,[status(thm)],[15,2]) ).
tff(17,plain,
( ( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( in(3,add(3,add(5,empty)))
<=> in(3,add(1,add(3,add(5,empty)))) ) )
<=> ( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( in(3,add(3,add(5,empty)))
<=> in(3,add(1,add(3,add(5,empty)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( ( in(3,add(3,add(5,empty)))
| ( $sum(1,$product(-1,3)) = 0 ) )
<=> in(3,add(1,add(3,add(5,empty)))) )
<=> ( in(3,add(3,add(5,empty)))
<=> in(3,add(1,add(3,add(5,empty)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( ( in(3,add(3,add(5,empty)))
| ( $sum(1,$product(-1,3)) = 0 ) )
<=> in(3,add(1,add(3,add(5,empty)))) ) )
<=> ( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( in(3,add(3,add(5,empty)))
<=> in(3,add(1,add(3,add(5,empty)))) ) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( ( in(3,add(3,add(5,empty)))
| ( $sum(1,$product(-1,3)) = 0 ) )
<=> in(3,add(1,add(3,add(5,empty)))) ) )
<=> ( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( in(3,add(3,add(5,empty)))
<=> in(3,add(1,add(3,add(5,empty)))) ) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( ( in(3,add(3,add(5,empty)))
| ( $sum(1,$product(-1,3)) = 0 ) )
<=> in(3,add(1,add(3,add(5,empty)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( in(3,add(3,add(5,empty)))
<=> in(3,add(1,add(3,add(5,empty)))) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( in(3,add(3,add(5,empty)))
<=> in(3,add(1,add(3,add(5,empty)))) ),
inference(unit_resolution,[status(thm)],[22,16]) ).
tff(24,plain,
^ [V: $int,W: collection] :
refl(
( in(V,add(V,W))
<=> in(V,add(V,W)) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [V: $int,W: collection] : in(V,add(V,W))
<=> ! [V: $int,W: collection] : in(V,add(V,W)) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [V: $int,W: collection] : in(V,add(V,W))
<=> ! [V: $int,W: collection] : in(V,add(V,W)) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
! [V: $int,W: collection] : in(V,add(V,W)),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=0.ax',ax2) ).
tff(28,plain,
! [V: $int,W: collection] : in(V,add(V,W)),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [V: $int,W: collection] : in(V,add(V,W)),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V: $int,W: collection] : in(V,add(V,W)),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [V: $int,W: collection] : in(V,add(V,W))
| in(3,add(3,add(5,empty))) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
in(3,add(3,add(5,empty))),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
( ~ in(3,add(1,add(3,add(5,empty))))
<=> ~ in(3,add(1,add(3,add(5,empty)))) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
~ in(3,add(1,add(3,add(5,empty)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(35,plain,
~ in(3,add(1,add(3,add(5,empty)))),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
( ~ ( in(3,add(3,add(5,empty)))
<=> in(3,add(1,add(3,add(5,empty)))) )
| ~ in(3,add(3,add(5,empty)))
| in(3,add(1,add(3,add(5,empty)))) ),
inference(tautology,[status(thm)],]) ).
tff(37,plain,
( ~ ( in(3,add(3,add(5,empty)))
<=> in(3,add(1,add(3,add(5,empty)))) )
| ~ in(3,add(3,add(5,empty))) ),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
$false,
inference(unit_resolution,[status(thm)],[37,32,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT019_1 : TPTP v8.1.0. Released v5.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 01:06:51 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------