TSTP Solution File: GRP017-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP017-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 22:25:27 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 33
% Syntax : Number of formulae : 66 ( 24 unt; 5 typ; 0 def)
% Number of atoms : 302 ( 37 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 434 ( 205 ~; 199 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 1 >; 2 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 230 ( 208 !; 0 ?; 230 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(c_type,type,
c: $i ).
tff(identity_type,type,
identity: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( product(X,identity,X)
<=> product(X,identity,X) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : product(X,identity,X)
<=> ! [X: $i] : product(X,identity,X) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : product(X,identity,X)
<=> ! [X: $i] : product(X,identity,X) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : product(X,identity,X),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
tff(5,plain,
! [X: $i] : product(X,identity,X),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : product(X,identity,X),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : product(X,identity,X),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : product(X,identity,X)
| product(b,identity,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
product(b,identity,b),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( product(a,c,identity)
<=> product(a,c,identity) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
product(a,c,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_identity) ).
tff(12,plain,
product(a,c,identity),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( product(b,a,identity)
<=> product(b,a,identity) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
product(b,a,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_is_identity) ).
tff(15,plain,
product(b,a,identity),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(
( ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
<=> ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W) )
<=> ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
( ( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) )
<=> ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W)
| product(U,Z,W) ) )),
rewrite(
( ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W)
| product(U,Z,W) )
<=> ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
( ( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) )
<=> ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
tff(22,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(b,a,identity)
| ~ product(b,identity,b)
| product(identity,c,b)
| ~ product(a,c,identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(b,a,identity)
| ~ product(b,identity,b)
| product(identity,c,b)
| ~ product(a,c,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( product(identity,c,b)
| ~ product(a,c,identity)
| ~ product(b,a,identity)
| ~ product(b,identity,b) )
<=> ( ~ product(b,a,identity)
| ~ product(b,identity,b)
| product(identity,c,b)
| ~ product(a,c,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(identity,c,b)
| ~ product(a,c,identity)
| ~ product(b,a,identity)
| ~ product(b,identity,b) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(b,a,identity)
| ~ product(b,identity,b)
| product(identity,c,b)
| ~ product(a,c,identity) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(identity,c,b)
| ~ product(a,c,identity)
| ~ product(b,a,identity)
| ~ product(b,identity,b) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(b,a,identity)
| ~ product(b,identity,b)
| product(identity,c,b)
| ~ product(a,c,identity) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(identity,c,b)
| ~ product(a,c,identity)
| ~ product(b,a,identity)
| ~ product(b,identity,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(b,a,identity)
| ~ product(b,identity,b)
| product(identity,c,b)
| ~ product(a,c,identity) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
product(identity,c,b),
inference(unit_resolution,[status(thm)],[31,25,15,12,9]) ).
tff(33,plain,
^ [X: $i] :
refl(
( product(identity,X,X)
<=> product(identity,X,X) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
! [X: $i] : product(identity,X,X),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
tff(37,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [X: $i] : product(identity,X,X),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
product(identity,c,c),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
( ( b != c )
<=> ( b != c ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
b != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_equals_c) ).
tff(44,plain,
b != c,
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
refl(
( ( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
<=> ( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
rewrite(
( ( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
<=> ( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).
tff(51,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[53,46]) ).
tff(55,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( b = c )
| ~ product(identity,c,b)
| ~ product(identity,c,c) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( b = c )
| ~ product(identity,c,b)
| ~ product(identity,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ( ( b = c )
| ~ product(identity,c,c)
| ~ product(identity,c,b) )
<=> ( ( b = c )
| ~ product(identity,c,b)
| ~ product(identity,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( b = c )
| ~ product(identity,c,c)
| ~ product(identity,c,b) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( b = c )
| ~ product(identity,c,b)
| ~ product(identity,c,c) ) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( b = c )
| ~ product(identity,c,c)
| ~ product(identity,c,b) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( b = c )
| ~ product(identity,c,b)
| ~ product(identity,c,c) ) ),
inference(transitivity,[status(thm)],[57,55]) ).
tff(59,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( b = c )
| ~ product(identity,c,c)
| ~ product(identity,c,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( b = c )
| ~ product(identity,c,b)
| ~ product(identity,c,c) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
$false,
inference(unit_resolution,[status(thm)],[60,54,44,41,32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP017-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 14:20:17 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------