TSTP Solution File: GRP042-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP042-2 : 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 22:25:38 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 26
% Syntax : Number of formulae : 51 ( 16 unt; 5 typ; 0 def)
% Number of atoms : 196 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 274 ( 129 ~; 125 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 2 >; 3 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 162 ( 145 !; 0 ?; 162 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(identity_type,type,
identity: $i ).
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(1,plain,
^ [X: $i] :
refl(
( product(identity,X,X)
<=> product(identity,X,X) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : product(identity,X,X),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',left_identity) ).
tff(5,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : product(identity,X,X),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
product(identity,a,a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( equalish(a,b)
<=> equalish(a,b) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b) ).
tff(12,plain,
equalish(a,b),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
refl(
( ( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) )
<=> ( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
rewrite(
( ( ~ equalish(X,Y)
| ~ product(W,Z,X)
| product(W,Z,Y) )
<=> ( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| ~ product(W,Z,X)
| product(W,Z,Y) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| ~ product(W,Z,X)
| product(W,Z,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',product_substitution3) ).
tff(19,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) )
| ~ product(identity,a,a)
| ~ equalish(a,b)
| product(identity,a,b) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) )
| ~ product(identity,a,a)
| ~ equalish(a,b)
| product(identity,a,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ product(identity,a,a)
| product(identity,a,b)
| ~ equalish(a,b) )
<=> ( ~ product(identity,a,a)
| ~ equalish(a,b)
| product(identity,a,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) )
| ~ product(identity,a,a)
| product(identity,a,b)
| ~ equalish(a,b) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) )
| ~ product(identity,a,a)
| ~ equalish(a,b)
| product(identity,a,b) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) )
| ~ product(identity,a,a)
| product(identity,a,b)
| ~ equalish(a,b) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) )
| ~ product(identity,a,a)
| ~ equalish(a,b)
| product(identity,a,b) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) )
| ~ product(identity,a,a)
| product(identity,a,b)
| ~ equalish(a,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(W,Z,X)
| product(W,Z,Y)
| ~ equalish(X,Y) )
| ~ product(identity,a,a)
| ~ equalish(a,b)
| product(identity,a,b) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
product(identity,a,b),
inference(unit_resolution,[status(thm)],[28,22,12,9]) ).
tff(30,plain,
( ~ equalish(b,a)
<=> ~ equalish(b,a) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
~ equalish(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetry) ).
tff(32,plain,
~ equalish(b,a),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
refl(
( ( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
<=> ( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
rewrite(
( ( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| equalish(Z,W) )
<=> ( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| equalish(Z,W) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| equalish(Z,W) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',total_function2) ).
tff(39,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(b,a)
| ~ product(identity,a,a)
| ~ product(identity,a,b) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(b,a)
| ~ product(identity,a,a)
| ~ product(identity,a,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(b,a)
| ~ product(identity,a,a)
| ~ product(identity,a,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(b,a)
| ~ product(identity,a,a)
| ~ product(identity,a,b) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
$false,
inference(unit_resolution,[status(thm)],[45,42,32,9,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP042-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 14:33:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.45 % SZS status Unsatisfiable
% 0.19/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------