TSTP Solution File: GRP047-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP047-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 22:25:40 EDT 2022
% Result : Unsatisfiable 17.06s 11.31s
% Output : Proof 17.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 61
% Syntax : Number of formulae : 128 ( 40 unt; 8 typ; 0 def)
% Number of atoms : 690 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1044 ( 497 ~; 489 |; 0 &)
% ( 58 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 23 ( 23 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 545 ( 501 !; 0 ?; 545 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(identity_type,type,
identity: $i ).
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(inverse_type,type,
inverse: $i > $i ).
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/sandbox2/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/sandbox2/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/sandbox2/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,
^ [X: $i] :
refl(
( product(inverse(X),X,identity)
<=> product(inverse(X),X,identity) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X: $i] : product(inverse(X),X,identity)
<=> ! [X: $i] : product(inverse(X),X,identity) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X: $i] : product(inverse(X),X,identity)
<=> ! [X: $i] : product(inverse(X),X,identity) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
! [X: $i] : product(inverse(X),X,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_inverse) ).
tff(34,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [X: $i] : product(inverse(X),X,identity)
| product(inverse(inverse(c)),inverse(c),identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
product(inverse(inverse(c)),inverse(c),identity),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
product(identity,c,c),
inference(unit_resolution,[status(thm)],[39,7]) ).
tff(41,plain,
( ~ ! [X: $i] : product(inverse(X),X,identity)
| product(inverse(c),c,identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
product(inverse(c),c,identity),
inference(unit_resolution,[status(thm)],[41,36]) ).
tff(43,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(
( ( product(X,V,W)
| ~ 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) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,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(U,Z,W) )
<=> ( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ) )),
( ( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) )
<=> ( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) )),
rewrite(
( ( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
<=> ( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ) )),
( ( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) )
<=> ( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',associativity1) ).
tff(49,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(modus_ponens,[status(thm)],[51,44]) ).
tff(53,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(inverse(c),c,identity)
| ~ product(identity,c,c)
| ~ product(inverse(inverse(c)),inverse(c),identity)
| product(inverse(inverse(c)),identity,c) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(inverse(c),c,identity)
| ~ product(identity,c,c)
| ~ product(inverse(inverse(c)),inverse(c),identity)
| product(inverse(inverse(c)),identity,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ( product(inverse(inverse(c)),identity,c)
| ~ product(identity,c,c)
| ~ product(inverse(c),c,identity)
| ~ product(inverse(inverse(c)),inverse(c),identity) )
<=> ( ~ product(inverse(c),c,identity)
| ~ product(identity,c,c)
| ~ product(inverse(inverse(c)),inverse(c),identity)
| product(inverse(inverse(c)),identity,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| product(inverse(inverse(c)),identity,c)
| ~ product(identity,c,c)
| ~ product(inverse(c),c,identity)
| ~ product(inverse(inverse(c)),inverse(c),identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(inverse(c),c,identity)
| ~ product(identity,c,c)
| ~ product(inverse(inverse(c)),inverse(c),identity)
| product(inverse(inverse(c)),identity,c) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| product(inverse(inverse(c)),identity,c)
| ~ product(identity,c,c)
| ~ product(inverse(c),c,identity)
| ~ product(inverse(inverse(c)),inverse(c),identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(inverse(c),c,identity)
| ~ product(identity,c,c)
| ~ product(inverse(inverse(c)),inverse(c),identity)
| product(inverse(inverse(c)),identity,c) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| product(inverse(inverse(c)),identity,c)
| ~ product(identity,c,c)
| ~ product(inverse(c),c,identity)
| ~ product(inverse(inverse(c)),inverse(c),identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(inverse(c),c,identity)
| ~ product(identity,c,c)
| ~ product(inverse(inverse(c)),inverse(c),identity)
| product(inverse(inverse(c)),identity,c) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
product(inverse(inverse(c)),identity,c),
inference(unit_resolution,[status(thm)],[58,52,42,40,38]) ).
tff(60,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,inverse(c),inverse(c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
product(identity,inverse(c),inverse(c)),
inference(unit_resolution,[status(thm)],[60,7]) ).
tff(62,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(inverse(c),c,identity)
| ~ product(identity,inverse(c),inverse(c))
| product(identity,identity,identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(inverse(c),c,identity)
| ~ product(identity,inverse(c),inverse(c))
| product(identity,identity,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ( product(identity,identity,identity)
| ~ product(inverse(c),c,identity)
| ~ product(inverse(c),c,identity)
| ~ product(identity,inverse(c),inverse(c)) )
<=> ( ~ product(inverse(c),c,identity)
| ~ product(identity,inverse(c),inverse(c))
| product(identity,identity,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| product(identity,identity,identity)
| ~ product(inverse(c),c,identity)
| ~ product(inverse(c),c,identity)
| ~ product(identity,inverse(c),inverse(c)) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(inverse(c),c,identity)
| ~ product(identity,inverse(c),inverse(c))
| product(identity,identity,identity) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| product(identity,identity,identity)
| ~ product(inverse(c),c,identity)
| ~ product(inverse(c),c,identity)
| ~ product(identity,inverse(c),inverse(c)) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(inverse(c),c,identity)
| ~ product(identity,inverse(c),inverse(c))
| product(identity,identity,identity) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| product(identity,identity,identity)
| ~ product(inverse(c),c,identity)
| ~ product(inverse(c),c,identity)
| ~ product(identity,inverse(c),inverse(c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(inverse(c),c,identity)
| ~ product(identity,inverse(c),inverse(c))
| product(identity,identity,identity) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
product(identity,identity,identity),
inference(unit_resolution,[status(thm)],[67,52,42,61]) ).
tff(69,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(70,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)],[69]) ).
tff(71,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(72,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(73,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)],[72]) ).
tff(74,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/sandbox2/benchmark/Axioms/GRP005-0.ax',associativity2) ).
tff(75,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)],[74,73]) ).
tff(76,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)],[75,71]) ).
tff(77,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)],[76]) ).
tff(78,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)],[77,70]) ).
tff(79,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(inverse(inverse(c)),identity,c)
| product(c,identity,c)
| ~ product(identity,identity,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(inverse(inverse(c)),identity,c)
| product(c,identity,c)
| ~ product(identity,identity,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ( product(c,identity,c)
| ~ product(identity,identity,identity)
| ~ product(inverse(inverse(c)),identity,c)
| ~ product(inverse(inverse(c)),identity,c) )
<=> ( ~ product(inverse(inverse(c)),identity,c)
| product(c,identity,c)
| ~ product(identity,identity,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,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(c,identity,c)
| ~ product(identity,identity,identity)
| ~ product(inverse(inverse(c)),identity,c)
| ~ product(inverse(inverse(c)),identity,c) )
<=> ( ~ ! [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(inverse(inverse(c)),identity,c)
| product(c,identity,c)
| ~ product(identity,identity,identity) ) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,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(c,identity,c)
| ~ product(identity,identity,identity)
| ~ product(inverse(inverse(c)),identity,c)
| ~ product(inverse(inverse(c)),identity,c) )
<=> ( ~ ! [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(inverse(inverse(c)),identity,c)
| product(c,identity,c)
| ~ product(identity,identity,identity) ) ),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,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(c,identity,c)
| ~ product(identity,identity,identity)
| ~ product(inverse(inverse(c)),identity,c)
| ~ product(inverse(inverse(c)),identity,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,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(inverse(inverse(c)),identity,c)
| product(c,identity,c)
| ~ product(identity,identity,identity) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
product(c,identity,c),
inference(unit_resolution,[status(thm)],[84,78,68,59]) ).
tff(86,plain,
^ [Y: $i,X: $i] :
refl(
( product(X,Y,multiply(X,Y))
<=> product(X,Y,multiply(X,Y)) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
<=> ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
( ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
<=> ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)) ),
inference(rewrite,[status(thm)],]) ).
tff(89,axiom,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function1) ).
tff(90,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(modus_ponens,[status(thm)],[91,87]) ).
tff(93,plain,
( ~ ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
| product(c,a,multiply(c,a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
product(c,a,multiply(c,a)),
inference(unit_resolution,[status(thm)],[93,92]) ).
tff(95,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(c,a,multiply(c,a))
| ~ product(identity,a,b)
| ~ product(c,identity,c)
| product(c,b,multiply(c,a)) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(c,a,multiply(c,a))
| ~ product(identity,a,b)
| ~ product(c,identity,c)
| product(c,b,multiply(c,a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ( product(c,b,multiply(c,a))
| ~ product(c,a,multiply(c,a))
| ~ product(identity,a,b)
| ~ product(c,identity,c) )
<=> ( ~ product(c,a,multiply(c,a))
| ~ product(identity,a,b)
| ~ product(c,identity,c)
| product(c,b,multiply(c,a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| product(c,b,multiply(c,a))
| ~ product(c,a,multiply(c,a))
| ~ product(identity,a,b)
| ~ product(c,identity,c) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(c,a,multiply(c,a))
| ~ product(identity,a,b)
| ~ product(c,identity,c)
| product(c,b,multiply(c,a)) ) ),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| product(c,b,multiply(c,a))
| ~ product(c,a,multiply(c,a))
| ~ product(identity,a,b)
| ~ product(c,identity,c) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(c,a,multiply(c,a))
| ~ product(identity,a,b)
| ~ product(c,identity,c)
| product(c,b,multiply(c,a)) ) ),
inference(transitivity,[status(thm)],[97,95]) ).
tff(99,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| product(c,b,multiply(c,a))
| ~ product(c,a,multiply(c,a))
| ~ product(identity,a,b)
| ~ product(c,identity,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(c,a,multiply(c,a))
| ~ product(identity,a,b)
| ~ product(c,identity,c)
| product(c,b,multiply(c,a)) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
product(c,b,multiply(c,a)),
inference(unit_resolution,[status(thm)],[100,52,94,85,29]) ).
tff(102,plain,
( ~ ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
| product(c,b,multiply(c,b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
product(c,b,multiply(c,b)),
inference(unit_resolution,[status(thm)],[102,92]) ).
tff(104,plain,
( ~ equalish(multiply(c,a),multiply(c,b))
<=> ~ equalish(multiply(c,a),multiply(c,b)) ),
inference(rewrite,[status(thm)],]) ).
tff(105,axiom,
~ equalish(multiply(c,a),multiply(c,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_multiply_substitution2) ).
tff(106,plain,
~ equalish(multiply(c,a),multiply(c,b)),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,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(108,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)],[107]) ).
tff(109,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(110,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(111,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)],[110]) ).
tff(112,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| equalish(Z,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function2) ).
tff(113,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)],[112,111]) ).
tff(114,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)],[113,109]) ).
tff(115,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(skolemize,[status(sab)],[114]) ).
tff(116,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)],[115,108]) ).
tff(117,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(multiply(c,a),multiply(c,b))
| ~ product(c,b,multiply(c,b))
| ~ product(c,b,multiply(c,a)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(multiply(c,a),multiply(c,b))
| ~ product(c,b,multiply(c,b))
| ~ product(c,b,multiply(c,a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(multiply(c,a),multiply(c,b))
| ~ product(c,b,multiply(c,b))
| ~ product(c,b,multiply(c,a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(multiply(c,a),multiply(c,b))
| ~ product(c,b,multiply(c,b))
| ~ product(c,b,multiply(c,a)) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
$false,
inference(unit_resolution,[status(thm)],[119,116,106,103,101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP047-2 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 14:19:47 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.
% 17.06/11.31 % SZS status Unsatisfiable
% 17.06/11.31 % SZS output start Proof
% See solution above
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