TSTP Solution File: GRP012-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP012-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 22:25:25 EDT 2022
% Result : Unsatisfiable 0.90s 0.81s
% Output : Proof 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 58
% Syntax : Number of formulae : 121 ( 43 unt; 7 typ; 0 def)
% Number of atoms : 642 ( 37 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 964 ( 458 ~; 450 |; 0 &)
% ( 56 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 22 ( 22 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 : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 474 ( 438 !; 0 ?; 474 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(c_type,type,
c: $i ).
tff(identity_type,type,
identity: $i ).
tff(d_type,type,
d: $i ).
tff(b_type,type,
b: $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/sandbox2/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(inverse(b),identity,inverse(b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
product(inverse(b),identity,inverse(b)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(
( product(inverse(X),X,identity)
<=> product(inverse(X),X,identity) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] : product(inverse(X),X,identity)
<=> ! [X: $i] : product(inverse(X),X,identity) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : product(inverse(X),X,identity)
<=> ! [X: $i] : product(inverse(X),X,identity) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X: $i] : product(inverse(X),X,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
tff(14,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : product(inverse(X),X,identity)
| product(inverse(a),a,identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
product(inverse(a),a,identity),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( product(inverse(b),inverse(a),d)
<=> product(inverse(b),inverse(a),d) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
product(inverse(b),inverse(a),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_b_multiply_inverse_a_is_d) ).
tff(21,plain,
product(inverse(b),inverse(a),d),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,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(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) )
<=> ! [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)],[22]) ).
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) )
<=> ! [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(25,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(26,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)],[25]) ).
tff(27,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/GRP003-0.ax',associativity2) ).
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) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
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) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
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) ),
inference(skolemize,[status(sab)],[29]) ).
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) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,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(d,a,inverse(b))
| ~ product(inverse(b),inverse(a),d)
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(a),a,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(d,a,inverse(b))
| ~ product(inverse(b),inverse(a),d)
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(a),a,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( product(d,a,inverse(b))
| ~ product(inverse(a),a,identity)
| ~ product(inverse(b),inverse(a),d)
| ~ product(inverse(b),identity,inverse(b)) )
<=> ( product(d,a,inverse(b))
| ~ product(inverse(b),inverse(a),d)
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(a),a,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,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(d,a,inverse(b))
| ~ product(inverse(a),a,identity)
| ~ product(inverse(b),inverse(a),d)
| ~ product(inverse(b),identity,inverse(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(d,a,inverse(b))
| ~ product(inverse(b),inverse(a),d)
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(a),a,identity) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,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(d,a,inverse(b))
| ~ product(inverse(a),a,identity)
| ~ product(inverse(b),inverse(a),d)
| ~ product(inverse(b),identity,inverse(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(d,a,inverse(b))
| ~ product(inverse(b),inverse(a),d)
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(a),a,identity) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,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(d,a,inverse(b))
| ~ product(inverse(a),a,identity)
| ~ product(inverse(b),inverse(a),d)
| ~ product(inverse(b),identity,inverse(b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,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(d,a,inverse(b))
| ~ product(inverse(b),inverse(a),d)
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(a),a,identity) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
product(d,a,inverse(b)),
inference(unit_resolution,[status(thm)],[37,31,21,18,9]) ).
tff(39,plain,
( ~ ! [X: $i] : product(inverse(X),X,identity)
| product(inverse(b),b,identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
product(inverse(b),b,identity),
inference(unit_resolution,[status(thm)],[39,16]) ).
tff(41,plain,
( product(a,b,c)
<=> product(a,b,c) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_multiply_b_is_c) ).
tff(43,plain,
product(a,b,c),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,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(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(quant_intro,[status(thm)],[44]) ).
tff(46,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(47,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(48,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)],[47]) ).
tff(49,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/GRP003-0.ax',associativity1) ).
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)],[49,48]) ).
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(modus_ponens,[status(thm)],[50,46]) ).
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(skolemize,[status(sab)],[51]) ).
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) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,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(d,a,inverse(b))
| product(d,c,identity)
| ~ product(inverse(b),b,identity)
| ~ product(a,b,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(d,a,inverse(b))
| product(d,c,identity)
| ~ product(inverse(b),b,identity)
| ~ product(a,b,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( product(d,c,identity)
| ~ product(inverse(b),b,identity)
| ~ product(a,b,c)
| ~ product(d,a,inverse(b)) )
<=> ( ~ product(d,a,inverse(b))
| product(d,c,identity)
| ~ product(inverse(b),b,identity)
| ~ product(a,b,c) ) ),
inference(rewrite,[status(thm)],]) ).
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(d,c,identity)
| ~ product(inverse(b),b,identity)
| ~ product(a,b,c)
| ~ product(d,a,inverse(b)) )
<=> ( ~ ! [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(d,a,inverse(b))
| product(d,c,identity)
| ~ product(inverse(b),b,identity)
| ~ product(a,b,c) ) ),
inference(monotonicity,[status(thm)],[55]) ).
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(d,c,identity)
| ~ product(inverse(b),b,identity)
| ~ product(a,b,c)
| ~ product(d,a,inverse(b)) )
<=> ( ~ ! [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(d,a,inverse(b))
| product(d,c,identity)
| ~ product(inverse(b),b,identity)
| ~ product(a,b,c) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
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(d,c,identity)
| ~ product(inverse(b),b,identity)
| ~ product(a,b,c)
| ~ product(d,a,inverse(b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,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(d,a,inverse(b))
| product(d,c,identity)
| ~ product(inverse(b),b,identity)
| ~ product(a,b,c) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
product(d,c,identity),
inference(unit_resolution,[status(thm)],[59,53,43,40,38]) ).
tff(61,plain,
^ [X: $i] :
refl(
( product(identity,X,X)
<=> product(identity,X,X) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
! [X: $i] : product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
tff(65,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [X: $i] : product(identity,X,X),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,inverse(c),inverse(c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
product(identity,inverse(c),inverse(c)),
inference(unit_resolution,[status(thm)],[68,67]) ).
tff(70,plain,
^ [X: $i] :
refl(
( product(X,inverse(X),identity)
<=> product(X,inverse(X),identity) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [X: $i] : product(X,inverse(X),identity)
<=> ! [X: $i] : product(X,inverse(X),identity) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [X: $i] : product(X,inverse(X),identity)
<=> ! [X: $i] : product(X,inverse(X),identity) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
! [X: $i] : product(X,inverse(X),identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
tff(74,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ~ ! [X: $i] : product(X,inverse(X),identity)
| product(c,inverse(c),identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
product(c,inverse(c),identity),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,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,inverse(c),inverse(c))
| ~ product(c,inverse(c),identity)
| ~ product(d,c,identity)
| product(d,identity,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(identity,inverse(c),inverse(c))
| ~ product(c,inverse(c),identity)
| ~ product(d,c,identity)
| product(d,identity,inverse(c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ( product(d,identity,inverse(c))
| ~ product(identity,inverse(c),inverse(c))
| ~ product(c,inverse(c),identity)
| ~ product(d,c,identity) )
<=> ( ~ product(identity,inverse(c),inverse(c))
| ~ product(c,inverse(c),identity)
| ~ product(d,c,identity)
| product(d,identity,inverse(c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,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(d,identity,inverse(c))
| ~ product(identity,inverse(c),inverse(c))
| ~ product(c,inverse(c),identity)
| ~ product(d,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(identity,inverse(c),inverse(c))
| ~ product(c,inverse(c),identity)
| ~ product(d,c,identity)
| product(d,identity,inverse(c)) ) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,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(d,identity,inverse(c))
| ~ product(identity,inverse(c),inverse(c))
| ~ product(c,inverse(c),identity)
| ~ product(d,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(identity,inverse(c),inverse(c))
| ~ product(c,inverse(c),identity)
| ~ product(d,c,identity)
| product(d,identity,inverse(c)) ) ),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,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(d,identity,inverse(c))
| ~ product(identity,inverse(c),inverse(c))
| ~ product(c,inverse(c),identity)
| ~ product(d,c,identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,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,inverse(c),inverse(c))
| ~ product(c,inverse(c),identity)
| ~ product(d,c,identity)
| product(d,identity,inverse(c)) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
product(d,identity,inverse(c)),
inference(unit_resolution,[status(thm)],[84,53,78,69,60]) ).
tff(86,plain,
( ~ ! [X: $i] : product(X,inverse(X),identity)
| product(a,inverse(a),identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
product(a,inverse(a),identity),
inference(unit_resolution,[status(thm)],[86,76]) ).
tff(88,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(d,a,inverse(b))
| ~ product(a,inverse(a),identity)
| ~ product(inverse(b),inverse(a),d)
| product(d,identity,d) )
<=> ( ~ ! [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(d,a,inverse(b))
| ~ product(a,inverse(a),identity)
| ~ product(inverse(b),inverse(a),d)
| product(d,identity,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( product(d,identity,d)
| ~ product(inverse(b),inverse(a),d)
| ~ product(a,inverse(a),identity)
| ~ product(d,a,inverse(b)) )
<=> ( ~ product(d,a,inverse(b))
| ~ product(a,inverse(a),identity)
| ~ product(inverse(b),inverse(a),d)
| product(d,identity,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,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(d,identity,d)
| ~ product(inverse(b),inverse(a),d)
| ~ product(a,inverse(a),identity)
| ~ product(d,a,inverse(b)) )
<=> ( ~ ! [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(d,a,inverse(b))
| ~ product(a,inverse(a),identity)
| ~ product(inverse(b),inverse(a),d)
| product(d,identity,d) ) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,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(d,identity,d)
| ~ product(inverse(b),inverse(a),d)
| ~ product(a,inverse(a),identity)
| ~ product(d,a,inverse(b)) )
<=> ( ~ ! [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(d,a,inverse(b))
| ~ product(a,inverse(a),identity)
| ~ product(inverse(b),inverse(a),d)
| product(d,identity,d) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,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(d,identity,d)
| ~ product(inverse(b),inverse(a),d)
| ~ product(a,inverse(a),identity)
| ~ product(d,a,inverse(b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,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(d,a,inverse(b))
| ~ product(a,inverse(a),identity)
| ~ product(inverse(b),inverse(a),d)
| product(d,identity,d) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
product(d,identity,d),
inference(unit_resolution,[status(thm)],[93,53,21,87,38]) ).
tff(95,plain,
( ( inverse(c) != d )
<=> ( inverse(c) != d ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,axiom,
inverse(c) != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_inverse_equals_d) ).
tff(97,plain,
inverse(c) != d,
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,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(99,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)],[98]) ).
tff(100,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(101,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(102,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)],[101]) ).
tff(103,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function2) ).
tff(104,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(skolemize,[status(sab)],[105]) ).
tff(107,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[106,99]) ).
tff(108,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(c) = d )
| ~ product(d,identity,inverse(c))
| ~ product(d,identity,d) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(c) = d )
| ~ product(d,identity,inverse(c))
| ~ product(d,identity,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ( ( inverse(c) = d )
| ~ product(d,identity,d)
| ~ product(d,identity,inverse(c)) )
<=> ( ( inverse(c) = d )
| ~ product(d,identity,inverse(c))
| ~ product(d,identity,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(c) = d )
| ~ product(d,identity,d)
| ~ product(d,identity,inverse(c)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(c) = d )
| ~ product(d,identity,inverse(c))
| ~ product(d,identity,d) ) ),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(c) = d )
| ~ product(d,identity,d)
| ~ product(d,identity,inverse(c)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(c) = d )
| ~ product(d,identity,inverse(c))
| ~ product(d,identity,d) ) ),
inference(transitivity,[status(thm)],[110,108]) ).
tff(112,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(c) = d )
| ~ product(d,identity,d)
| ~ product(d,identity,inverse(c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(c) = d )
| ~ product(d,identity,inverse(c))
| ~ product(d,identity,d) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
$false,
inference(unit_resolution,[status(thm)],[113,107,97,94,85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP012-2 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n018.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 : Wed Aug 31 14:08:41 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.
% 0.90/0.81 % SZS status Unsatisfiable
% 0.90/0.81 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------