TSTP Solution File: GRP001-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 22:25:18 EDT 2022
% Result : Unsatisfiable 0.55s 0.63s
% Output : Proof 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 82
% Syntax : Number of formulae : 191 ( 70 unt; 7 typ; 0 def)
% Number of atoms : 963 ( 75 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1437 ( 682 ~; 672 |; 0 &)
% ( 83 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 670 ( 631 !; 0 ?; 670 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(c_type,type,
c: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( product(X,X,identity)
<=> product(X,X,identity) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : product(X,X,identity)
<=> ! [X: $i] : product(X,X,identity) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : product(X,X,identity)
<=> ! [X: $i] : product(X,X,identity) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : product(X,X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square_element) ).
tff(5,plain,
! [X: $i] : product(X,X,identity),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : product(X,X,identity),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : product(X,X,identity),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : product(X,X,identity)
| product(inverse(b),inverse(b),identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
product(inverse(b),inverse(b),identity),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(
( product(identity,X,X)
<=> product(identity,X,X) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X: $i] : product(identity,X,X),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
tff(14,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : product(identity,X,X),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,b,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
product(identity,b,b),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X: $i] :
refl(
( product(inverse(X),X,identity)
<=> product(inverse(X),X,identity) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X: $i] : product(inverse(X),X,identity)
<=> ! [X: $i] : product(inverse(X),X,identity) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X: $i] : product(inverse(X),X,identity)
<=> ! [X: $i] : product(inverse(X),X,identity) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [X: $i] : product(inverse(X),X,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
tff(23,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [X: $i] : product(inverse(X),X,identity)
| product(inverse(b),b,identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
product(inverse(b),b,identity),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,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(29,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)],[28]) ).
tff(30,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(31,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(32,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)],[31]) ).
tff(33,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/sandbox/benchmark/Axioms/GRP003-0.ax',associativity1) ).
tff(34,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)],[33,32]) ).
tff(35,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)],[34,30]) ).
tff(36,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)],[35]) ).
tff(37,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)],[36,29]) ).
tff(38,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,b,b)
| product(inverse(b),identity,b)
| ~ product(inverse(b),b,identity)
| ~ product(inverse(b),inverse(b),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,b,b)
| product(inverse(b),identity,b)
| ~ product(inverse(b),b,identity)
| ~ product(inverse(b),inverse(b),identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ( product(inverse(b),identity,b)
| ~ product(identity,b,b)
| ~ product(inverse(b),b,identity)
| ~ product(inverse(b),inverse(b),identity) )
<=> ( ~ product(identity,b,b)
| product(inverse(b),identity,b)
| ~ product(inverse(b),b,identity)
| ~ product(inverse(b),inverse(b),identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,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(b),identity,b)
| ~ product(identity,b,b)
| ~ product(inverse(b),b,identity)
| ~ product(inverse(b),inverse(b),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,b,b)
| product(inverse(b),identity,b)
| ~ product(inverse(b),b,identity)
| ~ product(inverse(b),inverse(b),identity) ) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,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(b),identity,b)
| ~ product(identity,b,b)
| ~ product(inverse(b),b,identity)
| ~ product(inverse(b),inverse(b),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,b,b)
| product(inverse(b),identity,b)
| ~ product(inverse(b),b,identity)
| ~ product(inverse(b),inverse(b),identity) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,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(b),identity,b)
| ~ product(identity,b,b)
| ~ product(inverse(b),b,identity)
| ~ product(inverse(b),inverse(b),identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,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,b,b)
| product(inverse(b),identity,b)
| ~ product(inverse(b),b,identity)
| ~ product(inverse(b),inverse(b),identity) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
product(inverse(b),identity,b),
inference(unit_resolution,[status(thm)],[43,37,27,18,9]) ).
tff(45,plain,
^ [X: $i] :
refl(
( product(X,identity,X)
<=> product(X,identity,X) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [X: $i] : product(X,identity,X)
<=> ! [X: $i] : product(X,identity,X) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [X: $i] : product(X,identity,X)
<=> ! [X: $i] : product(X,identity,X) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
! [X: $i] : product(X,identity,X),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
tff(49,plain,
! [X: $i] : product(X,identity,X),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [X: $i] : product(X,identity,X),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [X: $i] : product(X,identity,X),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [X: $i] : product(X,identity,X)
| product(inverse(b),identity,inverse(b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
product(inverse(b),identity,inverse(b)),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,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(55,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)],[54]) ).
tff(56,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(57,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(58,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)],[57]) ).
tff(59,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(60,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[62,55]) ).
tff(64,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(b),identity,b)
| ( b = inverse(b) ) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(b),identity,b)
| ( b = inverse(b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ( ( b = inverse(b) )
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(b),identity,b) )
<=> ( ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(b),identity,b)
| ( b = inverse(b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( b = inverse(b) )
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(b),identity,b) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(b),identity,b)
| ( b = inverse(b) ) ) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( b = inverse(b) )
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(b),identity,b) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(b),identity,b)
| ( b = inverse(b) ) ) ),
inference(transitivity,[status(thm)],[66,64]) ).
tff(68,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( b = inverse(b) )
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(b),identity,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(inverse(b),identity,inverse(b))
| ~ product(inverse(b),identity,b)
| ( b = inverse(b) ) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
b = inverse(b),
inference(unit_resolution,[status(thm)],[69,63,53,44]) ).
tff(71,plain,
inverse(b) = b,
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( product(multiply(inverse(c),a),inverse(b),identity)
<=> product(multiply(inverse(c),a),b,identity) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( product(multiply(inverse(c),a),b,identity)
<=> product(multiply(inverse(c),a),inverse(b),identity) ),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
^ [X: $i] :
refl(
( product(X,inverse(X),identity)
<=> product(X,inverse(X),identity) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [X: $i] : product(X,inverse(X),identity)
<=> ! [X: $i] : product(X,inverse(X),identity) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [X: $i] : product(X,inverse(X),identity)
<=> ! [X: $i] : product(X,inverse(X),identity) ),
inference(rewrite,[status(thm)],]) ).
tff(77,axiom,
! [X: $i] : product(X,inverse(X),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
tff(78,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
( ~ ! [X: $i] : product(X,inverse(X),identity)
| product(c,inverse(c),identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
product(c,inverse(c),identity),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
( ~ ! [X: $i] : product(X,identity,X)
| product(c,identity,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
product(c,identity,c),
inference(unit_resolution,[status(thm)],[83,51]) ).
tff(85,plain,
( ~ ! [X: $i] : product(X,X,identity)
| product(c,c,identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
product(c,c,identity),
inference(unit_resolution,[status(thm)],[85,7]) ).
tff(87,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(88,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)],[87]) ).
tff(89,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(90,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(91,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)],[90]) ).
tff(92,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(93,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)],[92,91]) ).
tff(94,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)],[93,89]) ).
tff(95,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)],[94]) ).
tff(96,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)],[95,88]) ).
tff(97,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,inverse(c),identity)
| product(identity,inverse(c),c)
| ~ product(c,identity,c)
| ~ product(c,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(c,inverse(c),identity)
| product(identity,inverse(c),c)
| ~ product(c,identity,c)
| ~ product(c,c,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ( product(identity,inverse(c),c)
| ~ product(c,inverse(c),identity)
| ~ product(c,c,identity)
| ~ product(c,identity,c) )
<=> ( ~ product(c,inverse(c),identity)
| product(identity,inverse(c),c)
| ~ product(c,identity,c)
| ~ product(c,c,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,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,inverse(c),c)
| ~ product(c,inverse(c),identity)
| ~ product(c,c,identity)
| ~ product(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(c,inverse(c),identity)
| product(identity,inverse(c),c)
| ~ product(c,identity,c)
| ~ product(c,c,identity) ) ),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,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,inverse(c),c)
| ~ product(c,inverse(c),identity)
| ~ product(c,c,identity)
| ~ product(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(c,inverse(c),identity)
| product(identity,inverse(c),c)
| ~ product(c,identity,c)
| ~ product(c,c,identity) ) ),
inference(transitivity,[status(thm)],[99,97]) ).
tff(101,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,inverse(c),c)
| ~ product(c,inverse(c),identity)
| ~ product(c,c,identity)
| ~ product(c,identity,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,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,inverse(c),identity)
| product(identity,inverse(c),c)
| ~ product(c,identity,c)
| ~ product(c,c,identity) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
product(identity,inverse(c),c),
inference(unit_resolution,[status(thm)],[102,96,86,84,82]) ).
tff(104,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,inverse(c),inverse(c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
product(identity,inverse(c),inverse(c)),
inference(unit_resolution,[status(thm)],[104,16]) ).
tff(106,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(identity,inverse(c),c)
| ( inverse(c) = c )
| ~ product(identity,inverse(c),inverse(c)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(identity,inverse(c),c)
| ( inverse(c) = c )
| ~ product(identity,inverse(c),inverse(c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ( ( inverse(c) = c )
| ~ product(identity,inverse(c),c)
| ~ product(identity,inverse(c),inverse(c)) )
<=> ( ~ product(identity,inverse(c),c)
| ( inverse(c) = c )
| ~ product(identity,inverse(c),inverse(c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(c) = c )
| ~ product(identity,inverse(c),c)
| ~ product(identity,inverse(c),inverse(c)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(identity,inverse(c),c)
| ( inverse(c) = c )
| ~ product(identity,inverse(c),inverse(c)) ) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(c) = c )
| ~ product(identity,inverse(c),c)
| ~ product(identity,inverse(c),inverse(c)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(identity,inverse(c),c)
| ( inverse(c) = c )
| ~ product(identity,inverse(c),inverse(c)) ) ),
inference(transitivity,[status(thm)],[108,106]) ).
tff(110,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(c) = c )
| ~ product(identity,inverse(c),c)
| ~ product(identity,inverse(c),inverse(c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(identity,inverse(c),c)
| ( inverse(c) = c )
| ~ product(identity,inverse(c),inverse(c)) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
inverse(c) = c,
inference(unit_resolution,[status(thm)],[111,63,105,103]) ).
tff(113,plain,
c = inverse(c),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
( product(c,a,multiply(inverse(c),a))
<=> product(inverse(c),a,multiply(inverse(c),a)) ),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
( product(inverse(c),a,multiply(inverse(c),a))
<=> product(c,a,multiply(inverse(c),a)) ),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
^ [Y: $i,X: $i] :
refl(
( product(X,Y,multiply(X,Y))
<=> product(X,Y,multiply(X,Y)) )),
inference(bind,[status(th)],]) ).
tff(117,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)],[116]) ).
tff(118,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(119,axiom,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).
tff(120,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(skolemize,[status(sab)],[120]) ).
tff(122,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(modus_ponens,[status(thm)],[121,117]) ).
tff(123,plain,
( ~ ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
| product(inverse(c),a,multiply(inverse(c),a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(124,plain,
product(inverse(c),a,multiply(inverse(c),a)),
inference(unit_resolution,[status(thm)],[123,122]) ).
tff(125,plain,
product(c,a,multiply(inverse(c),a)),
inference(modus_ponens,[status(thm)],[124,115]) ).
tff(126,plain,
( product(a,b,c)
<=> product(a,b,c) ),
inference(rewrite,[status(thm)],]) ).
tff(127,axiom,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
tff(128,plain,
product(a,b,c),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,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(a,b,c)
| product(multiply(inverse(c),a),b,identity)
| ~ product(c,a,multiply(inverse(c),a))
| ~ product(c,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(a,b,c)
| product(multiply(inverse(c),a),b,identity)
| ~ product(c,a,multiply(inverse(c),a))
| ~ product(c,c,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
( ( product(multiply(inverse(c),a),b,identity)
| ~ product(a,b,c)
| ~ product(c,a,multiply(inverse(c),a))
| ~ product(c,c,identity) )
<=> ( ~ product(a,b,c)
| product(multiply(inverse(c),a),b,identity)
| ~ product(c,a,multiply(inverse(c),a))
| ~ product(c,c,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,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(multiply(inverse(c),a),b,identity)
| ~ product(a,b,c)
| ~ product(c,a,multiply(inverse(c),a))
| ~ product(c,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(a,b,c)
| product(multiply(inverse(c),a),b,identity)
| ~ product(c,a,multiply(inverse(c),a))
| ~ product(c,c,identity) ) ),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,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(multiply(inverse(c),a),b,identity)
| ~ product(a,b,c)
| ~ product(c,a,multiply(inverse(c),a))
| ~ product(c,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(a,b,c)
| product(multiply(inverse(c),a),b,identity)
| ~ product(c,a,multiply(inverse(c),a))
| ~ product(c,c,identity) ) ),
inference(transitivity,[status(thm)],[131,129]) ).
tff(133,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(multiply(inverse(c),a),b,identity)
| ~ product(a,b,c)
| ~ product(c,a,multiply(inverse(c),a))
| ~ product(c,c,identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,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(a,b,c)
| product(multiply(inverse(c),a),b,identity)
| ~ product(c,a,multiply(inverse(c),a))
| ~ product(c,c,identity) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
( product(multiply(inverse(c),a),b,identity)
| ~ product(c,a,multiply(inverse(c),a)) ),
inference(unit_resolution,[status(thm)],[134,96,128,86]) ).
tff(136,plain,
product(multiply(inverse(c),a),b,identity),
inference(unit_resolution,[status(thm)],[135,125]) ).
tff(137,plain,
product(multiply(inverse(c),a),inverse(b),identity),
inference(modus_ponens,[status(thm)],[136,73]) ).
tff(138,plain,
( ~ ! [X: $i] : product(X,X,identity)
| product(multiply(inverse(c),a),multiply(inverse(c),a),identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(139,plain,
product(multiply(inverse(c),a),multiply(inverse(c),a),identity),
inference(unit_resolution,[status(thm)],[138,7]) ).
tff(140,plain,
( ~ ! [X: $i] : product(X,identity,X)
| product(multiply(inverse(c),a),identity,multiply(inverse(c),a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(141,plain,
product(multiply(inverse(c),a),identity,multiply(inverse(c),a)),
inference(unit_resolution,[status(thm)],[140,51]) ).
tff(142,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(multiply(inverse(c),a),identity,multiply(inverse(c),a))
| product(identity,inverse(b),multiply(inverse(c),a))
| ~ product(multiply(inverse(c),a),inverse(b),identity)
| ~ product(multiply(inverse(c),a),multiply(inverse(c),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(multiply(inverse(c),a),identity,multiply(inverse(c),a))
| product(identity,inverse(b),multiply(inverse(c),a))
| ~ product(multiply(inverse(c),a),inverse(b),identity)
| ~ product(multiply(inverse(c),a),multiply(inverse(c),a),identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
( ( product(identity,inverse(b),multiply(inverse(c),a))
| ~ product(multiply(inverse(c),a),inverse(b),identity)
| ~ product(multiply(inverse(c),a),multiply(inverse(c),a),identity)
| ~ product(multiply(inverse(c),a),identity,multiply(inverse(c),a)) )
<=> ( ~ product(multiply(inverse(c),a),identity,multiply(inverse(c),a))
| product(identity,inverse(b),multiply(inverse(c),a))
| ~ product(multiply(inverse(c),a),inverse(b),identity)
| ~ product(multiply(inverse(c),a),multiply(inverse(c),a),identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(144,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,inverse(b),multiply(inverse(c),a))
| ~ product(multiply(inverse(c),a),inverse(b),identity)
| ~ product(multiply(inverse(c),a),multiply(inverse(c),a),identity)
| ~ product(multiply(inverse(c),a),identity,multiply(inverse(c),a)) )
<=> ( ~ ! [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(multiply(inverse(c),a),identity,multiply(inverse(c),a))
| product(identity,inverse(b),multiply(inverse(c),a))
| ~ product(multiply(inverse(c),a),inverse(b),identity)
| ~ product(multiply(inverse(c),a),multiply(inverse(c),a),identity) ) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,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,inverse(b),multiply(inverse(c),a))
| ~ product(multiply(inverse(c),a),inverse(b),identity)
| ~ product(multiply(inverse(c),a),multiply(inverse(c),a),identity)
| ~ product(multiply(inverse(c),a),identity,multiply(inverse(c),a)) )
<=> ( ~ ! [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(multiply(inverse(c),a),identity,multiply(inverse(c),a))
| product(identity,inverse(b),multiply(inverse(c),a))
| ~ product(multiply(inverse(c),a),inverse(b),identity)
| ~ product(multiply(inverse(c),a),multiply(inverse(c),a),identity) ) ),
inference(transitivity,[status(thm)],[144,142]) ).
tff(146,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,inverse(b),multiply(inverse(c),a))
| ~ product(multiply(inverse(c),a),inverse(b),identity)
| ~ product(multiply(inverse(c),a),multiply(inverse(c),a),identity)
| ~ product(multiply(inverse(c),a),identity,multiply(inverse(c),a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(147,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(multiply(inverse(c),a),identity,multiply(inverse(c),a))
| product(identity,inverse(b),multiply(inverse(c),a))
| ~ product(multiply(inverse(c),a),inverse(b),identity)
| ~ product(multiply(inverse(c),a),multiply(inverse(c),a),identity) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
( product(identity,inverse(b),multiply(inverse(c),a))
| ~ product(multiply(inverse(c),a),inverse(b),identity) ),
inference(unit_resolution,[status(thm)],[147,96,141,139]) ).
tff(149,plain,
product(identity,inverse(b),multiply(inverse(c),a)),
inference(unit_resolution,[status(thm)],[148,137]) ).
tff(150,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,inverse(b),inverse(b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(151,plain,
product(identity,inverse(b),inverse(b)),
inference(unit_resolution,[status(thm)],[150,16]) ).
tff(152,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(identity,inverse(b),inverse(b))
| ( multiply(inverse(c),a) = inverse(b) )
| ~ product(identity,inverse(b),multiply(inverse(c),a)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(identity,inverse(b),inverse(b))
| ( multiply(inverse(c),a) = inverse(b) )
| ~ product(identity,inverse(b),multiply(inverse(c),a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(153,plain,
( ( ( multiply(inverse(c),a) = inverse(b) )
| ~ product(identity,inverse(b),inverse(b))
| ~ product(identity,inverse(b),multiply(inverse(c),a)) )
<=> ( ~ product(identity,inverse(b),inverse(b))
| ( multiply(inverse(c),a) = inverse(b) )
| ~ product(identity,inverse(b),multiply(inverse(c),a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(154,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( multiply(inverse(c),a) = inverse(b) )
| ~ product(identity,inverse(b),inverse(b))
| ~ product(identity,inverse(b),multiply(inverse(c),a)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(identity,inverse(b),inverse(b))
| ( multiply(inverse(c),a) = inverse(b) )
| ~ product(identity,inverse(b),multiply(inverse(c),a)) ) ),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( multiply(inverse(c),a) = inverse(b) )
| ~ product(identity,inverse(b),inverse(b))
| ~ product(identity,inverse(b),multiply(inverse(c),a)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(identity,inverse(b),inverse(b))
| ( multiply(inverse(c),a) = inverse(b) )
| ~ product(identity,inverse(b),multiply(inverse(c),a)) ) ),
inference(transitivity,[status(thm)],[154,152]) ).
tff(156,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( multiply(inverse(c),a) = inverse(b) )
| ~ product(identity,inverse(b),inverse(b))
| ~ product(identity,inverse(b),multiply(inverse(c),a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(157,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(identity,inverse(b),inverse(b))
| ( multiply(inverse(c),a) = inverse(b) )
| ~ product(identity,inverse(b),multiply(inverse(c),a)) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
multiply(inverse(c),a) = inverse(b),
inference(unit_resolution,[status(thm)],[157,63,151,149]) ).
tff(159,plain,
inverse(b) = multiply(inverse(c),a),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
( product(c,a,inverse(b))
<=> product(inverse(c),a,multiply(inverse(c),a)) ),
inference(monotonicity,[status(thm)],[113,159]) ).
tff(161,plain,
( product(inverse(c),a,multiply(inverse(c),a))
<=> product(c,a,inverse(b)) ),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
product(c,a,inverse(b)),
inference(modus_ponens,[status(thm)],[124,161]) ).
tff(163,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(164,plain,
product(identity,a,a),
inference(unit_resolution,[status(thm)],[163,16]) ).
tff(165,plain,
( ~ product(b,a,c)
<=> ~ product(b,a,c) ),
inference(rewrite,[status(thm)],]) ).
tff(166,axiom,
~ product(b,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
tff(167,plain,
~ product(b,a,c),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,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,c)
| ~ product(identity,a,a)
| ~ product(inverse(b),a,c)
| ~ product(inverse(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,c)
| ~ product(identity,a,a)
| ~ product(inverse(b),a,c)
| ~ product(inverse(b),identity,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(169,plain,
( ( product(b,a,c)
| ~ product(identity,a,a)
| ~ product(inverse(b),identity,b)
| ~ product(inverse(b),a,c) )
<=> ( product(b,a,c)
| ~ product(identity,a,a)
| ~ product(inverse(b),a,c)
| ~ product(inverse(b),identity,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(170,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,c)
| ~ product(identity,a,a)
| ~ product(inverse(b),identity,b)
| ~ product(inverse(b),a,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(b,a,c)
| ~ product(identity,a,a)
| ~ product(inverse(b),a,c)
| ~ product(inverse(b),identity,b) ) ),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,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,c)
| ~ product(identity,a,a)
| ~ product(inverse(b),identity,b)
| ~ product(inverse(b),a,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(b,a,c)
| ~ product(identity,a,a)
| ~ product(inverse(b),a,c)
| ~ product(inverse(b),identity,b) ) ),
inference(transitivity,[status(thm)],[170,168]) ).
tff(172,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,c)
| ~ product(identity,a,a)
| ~ product(inverse(b),identity,b)
| ~ product(inverse(b),a,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(173,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,c)
| ~ product(identity,a,a)
| ~ product(inverse(b),a,c)
| ~ product(inverse(b),identity,b) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
~ product(inverse(b),a,c),
inference(unit_resolution,[status(thm)],[173,96,167,164,44]) ).
tff(175,plain,
( ~ ! [X: $i] : product(X,X,identity)
| product(a,a,identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(176,plain,
product(a,a,identity),
inference(unit_resolution,[status(thm)],[175,7]) ).
tff(177,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(b),a,c)
| ~ product(c,identity,c)
| ~ product(a,a,identity)
| ~ product(c,a,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(inverse(b),a,c)
| ~ product(c,identity,c)
| ~ product(a,a,identity)
| ~ product(c,a,inverse(b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(178,plain,
( ( product(inverse(b),a,c)
| ~ product(a,a,identity)
| ~ product(c,a,inverse(b))
| ~ product(c,identity,c) )
<=> ( product(inverse(b),a,c)
| ~ product(c,identity,c)
| ~ product(a,a,identity)
| ~ product(c,a,inverse(b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(179,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(b),a,c)
| ~ product(a,a,identity)
| ~ product(c,a,inverse(b))
| ~ product(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(b),a,c)
| ~ product(c,identity,c)
| ~ product(a,a,identity)
| ~ product(c,a,inverse(b)) ) ),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,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(b),a,c)
| ~ product(a,a,identity)
| ~ product(c,a,inverse(b))
| ~ product(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(b),a,c)
| ~ product(c,identity,c)
| ~ product(a,a,identity)
| ~ product(c,a,inverse(b)) ) ),
inference(transitivity,[status(thm)],[179,177]) ).
tff(181,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(b),a,c)
| ~ product(a,a,identity)
| ~ product(c,a,inverse(b))
| ~ product(c,identity,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,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(b),a,c)
| ~ product(c,identity,c)
| ~ product(a,a,identity)
| ~ product(c,a,inverse(b)) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
~ product(c,a,inverse(b)),
inference(unit_resolution,[status(thm)],[182,96,84,176,174]) ).
tff(184,plain,
$false,
inference(unit_resolution,[status(thm)],[183,162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GRP001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n011.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Aug 31 13:57:11 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.16/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.32 Usage: tptp [options] [-file:]file
% 0.16/0.32 -h, -? prints this message.
% 0.16/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.32 -m, -model generate model.
% 0.16/0.32 -p, -proof generate proof.
% 0.16/0.32 -c, -core generate unsat core of named formulas.
% 0.16/0.32 -st, -statistics display statistics.
% 0.16/0.32 -t:timeout set timeout (in second).
% 0.16/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.32 -<param>:<value> configuration parameter and value.
% 0.16/0.32 -o:<output-file> file to place output in.
% 0.55/0.63 % SZS status Unsatisfiable
% 0.55/0.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------