TSTP Solution File: GRP009-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP009-1 : 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 22:25:24 EDT 2022
% Result : Unsatisfiable 0.67s 0.69s
% Output : Proof 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 86
% Syntax : Number of formulae : 211 ( 74 unt; 7 typ; 0 def)
% Number of atoms : 1008 ( 128 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1479 ( 698 ~; 690 |; 0 &)
% ( 91 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 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 : 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 : 672 ( 634 !; 0 ?; 672 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(identity_type,type,
identity: $i ).
tff(c_type,type,
c: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( product(X,identity,X)
<=> product(X,identity,X) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : product(X,identity,X)
<=> ! [X: $i] : product(X,identity,X) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : product(X,identity,X)
<=> ! [X: $i] : product(X,identity,X) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : product(X,identity,X),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
tff(5,plain,
! [X: $i] : product(X,identity,X),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : product(X,identity,X),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : product(X,identity,X),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : product(X,identity,X)
| product(inverse(a),identity,inverse(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
product(inverse(a),identity,inverse(a)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(
( product(X,Y,multiply(X,Y))
<=> product(X,Y,multiply(X,Y)) )),
inference(bind,[status(th)],]) ).
tff(11,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)],[10]) ).
tff(12,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(13,axiom,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).
tff(14,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
| product(inverse(a),identity,multiply(inverse(a),identity)) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
product(inverse(a),identity,multiply(inverse(a),identity)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,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(20,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)],[19]) ).
tff(21,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(22,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(23,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)],[22]) ).
tff(24,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(25,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(inverse(a),identity,multiply(inverse(a),identity))
| ( inverse(a) = multiply(inverse(a),identity) )
| ~ product(inverse(a),identity,inverse(a)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(inverse(a),identity,multiply(inverse(a),identity))
| ( inverse(a) = multiply(inverse(a),identity) )
| ~ product(inverse(a),identity,inverse(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ( inverse(a) = multiply(inverse(a),identity) )
| ~ product(inverse(a),identity,multiply(inverse(a),identity))
| ~ product(inverse(a),identity,inverse(a)) )
<=> ( ~ product(inverse(a),identity,multiply(inverse(a),identity))
| ( inverse(a) = multiply(inverse(a),identity) )
| ~ product(inverse(a),identity,inverse(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(a) = multiply(inverse(a),identity) )
| ~ product(inverse(a),identity,multiply(inverse(a),identity))
| ~ product(inverse(a),identity,inverse(a)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(inverse(a),identity,multiply(inverse(a),identity))
| ( inverse(a) = multiply(inverse(a),identity) )
| ~ product(inverse(a),identity,inverse(a)) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(a) = multiply(inverse(a),identity) )
| ~ product(inverse(a),identity,multiply(inverse(a),identity))
| ~ product(inverse(a),identity,inverse(a)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(inverse(a),identity,multiply(inverse(a),identity))
| ( inverse(a) = multiply(inverse(a),identity) )
| ~ product(inverse(a),identity,inverse(a)) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(a) = multiply(inverse(a),identity) )
| ~ product(inverse(a),identity,multiply(inverse(a),identity))
| ~ product(inverse(a),identity,inverse(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(inverse(a),identity,multiply(inverse(a),identity))
| ( inverse(a) = multiply(inverse(a),identity) )
| ~ product(inverse(a),identity,inverse(a)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
inverse(a) = multiply(inverse(a),identity),
inference(unit_resolution,[status(thm)],[34,28,18,9]) ).
tff(36,plain,
multiply(inverse(a),identity) = inverse(a),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
( product(multiply(inverse(a),identity),a,identity)
<=> product(inverse(a),a,identity) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( product(inverse(a),a,identity)
<=> product(multiply(inverse(a),identity),a,identity) ),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
^ [X: $i] :
refl(
( product(inverse(X),X,identity)
<=> product(inverse(X),X,identity) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X: $i] : product(inverse(X),X,identity)
<=> ! [X: $i] : product(inverse(X),X,identity) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [X: $i] : product(inverse(X),X,identity)
<=> ! [X: $i] : product(inverse(X),X,identity) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
! [X: $i] : product(inverse(X),X,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
tff(43,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ~ ! [X: $i] : product(inverse(X),X,identity)
| product(inverse(a),a,identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
product(inverse(a),a,identity),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
product(multiply(inverse(a),identity),a,identity),
inference(modus_ponens,[status(thm)],[47,38]) ).
tff(49,plain,
( product(identity,multiply(inverse(a),identity),multiply(inverse(a),identity))
<=> product(identity,inverse(a),inverse(a)) ),
inference(monotonicity,[status(thm)],[36,36]) ).
tff(50,plain,
( product(identity,inverse(a),inverse(a))
<=> product(identity,multiply(inverse(a),identity),multiply(inverse(a),identity)) ),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
^ [X: $i] :
refl(
( product(identity,X,X)
<=> product(identity,X,X) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(rewrite,[status(thm)],]) ).
tff(54,axiom,
! [X: $i] : product(identity,X,X),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
tff(55,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [X: $i] : product(identity,X,X),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,inverse(a),inverse(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
product(identity,inverse(a),inverse(a)),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
product(identity,multiply(inverse(a),identity),multiply(inverse(a),identity)),
inference(modus_ponens,[status(thm)],[59,50]) ).
tff(61,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,inverse(identity),inverse(identity)) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
product(identity,inverse(identity),inverse(identity)),
inference(unit_resolution,[status(thm)],[61,57]) ).
tff(63,plain,
^ [X: $i] :
refl(
( product(X,inverse(X),identity)
<=> product(X,inverse(X),identity) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [X: $i] : product(X,inverse(X),identity)
<=> ! [X: $i] : product(X,inverse(X),identity) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [X: $i] : product(X,inverse(X),identity)
<=> ! [X: $i] : product(X,inverse(X),identity) ),
inference(rewrite,[status(thm)],]) ).
tff(66,axiom,
! [X: $i] : product(X,inverse(X),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
tff(67,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ~ ! [X: $i] : product(X,inverse(X),identity)
| product(identity,inverse(identity),identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
product(identity,inverse(identity),identity),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(identity,inverse(identity),identity)
| ( inverse(identity) = identity )
| ~ product(identity,inverse(identity),inverse(identity)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(identity,inverse(identity),identity)
| ( inverse(identity) = identity )
| ~ product(identity,inverse(identity),inverse(identity)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ( ( inverse(identity) = identity )
| ~ product(identity,inverse(identity),identity)
| ~ product(identity,inverse(identity),inverse(identity)) )
<=> ( ~ product(identity,inverse(identity),identity)
| ( inverse(identity) = identity )
| ~ product(identity,inverse(identity),inverse(identity)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(identity) = identity )
| ~ product(identity,inverse(identity),identity)
| ~ product(identity,inverse(identity),inverse(identity)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(identity,inverse(identity),identity)
| ( inverse(identity) = identity )
| ~ product(identity,inverse(identity),inverse(identity)) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(identity) = identity )
| ~ product(identity,inverse(identity),identity)
| ~ product(identity,inverse(identity),inverse(identity)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(identity,inverse(identity),identity)
| ( inverse(identity) = identity )
| ~ product(identity,inverse(identity),inverse(identity)) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( inverse(identity) = identity )
| ~ product(identity,inverse(identity),identity)
| ~ product(identity,inverse(identity),inverse(identity)) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(identity,inverse(identity),identity)
| ( inverse(identity) = identity )
| ~ product(identity,inverse(identity),inverse(identity)) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
inverse(identity) = identity,
inference(unit_resolution,[status(thm)],[77,28,71,62]) ).
tff(79,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
( product(multiply(b,a),identity,multiply(multiply(b,a),inverse(identity)))
<=> product(multiply(b,a),inverse(identity),multiply(multiply(b,a),inverse(identity))) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( product(multiply(b,a),inverse(identity),multiply(multiply(b,a),inverse(identity)))
<=> product(multiply(b,a),identity,multiply(multiply(b,a),inverse(identity))) ),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
| product(multiply(b,a),inverse(identity),multiply(multiply(b,a),inverse(identity))) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
product(multiply(b,a),inverse(identity),multiply(multiply(b,a),inverse(identity))),
inference(unit_resolution,[status(thm)],[82,16]) ).
tff(84,plain,
product(multiply(b,a),identity,multiply(multiply(b,a),inverse(identity))),
inference(modus_ponens,[status(thm)],[83,81]) ).
tff(85,plain,
( ~ ! [X: $i] : product(X,identity,X)
| product(multiply(b,a),identity,multiply(b,a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
product(multiply(b,a),identity,multiply(b,a)),
inference(unit_resolution,[status(thm)],[85,7]) ).
tff(87,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(multiply(b,a),identity,multiply(multiply(b,a),inverse(identity)))
| ( multiply(b,a) = multiply(multiply(b,a),inverse(identity)) )
| ~ product(multiply(b,a),identity,multiply(b,a)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(multiply(b,a),identity,multiply(multiply(b,a),inverse(identity)))
| ( multiply(b,a) = multiply(multiply(b,a),inverse(identity)) )
| ~ product(multiply(b,a),identity,multiply(b,a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ( ( multiply(b,a) = multiply(multiply(b,a),inverse(identity)) )
| ~ product(multiply(b,a),identity,multiply(multiply(b,a),inverse(identity)))
| ~ product(multiply(b,a),identity,multiply(b,a)) )
<=> ( ~ product(multiply(b,a),identity,multiply(multiply(b,a),inverse(identity)))
| ( multiply(b,a) = multiply(multiply(b,a),inverse(identity)) )
| ~ product(multiply(b,a),identity,multiply(b,a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( multiply(b,a) = multiply(multiply(b,a),inverse(identity)) )
| ~ product(multiply(b,a),identity,multiply(multiply(b,a),inverse(identity)))
| ~ product(multiply(b,a),identity,multiply(b,a)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(multiply(b,a),identity,multiply(multiply(b,a),inverse(identity)))
| ( multiply(b,a) = multiply(multiply(b,a),inverse(identity)) )
| ~ product(multiply(b,a),identity,multiply(b,a)) ) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( multiply(b,a) = multiply(multiply(b,a),inverse(identity)) )
| ~ product(multiply(b,a),identity,multiply(multiply(b,a),inverse(identity)))
| ~ product(multiply(b,a),identity,multiply(b,a)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(multiply(b,a),identity,multiply(multiply(b,a),inverse(identity)))
| ( multiply(b,a) = multiply(multiply(b,a),inverse(identity)) )
| ~ product(multiply(b,a),identity,multiply(b,a)) ) ),
inference(transitivity,[status(thm)],[89,87]) ).
tff(91,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( multiply(b,a) = multiply(multiply(b,a),inverse(identity)) )
| ~ product(multiply(b,a),identity,multiply(multiply(b,a),inverse(identity)))
| ~ product(multiply(b,a),identity,multiply(b,a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(multiply(b,a),identity,multiply(multiply(b,a),inverse(identity)))
| ( multiply(b,a) = multiply(multiply(b,a),inverse(identity)) )
| ~ product(multiply(b,a),identity,multiply(b,a)) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
( ~ product(multiply(b,a),identity,multiply(multiply(b,a),inverse(identity)))
| ( multiply(b,a) = multiply(multiply(b,a),inverse(identity)) ) ),
inference(unit_resolution,[status(thm)],[92,28,86]) ).
tff(94,plain,
multiply(b,a) = multiply(multiply(b,a),inverse(identity)),
inference(unit_resolution,[status(thm)],[93,84]) ).
tff(95,plain,
multiply(multiply(b,a),inverse(identity)) = multiply(b,a),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
( product(inverse(multiply(b,a)),multiply(multiply(b,a),inverse(identity)),identity)
<=> product(inverse(multiply(b,a)),multiply(b,a),identity) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( product(inverse(multiply(b,a)),multiply(b,a),identity)
<=> product(inverse(multiply(b,a)),multiply(multiply(b,a),inverse(identity)),identity) ),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
( ~ ! [X: $i] : product(inverse(X),X,identity)
| product(inverse(multiply(b,a)),multiply(b,a),identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
product(inverse(multiply(b,a)),multiply(b,a),identity),
inference(unit_resolution,[status(thm)],[98,45]) ).
tff(100,plain,
product(inverse(multiply(b,a)),multiply(multiply(b,a),inverse(identity)),identity),
inference(modus_ponens,[status(thm)],[99,97]) ).
tff(101,plain,
( product(b,a,multiply(multiply(b,a),inverse(identity)))
<=> product(b,a,multiply(b,a)) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(102,plain,
( product(b,a,multiply(b,a))
<=> product(b,a,multiply(multiply(b,a),inverse(identity))) ),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( ~ ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
| product(b,a,multiply(b,a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
product(b,a,multiply(b,a)),
inference(unit_resolution,[status(thm)],[103,16]) ).
tff(105,plain,
product(b,a,multiply(multiply(b,a),inverse(identity))),
inference(modus_ponens,[status(thm)],[104,102]) ).
tff(106,plain,
( ~ ! [X: $i] : product(X,identity,X)
| product(b,identity,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
product(b,identity,b),
inference(unit_resolution,[status(thm)],[106,7]) ).
tff(108,plain,
( product(a,b,identity)
<=> product(a,b,identity) ),
inference(rewrite,[status(thm)],]) ).
tff(109,axiom,
product(a,b,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_an_inverse_of_b) ).
tff(110,plain,
product(a,b,identity),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,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(112,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)],[111]) ).
tff(113,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(114,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(115,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)],[114]) ).
tff(116,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(117,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)],[116,115]) ).
tff(118,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)],[117,113]) ).
tff(119,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)],[118]) ).
tff(120,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)],[119,112]) ).
tff(121,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,identity)
| ~ product(b,a,multiply(b,a))
| ~ product(b,identity,b)
| product(multiply(b,a),b,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(a,b,identity)
| ~ product(b,a,multiply(b,a))
| ~ product(b,identity,b)
| product(multiply(b,a),b,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( ( product(multiply(b,a),b,b)
| ~ product(a,b,identity)
| ~ product(b,a,multiply(b,a))
| ~ product(b,identity,b) )
<=> ( ~ product(a,b,identity)
| ~ product(b,a,multiply(b,a))
| ~ product(b,identity,b)
| product(multiply(b,a),b,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,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(b,a),b,b)
| ~ product(a,b,identity)
| ~ product(b,a,multiply(b,a))
| ~ product(b,identity,b) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(a,b,identity)
| ~ product(b,a,multiply(b,a))
| ~ product(b,identity,b)
| product(multiply(b,a),b,b) ) ),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,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(b,a),b,b)
| ~ product(a,b,identity)
| ~ product(b,a,multiply(b,a))
| ~ product(b,identity,b) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(a,b,identity)
| ~ product(b,a,multiply(b,a))
| ~ product(b,identity,b)
| product(multiply(b,a),b,b) ) ),
inference(transitivity,[status(thm)],[123,121]) ).
tff(125,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(b,a),b,b)
| ~ product(a,b,identity)
| ~ product(b,a,multiply(b,a))
| ~ product(b,identity,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,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,identity)
| ~ product(b,a,multiply(b,a))
| ~ product(b,identity,b)
| product(multiply(b,a),b,b) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
product(multiply(b,a),b,b),
inference(unit_resolution,[status(thm)],[126,120,110,107,104]) ).
tff(128,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,b,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
product(identity,b,b),
inference(unit_resolution,[status(thm)],[128,57]) ).
tff(130,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(131,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)],[130]) ).
tff(132,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(133,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(134,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)],[133]) ).
tff(135,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(136,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)],[135,134]) ).
tff(137,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)],[136,132]) ).
tff(138,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)],[137]) ).
tff(139,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)],[138,131]) ).
tff(140,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(multiply(b,a)),b,b)
| ~ product(multiply(b,a),b,b)
| ~ product(inverse(multiply(b,a)),multiply(b,a),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(multiply(b,a)),b,b)
| ~ product(multiply(b,a),b,b)
| ~ product(inverse(multiply(b,a)),multiply(b,a),identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(141,plain,
( ( product(inverse(multiply(b,a)),b,b)
| ~ product(identity,b,b)
| ~ product(multiply(b,a),b,b)
| ~ product(inverse(multiply(b,a)),multiply(b,a),identity) )
<=> ( ~ product(identity,b,b)
| product(inverse(multiply(b,a)),b,b)
| ~ product(multiply(b,a),b,b)
| ~ product(inverse(multiply(b,a)),multiply(b,a),identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(142,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(multiply(b,a)),b,b)
| ~ product(identity,b,b)
| ~ product(multiply(b,a),b,b)
| ~ product(inverse(multiply(b,a)),multiply(b,a),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(multiply(b,a)),b,b)
| ~ product(multiply(b,a),b,b)
| ~ product(inverse(multiply(b,a)),multiply(b,a),identity) ) ),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,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(multiply(b,a)),b,b)
| ~ product(identity,b,b)
| ~ product(multiply(b,a),b,b)
| ~ product(inverse(multiply(b,a)),multiply(b,a),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(multiply(b,a)),b,b)
| ~ product(multiply(b,a),b,b)
| ~ product(inverse(multiply(b,a)),multiply(b,a),identity) ) ),
inference(transitivity,[status(thm)],[142,140]) ).
tff(144,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(multiply(b,a)),b,b)
| ~ product(identity,b,b)
| ~ product(multiply(b,a),b,b)
| ~ product(inverse(multiply(b,a)),multiply(b,a),identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(145,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(multiply(b,a)),b,b)
| ~ product(multiply(b,a),b,b)
| ~ product(inverse(multiply(b,a)),multiply(b,a),identity) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
product(inverse(multiply(b,a)),b,b),
inference(unit_resolution,[status(thm)],[145,139,129,99,127]) ).
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(inverse(multiply(b,a)),b,b)
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| product(b,a,identity)
| ~ product(inverse(multiply(b,a)),multiply(multiply(b,a),inverse(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(multiply(b,a)),b,b)
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| product(b,a,identity)
| ~ product(inverse(multiply(b,a)),multiply(multiply(b,a),inverse(identity)),identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,plain,
( ( product(b,a,identity)
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| ~ product(inverse(multiply(b,a)),b,b)
| ~ product(inverse(multiply(b,a)),multiply(multiply(b,a),inverse(identity)),identity) )
<=> ( ~ product(inverse(multiply(b,a)),b,b)
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| product(b,a,identity)
| ~ product(inverse(multiply(b,a)),multiply(multiply(b,a),inverse(identity)),identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(b,a,identity)
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| ~ product(inverse(multiply(b,a)),b,b)
| ~ product(inverse(multiply(b,a)),multiply(multiply(b,a),inverse(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(multiply(b,a)),b,b)
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| product(b,a,identity)
| ~ product(inverse(multiply(b,a)),multiply(multiply(b,a),inverse(identity)),identity) ) ),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(b,a,identity)
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| ~ product(inverse(multiply(b,a)),b,b)
| ~ product(inverse(multiply(b,a)),multiply(multiply(b,a),inverse(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(multiply(b,a)),b,b)
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| product(b,a,identity)
| ~ product(inverse(multiply(b,a)),multiply(multiply(b,a),inverse(identity)),identity) ) ),
inference(transitivity,[status(thm)],[149,147]) ).
tff(151,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(b,a,identity)
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| ~ product(inverse(multiply(b,a)),b,b)
| ~ product(inverse(multiply(b,a)),multiply(multiply(b,a),inverse(identity)),identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(152,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(multiply(b,a)),b,b)
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| product(b,a,identity)
| ~ product(inverse(multiply(b,a)),multiply(multiply(b,a),inverse(identity)),identity) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
( ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| product(b,a,identity)
| ~ product(inverse(multiply(b,a)),multiply(multiply(b,a),inverse(identity)),identity) ),
inference(unit_resolution,[status(thm)],[152,120,146]) ).
tff(154,plain,
product(b,a,identity),
inference(unit_resolution,[status(thm)],[153,105,100]) ).
tff(155,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| ( identity = multiply(multiply(b,a),inverse(identity)) )
| ~ product(b,a,identity) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| ( identity = multiply(multiply(b,a),inverse(identity)) )
| ~ product(b,a,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
( ( ( identity = multiply(multiply(b,a),inverse(identity)) )
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| ~ product(b,a,identity) )
<=> ( ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| ( identity = multiply(multiply(b,a),inverse(identity)) )
| ~ product(b,a,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(157,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( identity = multiply(multiply(b,a),inverse(identity)) )
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| ~ product(b,a,identity) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| ( identity = multiply(multiply(b,a),inverse(identity)) )
| ~ product(b,a,identity) ) ),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( identity = multiply(multiply(b,a),inverse(identity)) )
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| ~ product(b,a,identity) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| ( identity = multiply(multiply(b,a),inverse(identity)) )
| ~ product(b,a,identity) ) ),
inference(transitivity,[status(thm)],[157,155]) ).
tff(159,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( identity = multiply(multiply(b,a),inverse(identity)) )
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| ~ product(b,a,identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(160,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ~ product(b,a,multiply(multiply(b,a),inverse(identity)))
| ( identity = multiply(multiply(b,a),inverse(identity)) )
| ~ product(b,a,identity) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
identity = multiply(multiply(b,a),inverse(identity)),
inference(unit_resolution,[status(thm)],[160,28,105,154]) ).
tff(162,plain,
identity = multiply(b,a),
inference(transitivity,[status(thm)],[161,95]) ).
tff(163,plain,
( product(identity,multiply(inverse(a),identity),b)
<=> product(multiply(b,a),inverse(a),b) ),
inference(monotonicity,[status(thm)],[162,36]) ).
tff(164,plain,
( product(multiply(b,a),inverse(a),b)
<=> product(identity,multiply(inverse(a),identity),b) ),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
( ~ ! [X: $i] : product(X,inverse(X),identity)
| product(a,inverse(a),identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(166,plain,
product(a,inverse(a),identity),
inference(unit_resolution,[status(thm)],[165,69]) ).
tff(167,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(b,a),inverse(a),b)
| ~ product(a,inverse(a),identity)
| ~ product(b,a,multiply(b,a))
| ~ product(b,identity,b) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(multiply(b,a),inverse(a),b)
| ~ product(a,inverse(a),identity)
| ~ product(b,a,multiply(b,a))
| ~ product(b,identity,b) ) ),
inference(rewrite,[status(thm)],]) ).
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(multiply(b,a),inverse(a),b)
| ~ product(a,inverse(a),identity)
| ~ product(b,a,multiply(b,a))
| ~ product(b,identity,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(169,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(b,a),inverse(a),b)
| ~ product(a,inverse(a),identity)
| ~ product(b,a,multiply(b,a))
| ~ product(b,identity,b) ),
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
product(multiply(b,a),inverse(a),b),
inference(unit_resolution,[status(thm)],[169,120,107,104,166]) ).
tff(171,plain,
product(identity,multiply(inverse(a),identity),b),
inference(modus_ponens,[status(thm)],[170,164]) ).
tff(172,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( multiply(inverse(a),identity) = b )
| ~ product(identity,multiply(inverse(a),identity),b)
| ~ product(identity,multiply(inverse(a),identity),multiply(inverse(a),identity)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( multiply(inverse(a),identity) = b )
| ~ product(identity,multiply(inverse(a),identity),b)
| ~ product(identity,multiply(inverse(a),identity),multiply(inverse(a),identity)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(173,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( multiply(inverse(a),identity) = b )
| ~ product(identity,multiply(inverse(a),identity),b)
| ~ product(identity,multiply(inverse(a),identity),multiply(inverse(a),identity)) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( multiply(inverse(a),identity) = b )
| ~ product(identity,multiply(inverse(a),identity),b)
| ~ product(identity,multiply(inverse(a),identity),multiply(inverse(a),identity)) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
( ( multiply(inverse(a),identity) = b )
| ~ product(identity,multiply(inverse(a),identity),b)
| ~ product(identity,multiply(inverse(a),identity),multiply(inverse(a),identity)) ),
inference(unit_resolution,[status(thm)],[174,28]) ).
tff(176,plain,
multiply(inverse(a),identity) = b,
inference(unit_resolution,[status(thm)],[175,171,60]) ).
tff(177,plain,
( product(c,multiply(inverse(a),identity),identity)
<=> product(c,b,identity) ),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( product(c,b,identity)
<=> product(c,multiply(inverse(a),identity),identity) ),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
( product(c,b,identity)
<=> product(c,b,identity) ),
inference(rewrite,[status(thm)],]) ).
tff(180,axiom,
product(c,b,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_an_inverse_of_b) ).
tff(181,plain,
product(c,b,identity),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
product(c,multiply(inverse(a),identity),identity),
inference(modus_ponens,[status(thm)],[181,178]) ).
tff(183,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(184,plain,
product(identity,a,a),
inference(unit_resolution,[status(thm)],[183,57]) ).
tff(185,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,a,a)
| ~ product(c,multiply(inverse(a),identity),identity)
| product(c,identity,a)
| ~ product(multiply(inverse(a),identity),a,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,a,a)
| ~ product(c,multiply(inverse(a),identity),identity)
| product(c,identity,a)
| ~ product(multiply(inverse(a),identity),a,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(186,plain,
( ( product(c,identity,a)
| ~ product(identity,a,a)
| ~ product(multiply(inverse(a),identity),a,identity)
| ~ product(c,multiply(inverse(a),identity),identity) )
<=> ( ~ product(identity,a,a)
| ~ product(c,multiply(inverse(a),identity),identity)
| product(c,identity,a)
| ~ product(multiply(inverse(a),identity),a,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(187,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,identity,a)
| ~ product(identity,a,a)
| ~ product(multiply(inverse(a),identity),a,identity)
| ~ product(c,multiply(inverse(a),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(identity,a,a)
| ~ product(c,multiply(inverse(a),identity),identity)
| product(c,identity,a)
| ~ product(multiply(inverse(a),identity),a,identity) ) ),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,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,identity,a)
| ~ product(identity,a,a)
| ~ product(multiply(inverse(a),identity),a,identity)
| ~ product(c,multiply(inverse(a),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(identity,a,a)
| ~ product(c,multiply(inverse(a),identity),identity)
| product(c,identity,a)
| ~ product(multiply(inverse(a),identity),a,identity) ) ),
inference(transitivity,[status(thm)],[187,185]) ).
tff(189,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,identity,a)
| ~ product(identity,a,a)
| ~ product(multiply(inverse(a),identity),a,identity)
| ~ product(c,multiply(inverse(a),identity),identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(190,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,a,a)
| ~ product(c,multiply(inverse(a),identity),identity)
| product(c,identity,a)
| ~ product(multiply(inverse(a),identity),a,identity) ),
inference(modus_ponens,[status(thm)],[189,188]) ).
tff(191,plain,
( ~ product(c,multiply(inverse(a),identity),identity)
| product(c,identity,a)
| ~ product(multiply(inverse(a),identity),a,identity) ),
inference(unit_resolution,[status(thm)],[190,139,184]) ).
tff(192,plain,
product(c,identity,a),
inference(unit_resolution,[status(thm)],[191,182,48]) ).
tff(193,plain,
( ~ ! [X: $i] : product(X,identity,X)
| product(c,identity,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(194,plain,
product(c,identity,c),
inference(unit_resolution,[status(thm)],[193,7]) ).
tff(195,plain,
( ( a != c )
<=> ( a != c ) ),
inference(rewrite,[status(thm)],]) ).
tff(196,axiom,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_equals_c) ).
tff(197,plain,
a != c,
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( a = c )
| ~ product(c,identity,a)
| ~ product(c,identity,c) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( a = c )
| ~ product(c,identity,a)
| ~ product(c,identity,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(199,plain,
( ( ( a = c )
| ~ product(c,identity,c)
| ~ product(c,identity,a) )
<=> ( ( a = c )
| ~ product(c,identity,a)
| ~ product(c,identity,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(200,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( a = c )
| ~ product(c,identity,c)
| ~ product(c,identity,a) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( a = c )
| ~ product(c,identity,a)
| ~ product(c,identity,c) ) ),
inference(monotonicity,[status(thm)],[199]) ).
tff(201,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( a = c )
| ~ product(c,identity,c)
| ~ product(c,identity,a) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( a = c )
| ~ product(c,identity,a)
| ~ product(c,identity,c) ) ),
inference(transitivity,[status(thm)],[200,198]) ).
tff(202,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( a = c )
| ~ product(c,identity,c)
| ~ product(c,identity,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(203,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( a = c )
| ~ product(c,identity,a)
| ~ product(c,identity,c) ),
inference(modus_ponens,[status(thm)],[202,201]) ).
tff(204,plain,
$false,
inference(unit_resolution,[status(thm)],[203,28,197,194,192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n018.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 14:07:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.67/0.69 % SZS status Unsatisfiable
% 0.67/0.69 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------