TSTP Solution File: BOO012-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : BOO012-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 17:18:41 EDT 2022
% Result : Unsatisfiable 3.37s 2.48s
% Output : Proof 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 87
% Syntax : Number of formulae : 191 ( 64 unt; 7 typ; 0 def)
% Number of atoms : 927 ( 57 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 1342 ( 639 ~; 619 |; 0 &)
% ( 84 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 40 ( 40 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 4 >; 5 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 686 ( 631 !; 0 ?; 686 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(x_type,type,
x: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(multiplicative_identity_type,type,
multiplicative_identity: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( sum(X,Y,add(X,Y))
<=> sum(X,Y,add(X,Y)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : sum(X,Y,add(X,Y))
<=> ! [Y: $i,X: $i] : sum(X,Y,add(X,Y)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : sum(X,Y,add(X,Y))
<=> ! [Y: $i,X: $i] : sum(X,Y,add(X,Y)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i,X: $i] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
tff(5,plain,
! [Y: $i,X: $i] : sum(X,Y,add(X,Y)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : sum(X,Y,add(X,Y)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : sum(X,Y,add(X,Y)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : sum(X,Y,add(X,Y))
| sum(inverse(inverse(x)),x,add(inverse(inverse(x)),x)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
sum(inverse(inverse(x)),x,add(inverse(inverse(x)),x)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
<=> ( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_addition) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(inverse(inverse(x)),x,add(inverse(inverse(x)),x))
| sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(inverse(inverse(x)),x,add(inverse(inverse(x)),x))
| sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(inverse(inverse(x)),x,add(inverse(inverse(x)),x))
| sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x)) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(inverse(inverse(x)),x,add(inverse(inverse(x)),x))
| sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x)),
inference(unit_resolution,[status(thm)],[19,16,9]) ).
tff(21,plain,
^ [X: $i] :
refl(
( product(inverse(X),X,additive_identity)
<=> product(inverse(X),X,additive_identity) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [X: $i] : product(inverse(X),X,additive_identity)
<=> ! [X: $i] : product(inverse(X),X,additive_identity) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] : product(inverse(X),X,additive_identity)
<=> ! [X: $i] : product(inverse(X),X,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [X: $i] : product(inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
tff(25,plain,
! [X: $i] : product(inverse(X),X,additive_identity),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] : product(inverse(X),X,additive_identity),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] : product(inverse(X),X,additive_identity),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [X: $i] : product(inverse(X),X,additive_identity)
| product(inverse(inverse(x)),inverse(x),additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
product(inverse(inverse(x)),inverse(x),additive_identity),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ product(X,Y,Z)
| sum(X,Z,X) )
<=> ( ~ product(X,Y,Z)
| sum(X,Z,X) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_product_dual1) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) )
| ~ product(inverse(inverse(x)),inverse(x),additive_identity)
| sum(inverse(inverse(x)),additive_identity,inverse(inverse(x))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) )
| ~ product(inverse(inverse(x)),inverse(x),additive_identity)
| sum(inverse(inverse(x)),additive_identity,inverse(inverse(x))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) )
| ~ product(inverse(inverse(x)),inverse(x),additive_identity)
| sum(inverse(inverse(x)),additive_identity,inverse(inverse(x))) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) )
| ~ product(inverse(inverse(x)),inverse(x),additive_identity)
| sum(inverse(inverse(x)),additive_identity,inverse(inverse(x))) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
sum(inverse(inverse(x)),additive_identity,inverse(inverse(x))),
inference(unit_resolution,[status(thm)],[39,36,29]) ).
tff(41,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(inverse(inverse(x)),additive_identity,inverse(inverse(x)))
| sum(additive_identity,inverse(inverse(x)),inverse(inverse(x))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(inverse(inverse(x)),additive_identity,inverse(inverse(x)))
| sum(additive_identity,inverse(inverse(x)),inverse(inverse(x))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(inverse(inverse(x)),additive_identity,inverse(inverse(x)))
| sum(additive_identity,inverse(inverse(x)),inverse(inverse(x))) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(inverse(inverse(x)),additive_identity,inverse(inverse(x)))
| sum(additive_identity,inverse(inverse(x)),inverse(inverse(x))) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
sum(additive_identity,inverse(inverse(x)),inverse(inverse(x))),
inference(unit_resolution,[status(thm)],[43,16,40]) ).
tff(45,plain,
^ [X: $i] :
refl(
( sum(X,inverse(X),multiplicative_identity)
<=> sum(X,inverse(X),multiplicative_identity) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [X: $i] : sum(X,inverse(X),multiplicative_identity)
<=> ! [X: $i] : sum(X,inverse(X),multiplicative_identity) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [X: $i] : sum(X,inverse(X),multiplicative_identity)
<=> ! [X: $i] : sum(X,inverse(X),multiplicative_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
! [X: $i] : sum(X,inverse(X),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
tff(49,plain,
! [X: $i] : sum(X,inverse(X),multiplicative_identity),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [X: $i] : sum(X,inverse(X),multiplicative_identity),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [X: $i] : sum(X,inverse(X),multiplicative_identity),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [X: $i] : sum(X,inverse(X),multiplicative_identity)
| sum(inverse(x),inverse(inverse(x)),multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
sum(inverse(x),inverse(inverse(x)),multiplicative_identity),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
^ [X: $i] :
refl(
( product(X,inverse(X),additive_identity)
<=> product(X,inverse(X),additive_identity) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [X: $i] : product(X,inverse(X),additive_identity)
<=> ! [X: $i] : product(X,inverse(X),additive_identity) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [X: $i] : product(X,inverse(X),additive_identity)
<=> ! [X: $i] : product(X,inverse(X),additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
! [X: $i] : product(X,inverse(X),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
tff(58,plain,
! [X: $i] : product(X,inverse(X),additive_identity),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [X: $i] : product(X,inverse(X),additive_identity),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [X: $i] : product(X,inverse(X),additive_identity),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ~ ! [X: $i] : product(X,inverse(X),additive_identity)
| product(x,inverse(x),additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
product(x,inverse(x),additive_identity),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
refl(
( ( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) )
<=> ( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ sum(Y,X,V1)
| ~ sum(Z,X,V2)
| ~ product(Y,Z,V3) )
<=> ( ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ) )),
( ( ~ sum(Y,X,V1)
| ~ sum(Z,X,V2)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4) )
<=> ( ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1)
| ~ sum(V3,X,V4) ) )),
rewrite(
( ( ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1)
| ~ sum(V3,X,V4) )
<=> ( ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ) )),
( ( ~ sum(Y,X,V1)
| ~ sum(Z,X,V2)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4) )
<=> ( ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ) )),
( ( ~ sum(Y,X,V1)
| ~ sum(Z,X,V2)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| product(V1,V2,V4) )
<=> ( ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1)
| product(V1,V2,V4) ) )),
rewrite(
( ( ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1)
| product(V1,V2,V4) )
<=> ( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ) )),
( ( ~ sum(Y,X,V1)
| ~ sum(Z,X,V2)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| product(V1,V2,V4) )
<=> ( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,X,V1)
| ~ sum(Z,X,V2)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| product(V1,V2,V4) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,axiom,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,X,V1)
| ~ sum(Z,X,V2)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| product(V1,V2,V4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity7) ).
tff(69,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
inference(modus_ponens,[status(thm)],[71,64]) ).
tff(73,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) )
| ~ product(x,inverse(x),additive_identity)
| ~ sum(additive_identity,inverse(inverse(x)),inverse(inverse(x)))
| product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x))
| ~ sum(inverse(x),inverse(inverse(x)),multiplicative_identity) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) )
| ~ product(x,inverse(x),additive_identity)
| ~ sum(additive_identity,inverse(inverse(x)),inverse(inverse(x)))
| product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x))
| ~ sum(inverse(x),inverse(inverse(x)),multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ( product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ product(x,inverse(x),additive_identity)
| ~ sum(additive_identity,inverse(inverse(x)),inverse(inverse(x)))
| ~ sum(inverse(x),inverse(inverse(x)),multiplicative_identity)
| ~ sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x)) )
<=> ( ~ product(x,inverse(x),additive_identity)
| ~ sum(additive_identity,inverse(inverse(x)),inverse(inverse(x)))
| product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x))
| ~ sum(inverse(x),inverse(inverse(x)),multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) )
| product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ product(x,inverse(x),additive_identity)
| ~ sum(additive_identity,inverse(inverse(x)),inverse(inverse(x)))
| ~ sum(inverse(x),inverse(inverse(x)),multiplicative_identity)
| ~ sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x)) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) )
| ~ product(x,inverse(x),additive_identity)
| ~ sum(additive_identity,inverse(inverse(x)),inverse(inverse(x)))
| product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x))
| ~ sum(inverse(x),inverse(inverse(x)),multiplicative_identity) ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) )
| product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ product(x,inverse(x),additive_identity)
| ~ sum(additive_identity,inverse(inverse(x)),inverse(inverse(x)))
| ~ sum(inverse(x),inverse(inverse(x)),multiplicative_identity)
| ~ sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x)) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) )
| ~ product(x,inverse(x),additive_identity)
| ~ sum(additive_identity,inverse(inverse(x)),inverse(inverse(x)))
| product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x))
| ~ sum(inverse(x),inverse(inverse(x)),multiplicative_identity) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) )
| product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ product(x,inverse(x),additive_identity)
| ~ sum(additive_identity,inverse(inverse(x)),inverse(inverse(x)))
| ~ sum(inverse(x),inverse(inverse(x)),multiplicative_identity)
| ~ sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x)) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) )
| ~ product(x,inverse(x),additive_identity)
| ~ sum(additive_identity,inverse(inverse(x)),inverse(inverse(x)))
| product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x))
| ~ sum(inverse(x),inverse(inverse(x)),multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x))),
inference(unit_resolution,[status(thm)],[78,72,62,53,44,20]) ).
tff(80,plain,
^ [X: $i] :
refl(
( product(X,multiplicative_identity,X)
<=> product(X,multiplicative_identity,X) )),
inference(bind,[status(th)],]) ).
tff(81,plain,
( ! [X: $i] : product(X,multiplicative_identity,X)
<=> ! [X: $i] : product(X,multiplicative_identity,X) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [X: $i] : product(X,multiplicative_identity,X)
<=> ! [X: $i] : product(X,multiplicative_identity,X) ),
inference(rewrite,[status(thm)],]) ).
tff(83,axiom,
! [X: $i] : product(X,multiplicative_identity,X),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).
tff(84,plain,
! [X: $i] : product(X,multiplicative_identity,X),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [X: $i] : product(X,multiplicative_identity,X),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [X: $i] : product(X,multiplicative_identity,X),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
( ~ ! [X: $i] : product(X,multiplicative_identity,X)
| product(add(inverse(inverse(x)),x),multiplicative_identity,add(inverse(inverse(x)),x)) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
product(add(inverse(inverse(x)),x),multiplicative_identity,add(inverse(inverse(x)),x)),
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
<=> ( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
rewrite(
( ( ~ product(X,Y,U)
| ~ product(X,Y,V)
| ( U = V ) )
<=> ( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| ( U = V ) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).
tff(95,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,add(inverse(inverse(x)),x))
| ( add(inverse(inverse(x)),x) = inverse(inverse(x)) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,add(inverse(inverse(x)),x))
| ( add(inverse(inverse(x)),x) = inverse(inverse(x)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ( ( add(inverse(inverse(x)),x) = inverse(inverse(x)) )
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,add(inverse(inverse(x)),x)) )
<=> ( ~ product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,add(inverse(inverse(x)),x))
| ( add(inverse(inverse(x)),x) = inverse(inverse(x)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ( add(inverse(inverse(x)),x) = inverse(inverse(x)) )
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,add(inverse(inverse(x)),x)) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,add(inverse(inverse(x)),x))
| ( add(inverse(inverse(x)),x) = inverse(inverse(x)) ) ) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ( add(inverse(inverse(x)),x) = inverse(inverse(x)) )
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,add(inverse(inverse(x)),x)) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,add(inverse(inverse(x)),x))
| ( add(inverse(inverse(x)),x) = inverse(inverse(x)) ) ) ),
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ( add(inverse(inverse(x)),x) = inverse(inverse(x)) )
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,add(inverse(inverse(x)),x)) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,inverse(inverse(x)))
| ~ product(add(inverse(inverse(x)),x),multiplicative_identity,add(inverse(inverse(x)),x))
| ( add(inverse(inverse(x)),x) = inverse(inverse(x)) ) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
add(inverse(inverse(x)),x) = inverse(inverse(x)),
inference(unit_resolution,[status(thm)],[104,98,88,79]) ).
tff(106,plain,
inverse(inverse(x)) = add(inverse(inverse(x)),x),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
( product(x,inverse(inverse(x)),x)
<=> product(x,add(inverse(inverse(x)),x),x) ),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
( product(x,add(inverse(inverse(x)),x),x)
<=> product(x,inverse(inverse(x)),x) ),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ sum(X,Y,Z)
| product(X,Z,X) )
<=> ( ~ sum(X,Y,Z)
| product(X,Z,X) ) )),
inference(bind,[status(th)],]) ).
tff(110,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_product_dual2) ).
tff(113,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) )
| ~ sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x))
| product(x,add(inverse(inverse(x)),x),x) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) )
| ~ sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x))
| product(x,add(inverse(inverse(x)),x),x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) )
| ~ sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x))
| product(x,add(inverse(inverse(x)),x),x) ),
inference(quant_inst,[status(thm)],]) ).
tff(118,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) )
| ~ sum(x,inverse(inverse(x)),add(inverse(inverse(x)),x))
| product(x,add(inverse(inverse(x)),x),x) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
product(x,add(inverse(inverse(x)),x),x),
inference(unit_resolution,[status(thm)],[118,115,20]) ).
tff(120,plain,
product(x,inverse(inverse(x)),x),
inference(modus_ponens,[status(thm)],[119,108]) ).
tff(121,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) )
| ~ product(x,inverse(x),additive_identity)
| sum(x,additive_identity,x) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) )
| ~ product(x,inverse(x),additive_identity)
| sum(x,additive_identity,x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) )
| ~ product(x,inverse(x),additive_identity)
| sum(x,additive_identity,x) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| sum(X,Z,X) )
| ~ product(x,inverse(x),additive_identity)
| sum(x,additive_identity,x) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
sum(x,additive_identity,x),
inference(unit_resolution,[status(thm)],[123,36,62]) ).
tff(125,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(x,additive_identity,x)
| sum(additive_identity,x,x) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(x,additive_identity,x)
| sum(additive_identity,x,x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(x,additive_identity,x)
| sum(additive_identity,x,x) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(x,additive_identity,x)
| sum(additive_identity,x,x) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
sum(additive_identity,x,x),
inference(unit_resolution,[status(thm)],[127,16,124]) ).
tff(129,plain,
( ~ ! [X: $i] : product(X,inverse(X),additive_identity)
| product(inverse(x),inverse(inverse(x)),additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
product(inverse(x),inverse(inverse(x)),additive_identity),
inference(unit_resolution,[status(thm)],[129,60]) ).
tff(131,plain,
^ [X: $i] :
refl(
( sum(inverse(X),X,multiplicative_identity)
<=> sum(inverse(X),X,multiplicative_identity) )),
inference(bind,[status(th)],]) ).
tff(132,plain,
( ! [X: $i] : sum(inverse(X),X,multiplicative_identity)
<=> ! [X: $i] : sum(inverse(X),X,multiplicative_identity) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
( ! [X: $i] : sum(inverse(X),X,multiplicative_identity)
<=> ! [X: $i] : sum(inverse(X),X,multiplicative_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(134,axiom,
! [X: $i] : sum(inverse(X),X,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse1) ).
tff(135,plain,
! [X: $i] : sum(inverse(X),X,multiplicative_identity),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [X: $i] : sum(inverse(X),X,multiplicative_identity),
inference(skolemize,[status(sab)],[135]) ).
tff(137,plain,
! [X: $i] : sum(inverse(X),X,multiplicative_identity),
inference(modus_ponens,[status(thm)],[136,132]) ).
tff(138,plain,
( ~ ! [X: $i] : sum(inverse(X),X,multiplicative_identity)
| sum(inverse(x),x,multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(139,plain,
sum(inverse(x),x,multiplicative_identity),
inference(unit_resolution,[status(thm)],[138,137]) ).
tff(140,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
refl(
( ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
<=> ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
inference(bind,[status(th)],]) ).
tff(141,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
( ( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1)
| ~ sum(V1,V2,V4) ) )),
rewrite(
( ( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1)
| ~ sum(V1,V2,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
( ( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
( ( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1)
| product(V3,X,V4) ) )),
rewrite(
( ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1)
| product(V3,X,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
( ( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
inference(bind,[status(th)],]) ).
tff(144,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,axiom,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity4) ).
tff(146,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(modus_ponens,[status(thm)],[146,142]) ).
tff(148,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(skolemize,[status(sab)],[147]) ).
tff(149,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(modus_ponens,[status(thm)],[148,141]) ).
tff(150,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(inverse(x),x,multiplicative_identity)
| ~ sum(additive_identity,x,x)
| product(multiplicative_identity,inverse(inverse(x)),x)
| ~ product(inverse(x),inverse(inverse(x)),additive_identity)
| ~ product(x,inverse(inverse(x)),x) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(inverse(x),x,multiplicative_identity)
| ~ sum(additive_identity,x,x)
| product(multiplicative_identity,inverse(inverse(x)),x)
| ~ product(inverse(x),inverse(inverse(x)),additive_identity)
| ~ product(x,inverse(inverse(x)),x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(151,plain,
( ( ~ sum(inverse(x),x,multiplicative_identity)
| ~ sum(additive_identity,x,x)
| product(multiplicative_identity,inverse(inverse(x)),x)
| ~ product(x,inverse(inverse(x)),x)
| ~ product(inverse(x),inverse(inverse(x)),additive_identity) )
<=> ( ~ sum(inverse(x),x,multiplicative_identity)
| ~ sum(additive_identity,x,x)
| product(multiplicative_identity,inverse(inverse(x)),x)
| ~ product(inverse(x),inverse(inverse(x)),additive_identity)
| ~ product(x,inverse(inverse(x)),x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(inverse(x),x,multiplicative_identity)
| ~ sum(additive_identity,x,x)
| product(multiplicative_identity,inverse(inverse(x)),x)
| ~ product(x,inverse(inverse(x)),x)
| ~ product(inverse(x),inverse(inverse(x)),additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(inverse(x),x,multiplicative_identity)
| ~ sum(additive_identity,x,x)
| product(multiplicative_identity,inverse(inverse(x)),x)
| ~ product(inverse(x),inverse(inverse(x)),additive_identity)
| ~ product(x,inverse(inverse(x)),x) ) ),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(inverse(x),x,multiplicative_identity)
| ~ sum(additive_identity,x,x)
| product(multiplicative_identity,inverse(inverse(x)),x)
| ~ product(x,inverse(inverse(x)),x)
| ~ product(inverse(x),inverse(inverse(x)),additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(inverse(x),x,multiplicative_identity)
| ~ sum(additive_identity,x,x)
| product(multiplicative_identity,inverse(inverse(x)),x)
| ~ product(inverse(x),inverse(inverse(x)),additive_identity)
| ~ product(x,inverse(inverse(x)),x) ) ),
inference(transitivity,[status(thm)],[152,150]) ).
tff(154,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(inverse(x),x,multiplicative_identity)
| ~ sum(additive_identity,x,x)
| product(multiplicative_identity,inverse(inverse(x)),x)
| ~ product(x,inverse(inverse(x)),x)
| ~ product(inverse(x),inverse(inverse(x)),additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(155,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(inverse(x),x,multiplicative_identity)
| ~ sum(additive_identity,x,x)
| product(multiplicative_identity,inverse(inverse(x)),x)
| ~ product(inverse(x),inverse(inverse(x)),additive_identity)
| ~ product(x,inverse(inverse(x)),x) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
( product(multiplicative_identity,inverse(inverse(x)),x)
| ~ product(x,inverse(inverse(x)),x) ),
inference(unit_resolution,[status(thm)],[155,149,139,130,128]) ).
tff(157,plain,
product(multiplicative_identity,inverse(inverse(x)),x),
inference(unit_resolution,[status(thm)],[156,120]) ).
tff(158,plain,
( ~ ! [X: $i] : sum(inverse(X),X,multiplicative_identity)
| sum(inverse(inverse(x)),inverse(x),multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
sum(inverse(inverse(x)),inverse(x),multiplicative_identity),
inference(unit_resolution,[status(thm)],[158,137]) ).
tff(160,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) )
| ~ sum(inverse(inverse(x)),inverse(x),multiplicative_identity)
| product(inverse(inverse(x)),multiplicative_identity,inverse(inverse(x))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) )
| ~ sum(inverse(inverse(x)),inverse(x),multiplicative_identity)
| product(inverse(inverse(x)),multiplicative_identity,inverse(inverse(x))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(161,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) )
| ~ sum(inverse(inverse(x)),inverse(x),multiplicative_identity)
| product(inverse(inverse(x)),multiplicative_identity,inverse(inverse(x))) ),
inference(quant_inst,[status(thm)],]) ).
tff(162,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| product(X,Z,X) )
| ~ sum(inverse(inverse(x)),inverse(x),multiplicative_identity)
| product(inverse(inverse(x)),multiplicative_identity,inverse(inverse(x))) ),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
product(inverse(inverse(x)),multiplicative_identity,inverse(inverse(x))),
inference(unit_resolution,[status(thm)],[162,115,159]) ).
tff(164,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ product(X,Y,Z)
| product(Y,X,Z) )
<=> ( ~ product(X,Y,Z)
| product(Y,X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(165,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[164]) ).
tff(166,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(167,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).
tff(168,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(skolemize,[status(sab)],[168]) ).
tff(170,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[169,165]) ).
tff(171,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(inverse(inverse(x)),multiplicative_identity,inverse(inverse(x)))
| product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(inverse(inverse(x)),multiplicative_identity,inverse(inverse(x)))
| product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(172,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(inverse(inverse(x)),multiplicative_identity,inverse(inverse(x)))
| product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x))) ),
inference(quant_inst,[status(thm)],]) ).
tff(173,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(inverse(inverse(x)),multiplicative_identity,inverse(inverse(x)))
| product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x))) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x))),
inference(unit_resolution,[status(thm)],[173,170,163]) ).
tff(175,plain,
( ( inverse(inverse(x)) != x )
<=> ( inverse(inverse(x)) != x ) ),
inference(rewrite,[status(thm)],]) ).
tff(176,axiom,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
tff(177,plain,
inverse(inverse(x)) != x,
inference(modus_ponens,[status(thm)],[176,175]) ).
tff(178,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ( inverse(inverse(x)) = x )
| ~ product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x)))
| ~ product(multiplicative_identity,inverse(inverse(x)),x) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ( inverse(inverse(x)) = x )
| ~ product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x)))
| ~ product(multiplicative_identity,inverse(inverse(x)),x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(179,plain,
( ( ( inverse(inverse(x)) = x )
| ~ product(multiplicative_identity,inverse(inverse(x)),x)
| ~ product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x))) )
<=> ( ( inverse(inverse(x)) = x )
| ~ product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x)))
| ~ product(multiplicative_identity,inverse(inverse(x)),x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(180,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ( inverse(inverse(x)) = x )
| ~ product(multiplicative_identity,inverse(inverse(x)),x)
| ~ product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x))) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ( inverse(inverse(x)) = x )
| ~ product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x)))
| ~ product(multiplicative_identity,inverse(inverse(x)),x) ) ),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ( inverse(inverse(x)) = x )
| ~ product(multiplicative_identity,inverse(inverse(x)),x)
| ~ product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x))) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ( inverse(inverse(x)) = x )
| ~ product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x)))
| ~ product(multiplicative_identity,inverse(inverse(x)),x) ) ),
inference(transitivity,[status(thm)],[180,178]) ).
tff(182,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ( inverse(inverse(x)) = x )
| ~ product(multiplicative_identity,inverse(inverse(x)),x)
| ~ product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x))) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ product(X,Y,V)
| ~ product(X,Y,U) )
| ( inverse(inverse(x)) = x )
| ~ product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x)))
| ~ product(multiplicative_identity,inverse(inverse(x)),x) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
$false,
inference(unit_resolution,[status(thm)],[183,98,177,174,157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : BOO012-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Aug 30 03:05:15 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.18/0.34 Usage: tptp [options] [-file:]file
% 0.18/0.34 -h, -? prints this message.
% 0.18/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.18/0.34 -m, -model generate model.
% 0.18/0.34 -p, -proof generate proof.
% 0.18/0.34 -c, -core generate unsat core of named formulas.
% 0.18/0.34 -st, -statistics display statistics.
% 0.18/0.34 -t:timeout set timeout (in second).
% 0.18/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.18/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.18/0.34 -<param>:<value> configuration parameter and value.
% 0.18/0.34 -o:<output-file> file to place output in.
% 3.37/2.48 % SZS status Unsatisfiable
% 3.37/2.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------