TSTP Solution File: FLD014-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : FLD014-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 14:55:35 EDT 2022
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 56
% Syntax : Number of formulae : 111 ( 29 unt; 6 typ; 0 def)
% Number of atoms : 485 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 676 ( 317 ~; 312 |; 0 &)
% ( 47 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 21 ( 21 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 280 ( 257 !; 0 ?; 280 :)
% Comments :
%------------------------------------------------------------------------------
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(b_type,type,
b: $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( defined(b)
<=> defined(b) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
tff(3,plain,
defined(b),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i] :
refl(
( ( defined(additive_inverse(X))
| ~ defined(X) )
<=> ( defined(additive_inverse(X))
| ~ defined(X) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
<=> ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
<=> ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
tff(8,plain,
! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
| defined(additive_inverse(b))
| ~ defined(b) )
<=> ( ~ ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
| defined(additive_inverse(b))
| ~ defined(b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
| defined(additive_inverse(b))
| ~ defined(b) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
| defined(additive_inverse(b))
| ~ defined(b) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
defined(additive_inverse(b)),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [X: $i] :
refl(
( ( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,X) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
^ [X: $i] :
rewrite(
( ( sum(additive_identity,X,X)
| ~ defined(X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,X) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [X: $i] :
( sum(additive_identity,X,X)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [X: $i] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
tff(21,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_inverse(b))
| sum(additive_identity,additive_inverse(b),additive_inverse(b)) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_inverse(b))
| sum(additive_identity,additive_inverse(b),additive_inverse(b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_inverse(b))
| sum(additive_identity,additive_inverse(b),additive_inverse(b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_inverse(b))
| sum(additive_identity,additive_inverse(b),additive_inverse(b)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
sum(additive_identity,additive_inverse(b),additive_inverse(b)),
inference(unit_resolution,[status(thm)],[27,24,14]) ).
tff(29,plain,
^ [X: $i] :
refl(
( ( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
<=> ( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [X: $i] :
rewrite(
( ( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) )
<=> ( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X: $i] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [X: $i] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
tff(35,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(b)
| sum(additive_inverse(b),b,additive_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(b)
| sum(additive_inverse(b),b,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(b)
| sum(additive_inverse(b),b,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(b)
| sum(additive_inverse(b),b,additive_identity) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
sum(additive_inverse(b),b,additive_identity),
inference(unit_resolution,[status(thm)],[41,38,3]) ).
tff(43,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(44,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)],[43]) ).
tff(45,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(46,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(
( ( sum(Y,X,Z)
| ~ sum(X,Y,Z) )
<=> ( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [Z: $i,Y: $i,X: $i] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,axiom,
! [Z: $i,Y: $i,X: $i] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
tff(49,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[51,44]) ).
tff(53,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(b),b,additive_identity)
| sum(b,additive_inverse(b),additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(b),b,additive_identity)
| sum(b,additive_inverse(b),additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(b),b,additive_identity)
| sum(b,additive_inverse(b),additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(b),b,additive_identity)
| sum(b,additive_inverse(b),additive_identity) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
sum(b,additive_inverse(b),additive_identity),
inference(unit_resolution,[status(thm)],[55,52,42]) ).
tff(57,plain,
( defined(a)
<=> defined(a) ),
inference(rewrite,[status(thm)],]) ).
tff(58,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
tff(59,plain,
defined(a),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(a)
| sum(additive_inverse(a),a,additive_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(a)
| sum(additive_inverse(a),a,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(a)
| sum(additive_inverse(a),a,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(a)
| sum(additive_inverse(a),a,additive_identity) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
sum(additive_inverse(a),a,additive_identity),
inference(unit_resolution,[status(thm)],[62,38,59]) ).
tff(64,plain,
( defined(additive_identity)
<=> defined(additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(65,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
tff(66,plain,
defined(additive_identity),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(unit_resolution,[status(thm)],[69,24,66]) ).
tff(71,plain,
( sum(additive_identity,a,b)
<=> sum(additive_identity,a,b) ),
inference(rewrite,[status(thm)],]) ).
tff(72,axiom,
sum(additive_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).
tff(73,plain,
sum(additive_identity,a,b),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,a,b)
| sum(a,additive_identity,b) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,a,b)
| sum(a,additive_identity,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,a,b)
| sum(a,additive_identity,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,a,b)
| sum(a,additive_identity,b) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
sum(a,additive_identity,b),
inference(unit_resolution,[status(thm)],[76,52,73]) ).
tff(78,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
<=> ( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( sum(X,V,W)
| ~ sum(X,Y,U) )
<=> ( ~ sum(X,Y,U)
| sum(X,V,W) ) )),
( ( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V) )
<=> ( ~ sum(X,Y,U)
| sum(X,V,W)
| ~ sum(Y,Z,V) ) )),
rewrite(
( ( ~ sum(X,Y,U)
| sum(X,V,W)
| ~ sum(Y,Z,V) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
( ( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
( ( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W)
| ~ sum(U,Z,W) ) )),
rewrite(
( ( ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W)
| ~ sum(U,Z,W) )
<=> ( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
( ( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) )
<=> ( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
tff(84,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[86,79]) ).
tff(88,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(a,additive_identity,b)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_inverse(a),a,additive_identity)
| sum(additive_inverse(a),b,additive_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(a,additive_identity,b)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_inverse(a),a,additive_identity)
| sum(additive_inverse(a),b,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(a,additive_identity,b)
| ~ sum(additive_inverse(a),a,additive_identity)
| sum(additive_inverse(a),b,additive_identity) )
<=> ( ~ sum(a,additive_identity,b)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_inverse(a),a,additive_identity)
| sum(additive_inverse(a),b,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(a,additive_identity,b)
| ~ sum(additive_inverse(a),a,additive_identity)
| sum(additive_inverse(a),b,additive_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(a,additive_identity,b)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_inverse(a),a,additive_identity)
| sum(additive_inverse(a),b,additive_identity) ) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(a,additive_identity,b)
| ~ sum(additive_inverse(a),a,additive_identity)
| sum(additive_inverse(a),b,additive_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(a,additive_identity,b)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_inverse(a),a,additive_identity)
| sum(additive_inverse(a),b,additive_identity) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(a,additive_identity,b)
| ~ sum(additive_inverse(a),a,additive_identity)
| sum(additive_inverse(a),b,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(a,additive_identity,b)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_inverse(a),a,additive_identity)
| sum(additive_inverse(a),b,additive_identity) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
sum(additive_inverse(a),b,additive_identity),
inference(unit_resolution,[status(thm)],[93,87,77,70,63]) ).
tff(95,plain,
( ~ sum(additive_identity,additive_inverse(a),additive_inverse(b))
<=> ~ sum(additive_identity,additive_inverse(a),additive_inverse(b)) ),
inference(rewrite,[status(thm)],]) ).
tff(96,axiom,
~ sum(additive_identity,additive_inverse(a),additive_inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
tff(97,plain,
~ sum(additive_identity,additive_inverse(a),additive_inverse(b)),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(a),additive_identity,additive_inverse(b))
| sum(additive_identity,additive_inverse(a),additive_inverse(b)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(a),additive_identity,additive_inverse(b))
| sum(additive_identity,additive_inverse(a),additive_inverse(b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(a),additive_identity,additive_inverse(b))
| sum(additive_identity,additive_inverse(a),additive_inverse(b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(a),additive_identity,additive_inverse(b))
| sum(additive_identity,additive_inverse(a),additive_inverse(b)) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
~ sum(additive_inverse(a),additive_identity,additive_inverse(b)),
inference(unit_resolution,[status(thm)],[100,52,97]) ).
tff(102,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,additive_inverse(b),additive_inverse(b))
| ~ sum(b,additive_inverse(b),additive_identity)
| ~ sum(additive_inverse(a),b,additive_identity)
| sum(additive_inverse(a),additive_identity,additive_inverse(b)) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,additive_inverse(b),additive_inverse(b))
| ~ sum(b,additive_inverse(b),additive_identity)
| ~ sum(additive_inverse(a),b,additive_identity)
| sum(additive_inverse(a),additive_identity,additive_inverse(b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,additive_inverse(b),additive_inverse(b))
| ~ sum(b,additive_inverse(b),additive_identity)
| ~ sum(additive_inverse(a),b,additive_identity)
| sum(additive_inverse(a),additive_identity,additive_inverse(b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,additive_inverse(b),additive_inverse(b))
| ~ sum(b,additive_inverse(b),additive_identity)
| ~ sum(additive_inverse(a),b,additive_identity)
| sum(additive_inverse(a),additive_identity,additive_inverse(b)) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
$false,
inference(unit_resolution,[status(thm)],[104,87,101,94,56,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : FLD014-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 02:44:06 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------