TSTP Solution File: RNG008-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 20 03:17:38 EDT 2022
% Result : Unsatisfiable 205.99s 132.19s
% Output : Proof 206.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 94
% Syntax : Number of formulae : 296 ( 218 unt; 7 typ; 0 def)
% Number of atoms : 388 ( 373 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 131 ( 46 ~; 39 |; 0 &)
% ( 46 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 315 ( 289 !; 0 ?; 315 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(c_type,type,
c: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( multiply(X,X) = X )
<=> ( multiply(X,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(X,X) = X )
<=> ! [X: $i] : ( multiply(X,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(X,X) = X )
<=> ! [X: $i] : ( multiply(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( multiply(X,X) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',boolean_ring) ).
tff(5,plain,
! [X: $i] : ( multiply(X,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(X,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(X,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(X,X) = X )
| ( multiply(b,b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
multiply(b,b) = b,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
b = multiply(b,b),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
multiply(a,b) = multiply(a,multiply(b,b)),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
multiply(a,multiply(b,b)) = multiply(a,b),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ~ ! [X: $i] : ( multiply(X,X) = X )
| ( multiply(multiply(a,multiply(b,b)),multiply(a,multiply(b,b))) = multiply(a,multiply(b,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(14,plain,
multiply(multiply(a,multiply(b,b)),multiply(a,multiply(b,b))) = multiply(a,multiply(b,b)),
inference(unit_resolution,[status(thm)],[13,7]) ).
tff(15,plain,
^ [Y: $i,X: $i] :
refl(
( ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
<=> ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
<=> ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
<=> ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse2) ).
tff(19,plain,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(additive_inverse(a)),multiply(a,b)) = additive_inverse(multiply(additive_inverse(a),multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
multiply(additive_inverse(additive_inverse(a)),multiply(a,b)) = additive_inverse(multiply(additive_inverse(a),multiply(a,b))),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
( ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X )
<=> ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X )
<=> ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',additive_inverse_additive_inverse) ).
tff(27,plain,
! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X )
| ( additive_inverse(additive_inverse(a)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
additive_inverse(additive_inverse(a)) = a,
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
multiply(additive_inverse(additive_inverse(a)),multiply(a,b)) = multiply(a,multiply(a,b)),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
multiply(a,multiply(a,b)) = multiply(additive_inverse(additive_inverse(a)),multiply(a,b)),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',associative_multiplication) ).
tff(38,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),b) = multiply(a,multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
multiply(multiply(a,a),b) = multiply(a,multiply(a,b)),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
( ~ ! [X: $i] : ( multiply(X,X) = X )
| ( multiply(a,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
multiply(a,a) = a,
inference(unit_resolution,[status(thm)],[43,7]) ).
tff(45,plain,
multiply(multiply(a,a),b) = multiply(a,b),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
multiply(a,b) = multiply(multiply(a,a),b),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
multiply(a,multiply(b,b)) = additive_inverse(multiply(additive_inverse(a),multiply(a,b))),
inference(transitivity,[status(thm)],[12,46,42,33,23]) ).
tff(48,plain,
multiply(multiply(a,multiply(b,b)),multiply(a,multiply(b,b))) = multiply(multiply(a,multiply(b,b)),additive_inverse(multiply(additive_inverse(a),multiply(a,b)))),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
multiply(multiply(a,multiply(b,b)),additive_inverse(multiply(additive_inverse(a),multiply(a,b)))) = multiply(multiply(a,multiply(b,b)),multiply(a,multiply(b,b))),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
^ [Y: $i,X: $i] :
refl(
( ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) )
<=> ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) )
<=> ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) )
<=> ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse1) ).
tff(54,plain,
! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) )
| ( multiply(multiply(a,multiply(b,b)),additive_inverse(multiply(additive_inverse(a),multiply(a,b)))) = additive_inverse(multiply(multiply(a,multiply(b,b)),multiply(additive_inverse(a),multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
multiply(multiply(a,multiply(b,b)),additive_inverse(multiply(additive_inverse(a),multiply(a,b)))) = additive_inverse(multiply(multiply(a,multiply(b,b)),multiply(additive_inverse(a),multiply(a,b)))),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
additive_inverse(multiply(multiply(a,multiply(b,b)),multiply(additive_inverse(a),multiply(a,b)))) = multiply(multiply(a,multiply(b,b)),additive_inverse(multiply(additive_inverse(a),multiply(a,b)))),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(multiply(a,multiply(b,b))),multiply(additive_inverse(a),multiply(a,b))) = additive_inverse(multiply(multiply(a,multiply(b,b)),multiply(additive_inverse(a),multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
multiply(additive_inverse(multiply(a,multiply(b,b))),multiply(additive_inverse(a),multiply(a,b))) = additive_inverse(multiply(multiply(a,multiply(b,b)),multiply(additive_inverse(a),multiply(a,b)))),
inference(unit_resolution,[status(thm)],[60,21]) ).
tff(62,plain,
( ~ ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X )
| ( additive_inverse(additive_inverse(multiply(additive_inverse(a),multiply(a,b)))) = multiply(additive_inverse(a),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
additive_inverse(additive_inverse(multiply(additive_inverse(a),multiply(a,b)))) = multiply(additive_inverse(a),multiply(a,b)),
inference(unit_resolution,[status(thm)],[62,29]) ).
tff(64,plain,
additive_inverse(multiply(a,multiply(b,b))) = additive_inverse(additive_inverse(multiply(additive_inverse(a),multiply(a,b)))),
inference(monotonicity,[status(thm)],[47]) ).
tff(65,plain,
additive_inverse(multiply(a,multiply(b,b))) = multiply(additive_inverse(a),multiply(a,b)),
inference(transitivity,[status(thm)],[64,63]) ).
tff(66,plain,
multiply(additive_inverse(multiply(a,multiply(b,b))),multiply(additive_inverse(a),multiply(a,b))) = multiply(multiply(additive_inverse(a),multiply(a,b)),multiply(additive_inverse(a),multiply(a,b))),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
multiply(multiply(additive_inverse(a),multiply(a,b)),multiply(additive_inverse(a),multiply(a,b))) = multiply(additive_inverse(multiply(a,multiply(b,b))),multiply(additive_inverse(a),multiply(a,b))),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
( ~ ! [X: $i] : ( multiply(X,X) = X )
| ( multiply(multiply(additive_inverse(a),multiply(a,b)),multiply(additive_inverse(a),multiply(a,b))) = multiply(additive_inverse(a),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
multiply(multiply(additive_inverse(a),multiply(a,b)),multiply(additive_inverse(a),multiply(a,b))) = multiply(additive_inverse(a),multiply(a,b)),
inference(unit_resolution,[status(thm)],[68,7]) ).
tff(70,plain,
multiply(additive_inverse(a),multiply(a,b)) = multiply(multiply(additive_inverse(a),multiply(a,b)),multiply(additive_inverse(a),multiply(a,b))),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
^ [X: $i] :
refl(
( ( add(additive_identity,X) = X )
<=> ( add(additive_identity,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
! [X: $i] : ( add(additive_identity,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',left_identity) ).
tff(75,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,multiply(additive_inverse(a),multiply(a,b))) = multiply(additive_inverse(a),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
add(additive_identity,multiply(additive_inverse(a),multiply(a,b))) = multiply(additive_inverse(a),multiply(a,b)),
inference(unit_resolution,[status(thm)],[78,77]) ).
tff(80,plain,
multiply(additive_inverse(additive_inverse(a)),b) = multiply(a,b),
inference(monotonicity,[status(thm)],[31]) ).
tff(81,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(additive_inverse(a)),b) = additive_inverse(multiply(additive_inverse(a),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
multiply(additive_inverse(additive_inverse(a)),b) = additive_inverse(multiply(additive_inverse(a),b)),
inference(unit_resolution,[status(thm)],[81,21]) ).
tff(83,plain,
additive_inverse(multiply(additive_inverse(a),b)) = multiply(additive_inverse(additive_inverse(a)),b),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
additive_inverse(multiply(additive_inverse(a),b)) = multiply(a,multiply(b,b)),
inference(transitivity,[status(thm)],[83,80,11]) ).
tff(85,plain,
additive_inverse(additive_inverse(multiply(additive_inverse(a),b))) = additive_inverse(multiply(a,multiply(b,b))),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
( ~ ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X )
| ( additive_inverse(additive_inverse(multiply(additive_inverse(a),b))) = multiply(additive_inverse(a),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
additive_inverse(additive_inverse(multiply(additive_inverse(a),b))) = multiply(additive_inverse(a),b),
inference(unit_resolution,[status(thm)],[86,29]) ).
tff(88,plain,
multiply(additive_inverse(a),b) = additive_inverse(additive_inverse(multiply(additive_inverse(a),b))),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
multiply(additive_inverse(a),b) = multiply(additive_inverse(a),multiply(a,b)),
inference(transitivity,[status(thm)],[88,85,64,63]) ).
tff(90,plain,
add(additive_identity,multiply(additive_inverse(a),b)) = add(additive_identity,multiply(additive_inverse(a),multiply(a,b))),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
additive_inverse(multiply(a,multiply(b,b))) = additive_inverse(additive_inverse(multiply(additive_inverse(a),b))),
inference(symmetry,[status(thm)],[85]) ).
tff(92,plain,
additive_inverse(additive_inverse(multiply(additive_inverse(a),multiply(a,b)))) = additive_inverse(multiply(a,multiply(b,b))),
inference(symmetry,[status(thm)],[64]) ).
tff(93,plain,
multiply(additive_inverse(a),multiply(a,b)) = additive_inverse(additive_inverse(multiply(additive_inverse(a),multiply(a,b)))),
inference(symmetry,[status(thm)],[63]) ).
tff(94,plain,
multiply(additive_inverse(a),multiply(a,b)) = multiply(additive_inverse(a),b),
inference(transitivity,[status(thm)],[93,92,91,87]) ).
tff(95,plain,
^ [X: $i] :
refl(
( ( add(additive_inverse(X),X) = additive_identity )
<=> ( add(additive_inverse(X),X) = additive_identity ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,axiom,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',left_additive_inverse) ).
tff(99,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(b),b) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
add(additive_inverse(b),b) = additive_identity,
inference(unit_resolution,[status(thm)],[102,101]) ).
tff(104,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
<=> ( add(add(X,Y),Z) = add(X,add(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(105,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',associative_addition) ).
tff(108,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(additive_inverse(a),additive_inverse(additive_identity)),a),b) = add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
add(add(add(additive_inverse(a),additive_inverse(additive_identity)),a),b) = add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
^ [X: $i] :
refl(
( ( add(X,additive_inverse(X)) = additive_identity )
<=> ( add(X,additive_inverse(X)) = additive_identity ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
<=> ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
<=> ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,axiom,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
tff(117,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
( ~ ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
| ( add(additive_inverse(a),additive_inverse(additive_inverse(a))) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
add(additive_inverse(a),additive_inverse(additive_inverse(a))) = additive_identity,
inference(unit_resolution,[status(thm)],[120,119]) ).
tff(122,plain,
a = additive_inverse(additive_inverse(a)),
inference(symmetry,[status(thm)],[31]) ).
tff(123,plain,
^ [X: $i] :
refl(
( ( add(X,additive_identity) = X )
<=> ( add(X,additive_identity) = X ) )),
inference(bind,[status(th)],]) ).
tff(124,plain,
( ! [X: $i] : ( add(X,additive_identity) = X )
<=> ! [X: $i] : ( add(X,additive_identity) = X ) ),
inference(quant_intro,[status(thm)],[123]) ).
tff(125,plain,
( ! [X: $i] : ( add(X,additive_identity) = X )
<=> ! [X: $i] : ( add(X,additive_identity) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,axiom,
! [X: $i] : ( add(X,additive_identity) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
tff(127,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(skolemize,[status(sab)],[127]) ).
tff(129,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(modus_ponens,[status(thm)],[128,124]) ).
tff(130,plain,
( ~ ! [X: $i] : ( add(X,additive_identity) = X )
| ( add(a,additive_identity) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
add(a,additive_identity) = a,
inference(unit_resolution,[status(thm)],[130,129]) ).
tff(132,plain,
a = add(a,additive_identity),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
additive_inverse(a) = additive_inverse(add(a,additive_identity)),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
additive_inverse(add(a,additive_identity)) = additive_inverse(a),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
^ [Y: $i,X: $i] :
refl(
( ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
<=> ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ) )),
inference(bind,[status(th)],]) ).
tff(136,plain,
( ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
<=> ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
( ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
<=> ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(138,axiom,
! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',distribute_additive_inverse) ).
tff(139,plain,
! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ),
inference(skolemize,[status(sab)],[139]) ).
tff(141,plain,
! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ),
inference(modus_ponens,[status(thm)],[140,136]) ).
tff(142,plain,
( ~ ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
| ( additive_inverse(add(a,additive_identity)) = add(additive_inverse(a),additive_inverse(additive_identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
additive_inverse(add(a,additive_identity)) = add(additive_inverse(a),additive_inverse(additive_identity)),
inference(unit_resolution,[status(thm)],[142,141]) ).
tff(144,plain,
add(additive_inverse(a),additive_inverse(additive_identity)) = additive_inverse(add(a,additive_identity)),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
add(additive_inverse(a),additive_inverse(additive_identity)) = additive_inverse(a),
inference(transitivity,[status(thm)],[144,134]) ).
tff(146,plain,
add(add(additive_inverse(a),additive_inverse(additive_identity)),a) = add(additive_inverse(a),additive_inverse(additive_inverse(a))),
inference(monotonicity,[status(thm)],[145,122]) ).
tff(147,plain,
add(add(additive_inverse(a),additive_inverse(additive_identity)),a) = additive_identity,
inference(transitivity,[status(thm)],[146,121]) ).
tff(148,plain,
add(add(add(additive_inverse(a),additive_inverse(additive_identity)),a),b) = add(additive_identity,b),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
add(additive_identity,b) = add(add(add(additive_inverse(a),additive_inverse(additive_identity)),a),b),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
^ [Y: $i,X: $i] :
refl(
( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(151,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(quant_intro,[status(thm)],[150]) ).
tff(152,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(153,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',commutative_addition) ).
tff(154,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[154]) ).
tff(156,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[155,151]) ).
tff(157,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_identity,b) = add(b,additive_identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(158,plain,
add(additive_identity,b) = add(b,additive_identity),
inference(unit_resolution,[status(thm)],[157,156]) ).
tff(159,plain,
add(b,additive_identity) = add(additive_identity,b),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
( ~ ! [X: $i] : ( add(X,additive_identity) = X )
| ( add(b,additive_identity) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(161,plain,
add(b,additive_identity) = b,
inference(unit_resolution,[status(thm)],[160,129]) ).
tff(162,plain,
b = add(b,additive_identity),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
b = add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),
inference(transitivity,[status(thm)],[162,159,149,112]) ).
tff(164,plain,
additive_inverse(b) = additive_inverse(add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b))),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
additive_inverse(add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b))) = additive_inverse(b),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
( ~ ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
| ( additive_inverse(add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b))) = add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(167,plain,
additive_inverse(add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b))) = add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),
inference(unit_resolution,[status(thm)],[166,141]) ).
tff(168,plain,
add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))) = additive_inverse(add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b))),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))) = additive_inverse(b),
inference(transitivity,[status(thm)],[168,165]) ).
tff(170,plain,
add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),b) = add(additive_inverse(b),b),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),b) = additive_identity,
inference(transitivity,[status(thm)],[170,103]) ).
tff(172,plain,
add(add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),b),multiply(additive_inverse(a),multiply(a,b))) = add(additive_identity,multiply(additive_inverse(a),b)),
inference(monotonicity,[status(thm)],[171,94]) ).
tff(173,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),b),multiply(additive_inverse(a),multiply(a,b))) = add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),add(b,multiply(additive_inverse(a),multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
add(add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),b),multiply(additive_inverse(a),multiply(a,b))) = add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),add(b,multiply(additive_inverse(a),multiply(a,b)))),
inference(unit_resolution,[status(thm)],[173,110]) ).
tff(175,plain,
add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),add(b,multiply(additive_inverse(a),multiply(a,b)))) = add(add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),b),multiply(additive_inverse(a),multiply(a,b))),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(multiply(additive_inverse(a),multiply(a,b)),b) = add(b,multiply(additive_inverse(a),multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(177,plain,
add(multiply(additive_inverse(a),multiply(a,b)),b) = add(b,multiply(additive_inverse(a),multiply(a,b))),
inference(unit_resolution,[status(thm)],[176,156]) ).
tff(178,plain,
add(multiply(additive_inverse(a),multiply(a,b)),b) = add(multiply(additive_inverse(a),multiply(a,b)),add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b))),
inference(monotonicity,[status(thm)],[163]) ).
tff(179,plain,
add(multiply(additive_inverse(a),multiply(a,b)),add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b))) = add(multiply(additive_inverse(a),multiply(a,b)),b),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(multiply(additive_inverse(a),multiply(a,b)),add(additive_inverse(a),additive_inverse(additive_identity))),add(a,b)) = add(multiply(additive_inverse(a),multiply(a,b)),add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(181,plain,
add(add(multiply(additive_inverse(a),multiply(a,b)),add(additive_inverse(a),additive_inverse(additive_identity))),add(a,b)) = add(multiply(additive_inverse(a),multiply(a,b)),add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b))),
inference(unit_resolution,[status(thm)],[180,110]) ).
tff(182,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(b,a) = add(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,plain,
add(b,a) = add(a,b),
inference(unit_resolution,[status(thm)],[182,156]) ).
tff(184,plain,
multiply(add(additive_inverse(a),additive_inverse(additive_identity)),add(b,a)) = multiply(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(186,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
inference(quant_intro,[status(thm)],[185]) ).
tff(187,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(188,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',distribute1) ).
tff(189,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[189]) ).
tff(191,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[190,186]) ).
tff(192,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(add(additive_inverse(a),additive_inverse(additive_identity)),add(b,a)) = add(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),b),multiply(add(additive_inverse(a),additive_inverse(additive_identity)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(193,plain,
multiply(add(additive_inverse(a),additive_inverse(additive_identity)),add(b,a)) = add(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),b),multiply(add(additive_inverse(a),additive_inverse(additive_identity)),a)),
inference(unit_resolution,[status(thm)],[192,191]) ).
tff(194,plain,
add(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),b),multiply(add(additive_inverse(a),additive_inverse(additive_identity)),a)) = multiply(add(additive_inverse(a),additive_inverse(additive_identity)),add(b,a)),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
( ~ ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X )
| ( additive_inverse(additive_inverse(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),a))) = multiply(add(additive_inverse(a),additive_inverse(additive_identity)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(196,plain,
additive_inverse(additive_inverse(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),a))) = multiply(add(additive_inverse(a),additive_inverse(additive_identity)),a),
inference(unit_resolution,[status(thm)],[195,29]) ).
tff(197,plain,
additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))) = additive_inverse(additive_inverse(a)),
inference(monotonicity,[status(thm)],[145]) ).
tff(198,plain,
additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))) = a,
inference(transitivity,[status(thm)],[197,31]) ).
tff(199,plain,
multiply(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),a) = multiply(a,a),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),a) = additive_inverse(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(201,plain,
multiply(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),a) = additive_inverse(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),a)),
inference(unit_resolution,[status(thm)],[200,21]) ).
tff(202,plain,
additive_inverse(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),a)) = multiply(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),a),
inference(symmetry,[status(thm)],[201]) ).
tff(203,plain,
additive_inverse(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),a)) = a,
inference(transitivity,[status(thm)],[202,199,44]) ).
tff(204,plain,
additive_inverse(additive_inverse(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),a))) = additive_inverse(a),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
additive_inverse(a) = additive_inverse(additive_inverse(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),a))),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
add(additive_inverse(a),additive_inverse(additive_identity)) = multiply(add(additive_inverse(a),additive_inverse(additive_identity)),a),
inference(transitivity,[status(thm)],[144,134,205,196]) ).
tff(207,plain,
multiply(add(additive_inverse(a),additive_inverse(additive_identity)),b) = multiply(additive_inverse(a),b),
inference(monotonicity,[status(thm)],[145]) ).
tff(208,plain,
multiply(additive_inverse(a),b) = multiply(add(additive_inverse(a),additive_inverse(additive_identity)),b),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
multiply(additive_inverse(a),multiply(a,b)) = multiply(add(additive_inverse(a),additive_inverse(additive_identity)),b),
inference(transitivity,[status(thm)],[93,92,91,87,208]) ).
tff(210,plain,
add(multiply(additive_inverse(a),multiply(a,b)),add(additive_inverse(a),additive_inverse(additive_identity))) = add(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),b),multiply(add(additive_inverse(a),additive_inverse(additive_identity)),a)),
inference(monotonicity,[status(thm)],[209,206]) ).
tff(211,plain,
add(multiply(additive_inverse(a),multiply(a,b)),add(additive_inverse(a),additive_inverse(additive_identity))) = multiply(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),
inference(transitivity,[status(thm)],[210,194,184]) ).
tff(212,plain,
add(add(multiply(additive_inverse(a),multiply(a,b)),add(additive_inverse(a),additive_inverse(additive_identity))),add(a,b)) = add(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),add(a,b)),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
add(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),add(a,b)) = add(add(multiply(additive_inverse(a),multiply(a,b)),add(additive_inverse(a),additive_inverse(additive_identity))),add(a,b)),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
( ~ ! [X: $i] : ( multiply(X,X) = X )
| ( multiply(add(a,b),add(a,b)) = add(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(215,plain,
multiply(add(a,b),add(a,b)) = add(a,b),
inference(unit_resolution,[status(thm)],[214,7]) ).
tff(216,plain,
add(a,b) = multiply(add(a,b),add(a,b)),
inference(symmetry,[status(thm)],[215]) ).
tff(217,plain,
add(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),add(a,b)) = add(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),multiply(add(a,b),add(a,b))),
inference(monotonicity,[status(thm)],[216]) ).
tff(218,plain,
add(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),multiply(add(a,b),add(a,b))) = add(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),add(a,b)),
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(220,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[219]) ).
tff(221,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(222,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',distribute2) ).
tff(223,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[222,221]) ).
tff(224,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[223]) ).
tff(225,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[224,220]) ).
tff(226,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),add(a,b)) = add(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),multiply(add(a,b),add(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(227,plain,
multiply(add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),add(a,b)) = add(multiply(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),multiply(add(a,b),add(a,b))),
inference(unit_resolution,[status(thm)],[226,225]) ).
tff(228,plain,
add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)) = add(add(add(additive_inverse(a),additive_inverse(additive_identity)),a),b),
inference(symmetry,[status(thm)],[112]) ).
tff(229,plain,
add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)) = b,
inference(transitivity,[status(thm)],[228,148,158,161]) ).
tff(230,plain,
multiply(add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),add(a,b)) = multiply(b,add(a,b)),
inference(monotonicity,[status(thm)],[229]) ).
tff(231,plain,
multiply(b,add(a,b)) = multiply(add(add(additive_inverse(a),additive_inverse(additive_identity)),add(a,b)),add(a,b)),
inference(symmetry,[status(thm)],[230]) ).
tff(232,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(b,add(a,b)) = add(multiply(b,a),multiply(b,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(233,plain,
multiply(b,add(a,b)) = add(multiply(b,a),multiply(b,b)),
inference(unit_resolution,[status(thm)],[232,191]) ).
tff(234,plain,
add(multiply(b,a),multiply(b,b)) = multiply(b,add(a,b)),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
add(multiply(b,a),multiply(b,b)) = add(multiply(b,a),b),
inference(monotonicity,[status(thm)],[9]) ).
tff(236,plain,
add(multiply(b,a),b) = add(multiply(b,a),multiply(b,b)),
inference(symmetry,[status(thm)],[235]) ).
tff(237,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(multiply(b,a),b) = add(b,multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(238,plain,
add(multiply(b,a),b) = add(b,multiply(b,a)),
inference(unit_resolution,[status(thm)],[237,156]) ).
tff(239,plain,
add(b,multiply(b,a)) = add(multiply(b,a),b),
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
add(b,multiply(b,a)) = add(b,multiply(additive_inverse(a),multiply(a,b))),
inference(transitivity,[status(thm)],[239,236,234,231,227,218,213,181,179,177]) ).
tff(241,plain,
add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),add(b,multiply(b,a))) = add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),add(b,multiply(additive_inverse(a),multiply(a,b)))),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
a = multiply(a,a),
inference(symmetry,[status(thm)],[44]) ).
tff(243,plain,
multiply(b,a) = multiply(b,multiply(a,a)),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
multiply(b,multiply(a,a)) = multiply(b,a),
inference(symmetry,[status(thm)],[243]) ).
tff(245,plain,
add(b,multiply(b,multiply(a,a))) = add(b,multiply(b,a)),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),add(b,multiply(b,multiply(a,a)))) = add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),add(b,multiply(b,a))),
inference(monotonicity,[status(thm)],[245]) ).
tff(247,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),b),multiply(b,multiply(a,a))) = add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),add(b,multiply(b,multiply(a,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(248,plain,
add(add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),b),multiply(b,multiply(a,a))) = add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),add(b,multiply(b,multiply(a,a)))),
inference(unit_resolution,[status(thm)],[247,110]) ).
tff(249,plain,
add(additive_inverse(b),b) = add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),b),
inference(symmetry,[status(thm)],[170]) ).
tff(250,plain,
additive_identity = add(additive_inverse(b),b),
inference(symmetry,[status(thm)],[103]) ).
tff(251,plain,
^ [X: $i] :
refl(
( ( multiply(X,additive_identity) = additive_identity )
<=> ( multiply(X,additive_identity) = additive_identity ) )),
inference(bind,[status(th)],]) ).
tff(252,plain,
( ! [X: $i] : ( multiply(X,additive_identity) = additive_identity )
<=> ! [X: $i] : ( multiply(X,additive_identity) = additive_identity ) ),
inference(quant_intro,[status(thm)],[251]) ).
tff(253,plain,
( ! [X: $i] : ( multiply(X,additive_identity) = additive_identity )
<=> ! [X: $i] : ( multiply(X,additive_identity) = additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(254,axiom,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',multiply_additive_id1) ).
tff(255,plain,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
inference(modus_ponens,[status(thm)],[254,253]) ).
tff(256,plain,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
inference(skolemize,[status(sab)],[255]) ).
tff(257,plain,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
inference(modus_ponens,[status(thm)],[256,252]) ).
tff(258,plain,
( ~ ! [X: $i] : ( multiply(X,additive_identity) = additive_identity )
| ( multiply(b,additive_identity) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(259,plain,
multiply(b,additive_identity) = additive_identity,
inference(unit_resolution,[status(thm)],[258,257]) ).
tff(260,plain,
multiply(b,additive_identity) = add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),b),
inference(transitivity,[status(thm)],[259,250,249]) ).
tff(261,plain,
add(multiply(b,additive_identity),multiply(b,multiply(a,a))) = add(add(add(additive_inverse(add(additive_inverse(a),additive_inverse(additive_identity))),additive_inverse(add(a,b))),b),multiply(b,multiply(a,a))),
inference(monotonicity,[status(thm)],[260]) ).
tff(262,plain,
additive_identity = multiply(b,additive_identity),
inference(symmetry,[status(thm)],[259]) ).
tff(263,plain,
( ~ ! [X: $i] : ( multiply(X,additive_identity) = additive_identity )
| ( multiply(add(multiply(b,a),multiply(b,additive_identity)),additive_identity) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(264,plain,
multiply(add(multiply(b,a),multiply(b,additive_identity)),additive_identity) = additive_identity,
inference(unit_resolution,[status(thm)],[263,257]) ).
tff(265,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(b,add(a,additive_identity)) = add(multiply(b,a),multiply(b,additive_identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(266,plain,
multiply(b,add(a,additive_identity)) = add(multiply(b,a),multiply(b,additive_identity)),
inference(unit_resolution,[status(thm)],[265,191]) ).
tff(267,plain,
multiply(b,add(a,additive_identity)) = multiply(b,a),
inference(monotonicity,[status(thm)],[131]) ).
tff(268,plain,
multiply(b,a) = multiply(b,add(a,additive_identity)),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
multiply(b,a) = add(multiply(b,a),multiply(b,additive_identity)),
inference(transitivity,[status(thm)],[268,266]) ).
tff(270,plain,
multiply(multiply(b,a),additive_identity) = multiply(add(multiply(b,a),multiply(b,additive_identity)),additive_identity),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
multiply(multiply(b,a),additive_identity) = multiply(b,additive_identity),
inference(transitivity,[status(thm)],[270,264,262]) ).
tff(272,plain,
add(multiply(multiply(b,a),additive_identity),multiply(b,multiply(a,a))) = add(multiply(b,additive_identity),multiply(b,multiply(a,a))),
inference(monotonicity,[status(thm)],[271]) ).
tff(273,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(multiply(multiply(b,a),additive_identity),multiply(b,multiply(a,a))) = add(multiply(b,multiply(a,a)),multiply(multiply(b,a),additive_identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(274,plain,
add(multiply(multiply(b,a),additive_identity),multiply(b,multiply(a,a))) = add(multiply(b,multiply(a,a)),multiply(multiply(b,a),additive_identity)),
inference(unit_resolution,[status(thm)],[273,156]) ).
tff(275,plain,
add(multiply(b,multiply(a,a)),multiply(multiply(b,a),additive_identity)) = add(multiply(multiply(b,a),additive_identity),multiply(b,multiply(a,a))),
inference(symmetry,[status(thm)],[274]) ).
tff(276,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,a),a) = multiply(b,multiply(a,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(277,plain,
multiply(multiply(b,a),a) = multiply(b,multiply(a,a)),
inference(unit_resolution,[status(thm)],[276,40]) ).
tff(278,plain,
add(multiply(multiply(b,a),a),multiply(multiply(b,a),additive_identity)) = add(multiply(b,multiply(a,a)),multiply(multiply(b,a),additive_identity)),
inference(monotonicity,[status(thm)],[277]) ).
tff(279,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(multiply(b,a),add(a,additive_identity)) = add(multiply(multiply(b,a),a),multiply(multiply(b,a),additive_identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(280,plain,
multiply(multiply(b,a),add(a,additive_identity)) = add(multiply(multiply(b,a),a),multiply(multiply(b,a),additive_identity)),
inference(unit_resolution,[status(thm)],[279,191]) ).
tff(281,plain,
multiply(multiply(b,a),a) = multiply(multiply(b,a),add(a,additive_identity)),
inference(monotonicity,[status(thm)],[132]) ).
tff(282,plain,
multiply(b,multiply(a,a)) = multiply(multiply(b,a),a),
inference(symmetry,[status(thm)],[277]) ).
tff(283,plain,
multiply(b,a) = multiply(a,b),
inference(transitivity,[status(thm)],[243,282,281,280,278,275,272,261,248,246,241,175,172,90,79,70,67,61,59,49,14,12]) ).
tff(284,plain,
( ( multiply(b,a) != c )
<=> ( multiply(b,a) != multiply(a,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(285,plain,
( ( multiply(b,a) != c )
<=> ( multiply(b,a) != c ) ),
inference(rewrite,[status(thm)],]) ).
tff(286,axiom,
multiply(b,a) != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
tff(287,plain,
multiply(b,a) != c,
inference(modus_ponens,[status(thm)],[286,285]) ).
tff(288,plain,
multiply(b,a) != multiply(a,b),
inference(modus_ponens,[status(thm)],[287,284]) ).
tff(289,plain,
$false,
inference(unit_resolution,[status(thm)],[288,283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 : Fri Sep 2 21:19:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 205.99/132.19 % SZS status Unsatisfiable
% 205.99/132.19 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------