TSTP Solution File: RNG008-4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG008-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 109.62s 70.64s
% Output : Proof 109.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 85
% Syntax : Number of formulae : 289 ( 216 unt; 7 typ; 0 def)
% Number of atoms : 366 ( 356 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 125 ( 50 ~; 43 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 9 ( 9 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 : 256 ( 238 !; 0 ?; 256 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(c_type,type,
c: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( add(additive_identity,X) = X )
<=> ( add(additive_identity,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( add(additive_identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',left_identity) ).
tff(5,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,multiply(a,b)) = multiply(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
add(additive_identity,multiply(a,b)) = multiply(a,b),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(
( ( multiply(X,X) = X )
<=> ( multiply(X,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] : ( multiply(X,X) = X )
<=> ! [X: $i] : ( multiply(X,X) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( multiply(X,X) = X )
<=> ! [X: $i] : ( multiply(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X: $i] : ( multiply(X,X) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolean_ring) ).
tff(14,plain,
! [X: $i] : ( multiply(X,X) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( multiply(X,X) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( multiply(X,X) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( multiply(X,X) = X )
| ( multiply(b,b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
multiply(b,b) = b,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
multiply(a,multiply(b,b)) = multiply(a,b),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
^ [X: $i] :
refl(
( ( add(additive_inverse(X),X) = additive_identity )
<=> ( add(additive_inverse(X),X) = additive_identity ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',left_additive_inverse) ).
tff(24,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(b),b) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
add(additive_inverse(b),b) = additive_identity,
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
add(additive_identity,b) = b,
inference(unit_resolution,[status(thm)],[29,7]) ).
tff(31,plain,
^ [Y: $i,X: $i] :
refl(
( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(32,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)],[31]) ).
tff(33,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(34,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',commutative_addition) ).
tff(35,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,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(39,plain,
add(additive_identity,b) = add(b,additive_identity),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
add(b,additive_identity) = add(additive_identity,b),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
add(b,additive_identity) = b,
inference(transitivity,[status(thm)],[40,30]) ).
tff(42,plain,
b = multiply(b,b),
inference(symmetry,[status(thm)],[18]) ).
tff(43,plain,
additive_inverse(b) = additive_inverse(multiply(b,b)),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
additive_inverse(multiply(b,b)) = additive_inverse(b),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
add(additive_inverse(multiply(b,b)),add(b,additive_identity)) = add(additive_inverse(b),b),
inference(monotonicity,[status(thm)],[44,41]) ).
tff(46,plain,
add(additive_inverse(multiply(b,b)),add(b,additive_identity)) = additive_identity,
inference(transitivity,[status(thm)],[45,28]) ).
tff(47,plain,
add(add(additive_inverse(multiply(b,b)),add(b,additive_identity)),multiply(a,multiply(b,b))) = add(additive_identity,multiply(a,b)),
inference(monotonicity,[status(thm)],[46,19]) ).
tff(48,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(49,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)],[48]) ).
tff(50,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(51,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',associative_addition) ).
tff(52,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(additive_inverse(multiply(b,b)),add(b,additive_identity)),multiply(a,multiply(b,b))) = add(additive_inverse(multiply(b,b)),add(add(b,additive_identity),multiply(a,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
add(add(additive_inverse(multiply(b,b)),add(b,additive_identity)),multiply(a,multiply(b,b))) = add(additive_inverse(multiply(b,b)),add(add(b,additive_identity),multiply(a,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
add(additive_inverse(multiply(b,b)),add(add(b,additive_identity),multiply(a,multiply(b,b)))) = add(add(additive_inverse(multiply(b,b)),add(b,additive_identity)),multiply(a,multiply(b,b))),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(b,additive_identity),multiply(a,multiply(b,b))) = add(b,add(additive_identity,multiply(a,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
add(add(b,additive_identity),multiply(a,multiply(b,b))) = add(b,add(additive_identity,multiply(a,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[58,54]) ).
tff(60,plain,
add(b,add(additive_identity,multiply(a,multiply(b,b)))) = add(add(b,additive_identity),multiply(a,multiply(b,b))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
add(additive_identity,multiply(a,multiply(b,b))) = add(additive_identity,multiply(a,b)),
inference(monotonicity,[status(thm)],[19]) ).
tff(62,plain,
add(additive_identity,multiply(a,multiply(b,b))) = multiply(a,b),
inference(transitivity,[status(thm)],[61,9]) ).
tff(63,plain,
add(b,add(additive_identity,multiply(a,multiply(b,b)))) = add(b,multiply(a,b)),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
add(b,multiply(a,b)) = add(b,add(additive_identity,multiply(a,multiply(b,b)))),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(b,multiply(a,b)) = add(multiply(a,b),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
add(b,multiply(a,b)) = add(multiply(a,b),b),
inference(unit_resolution,[status(thm)],[65,37]) ).
tff(67,plain,
add(multiply(a,b),b) = add(b,multiply(a,b)),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
add(multiply(a,b),b) = add(add(b,additive_identity),multiply(a,multiply(b,b))),
inference(transitivity,[status(thm)],[67,64,60]) ).
tff(69,plain,
add(additive_inverse(multiply(b,b)),add(multiply(a,b),b)) = add(additive_inverse(multiply(b,b)),add(add(b,additive_identity),multiply(a,multiply(b,b)))),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_inverse(multiply(b,b)),add(multiply(a,b),b)) = add(add(multiply(a,b),b),additive_inverse(multiply(b,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
add(additive_inverse(multiply(b,b)),add(multiply(a,b),b)) = add(add(multiply(a,b),b),additive_inverse(multiply(b,b))),
inference(unit_resolution,[status(thm)],[70,37]) ).
tff(72,plain,
add(add(multiply(a,b),b),additive_inverse(multiply(b,b))) = add(additive_inverse(multiply(b,b)),add(multiply(a,b),b)),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( ~ ! [X: $i] : ( multiply(X,X) = X )
| ( multiply(additive_inverse(multiply(b,b)),additive_inverse(multiply(b,b))) = additive_inverse(multiply(b,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
multiply(additive_inverse(multiply(b,b)),additive_inverse(multiply(b,b))) = additive_inverse(multiply(b,b)),
inference(unit_resolution,[status(thm)],[73,16]) ).
tff(75,plain,
additive_inverse(add(b,additive_identity)) = additive_inverse(b),
inference(monotonicity,[status(thm)],[41]) ).
tff(76,plain,
additive_inverse(b) = additive_inverse(add(b,additive_identity)),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
additive_inverse(multiply(b,b)) = additive_inverse(add(b,additive_identity)),
inference(transitivity,[status(thm)],[44,76]) ).
tff(78,plain,
multiply(additive_inverse(multiply(b,b)),additive_inverse(multiply(b,b))) = multiply(additive_inverse(multiply(b,b)),additive_inverse(add(b,additive_identity))),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
multiply(additive_inverse(multiply(b,b)),additive_inverse(add(b,additive_identity))) = multiply(additive_inverse(multiply(b,b)),additive_inverse(multiply(b,b))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,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(81,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)],[80]) ).
tff(82,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(83,axiom,
! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse1) ).
tff(84,plain,
! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(multiply(b,b)),additive_inverse(add(b,additive_identity))) = additive_inverse(multiply(additive_inverse(multiply(b,b)),add(b,additive_identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
multiply(additive_inverse(multiply(b,b)),additive_inverse(add(b,additive_identity))) = additive_inverse(multiply(additive_inverse(multiply(b,b)),add(b,additive_identity))),
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
additive_inverse(multiply(additive_inverse(multiply(b,b)),add(b,additive_identity))) = multiply(additive_inverse(multiply(b,b)),additive_inverse(add(b,additive_identity))),
inference(symmetry,[status(thm)],[88]) ).
tff(90,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(91,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)],[90]) ).
tff(92,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(93,axiom,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse2) ).
tff(94,plain,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(b),b) = additive_inverse(multiply(b,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
multiply(additive_inverse(b),b) = additive_inverse(multiply(b,b)),
inference(unit_resolution,[status(thm)],[97,96]) ).
tff(99,plain,
multiply(additive_inverse(multiply(b,b)),add(b,additive_identity)) = multiply(additive_inverse(b),b),
inference(monotonicity,[status(thm)],[44,41]) ).
tff(100,plain,
multiply(additive_inverse(multiply(b,b)),add(b,additive_identity)) = additive_inverse(b),
inference(transitivity,[status(thm)],[99,98,44]) ).
tff(101,plain,
additive_inverse(multiply(additive_inverse(multiply(b,b)),add(b,additive_identity))) = additive_inverse(additive_inverse(b)),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
additive_inverse(additive_inverse(b)) = additive_inverse(multiply(additive_inverse(multiply(b,b)),add(b,additive_identity))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X )
<=> ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X )
<=> ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,axiom,
! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',additive_inverse_additive_inverse) ).
tff(106,plain,
! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
( ~ ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X )
| ( additive_inverse(additive_inverse(b)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
additive_inverse(additive_inverse(b)) = b,
inference(unit_resolution,[status(thm)],[109,108]) ).
tff(111,plain,
b = additive_inverse(additive_inverse(b)),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
add(b,additive_identity) = additive_inverse(multiply(b,b)),
inference(transitivity,[status(thm)],[40,30,111,102,89,79,74]) ).
tff(113,plain,
add(add(multiply(a,b),b),add(b,additive_identity)) = add(add(multiply(a,b),b),additive_inverse(multiply(b,b))),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(multiply(a,b),b),add(b,additive_identity)) = add(add(b,additive_identity),add(multiply(a,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(115,plain,
add(add(multiply(a,b),b),add(b,additive_identity)) = add(add(b,additive_identity),add(multiply(a,b),b)),
inference(unit_resolution,[status(thm)],[114,37]) ).
tff(116,plain,
add(add(b,additive_identity),add(multiply(a,b),b)) = add(add(multiply(a,b),b),add(b,additive_identity)),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
add(add(additive_identity,multiply(a,b)),b) = add(multiply(a,b),b),
inference(monotonicity,[status(thm)],[9]) ).
tff(118,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(additive_identity,multiply(a,b)),b) = add(additive_identity,add(multiply(a,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
add(add(additive_identity,multiply(a,b)),b) = add(additive_identity,add(multiply(a,b),b)),
inference(unit_resolution,[status(thm)],[118,54]) ).
tff(120,plain,
add(additive_identity,add(multiply(a,b),b)) = add(add(additive_identity,multiply(a,b)),b),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(additive_inverse(a)),additive_inverse(a)) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
add(additive_inverse(additive_inverse(a)),additive_inverse(a)) = additive_identity,
inference(unit_resolution,[status(thm)],[121,26]) ).
tff(123,plain,
( ~ ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X )
| ( additive_inverse(additive_inverse(a)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(124,plain,
additive_inverse(additive_inverse(a)) = a,
inference(unit_resolution,[status(thm)],[123,108]) ).
tff(125,plain,
a = additive_inverse(additive_inverse(a)),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
add(a,additive_inverse(a)) = add(additive_inverse(additive_inverse(a)),additive_inverse(a)),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
add(a,additive_inverse(a)) = additive_identity,
inference(transitivity,[status(thm)],[126,122]) ).
tff(128,plain,
add(add(a,additive_inverse(a)),add(multiply(a,b),b)) = add(additive_identity,add(multiply(a,b),b)),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(a,additive_inverse(a)),add(multiply(a,b),b)) = add(a,add(additive_inverse(a),add(multiply(a,b),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
add(add(a,additive_inverse(a)),add(multiply(a,b),b)) = add(a,add(additive_inverse(a),add(multiply(a,b),b))),
inference(unit_resolution,[status(thm)],[129,54]) ).
tff(131,plain,
add(a,add(additive_inverse(a),add(multiply(a,b),b))) = add(add(a,additive_inverse(a)),add(multiply(a,b),b)),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
add(a,add(additive_inverse(a),add(multiply(a,b),b))) = add(multiply(a,b),b),
inference(transitivity,[status(thm)],[131,128,120,117]) ).
tff(133,plain,
add(add(b,additive_identity),add(a,add(additive_inverse(a),add(multiply(a,b),b)))) = add(add(b,additive_identity),add(multiply(a,b),b)),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(b,additive_identity),a),add(additive_inverse(a),add(multiply(a,b),b))) = add(add(b,additive_identity),add(a,add(additive_inverse(a),add(multiply(a,b),b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
add(add(add(b,additive_identity),a),add(additive_inverse(a),add(multiply(a,b),b))) = add(add(b,additive_identity),add(a,add(additive_inverse(a),add(multiply(a,b),b)))),
inference(unit_resolution,[status(thm)],[134,54]) ).
tff(136,plain,
add(add(b,additive_identity),a) = add(b,a),
inference(monotonicity,[status(thm)],[41]) ).
tff(137,plain,
add(b,a) = add(add(b,additive_identity),a),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(a,b) = add(b,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(139,plain,
add(a,b) = add(b,a),
inference(unit_resolution,[status(thm)],[138,37]) ).
tff(140,plain,
b = add(additive_identity,b),
inference(symmetry,[status(thm)],[30]) ).
tff(141,plain,
b = add(b,additive_identity),
inference(transitivity,[status(thm)],[140,39]) ).
tff(142,plain,
add(a,b) = add(a,add(b,additive_identity)),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
add(a,add(b,additive_identity)) = add(a,b),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [X: $i] : ( multiply(X,X) = X )
| ( multiply(add(a,add(b,additive_identity)),add(a,add(b,additive_identity))) = add(a,add(b,additive_identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(145,plain,
multiply(add(a,add(b,additive_identity)),add(a,add(b,additive_identity))) = add(a,add(b,additive_identity)),
inference(unit_resolution,[status(thm)],[144,16]) ).
tff(146,plain,
add(b,a) = add(a,b),
inference(symmetry,[status(thm)],[139]) ).
tff(147,plain,
( ~ ! [X: $i] : ( multiply(X,X) = X )
| ( multiply(a,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(148,plain,
multiply(a,a) = a,
inference(unit_resolution,[status(thm)],[147,16]) ).
tff(149,plain,
multiply(a,additive_inverse(additive_inverse(a))) = multiply(a,a),
inference(monotonicity,[status(thm)],[124]) ).
tff(150,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) )
| ( multiply(a,additive_inverse(additive_inverse(a))) = additive_inverse(multiply(a,additive_inverse(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(151,plain,
multiply(a,additive_inverse(additive_inverse(a))) = additive_inverse(multiply(a,additive_inverse(a))),
inference(unit_resolution,[status(thm)],[150,86]) ).
tff(152,plain,
additive_inverse(multiply(a,additive_inverse(a))) = multiply(a,additive_inverse(additive_inverse(a))),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(a),additive_inverse(a)) = additive_inverse(multiply(a,additive_inverse(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
multiply(additive_inverse(a),additive_inverse(a)) = additive_inverse(multiply(a,additive_inverse(a))),
inference(unit_resolution,[status(thm)],[153,96]) ).
tff(155,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,additive_inverse(a)) = additive_inverse(a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,plain,
add(additive_identity,additive_inverse(a)) = additive_inverse(a),
inference(unit_resolution,[status(thm)],[155,7]) ).
tff(157,plain,
multiply(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(a))) = multiply(additive_inverse(a),additive_inverse(a)),
inference(monotonicity,[status(thm)],[156,156]) ).
tff(158,plain,
( ~ ! [X: $i] : ( multiply(X,X) = X )
| ( multiply(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(a))) = add(additive_identity,additive_inverse(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
multiply(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(a))) = add(additive_identity,additive_inverse(a)),
inference(unit_resolution,[status(thm)],[158,16]) ).
tff(160,plain,
add(additive_identity,additive_inverse(a)) = multiply(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(a))),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
add(additive_identity,additive_inverse(a)) = a,
inference(transitivity,[status(thm)],[160,157,154,152,149,148]) ).
tff(162,plain,
add(b,add(additive_identity,additive_inverse(a))) = add(add(b,additive_identity),a),
inference(monotonicity,[status(thm)],[141,161]) ).
tff(163,plain,
additive_inverse(a) = add(additive_identity,additive_inverse(a)),
inference(symmetry,[status(thm)],[156]) ).
tff(164,plain,
add(add(b,additive_identity),additive_inverse(a)) = add(b,add(additive_identity,additive_inverse(a))),
inference(monotonicity,[status(thm)],[41,163]) ).
tff(165,plain,
add(add(b,additive_identity),additive_inverse(a)) = add(a,add(b,additive_identity)),
inference(transitivity,[status(thm)],[164,162,136,146,142]) ).
tff(166,plain,
multiply(add(a,add(b,additive_identity)),add(add(b,additive_identity),additive_inverse(a))) = multiply(add(a,add(b,additive_identity)),add(a,add(b,additive_identity))),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
multiply(add(a,add(b,additive_identity)),add(add(b,additive_identity),additive_inverse(a))) = add(add(b,additive_identity),a),
inference(transitivity,[status(thm)],[166,145,143,139,137]) ).
tff(168,plain,
add(multiply(add(a,add(b,additive_identity)),add(add(b,additive_identity),additive_inverse(a))),add(additive_inverse(a),add(multiply(a,b),b))) = add(add(add(b,additive_identity),a),add(additive_inverse(a),add(multiply(a,b),b))),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(multiply(a,b),b),additive_inverse(a)) = add(additive_inverse(a),add(multiply(a,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(170,plain,
add(add(multiply(a,b),b),additive_inverse(a)) = add(additive_inverse(a),add(multiply(a,b),b)),
inference(unit_resolution,[status(thm)],[169,37]) ).
tff(171,plain,
add(add(multiply(a,b),b),add(additive_identity,additive_inverse(a))) = add(add(multiply(a,b),b),additive_inverse(a)),
inference(monotonicity,[status(thm)],[156]) ).
tff(172,plain,
multiply(additive_inverse(a),additive_inverse(a)) = multiply(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(a))),
inference(symmetry,[status(thm)],[157]) ).
tff(173,plain,
additive_inverse(multiply(a,additive_inverse(a))) = multiply(additive_inverse(a),additive_inverse(a)),
inference(symmetry,[status(thm)],[154]) ).
tff(174,plain,
multiply(a,a) = multiply(a,additive_inverse(additive_inverse(a))),
inference(symmetry,[status(thm)],[149]) ).
tff(175,plain,
a = multiply(a,a),
inference(symmetry,[status(thm)],[148]) ).
tff(176,plain,
a = add(additive_identity,additive_inverse(a)),
inference(transitivity,[status(thm)],[175,174,151,173,172,159]) ).
tff(177,plain,
add(add(multiply(a,b),b),a) = add(add(multiply(a,b),b),add(additive_identity,additive_inverse(a))),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(multiply(a,b),b),a) = add(a,add(multiply(a,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(179,plain,
add(add(multiply(a,b),b),a) = add(a,add(multiply(a,b),b)),
inference(unit_resolution,[status(thm)],[178,37]) ).
tff(180,plain,
add(a,add(multiply(a,b),b)) = add(add(multiply(a,b),b),a),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
add(add(b,additive_identity),multiply(a,multiply(b,b))) = add(multiply(a,b),b),
inference(transitivity,[status(thm)],[59,63,66]) ).
tff(182,plain,
add(a,add(add(b,additive_identity),multiply(a,multiply(b,b)))) = add(a,add(multiply(a,b),b)),
inference(monotonicity,[status(thm)],[181]) ).
tff(183,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(a,add(b,additive_identity)),multiply(a,multiply(b,b))) = add(a,add(add(b,additive_identity),multiply(a,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(184,plain,
add(add(a,add(b,additive_identity)),multiply(a,multiply(b,b))) = add(a,add(add(b,additive_identity),multiply(a,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[183,54]) ).
tff(185,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(multiply(a,multiply(b,b)),add(a,add(b,additive_identity))) = add(add(a,add(b,additive_identity)),multiply(a,multiply(b,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(186,plain,
add(multiply(a,multiply(b,b)),add(a,add(b,additive_identity))) = add(add(a,add(b,additive_identity)),multiply(a,multiply(b,b))),
inference(unit_resolution,[status(thm)],[185,37]) ).
tff(187,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(multiply(a,multiply(b,b)),a),add(b,additive_identity)) = add(multiply(a,multiply(b,b)),add(a,add(b,additive_identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
add(add(multiply(a,multiply(b,b)),a),add(b,additive_identity)) = add(multiply(a,multiply(b,b)),add(a,add(b,additive_identity))),
inference(unit_resolution,[status(thm)],[187,54]) ).
tff(189,plain,
add(add(multiply(a,multiply(b,b)),a),add(b,additive_identity)) = add(additive_inverse(a),add(multiply(a,b),b)),
inference(transitivity,[status(thm)],[188,186,184,182,180,177,171,170]) ).
tff(190,plain,
add(multiply(add(a,add(b,additive_identity)),add(add(b,additive_identity),additive_inverse(a))),add(add(multiply(a,multiply(b,b)),a),add(b,additive_identity))) = add(multiply(add(a,add(b,additive_identity)),add(add(b,additive_identity),additive_inverse(a))),add(additive_inverse(a),add(multiply(a,b),b))),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(multiply(add(a,add(b,additive_identity)),add(add(b,additive_identity),additive_inverse(a))),add(multiply(a,multiply(b,b)),a)),add(b,additive_identity)) = add(multiply(add(a,add(b,additive_identity)),add(add(b,additive_identity),additive_inverse(a))),add(add(multiply(a,multiply(b,b)),a),add(b,additive_identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(192,plain,
add(add(multiply(add(a,add(b,additive_identity)),add(add(b,additive_identity),additive_inverse(a))),add(multiply(a,multiply(b,b)),a)),add(b,additive_identity)) = add(multiply(add(a,add(b,additive_identity)),add(add(b,additive_identity),additive_inverse(a))),add(add(multiply(a,multiply(b,b)),a),add(b,additive_identity))),
inference(unit_resolution,[status(thm)],[191,54]) ).
tff(193,plain,
add(a,add(b,additive_identity)) = add(b,a),
inference(transitivity,[status(thm)],[143,139]) ).
tff(194,plain,
multiply(add(additive_identity,additive_inverse(a)),add(a,add(b,additive_identity))) = multiply(additive_inverse(a),add(b,a)),
inference(monotonicity,[status(thm)],[156,193]) ).
tff(195,plain,
multiply(additive_inverse(a),add(b,a)) = multiply(add(additive_identity,additive_inverse(a)),add(a,add(b,additive_identity))),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
additive_inverse(a) = a,
inference(transitivity,[status(thm)],[163,160,157,154,152,149,148]) ).
tff(197,plain,
multiply(additive_inverse(a),add(b,a)) = multiply(a,add(b,a)),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
multiply(a,add(b,a)) = multiply(additive_inverse(a),add(b,a)),
inference(symmetry,[status(thm)],[197]) ).
tff(199,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(200,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)],[199]) ).
tff(201,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(202,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',distribute1) ).
tff(203,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[202,201]) ).
tff(204,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[203]) ).
tff(205,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[204,200]) ).
tff(206,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(a,add(b,a)) = add(multiply(a,b),multiply(a,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(207,plain,
multiply(a,add(b,a)) = add(multiply(a,b),multiply(a,a)),
inference(unit_resolution,[status(thm)],[206,205]) ).
tff(208,plain,
add(multiply(a,b),multiply(a,a)) = multiply(a,add(b,a)),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
multiply(a,b) = multiply(a,multiply(b,b)),
inference(symmetry,[status(thm)],[19]) ).
tff(210,plain,
add(multiply(a,b),multiply(a,a)) = add(multiply(a,multiply(b,b)),a),
inference(monotonicity,[status(thm)],[209,148]) ).
tff(211,plain,
add(multiply(a,multiply(b,b)),a) = add(multiply(a,b),multiply(a,a)),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
add(multiply(a,multiply(b,b)),a) = multiply(add(additive_identity,additive_inverse(a)),add(a,add(b,additive_identity))),
inference(transitivity,[status(thm)],[211,208,198,195]) ).
tff(213,plain,
add(multiply(add(a,add(b,additive_identity)),add(add(b,additive_identity),additive_inverse(a))),add(multiply(a,multiply(b,b)),a)) = add(multiply(add(a,add(b,additive_identity)),add(a,add(b,additive_identity))),multiply(add(additive_identity,additive_inverse(a)),add(a,add(b,additive_identity)))),
inference(monotonicity,[status(thm)],[166,212]) ).
tff(214,plain,
add(multiply(add(a,add(b,additive_identity)),add(a,add(b,additive_identity))),multiply(add(additive_identity,additive_inverse(a)),add(a,add(b,additive_identity)))) = add(multiply(add(a,add(b,additive_identity)),add(add(b,additive_identity),additive_inverse(a))),add(multiply(a,multiply(b,b)),a)),
inference(symmetry,[status(thm)],[213]) ).
tff(215,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(216,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)],[215]) ).
tff(217,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(218,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',distribute2) ).
tff(219,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[218,217]) ).
tff(220,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[219]) ).
tff(221,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[220,216]) ).
tff(222,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(add(a,add(b,additive_identity)),add(additive_identity,additive_inverse(a))),add(a,add(b,additive_identity))) = add(multiply(add(a,add(b,additive_identity)),add(a,add(b,additive_identity))),multiply(add(additive_identity,additive_inverse(a)),add(a,add(b,additive_identity)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(223,plain,
multiply(add(add(a,add(b,additive_identity)),add(additive_identity,additive_inverse(a))),add(a,add(b,additive_identity))) = add(multiply(add(a,add(b,additive_identity)),add(a,add(b,additive_identity))),multiply(add(additive_identity,additive_inverse(a)),add(a,add(b,additive_identity)))),
inference(unit_resolution,[status(thm)],[222,221]) ).
tff(224,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(additive_identity),additive_identity) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(225,plain,
add(additive_inverse(additive_identity),additive_identity) = additive_identity,
inference(unit_resolution,[status(thm)],[224,26]) ).
tff(226,plain,
( ( additive_inverse(additive_identity) = additive_identity )
<=> ( additive_inverse(additive_identity) = additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(227,axiom,
additive_inverse(additive_identity) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',additive_inverse_identity) ).
tff(228,plain,
additive_inverse(additive_identity) = additive_identity,
inference(modus_ponens,[status(thm)],[227,226]) ).
tff(229,plain,
additive_identity = additive_inverse(additive_identity),
inference(symmetry,[status(thm)],[228]) ).
tff(230,plain,
add(a,additive_inverse(a)) = additive_inverse(additive_identity),
inference(transitivity,[status(thm)],[126,122,229]) ).
tff(231,plain,
add(add(a,additive_inverse(a)),additive_identity) = add(additive_inverse(additive_identity),additive_identity),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(a,additive_inverse(a)),additive_identity) = add(a,add(additive_inverse(a),additive_identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(233,plain,
add(add(a,additive_inverse(a)),additive_identity) = add(a,add(additive_inverse(a),additive_identity)),
inference(unit_resolution,[status(thm)],[232,54]) ).
tff(234,plain,
add(a,add(additive_inverse(a),additive_identity)) = add(add(a,additive_inverse(a)),additive_identity),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
add(a,add(additive_inverse(a),additive_identity)) = additive_identity,
inference(transitivity,[status(thm)],[234,231,225]) ).
tff(236,plain,
add(b,add(a,add(additive_inverse(a),additive_identity))) = add(b,additive_identity),
inference(monotonicity,[status(thm)],[235]) ).
tff(237,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(b,a),add(additive_inverse(a),additive_identity)) = add(b,add(a,add(additive_inverse(a),additive_identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(238,plain,
add(add(b,a),add(additive_inverse(a),additive_identity)) = add(b,add(a,add(additive_inverse(a),additive_identity))),
inference(unit_resolution,[status(thm)],[237,54]) ).
tff(239,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_inverse(a),additive_identity) = add(additive_identity,additive_inverse(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(240,plain,
add(additive_inverse(a),additive_identity) = add(additive_identity,additive_inverse(a)),
inference(unit_resolution,[status(thm)],[239,37]) ).
tff(241,plain,
add(additive_identity,additive_inverse(a)) = add(additive_inverse(a),additive_identity),
inference(symmetry,[status(thm)],[240]) ).
tff(242,plain,
add(add(a,add(b,additive_identity)),add(additive_identity,additive_inverse(a))) = add(add(b,a),add(additive_inverse(a),additive_identity)),
inference(monotonicity,[status(thm)],[193,241]) ).
tff(243,plain,
add(add(a,add(b,additive_identity)),add(additive_identity,additive_inverse(a))) = b,
inference(transitivity,[status(thm)],[242,238,236,40,30]) ).
tff(244,plain,
multiply(add(add(a,add(b,additive_identity)),add(additive_identity,additive_inverse(a))),add(a,add(b,additive_identity))) = multiply(b,add(b,a)),
inference(monotonicity,[status(thm)],[243,193]) ).
tff(245,plain,
multiply(b,add(b,a)) = multiply(add(add(a,add(b,additive_identity)),add(additive_identity,additive_inverse(a))),add(a,add(b,additive_identity))),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(b,add(b,a)) = add(multiply(b,b),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(247,plain,
multiply(b,add(b,a)) = add(multiply(b,b),multiply(b,a)),
inference(unit_resolution,[status(thm)],[246,205]) ).
tff(248,plain,
add(multiply(b,b),multiply(b,a)) = multiply(b,add(b,a)),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
add(multiply(b,b),multiply(b,a)) = add(b,multiply(b,a)),
inference(monotonicity,[status(thm)],[18]) ).
tff(250,plain,
add(b,multiply(b,a)) = add(multiply(b,b),multiply(b,a)),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(b,multiply(b,a)) = add(multiply(b,a),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(252,plain,
add(b,multiply(b,a)) = add(multiply(b,a),b),
inference(unit_resolution,[status(thm)],[251,37]) ).
tff(253,plain,
add(multiply(b,a),b) = add(b,multiply(b,a)),
inference(symmetry,[status(thm)],[252]) ).
tff(254,plain,
add(multiply(b,a),b) = add(multiply(add(a,add(b,additive_identity)),add(add(b,additive_identity),additive_inverse(a))),add(multiply(a,multiply(b,b)),a)),
inference(transitivity,[status(thm)],[253,250,248,245,223,214]) ).
tff(255,plain,
add(add(multiply(b,a),b),add(b,additive_identity)) = add(add(multiply(add(a,add(b,additive_identity)),add(add(b,additive_identity),additive_inverse(a))),add(multiply(a,multiply(b,b)),a)),add(b,additive_identity)),
inference(monotonicity,[status(thm)],[254]) ).
tff(256,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(multiply(b,a),b),add(b,additive_identity)) = add(add(b,additive_identity),add(multiply(b,a),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(257,plain,
add(add(multiply(b,a),b),add(b,additive_identity)) = add(add(b,additive_identity),add(multiply(b,a),b)),
inference(unit_resolution,[status(thm)],[256,37]) ).
tff(258,plain,
add(add(b,additive_identity),add(multiply(b,a),b)) = add(add(multiply(b,a),b),add(b,additive_identity)),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
additive_inverse(multiply(b,b)) = multiply(additive_inverse(multiply(b,b)),additive_inverse(multiply(b,b))),
inference(symmetry,[status(thm)],[74]) ).
tff(260,plain,
additive_inverse(multiply(b,b)) = add(b,additive_identity),
inference(transitivity,[status(thm)],[259,78,88,101,110,140,39]) ).
tff(261,plain,
add(additive_inverse(multiply(b,b)),add(multiply(b,a),b)) = add(add(b,additive_identity),add(multiply(b,a),b)),
inference(monotonicity,[status(thm)],[260]) ).
tff(262,plain,
multiply(b,a) = multiply(b,multiply(a,a)),
inference(monotonicity,[status(thm)],[175]) ).
tff(263,plain,
multiply(b,multiply(a,a)) = multiply(b,a),
inference(symmetry,[status(thm)],[262]) ).
tff(264,plain,
add(add(b,additive_identity),multiply(b,multiply(a,a))) = add(b,multiply(b,a)),
inference(monotonicity,[status(thm)],[41,263]) ).
tff(265,plain,
add(add(b,additive_identity),multiply(b,multiply(a,a))) = add(multiply(b,a),b),
inference(transitivity,[status(thm)],[264,252]) ).
tff(266,plain,
add(additive_inverse(multiply(b,b)),add(add(b,additive_identity),multiply(b,multiply(a,a)))) = add(additive_inverse(multiply(b,b)),add(multiply(b,a),b)),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(additive_inverse(multiply(b,b)),add(b,additive_identity)),multiply(b,multiply(a,a))) = add(additive_inverse(multiply(b,b)),add(add(b,additive_identity),multiply(b,multiply(a,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(268,plain,
add(add(additive_inverse(multiply(b,b)),add(b,additive_identity)),multiply(b,multiply(a,a))) = add(additive_inverse(multiply(b,b)),add(add(b,additive_identity),multiply(b,multiply(a,a)))),
inference(unit_resolution,[status(thm)],[267,54]) ).
tff(269,plain,
add(additive_inverse(b),b) = add(additive_inverse(multiply(b,b)),add(b,additive_identity)),
inference(symmetry,[status(thm)],[45]) ).
tff(270,plain,
additive_identity = add(additive_inverse(b),b),
inference(symmetry,[status(thm)],[28]) ).
tff(271,plain,
additive_identity = add(additive_inverse(multiply(b,b)),add(b,additive_identity)),
inference(transitivity,[status(thm)],[270,269]) ).
tff(272,plain,
add(additive_identity,multiply(b,multiply(a,a))) = add(add(additive_inverse(multiply(b,b)),add(b,additive_identity)),multiply(b,multiply(a,a))),
inference(monotonicity,[status(thm)],[271]) ).
tff(273,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,multiply(b,multiply(a,a))) = multiply(b,multiply(a,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(274,plain,
add(additive_identity,multiply(b,multiply(a,a))) = multiply(b,multiply(a,a)),
inference(unit_resolution,[status(thm)],[273,7]) ).
tff(275,plain,
multiply(b,multiply(a,a)) = add(additive_identity,multiply(b,multiply(a,a))),
inference(symmetry,[status(thm)],[274]) ).
tff(276,plain,
multiply(b,a) = multiply(a,b),
inference(transitivity,[status(thm)],[262,275,272,268,266,261,258,255,192,190,168,135,133,116,113,72,69,57,47,9]) ).
tff(277,plain,
( ( multiply(b,a) != c )
<=> ( multiply(b,a) != multiply(a,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(278,plain,
( ( multiply(b,a) != c )
<=> ( multiply(b,a) != c ) ),
inference(rewrite,[status(thm)],]) ).
tff(279,axiom,
multiply(b,a) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
tff(280,plain,
multiply(b,a) != c,
inference(modus_ponens,[status(thm)],[279,278]) ).
tff(281,plain,
multiply(b,a) != multiply(a,b),
inference(modus_ponens,[status(thm)],[280,277]) ).
tff(282,plain,
$false,
inference(unit_resolution,[status(thm)],[281,276]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG008-4 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n003.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 21:18:55 EDT 2022
% 0.12/0.34 % 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.
% 109.62/70.64 % SZS status Unsatisfiable
% 109.62/70.64 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------