TSTP Solution File: RNG020-7 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG020-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 03:17:43 EDT 2022
% Result : Unsatisfiable 0.19s 0.50s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 47
% Syntax : Number of formulae : 117 ( 78 unt; 8 typ; 0 def)
% Number of atoms : 154 ( 146 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 58 ( 20 ~; 16 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 213 ( 194 !; 0 ?; 213 :)
% Comments :
%------------------------------------------------------------------------------
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(associator_type,type,
associator: ( $i * $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(v_type,type,
v: $i ).
tff(x_type,type,
x: $i ).
tff(u_type,type,
u: $i ).
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
tff(5,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(associator(x,v,y),associator(x,u,y)) = add(associator(x,u,y),associator(x,v,y)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
add(associator(x,v,y),associator(x,u,y)) = add(associator(x,u,y),associator(x,v,y)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
<=> ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associator) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
| ( associator(x,u,y) = add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
associator(x,u,y) = add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y)))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
| ( associator(x,v,y) = add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
associator(x,v,y) = add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,plain,
add(associator(x,v,y),associator(x,u,y)) = add(add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))),add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y))))),
inference(monotonicity,[status(thm)],[20,18]) ).
tff(22,plain,
add(add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))),add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y))))) = add(associator(x,v,y),associator(x,u,y)),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
<=> ( add(X,add(Y,Z)) = add(add(X,Y),Z) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(multiply(multiply(x,v),y),add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y)))))) = add(add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))),add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
add(multiply(multiply(x,v),y),add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y)))))) = add(add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))),add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y))))),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y))))),multiply(multiply(x,v),y)) = add(multiply(multiply(x,v),y),add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
add(add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y))))),multiply(multiply(x,v),y)) = add(multiply(multiply(x,v),y),add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y)))))),
inference(unit_resolution,[status(thm)],[32,7]) ).
tff(34,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(additive_inverse(X),add(Y,Z)) = add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))) )
<=> ( multiply(additive_inverse(X),add(Y,Z)) = add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(additive_inverse(X),add(Y,Z)) = add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(additive_inverse(X),add(Y,Z)) = add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(additive_inverse(X),add(Y,Z)) = add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(additive_inverse(X),add(Y,Z)) = add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(additive_inverse(X),add(Y,Z)) = add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_of_difference3) ).
tff(38,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(additive_inverse(X),add(Y,Z)) = add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(additive_inverse(X),add(Y,Z)) = add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(additive_inverse(X),add(Y,Z)) = add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(additive_inverse(X),add(Y,Z)) = add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))) )
| ( multiply(additive_inverse(x),add(multiply(v,y),multiply(u,y))) = add(additive_inverse(multiply(x,multiply(v,y))),additive_inverse(multiply(x,multiply(u,y)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
multiply(additive_inverse(x),add(multiply(v,y),multiply(u,y))) = add(additive_inverse(multiply(x,multiply(v,y))),additive_inverse(multiply(x,multiply(u,y)))),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(v,u) = add(u,v) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
add(v,u) = add(u,v),
inference(unit_resolution,[status(thm)],[43,7]) ).
tff(45,plain,
multiply(add(v,u),y) = multiply(add(u,v),y),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,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(47,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)],[46]) ).
tff(48,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(49,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/RNG003-0.ax',distribute2) ).
tff(50,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(v,u),y) = add(multiply(v,y),multiply(u,y)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
multiply(add(v,u),y) = add(multiply(v,y),multiply(u,y)),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
add(multiply(v,y),multiply(u,y)) = multiply(add(v,u),y),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
add(multiply(v,y),multiply(u,y)) = multiply(add(u,v),y),
inference(transitivity,[status(thm)],[55,45]) ).
tff(57,plain,
multiply(additive_inverse(x),add(multiply(v,y),multiply(u,y))) = multiply(additive_inverse(x),multiply(add(u,v),y)),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
multiply(additive_inverse(x),multiply(add(u,v),y)) = multiply(additive_inverse(x),add(multiply(v,y),multiply(u,y))),
inference(symmetry,[status(thm)],[57]) ).
tff(59,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(60,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)],[59]) ).
tff(61,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(62,axiom,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product1) ).
tff(63,plain,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(x),multiply(add(u,v),y)) = additive_inverse(multiply(x,multiply(add(u,v),y))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
multiply(additive_inverse(x),multiply(add(u,v),y)) = additive_inverse(multiply(x,multiply(add(u,v),y))),
inference(unit_resolution,[status(thm)],[66,65]) ).
tff(68,plain,
additive_inverse(multiply(x,multiply(add(u,v),y))) = multiply(additive_inverse(x),multiply(add(u,v),y)),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
additive_inverse(multiply(x,multiply(add(u,v),y))) = add(additive_inverse(multiply(x,multiply(v,y))),additive_inverse(multiply(x,multiply(u,y)))),
inference(transitivity,[status(thm)],[68,58,42]) ).
tff(70,plain,
add(additive_inverse(multiply(x,multiply(add(u,v),y))),multiply(multiply(x,u),y)) = add(add(additive_inverse(multiply(x,multiply(v,y))),additive_inverse(multiply(x,multiply(u,y)))),multiply(multiply(x,u),y)),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
add(add(additive_inverse(multiply(x,multiply(v,y))),additive_inverse(multiply(x,multiply(u,y)))),multiply(multiply(x,u),y)) = add(additive_inverse(multiply(x,multiply(add(u,v),y))),multiply(multiply(x,u),y)),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(additive_inverse(multiply(x,multiply(v,y))),add(additive_inverse(multiply(x,multiply(u,y))),multiply(multiply(x,u),y))) = add(add(additive_inverse(multiply(x,multiply(v,y))),additive_inverse(multiply(x,multiply(u,y)))),multiply(multiply(x,u),y)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
add(additive_inverse(multiply(x,multiply(v,y))),add(additive_inverse(multiply(x,multiply(u,y))),multiply(multiply(x,u),y))) = add(add(additive_inverse(multiply(x,multiply(v,y))),additive_inverse(multiply(x,multiply(u,y)))),multiply(multiply(x,u),y)),
inference(unit_resolution,[status(thm)],[72,29]) ).
tff(74,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_inverse(multiply(x,multiply(u,y))),multiply(multiply(x,u),y)) = add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
add(additive_inverse(multiply(x,multiply(u,y))),multiply(multiply(x,u),y)) = add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y)))),
inference(unit_resolution,[status(thm)],[74,7]) ).
tff(76,plain,
add(additive_inverse(multiply(x,multiply(v,y))),add(additive_inverse(multiply(x,multiply(u,y))),multiply(multiply(x,u),y))) = add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y))))),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y))))) = add(additive_inverse(multiply(x,multiply(v,y))),add(additive_inverse(multiply(x,multiply(u,y))),multiply(multiply(x,u),y))),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y))))) = add(additive_inverse(multiply(x,multiply(add(u,v),y))),multiply(multiply(x,u),y)),
inference(transitivity,[status(thm)],[77,73,71]) ).
tff(79,plain,
add(add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y))))),multiply(multiply(x,v),y)) = add(add(additive_inverse(multiply(x,multiply(add(u,v),y))),multiply(multiply(x,u),y)),multiply(multiply(x,v),y)),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
add(add(additive_inverse(multiply(x,multiply(add(u,v),y))),multiply(multiply(x,u),y)),multiply(multiply(x,v),y)) = add(add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y))))),multiply(multiply(x,v),y)),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(additive_inverse(multiply(x,multiply(add(u,v),y))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y))) = add(add(additive_inverse(multiply(x,multiply(add(u,v),y))),multiply(multiply(x,u),y)),multiply(multiply(x,v),y)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
add(additive_inverse(multiply(x,multiply(add(u,v),y))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y))) = add(add(additive_inverse(multiply(x,multiply(add(u,v),y))),multiply(multiply(x,u),y)),multiply(multiply(x,v),y)),
inference(unit_resolution,[status(thm)],[81,29]) ).
tff(83,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(84,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)],[83]) ).
tff(85,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(86,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/RNG003-0.ax',distribute1) ).
tff(87,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(x,add(u,v)) = add(multiply(x,u),multiply(x,v)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
multiply(x,add(u,v)) = add(multiply(x,u),multiply(x,v)),
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,plain,
add(multiply(x,u),multiply(x,v)) = multiply(x,add(u,v)),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
multiply(add(multiply(x,u),multiply(x,v)),y) = multiply(multiply(x,add(u,v)),y),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(multiply(x,u),multiply(x,v)),y) = add(multiply(multiply(x,u),y),multiply(multiply(x,v),y)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
multiply(add(multiply(x,u),multiply(x,v)),y) = add(multiply(multiply(x,u),y),multiply(multiply(x,v),y)),
inference(unit_resolution,[status(thm)],[94,52]) ).
tff(96,plain,
add(multiply(multiply(x,u),y),multiply(multiply(x,v),y)) = multiply(add(multiply(x,u),multiply(x,v)),y),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
add(multiply(multiply(x,u),y),multiply(multiply(x,v),y)) = multiply(multiply(x,add(u,v)),y),
inference(transitivity,[status(thm)],[96,93]) ).
tff(98,plain,
add(additive_inverse(multiply(x,multiply(add(u,v),y))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y))) = add(additive_inverse(multiply(x,multiply(add(u,v),y))),multiply(multiply(x,add(u,v)),y)),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
add(additive_inverse(multiply(x,multiply(add(u,v),y))),multiply(multiply(x,add(u,v)),y)) = add(additive_inverse(multiply(x,multiply(add(u,v),y))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_inverse(multiply(x,multiply(add(u,v),y))),multiply(multiply(x,add(u,v)),y)) = add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
add(additive_inverse(multiply(x,multiply(add(u,v),y))),multiply(multiply(x,add(u,v)),y)) = add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(unit_resolution,[status(thm)],[100,7]) ).
tff(102,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) = add(additive_inverse(multiply(x,multiply(add(u,v),y))),multiply(multiply(x,add(u,v)),y)),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
| ( associator(x,add(u,v),y) = add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
associator(x,add(u,v),y) = add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(unit_resolution,[status(thm)],[103,16]) ).
tff(105,plain,
associator(x,add(u,v),y) = add(associator(x,u,y),associator(x,v,y)),
inference(transitivity,[status(thm)],[104,102,99,82,80,33,31,22,9]) ).
tff(106,plain,
( ( associator(x,add(u,v),y) != add(associator(x,u,y),associator(x,v,y)) )
<=> ( associator(x,add(u,v),y) != add(associator(x,u,y),associator(x,v,y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,axiom,
associator(x,add(u,v),y) != add(associator(x,u,y),associator(x,v,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_linearised_form2) ).
tff(108,plain,
associator(x,add(u,v),y) != add(associator(x,u,y),associator(x,v,y)),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
$false,
inference(unit_resolution,[status(thm)],[108,105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : RNG020-7 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.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 21:41:34 EDT 2022
% 0.12/0.33 % 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.
% 0.19/0.50 % SZS status Unsatisfiable
% 0.19/0.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------