%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG019-7 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 : Sat Jun 21 05:23:54 AM UTC 2025
% Result : Unsatisfiable 0.86s 1.01s
% Output : Proof 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 34
% Syntax : Number of formulae : 93 ( 66 unt; 0 typ; 0 def)
% Number of atoms : 132 ( 125 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 51 ( 18 ~; 14 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 181 ( 165 !; 0 ?; 181 :)
% Comments :
%------------------------------------------------------------------------------
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(associator_type,type,
associator: ( $i * $i * $i ) > $i ).
tff(v_type,type,
v: $i ).
tff(y_type,type,
y: $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,
^ [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(2,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)],[1]) ).
tff(3,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(4,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/sandbox2/benchmark/Axioms/RNG003-0.ax',associator) ).
tff(5,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)],[4,3]) ).
tff(6,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)],[5]) ).
tff(7,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)],[6,2]) ).
tff(8,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,y,v) = add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
associator(x,y,v) = add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v)))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v)))) = associator(x,y,v),
inference(symmetry,[status(thm)],[9]) ).
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)))) )
| ( associator(x,y,u) = add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
associator(x,y,u) = add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))) = associator(x,y,u),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))) = add(associator(x,y,u),associator(x,y,v)),
inference(monotonicity,[status(thm)],[13,10]) ).
tff(15,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(16,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)],[15]) ).
tff(17,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(18,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
tff(19,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(multiply(multiply(x,y),u),add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v)))))) = add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
add(multiply(multiply(x,y),u),add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v)))))) = add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
^ [Y: $i,X: $i] :
refl(( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(25,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)],[24]) ).
tff(26,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(27,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
tff(28,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))),multiply(multiply(x,y),u)) = add(multiply(multiply(x,y),u),add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
add(add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))),multiply(multiply(x,y),u)) = add(multiply(multiply(x,y),u),add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v)))))),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_inverse(multiply(x,multiply(y,v))),multiply(multiply(x,y),v)) = add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
add(additive_inverse(multiply(x,multiply(y,v))),multiply(multiply(x,y),v)) = add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v)))),
inference(unit_resolution,[status(thm)],[33,30]) ).
tff(35,plain,
add(additive_inverse(multiply(x,multiply(y,u))),add(additive_inverse(multiply(x,multiply(y,v))),multiply(multiply(x,y),v))) = add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(additive_inverse(multiply(x,multiply(y,u))),add(additive_inverse(multiply(x,multiply(y,v))),multiply(multiply(x,y),v))) = add(add(additive_inverse(multiply(x,multiply(y,u))),additive_inverse(multiply(x,multiply(y,v)))),multiply(multiply(x,y),v)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
add(additive_inverse(multiply(x,multiply(y,u))),add(additive_inverse(multiply(x,multiply(y,v))),multiply(multiply(x,y),v))) = add(add(additive_inverse(multiply(x,multiply(y,u))),additive_inverse(multiply(x,multiply(y,v)))),multiply(multiply(x,y),v)),
inference(unit_resolution,[status(thm)],[36,21]) ).
tff(38,plain,
add(add(additive_inverse(multiply(x,multiply(y,u))),additive_inverse(multiply(x,multiply(y,v)))),multiply(multiply(x,y),v)) = add(additive_inverse(multiply(x,multiply(y,u))),add(additive_inverse(multiply(x,multiply(y,v))),multiply(multiply(x,y),v))),
inference(symmetry,[status(thm)],[37]) ).
tff(39,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(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))) )
<=> ! [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)],[39]) ).
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))) )
<=> ! [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(42,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/sandbox2/benchmark/theBenchmark.p',distributivity_of_difference3) ).
tff(43,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)],[42,41]) ).
tff(44,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)],[43]) ).
tff(45,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)],[44,40]) ).
tff(46,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(y,u),multiply(y,v))) = add(additive_inverse(multiply(x,multiply(y,u))),additive_inverse(multiply(x,multiply(y,v)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
multiply(additive_inverse(x),add(multiply(y,u),multiply(y,v))) = add(additive_inverse(multiply(x,multiply(y,u))),additive_inverse(multiply(x,multiply(y,v)))),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,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(49,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)],[48]) ).
tff(50,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(51,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/RNG003-0.ax',distribute1) ).
tff(52,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(y,add(u,v)) = add(multiply(y,u),multiply(y,v)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
multiply(y,add(u,v)) = add(multiply(y,u),multiply(y,v)),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
add(multiply(y,u),multiply(y,v)) = multiply(y,add(u,v)),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
multiply(additive_inverse(x),add(multiply(y,u),multiply(y,v))) = multiply(additive_inverse(x),multiply(y,add(u,v))),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
multiply(additive_inverse(x),multiply(y,add(u,v))) = multiply(additive_inverse(x),add(multiply(y,u),multiply(y,v))),
inference(symmetry,[status(thm)],[58]) ).
tff(60,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(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(quant_intro,[status(thm)],[60]) ).
tff(62,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(63,axiom,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product1) ).
tff(64,plain,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(x),multiply(y,add(u,v))) = additive_inverse(multiply(x,multiply(y,add(u,v)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
multiply(additive_inverse(x),multiply(y,add(u,v))) = additive_inverse(multiply(x,multiply(y,add(u,v)))),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
additive_inverse(multiply(x,multiply(y,add(u,v)))) = multiply(additive_inverse(x),multiply(y,add(u,v))),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
additive_inverse(multiply(x,multiply(y,add(u,v)))) = add(additive_inverse(multiply(x,multiply(y,u))),additive_inverse(multiply(x,multiply(y,v)))),
inference(transitivity,[status(thm)],[69,59,47]) ).
tff(71,plain,
add(additive_inverse(multiply(x,multiply(y,add(u,v)))),multiply(multiply(x,y),v)) = add(add(additive_inverse(multiply(x,multiply(y,u))),additive_inverse(multiply(x,multiply(y,v)))),multiply(multiply(x,y),v)),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
add(additive_inverse(multiply(x,multiply(y,add(u,v)))),multiply(multiply(x,y),v)) = add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))),
inference(transitivity,[status(thm)],[71,38,35]) ).
tff(73,plain,
add(add(additive_inverse(multiply(x,multiply(y,add(u,v)))),multiply(multiply(x,y),v)),multiply(multiply(x,y),u)) = add(add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))),multiply(multiply(x,y),u)),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(additive_inverse(multiply(x,multiply(y,add(u,v)))),add(multiply(multiply(x,y),v),multiply(multiply(x,y),u))) = add(add(additive_inverse(multiply(x,multiply(y,add(u,v)))),multiply(multiply(x,y),v)),multiply(multiply(x,y),u)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
add(additive_inverse(multiply(x,multiply(y,add(u,v)))),add(multiply(multiply(x,y),v),multiply(multiply(x,y),u))) = add(add(additive_inverse(multiply(x,multiply(y,add(u,v)))),multiply(multiply(x,y),v)),multiply(multiply(x,y),u)),
inference(unit_resolution,[status(thm)],[74,21]) ).
tff(76,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(multiply(x,y),add(v,u)) = add(multiply(multiply(x,y),v),multiply(multiply(x,y),u)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
multiply(multiply(x,y),add(v,u)) = add(multiply(multiply(x,y),v),multiply(multiply(x,y),u)),
inference(unit_resolution,[status(thm)],[76,54]) ).
tff(78,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(v,u) = add(u,v) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
add(v,u) = add(u,v),
inference(unit_resolution,[status(thm)],[78,30]) ).
tff(80,plain,
multiply(multiply(x,y),add(v,u)) = multiply(multiply(x,y),add(u,v)),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
multiply(multiply(x,y),add(u,v)) = multiply(multiply(x,y),add(v,u)),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
multiply(multiply(x,y),add(u,v)) = add(multiply(multiply(x,y),v),multiply(multiply(x,y),u)),
inference(transitivity,[status(thm)],[81,77]) ).
tff(83,plain,
add(additive_inverse(multiply(x,multiply(y,add(u,v)))),multiply(multiply(x,y),add(u,v))) = add(additive_inverse(multiply(x,multiply(y,add(u,v)))),add(multiply(multiply(x,y),v),multiply(multiply(x,y),u))),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_inverse(multiply(x,multiply(y,add(u,v)))),multiply(multiply(x,y),add(u,v))) = add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
add(additive_inverse(multiply(x,multiply(y,add(u,v)))),multiply(multiply(x,y),add(u,v))) = add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))),
inference(unit_resolution,[status(thm)],[84,30]) ).
tff(86,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) = add(additive_inverse(multiply(x,multiply(y,add(u,v)))),multiply(multiply(x,y),add(u,v))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,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,y,add(u,v)) = add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
associator(x,y,add(u,v)) = add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))),
inference(unit_resolution,[status(thm)],[87,7]) ).
tff(89,plain,
associator(x,y,add(u,v)) = add(associator(x,y,u),associator(x,y,v)),
inference(transitivity,[status(thm)],[88,86,83,75,73,32,23,14]) ).
tff(90,plain,
( ( associator(x,y,add(u,v)) != add(associator(x,y,u),associator(x,y,v)) )
<=> ( associator(x,y,add(u,v)) != add(associator(x,y,u),associator(x,y,v)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,axiom,
associator(x,y,add(u,v)) != add(associator(x,y,u),associator(x,y,v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_linearised_form1) ).
tff(92,plain,
associator(x,y,add(u,v)) != add(associator(x,y,u),associator(x,y,v)),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
$false,
inference(unit_resolution,[status(thm)],[92,89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG019-7 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 03:09:18 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.86/1.01 % SZS status Unsatisfiable
% 0.86/1.01 % SZS output start Proof
% See solution above
% 0.86/1.02 % E exiting
%------------------------------------------------------------------------------