%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG016-6 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 7.01s 7.19s
% Output : Proof 7.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 41
% Syntax : Number of formulae : 124 ( 92 unt; 0 typ; 0 def)
% Number of atoms : 172 ( 163 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 59 ( 19 ~; 15 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 8 ( 8 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 143 ( 130 !; 0 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(z_type,type,
z: $i ).
tff(y_type,type,
y: $i ).
tff(x_type,type,
x: $i ).
tff(additive_identity_type,type,
additive_identity: $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(add(multiply(x,z),multiply(additive_inverse(y),z)),multiply(y,z)) = add(multiply(y,z),add(multiply(x,z),multiply(additive_inverse(y),z))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
add(add(multiply(x,z),multiply(additive_inverse(y),z)),multiply(y,z)) = add(multiply(y,z),add(multiply(x,z),multiply(additive_inverse(y),z))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
add(multiply(y,z),add(multiply(x,z),multiply(additive_inverse(y),z))) = add(add(multiply(x,z),multiply(additive_inverse(y),z)),multiply(y,z)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,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(12,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)],[11]) ).
tff(13,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(14,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(15,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(x,additive_inverse(y)),z) = add(multiply(x,z),multiply(additive_inverse(y),z)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
multiply(add(x,additive_inverse(y)),z) = add(multiply(x,z),multiply(additive_inverse(y),z)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
add(multiply(y,z),multiply(add(x,additive_inverse(y)),z)) = add(multiply(y,z),add(multiply(x,z),multiply(additive_inverse(y),z))),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
add(multiply(x,z),multiply(additive_inverse(y),z)) = multiply(add(x,additive_inverse(y)),z),
inference(symmetry,[status(thm)],[19]) ).
tff(22,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(multiply(additive_inverse(y),z),multiply(x,z)) = add(multiply(x,z),multiply(additive_inverse(y),z)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
add(multiply(additive_inverse(y),z),multiply(x,z)) = add(multiply(x,z),multiply(additive_inverse(y),z)),
inference(unit_resolution,[status(thm)],[22,7]) ).
tff(24,plain,
add(multiply(additive_inverse(y),z),multiply(x,z)) = multiply(add(x,additive_inverse(y)),z),
inference(transitivity,[status(thm)],[23,21]) ).
tff(25,plain,
add(multiply(y,z),add(multiply(additive_inverse(y),z),multiply(x,z))) = add(multiply(y,z),multiply(add(x,additive_inverse(y)),z)),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,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(27,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)],[26]) ).
tff(28,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(29,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(30,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(multiply(y,z),add(multiply(additive_inverse(y),z),multiply(x,z))) = add(add(multiply(y,z),multiply(additive_inverse(y),z)),multiply(x,z)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
add(multiply(y,z),add(multiply(additive_inverse(y),z),multiply(x,z))) = add(add(multiply(y,z),multiply(additive_inverse(y),z)),multiply(x,z)),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
add(add(multiply(y,z),multiply(additive_inverse(y),z)),multiply(x,z)) = add(multiply(y,z),add(multiply(additive_inverse(y),z),multiply(x,z))),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(y,additive_inverse(y)),z) = add(multiply(y,z),multiply(additive_inverse(y),z)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
multiply(add(y,additive_inverse(y)),z) = add(multiply(y,z),multiply(additive_inverse(y),z)),
inference(unit_resolution,[status(thm)],[36,17]) ).
tff(38,plain,
^ [X: $i] :
refl(( ( add(additive_inverse(X),X) = additive_identity )
<=> ( add(additive_inverse(X),X) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_additive_inverse) ).
tff(42,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(y),y) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
add(additive_inverse(y),y) = additive_identity,
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
additive_identity = add(additive_inverse(y),y),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
^ [X: $i] :
refl(( ( add(X,additive_inverse(X)) = additive_identity )
<=> ( add(X,additive_inverse(X)) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
<=> ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
<=> ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).
tff(52,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
| ( add(y,additive_inverse(y)) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
add(y,additive_inverse(y)) = additive_identity,
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
add(y,additive_inverse(y)) = add(additive_inverse(y),y),
inference(transitivity,[status(thm)],[56,47]) ).
tff(58,plain,
multiply(add(y,additive_inverse(y)),z) = multiply(add(additive_inverse(y),y),z),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
multiply(add(additive_inverse(y),y),z) = multiply(add(y,additive_inverse(y)),z),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
multiply(add(additive_inverse(y),y),z) = multiply(additive_identity,z),
inference(monotonicity,[status(thm)],[46]) ).
tff(61,plain,
multiply(additive_identity,z) = multiply(add(additive_inverse(y),y),z),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
^ [X: $i] :
refl(( ( multiply(additive_identity,X) = additive_identity )
<=> ( multiply(additive_identity,X) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [X: $i] : ( multiply(additive_identity,X) = additive_identity )
<=> ! [X: $i] : ( multiply(additive_identity,X) = additive_identity ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [X: $i] : ( multiply(additive_identity,X) = additive_identity )
<=> ! [X: $i] : ( multiply(additive_identity,X) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
! [X: $i] : ( multiply(additive_identity,X) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_multiplicative_zero) ).
tff(66,plain,
! [X: $i] : ( multiply(additive_identity,X) = additive_identity ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [X: $i] : ( multiply(additive_identity,X) = additive_identity ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [X: $i] : ( multiply(additive_identity,X) = additive_identity ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
( ~ ! [X: $i] : ( multiply(additive_identity,X) = additive_identity )
| ( multiply(additive_identity,z) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
multiply(additive_identity,z) = additive_identity,
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
additive_identity = multiply(additive_identity,z),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
additive_identity = add(multiply(y,z),multiply(additive_inverse(y),z)),
inference(transitivity,[status(thm)],[71,61,59,37]) ).
tff(73,plain,
add(additive_identity,multiply(x,z)) = add(add(multiply(y,z),multiply(additive_inverse(y),z)),multiply(x,z)),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
^ [X: $i] :
refl(( ( add(additive_identity,X) = X )
<=> ( add(additive_identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,axiom,
! [X: $i] : ( add(additive_identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).
tff(78,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,multiply(x,z)) = multiply(x,z) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
add(additive_identity,multiply(x,z)) = multiply(x,z),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
multiply(x,z) = add(additive_identity,multiply(x,z)),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
multiply(x,z) = add(add(multiply(x,z),multiply(additive_inverse(y),z)),multiply(y,z)),
inference(transitivity,[status(thm)],[83,73,35,25,20,10]) ).
tff(85,plain,
add(multiply(x,z),additive_inverse(multiply(y,z))) = add(add(add(multiply(x,z),multiply(additive_inverse(y),z)),multiply(y,z)),additive_inverse(multiply(y,z))),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
add(add(add(multiply(x,z),multiply(additive_inverse(y),z)),multiply(y,z)),additive_inverse(multiply(y,z))) = add(multiply(x,z),additive_inverse(multiply(y,z))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(add(multiply(x,z),multiply(additive_inverse(y),z)),add(multiply(y,z),additive_inverse(multiply(y,z)))) = add(add(add(multiply(x,z),multiply(additive_inverse(y),z)),multiply(y,z)),additive_inverse(multiply(y,z))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
add(add(multiply(x,z),multiply(additive_inverse(y),z)),add(multiply(y,z),additive_inverse(multiply(y,z)))) = add(add(add(multiply(x,z),multiply(additive_inverse(y),z)),multiply(y,z)),additive_inverse(multiply(y,z))),
inference(unit_resolution,[status(thm)],[87,32]) ).
tff(89,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,additive_inverse(multiply(additive_identity,z))) = additive_inverse(multiply(additive_identity,z)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
add(additive_identity,additive_inverse(multiply(additive_identity,z))) = additive_inverse(multiply(additive_identity,z)),
inference(unit_resolution,[status(thm)],[89,80]) ).
tff(91,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_inverse(multiply(additive_identity,z)),additive_identity) = add(additive_identity,additive_inverse(multiply(additive_identity,z))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
add(additive_inverse(multiply(additive_identity,z)),additive_identity) = add(additive_identity,additive_inverse(multiply(additive_identity,z))),
inference(unit_resolution,[status(thm)],[91,7]) ).
tff(93,plain,
additive_inverse(additive_identity) = additive_inverse(multiply(additive_identity,z)),
inference(monotonicity,[status(thm)],[71]) ).
tff(94,plain,
additive_inverse(multiply(additive_identity,z)) = additive_inverse(additive_identity),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
add(additive_inverse(multiply(additive_identity,z)),additive_identity) = add(additive_inverse(additive_identity),additive_identity),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
add(additive_inverse(additive_identity),additive_identity) = add(additive_inverse(multiply(additive_identity,z)),additive_identity),
inference(symmetry,[status(thm)],[95]) ).
tff(97,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(98,plain,
add(additive_inverse(additive_identity),additive_identity) = additive_identity,
inference(unit_resolution,[status(thm)],[97,44]) ).
tff(99,plain,
additive_identity = add(additive_inverse(additive_identity),additive_identity),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
| ( add(multiply(y,z),additive_inverse(multiply(y,z))) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
add(multiply(y,z),additive_inverse(multiply(y,z))) = additive_identity,
inference(unit_resolution,[status(thm)],[100,54]) ).
tff(102,plain,
add(multiply(y,z),additive_inverse(multiply(y,z))) = additive_inverse(multiply(additive_identity,z)),
inference(transitivity,[status(thm)],[101,99,96,92,90]) ).
tff(103,plain,
add(add(multiply(x,z),multiply(additive_inverse(y),z)),add(multiply(y,z),additive_inverse(multiply(y,z)))) = add(add(multiply(x,z),multiply(additive_inverse(y),z)),additive_inverse(multiply(additive_identity,z))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
add(add(multiply(x,z),multiply(additive_inverse(y),z)),additive_inverse(multiply(additive_identity,z))) = add(add(multiply(x,z),multiply(additive_inverse(y),z)),add(multiply(y,z),additive_inverse(multiply(y,z)))),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
add(additive_identity,additive_inverse(multiply(additive_identity,z))) = add(additive_inverse(multiply(additive_identity,z)),additive_identity),
inference(symmetry,[status(thm)],[92]) ).
tff(106,plain,
additive_inverse(multiply(additive_identity,z)) = add(additive_identity,additive_inverse(multiply(additive_identity,z))),
inference(symmetry,[status(thm)],[90]) ).
tff(107,plain,
additive_inverse(multiply(additive_identity,z)) = additive_identity,
inference(transitivity,[status(thm)],[106,105,95,98]) ).
tff(108,plain,
add(add(multiply(x,z),multiply(additive_inverse(y),z)),additive_inverse(multiply(additive_identity,z))) = add(add(multiply(x,z),multiply(additive_inverse(y),z)),additive_identity),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
add(add(multiply(x,z),multiply(additive_inverse(y),z)),additive_identity) = add(add(multiply(x,z),multiply(additive_inverse(y),z)),additive_inverse(multiply(additive_identity,z))),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
^ [X: $i] :
refl(( ( add(X,additive_identity) = X )
<=> ( add(X,additive_identity) = X ) )),
inference(bind,[status(th)],[]) ).
tff(111,plain,
( ! [X: $i] : ( add(X,additive_identity) = X )
<=> ! [X: $i] : ( add(X,additive_identity) = X ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,plain,
( ! [X: $i] : ( add(X,additive_identity) = X )
<=> ! [X: $i] : ( add(X,additive_identity) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,axiom,
! [X: $i] : ( add(X,additive_identity) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
tff(114,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(skolemize,[status(sab)],[114]) ).
tff(116,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(modus_ponens,[status(thm)],[115,111]) ).
tff(117,plain,
( ~ ! [X: $i] : ( add(X,additive_identity) = X )
| ( add(add(multiply(x,z),multiply(additive_inverse(y),z)),additive_identity) = add(multiply(x,z),multiply(additive_inverse(y),z)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
add(add(multiply(x,z),multiply(additive_inverse(y),z)),additive_identity) = add(multiply(x,z),multiply(additive_inverse(y),z)),
inference(unit_resolution,[status(thm)],[117,116]) ).
tff(119,plain,
add(multiply(x,z),multiply(additive_inverse(y),z)) = add(add(multiply(x,z),multiply(additive_inverse(y),z)),additive_identity),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
multiply(add(x,additive_inverse(y)),z) = add(multiply(x,z),additive_inverse(multiply(y,z))),
inference(transitivity,[status(thm)],[19,119,109,104,88,86]) ).
tff(121,plain,
( ( multiply(add(x,additive_inverse(y)),z) != add(multiply(x,z),additive_inverse(multiply(y,z))) )
<=> ( multiply(add(x,additive_inverse(y)),z) != add(multiply(x,z),additive_inverse(multiply(y,z))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,axiom,
multiply(add(x,additive_inverse(y)),z) != add(multiply(x,z),additive_inverse(multiply(y,z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
tff(123,plain,
multiply(add(x,additive_inverse(y)),z) != add(multiply(x,z),additive_inverse(multiply(y,z))),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
$false,
inference(unit_resolution,[status(thm)],[123,120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG016-6 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 03:08:25 EDT 2025
% 0.12/0.34 % CPUTime :
% 7.01/7.19 % SZS status Unsatisfiable
% 7.01/7.19 % SZS output start Proof
% See solution above
% 7.01/7.21 % E exiting
%------------------------------------------------------------------------------