%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG017-6 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 175.60s 175.75s
% Output : Proof 175.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 56
% Syntax : Number of formulae : 179 ( 134 unt; 0 typ; 0 def)
% Number of atoms : 244 ( 233 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 83 ( 28 ~; 24 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 10 ( 10 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 : 198 ( 181 !; 0 ?; 198 :)
% 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(x_type,type,
x: $i ).
tff(y_type,type,
y: $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(additive_inverse(multiply(x,z)),additive_inverse(multiply(x,y))) = add(additive_inverse(multiply(x,y)),additive_inverse(multiply(x,z))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
add(additive_inverse(multiply(x,z)),additive_inverse(multiply(x,y))) = add(additive_inverse(multiply(x,y)),additive_inverse(multiply(x,z))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( ( add(X,additive_identity) = X )
<=> ( add(X,additive_identity) = X ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : ( add(X,additive_identity) = X )
<=> ! [X: $i] : ( add(X,additive_identity) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( add(X,additive_identity) = X )
<=> ! [X: $i] : ( add(X,additive_identity) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : ( add(X,additive_identity) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
tff(14,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( add(X,additive_identity) = X )
| ( add(multiply(additive_inverse(x),z),additive_identity) = multiply(additive_inverse(x),z) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
add(multiply(additive_inverse(x),z),additive_identity) = multiply(additive_inverse(x),z),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X: $i] :
refl(( ( add(additive_inverse(X),X) = additive_identity )
<=> ( add(additive_inverse(X),X) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_additive_inverse) ).
tff(23,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,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(27,plain,
add(additive_inverse(additive_identity),additive_identity) = additive_identity,
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
^ [X: $i] :
refl(( ( multiply(additive_identity,X) = additive_identity )
<=> ( multiply(additive_identity,X) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [X: $i] : ( multiply(additive_identity,X) = additive_identity )
<=> ! [X: $i] : ( multiply(additive_identity,X) = additive_identity ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [X: $i] : ( multiply(additive_identity,X) = additive_identity )
<=> ! [X: $i] : ( multiply(additive_identity,X) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
! [X: $i] : ( multiply(additive_identity,X) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_multiplicative_zero) ).
tff(32,plain,
! [X: $i] : ( multiply(additive_identity,X) = additive_identity ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [X: $i] : ( multiply(additive_identity,X) = additive_identity ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [X: $i] : ( multiply(additive_identity,X) = additive_identity ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [X: $i] : ( multiply(additive_identity,X) = additive_identity )
| ( multiply(additive_identity,y) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
multiply(additive_identity,y) = additive_identity,
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
additive_identity = multiply(additive_identity,y),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
additive_inverse(additive_identity) = additive_inverse(multiply(additive_identity,y)),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
additive_inverse(multiply(additive_identity,y)) = additive_inverse(additive_identity),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
add(additive_inverse(multiply(additive_identity,y)),additive_identity) = add(additive_inverse(additive_identity),additive_identity),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_inverse(multiply(additive_identity,y)),additive_identity) = add(additive_identity,additive_inverse(multiply(additive_identity,y))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
add(additive_inverse(multiply(additive_identity,y)),additive_identity) = add(additive_identity,additive_inverse(multiply(additive_identity,y))),
inference(unit_resolution,[status(thm)],[41,7]) ).
tff(43,plain,
add(additive_identity,additive_inverse(multiply(additive_identity,y))) = add(additive_inverse(multiply(additive_identity,y)),additive_identity),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
^ [X: $i] :
refl(( ( add(additive_identity,X) = X )
<=> ( add(additive_identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
! [X: $i] : ( add(additive_identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).
tff(48,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,additive_inverse(multiply(additive_identity,y))) = additive_inverse(multiply(additive_identity,y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
add(additive_identity,additive_inverse(multiply(additive_identity,y))) = additive_inverse(multiply(additive_identity,y)),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
additive_inverse(multiply(additive_identity,y)) = add(additive_identity,additive_inverse(multiply(additive_identity,y))),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
additive_inverse(multiply(additive_identity,y)) = additive_identity,
inference(transitivity,[status(thm)],[53,43,40,27]) ).
tff(55,plain,
add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y))) = add(multiply(additive_inverse(x),z),additive_identity),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
^ [X: $i] :
refl(( ( multiply(X,additive_identity) = additive_identity )
<=> ( multiply(X,additive_identity) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [X: $i] : ( multiply(X,additive_identity) = additive_identity )
<=> ! [X: $i] : ( multiply(X,additive_identity) = additive_identity ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [X: $i] : ( multiply(X,additive_identity) = additive_identity )
<=> ! [X: $i] : ( multiply(X,additive_identity) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_multiplicative_zero) ).
tff(60,plain,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
( ~ ! [X: $i] : ( multiply(X,additive_identity) = additive_identity )
| ( multiply(y,additive_identity) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
multiply(y,additive_identity) = additive_identity,
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
add(multiply(y,additive_identity),additive_inverse(multiply(additive_identity,y))) = add(additive_identity,additive_inverse(multiply(additive_identity,y))),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
additive_identity = multiply(y,additive_identity),
inference(symmetry,[status(thm)],[64]) ).
tff(67,plain,
( ~ ! [X: $i] : ( multiply(additive_identity,X) = additive_identity )
| ( multiply(additive_identity,z) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
multiply(additive_identity,z) = additive_identity,
inference(unit_resolution,[status(thm)],[67,34]) ).
tff(69,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(x),x) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
add(additive_inverse(x),x) = additive_identity,
inference(unit_resolution,[status(thm)],[69,25]) ).
tff(71,plain,
multiply(add(additive_inverse(x),x),z) = multiply(additive_identity,z),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
additive_identity = add(additive_inverse(x),x),
inference(symmetry,[status(thm)],[70]) ).
tff(73,plain,
^ [X: $i] :
refl(( ( add(X,additive_inverse(X)) = additive_identity )
<=> ( add(X,additive_inverse(X)) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
<=> ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
<=> ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,axiom,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).
tff(77,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
( ~ ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
| ( add(x,additive_inverse(x)) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
add(x,additive_inverse(x)) = additive_identity,
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
add(x,additive_inverse(x)) = add(additive_inverse(x),x),
inference(transitivity,[status(thm)],[81,72]) ).
tff(83,plain,
multiply(add(x,additive_inverse(x)),z) = multiply(add(additive_inverse(x),x),z),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,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(85,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)],[84]) ).
tff(86,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(87,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(88,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(x,additive_inverse(x)),z) = add(multiply(x,z),multiply(additive_inverse(x),z)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
multiply(add(x,additive_inverse(x)),z) = add(multiply(x,z),multiply(additive_inverse(x),z)),
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
add(multiply(x,z),multiply(additive_inverse(x),z)) = multiply(add(x,additive_inverse(x)),z),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
add(multiply(x,z),multiply(additive_inverse(x),z)) = multiply(y,additive_identity),
inference(transitivity,[status(thm)],[93,83,71,68,66]) ).
tff(95,plain,
add(add(multiply(x,z),multiply(additive_inverse(x),z)),additive_inverse(multiply(additive_identity,y))) = add(multiply(y,additive_identity),additive_inverse(multiply(additive_identity,y))),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,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(97,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)],[96]) ).
tff(98,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(99,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(100,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[101,97]) ).
tff(103,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(multiply(x,z),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y)))) = add(add(multiply(x,z),multiply(additive_inverse(x),z)),additive_inverse(multiply(additive_identity,y))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
add(multiply(x,z),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y)))) = add(add(multiply(x,z),multiply(additive_inverse(x),z)),additive_inverse(multiply(additive_identity,y))),
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
add(multiply(x,z),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y)))) = additive_inverse(multiply(additive_identity,y)),
inference(transitivity,[status(thm)],[104,95,65,52]) ).
tff(106,plain,
add(multiply(additive_inverse(x),z),add(multiply(x,z),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y))))) = add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y))),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(multiply(additive_inverse(x),z),add(multiply(x,z),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y))))) = add(add(multiply(additive_inverse(x),z),multiply(x,z)),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
add(multiply(additive_inverse(x),z),add(multiply(x,z),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y))))) = add(add(multiply(additive_inverse(x),z),multiply(x,z)),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y)))),
inference(unit_resolution,[status(thm)],[107,102]) ).
tff(109,plain,
add(add(multiply(additive_inverse(x),z),multiply(x,z)),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y)))) = add(multiply(additive_inverse(x),z),add(multiply(x,z),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y))))),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(additive_inverse(x),x),z) = add(multiply(additive_inverse(x),z),multiply(x,z)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
multiply(add(additive_inverse(x),x),z) = add(multiply(additive_inverse(x),z),multiply(x,z)),
inference(unit_resolution,[status(thm)],[110,90]) ).
tff(112,plain,
multiply(additive_identity,z) = multiply(add(additive_inverse(x),x),z),
inference(symmetry,[status(thm)],[71]) ).
tff(113,plain,
additive_identity = multiply(additive_identity,z),
inference(symmetry,[status(thm)],[68]) ).
tff(114,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(multiply(x,z)),multiply(x,z)) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
add(additive_inverse(multiply(x,z)),multiply(x,z)) = additive_identity,
inference(unit_resolution,[status(thm)],[114,25]) ).
tff(116,plain,
add(additive_inverse(multiply(x,z)),multiply(x,z)) = add(multiply(additive_inverse(x),z),multiply(x,z)),
inference(transitivity,[status(thm)],[115,113,112,111]) ).
tff(117,plain,
add(add(additive_inverse(multiply(x,z)),multiply(x,z)),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y)))) = add(add(multiply(additive_inverse(x),z),multiply(x,z)),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y)))),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(additive_inverse(multiply(x,z)),add(multiply(x,z),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y))))) = add(add(additive_inverse(multiply(x,z)),multiply(x,z)),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
add(additive_inverse(multiply(x,z)),add(multiply(x,z),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y))))) = add(add(additive_inverse(multiply(x,z)),multiply(x,z)),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y)))),
inference(unit_resolution,[status(thm)],[118,102]) ).
tff(120,plain,
add(add(multiply(x,z),multiply(additive_inverse(x),z)),additive_inverse(multiply(additive_identity,y))) = add(multiply(x,z),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y)))),
inference(symmetry,[status(thm)],[104]) ).
tff(121,plain,
add(multiply(y,additive_identity),additive_inverse(multiply(additive_identity,y))) = add(add(multiply(x,z),multiply(additive_inverse(x),z)),additive_inverse(multiply(additive_identity,y))),
inference(symmetry,[status(thm)],[95]) ).
tff(122,plain,
add(additive_identity,additive_inverse(multiply(additive_identity,y))) = add(multiply(y,additive_identity),additive_inverse(multiply(additive_identity,y))),
inference(symmetry,[status(thm)],[65]) ).
tff(123,plain,
additive_inverse(multiply(additive_identity,y)) = add(multiply(x,z),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y)))),
inference(transitivity,[status(thm)],[53,122,121,120]) ).
tff(124,plain,
add(additive_inverse(multiply(x,z)),additive_inverse(multiply(additive_identity,y))) = add(additive_inverse(multiply(x,z)),add(multiply(x,z),add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y))))),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
add(additive_inverse(additive_identity),additive_identity) = add(additive_inverse(multiply(additive_identity,y)),additive_identity),
inference(symmetry,[status(thm)],[40]) ).
tff(126,plain,
additive_identity = add(additive_inverse(additive_identity),additive_identity),
inference(symmetry,[status(thm)],[27]) ).
tff(127,plain,
additive_identity = additive_inverse(multiply(additive_identity,y)),
inference(transitivity,[status(thm)],[126,125,42,52]) ).
tff(128,plain,
add(additive_inverse(multiply(x,z)),additive_identity) = add(additive_inverse(multiply(x,z)),additive_inverse(multiply(additive_identity,y))),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ~ ! [X: $i] : ( add(X,additive_identity) = X )
| ( add(additive_inverse(multiply(x,z)),additive_identity) = additive_inverse(multiply(x,z)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(130,plain,
add(additive_inverse(multiply(x,z)),additive_identity) = additive_inverse(multiply(x,z)),
inference(unit_resolution,[status(thm)],[129,16]) ).
tff(131,plain,
additive_inverse(multiply(x,z)) = add(additive_inverse(multiply(x,z)),additive_identity),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
additive_inverse(multiply(x,z)) = multiply(additive_inverse(x),z),
inference(transitivity,[status(thm)],[131,128,124,119,117,109,106,55,18]) ).
tff(133,plain,
add(additive_inverse(multiply(x,z)),additive_inverse(multiply(x,y))) = add(multiply(additive_inverse(x),z),additive_inverse(multiply(x,y))),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
add(multiply(additive_inverse(x),z),additive_inverse(multiply(x,y))) = add(additive_inverse(multiply(x,z)),additive_inverse(multiply(x,y))),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(multiply(additive_inverse(x),z),multiply(additive_inverse(x),y)) = add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
add(multiply(additive_inverse(x),z),multiply(additive_inverse(x),y)) = add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),
inference(unit_resolution,[status(thm)],[135,7]) ).
tff(137,plain,
add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)) = add(multiply(additive_inverse(x),z),multiply(additive_inverse(x),y)),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),multiply(x,y)) = add(add(multiply(additive_inverse(x),z),multiply(additive_inverse(x),y)),multiply(x,y)),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
add(add(multiply(additive_inverse(x),z),multiply(additive_inverse(x),y)),multiply(x,y)) = add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),multiply(x,y)),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(multiply(additive_inverse(x),z),add(multiply(additive_inverse(x),y),multiply(x,y))) = add(add(multiply(additive_inverse(x),z),multiply(additive_inverse(x),y)),multiply(x,y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
add(multiply(additive_inverse(x),z),add(multiply(additive_inverse(x),y),multiply(x,y))) = add(add(multiply(additive_inverse(x),z),multiply(additive_inverse(x),y)),multiply(x,y)),
inference(unit_resolution,[status(thm)],[140,102]) ).
tff(142,plain,
multiply(add(additive_inverse(x),x),y) = multiply(additive_identity,y),
inference(monotonicity,[status(thm)],[70]) ).
tff(143,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(additive_inverse(x),x),y) = add(multiply(additive_inverse(x),y),multiply(x,y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(144,plain,
multiply(add(additive_inverse(x),x),y) = add(multiply(additive_inverse(x),y),multiply(x,y)),
inference(unit_resolution,[status(thm)],[143,90]) ).
tff(145,plain,
add(multiply(additive_inverse(x),y),multiply(x,y)) = multiply(add(additive_inverse(x),x),y),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
add(multiply(additive_inverse(x),y),multiply(x,y)) = additive_inverse(multiply(additive_identity,y)),
inference(transitivity,[status(thm)],[145,142,36,126,125,42,52]) ).
tff(147,plain,
add(multiply(additive_inverse(x),z),add(multiply(additive_inverse(x),y),multiply(x,y))) = add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y))),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y))) = add(multiply(additive_inverse(x),z),add(multiply(additive_inverse(x),y),multiply(x,y))),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
add(multiply(additive_inverse(x),z),additive_identity) = add(multiply(additive_inverse(x),z),additive_inverse(multiply(additive_identity,y))),
inference(symmetry,[status(thm)],[55]) ).
tff(150,plain,
multiply(additive_inverse(x),z) = add(multiply(additive_inverse(x),z),additive_identity),
inference(symmetry,[status(thm)],[18]) ).
tff(151,plain,
multiply(additive_inverse(x),z) = add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),multiply(x,y)),
inference(transitivity,[status(thm)],[150,149,148,141,139]) ).
tff(152,plain,
add(multiply(additive_inverse(x),z),additive_inverse(multiply(x,y))) = add(add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),multiply(x,y)),additive_inverse(multiply(x,y))),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
add(add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),multiply(x,y)),additive_inverse(multiply(x,y))) = add(multiply(additive_inverse(x),z),additive_inverse(multiply(x,y))),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),add(multiply(x,y),additive_inverse(multiply(x,y)))) = add(add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),multiply(x,y)),additive_inverse(multiply(x,y))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),add(multiply(x,y),additive_inverse(multiply(x,y)))) = add(add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),multiply(x,y)),additive_inverse(multiply(x,y))),
inference(unit_resolution,[status(thm)],[154,102]) ).
tff(156,plain,
( ~ ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
| ( add(multiply(x,y),additive_inverse(multiply(x,y))) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(157,plain,
add(multiply(x,y),additive_inverse(multiply(x,y))) = additive_identity,
inference(unit_resolution,[status(thm)],[156,79]) ).
tff(158,plain,
add(multiply(x,y),additive_inverse(multiply(x,y))) = additive_inverse(multiply(additive_identity,y)),
inference(transitivity,[status(thm)],[157,126,125,42,52]) ).
tff(159,plain,
add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),add(multiply(x,y),additive_inverse(multiply(x,y)))) = add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),additive_inverse(multiply(additive_identity,y))),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),additive_inverse(multiply(additive_identity,y))) = add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),add(multiply(x,y),additive_inverse(multiply(x,y)))),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),additive_inverse(multiply(additive_identity,y))) = add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),additive_identity),
inference(monotonicity,[status(thm)],[54]) ).
tff(162,plain,
add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),additive_identity) = add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),additive_inverse(multiply(additive_identity,y))),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
( ~ ! [X: $i] : ( add(X,additive_identity) = X )
| ( add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),additive_identity) = add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,plain,
add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),additive_identity) = add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),
inference(unit_resolution,[status(thm)],[163,16]) ).
tff(165,plain,
add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)) = add(add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),additive_identity),
inference(symmetry,[status(thm)],[164]) ).
tff(166,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(167,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)],[166]) ).
tff(168,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(169,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(170,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[170]) ).
tff(172,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[171,167]) ).
tff(173,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(additive_inverse(x),add(y,z)) = add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(174,plain,
multiply(additive_inverse(x),add(y,z)) = add(multiply(additive_inverse(x),y),multiply(additive_inverse(x),z)),
inference(unit_resolution,[status(thm)],[173,172]) ).
tff(175,plain,
multiply(additive_inverse(x),add(y,z)) = add(additive_inverse(multiply(x,y)),additive_inverse(multiply(x,z))),
inference(transitivity,[status(thm)],[174,165,162,160,155,153,134,9]) ).
tff(176,plain,
( ( 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(rewrite,[status(thm)],[]) ).
tff(177,axiom,
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',prove_distributivity) ).
tff(178,plain,
multiply(additive_inverse(x),add(y,z)) != add(additive_inverse(multiply(x,y)),additive_inverse(multiply(x,z))),
inference(modus_ponens,[status(thm)],[177,176]) ).
tff(179,plain,
$false,
inference(unit_resolution,[status(thm)],[178,175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : RNG017-6 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.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 03:07:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 175.60/175.75 % SZS status Unsatisfiable
% 175.60/175.75 % SZS output start Proof
% See solution above
% 175.60/175.77 % E exiting
%------------------------------------------------------------------------------