%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG014-6 : 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 05:23:53 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 44
% Syntax : Number of formulae : 133 ( 99 unt; 0 typ; 0 def)
% Number of atoms : 185 ( 175 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 62 ( 19 ~; 15 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 152 ( 138 !; 0 ?; 152 :)
% Comments :
%------------------------------------------------------------------------------
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( add(X,additive_identity) = X )
<=> ( add(X,additive_identity) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( add(X,additive_identity) = X )
<=> ! [X: $i] : ( add(X,additive_identity) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( add(X,additive_identity) = X )
<=> ! [X: $i] : ( add(X,additive_identity) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( add(X,additive_identity) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
tff(5,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( add(X,additive_identity) = X )
| ( add(additive_inverse(multiply(a,b)),additive_identity) = additive_inverse(multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
add(additive_inverse(multiply(a,b)),additive_identity) = additive_inverse(multiply(a,b)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( ( add(additive_identity,X) = X )
<=> ( add(additive_identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : ( add(additive_identity,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).
tff(14,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,additive_inverse(multiply(a,additive_identity))) = additive_inverse(multiply(a,additive_identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
add(additive_identity,additive_inverse(multiply(a,additive_identity))) = additive_inverse(multiply(a,additive_identity)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Y: $i,X: $i] :
refl(( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(20,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)],[19]) ).
tff(21,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(22,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
tff(23,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_inverse(multiply(a,additive_identity)),additive_identity) = add(additive_identity,additive_inverse(multiply(a,additive_identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
add(additive_inverse(multiply(a,additive_identity)),additive_identity) = add(additive_identity,additive_inverse(multiply(a,additive_identity))),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
^ [X: $i] :
refl(( ( multiply(X,additive_identity) = additive_identity )
<=> ( multiply(X,additive_identity) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [X: $i] : ( multiply(X,additive_identity) = additive_identity )
<=> ! [X: $i] : ( multiply(X,additive_identity) = additive_identity ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [X: $i] : ( multiply(X,additive_identity) = additive_identity )
<=> ! [X: $i] : ( multiply(X,additive_identity) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_multiplicative_zero) ).
tff(32,plain,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [X: $i] : ( multiply(X,additive_identity) = additive_identity )
| ( multiply(a,additive_identity) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
multiply(a,additive_identity) = additive_identity,
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
additive_identity = multiply(a,additive_identity),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
additive_inverse(additive_identity) = additive_inverse(multiply(a,additive_identity)),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
additive_inverse(multiply(a,additive_identity)) = additive_inverse(additive_identity),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
add(additive_inverse(multiply(a,additive_identity)),additive_identity) = add(additive_inverse(additive_identity),additive_identity),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
add(additive_inverse(additive_identity),additive_identity) = add(additive_inverse(multiply(a,additive_identity)),additive_identity),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
^ [X: $i] :
refl(( ( add(additive_inverse(X),X) = additive_identity )
<=> ( add(additive_inverse(X),X) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',left_additive_inverse) ).
tff(46,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,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(50,plain,
add(additive_inverse(additive_identity),additive_identity) = additive_identity,
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
additive_identity = add(additive_inverse(additive_identity),additive_identity),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
additive_identity = additive_inverse(multiply(a,additive_identity)),
inference(transitivity,[status(thm)],[51,41,27,18]) ).
tff(53,plain,
add(additive_inverse(multiply(a,b)),additive_identity) = add(additive_inverse(multiply(a,b)),additive_inverse(multiply(a,additive_identity))),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
add(additive_inverse(multiply(a,b)),additive_inverse(multiply(a,additive_identity))) = add(additive_inverse(multiply(a,b)),additive_identity),
inference(symmetry,[status(thm)],[53]) ).
tff(55,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(56,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)],[55]) ).
tff(57,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(58,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(59,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(multiply(a,b),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity)))) = add(add(multiply(a,b),multiply(a,additive_inverse(b))),additive_inverse(multiply(a,additive_identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
add(multiply(a,b),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity)))) = add(add(multiply(a,b),multiply(a,additive_inverse(b))),additive_inverse(multiply(a,additive_identity))),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
add(add(multiply(a,b),multiply(a,additive_inverse(b))),additive_inverse(multiply(a,additive_identity))) = add(multiply(a,b),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity)))),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
^ [X: $i] :
refl(( ( multiply(additive_identity,X) = additive_identity )
<=> ( multiply(additive_identity,X) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [X: $i] : ( multiply(additive_identity,X) = additive_identity )
<=> ! [X: $i] : ( multiply(additive_identity,X) = additive_identity ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [X: $i] : ( multiply(additive_identity,X) = additive_identity )
<=> ! [X: $i] : ( multiply(additive_identity,X) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,axiom,
! [X: $i] : ( multiply(additive_identity,X) = additive_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',left_multiplicative_zero) ).
tff(69,plain,
! [X: $i] : ( multiply(additive_identity,X) = additive_identity ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [X: $i] : ( multiply(additive_identity,X) = additive_identity ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [X: $i] : ( multiply(additive_identity,X) = additive_identity ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
( ~ ! [X: $i] : ( multiply(additive_identity,X) = additive_identity )
| ( multiply(additive_identity,a) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
multiply(additive_identity,a) = additive_identity,
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
additive_identity = multiply(additive_identity,a),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(b),b) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
add(additive_inverse(b),b) = additive_identity,
inference(unit_resolution,[status(thm)],[75,48]) ).
tff(77,plain,
multiply(a,add(additive_inverse(b),b)) = multiply(a,additive_identity),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
additive_identity = add(additive_inverse(b),b),
inference(symmetry,[status(thm)],[76]) ).
tff(79,plain,
^ [X: $i] :
refl(( ( add(X,additive_inverse(X)) = additive_identity )
<=> ( add(X,additive_inverse(X)) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
<=> ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
<=> ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,axiom,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).
tff(83,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
( ~ ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
| ( add(b,additive_inverse(b)) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
add(b,additive_inverse(b)) = additive_identity,
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
add(b,additive_inverse(b)) = add(additive_inverse(b),b),
inference(transitivity,[status(thm)],[87,78]) ).
tff(89,plain,
multiply(a,add(b,additive_inverse(b))) = multiply(a,add(additive_inverse(b),b)),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,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(91,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)],[90]) ).
tff(92,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(93,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(94,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(a,add(b,additive_inverse(b))) = add(multiply(a,b),multiply(a,additive_inverse(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
multiply(a,add(b,additive_inverse(b))) = add(multiply(a,b),multiply(a,additive_inverse(b))),
inference(unit_resolution,[status(thm)],[97,96]) ).
tff(99,plain,
add(multiply(a,b),multiply(a,additive_inverse(b))) = multiply(a,add(b,additive_inverse(b))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
add(multiply(a,b),multiply(a,additive_inverse(b))) = multiply(additive_identity,a),
inference(transitivity,[status(thm)],[99,89,77,36,74]) ).
tff(101,plain,
add(add(multiply(a,b),multiply(a,additive_inverse(b))),additive_inverse(multiply(a,additive_identity))) = add(multiply(additive_identity,a),additive_inverse(multiply(a,additive_identity))),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
add(multiply(additive_identity,a),additive_inverse(multiply(a,additive_identity))) = add(add(multiply(a,b),multiply(a,additive_inverse(b))),additive_inverse(multiply(a,additive_identity))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
add(multiply(additive_identity,a),additive_inverse(multiply(a,additive_identity))) = add(additive_identity,additive_inverse(multiply(a,additive_identity))),
inference(monotonicity,[status(thm)],[73]) ).
tff(104,plain,
add(additive_identity,additive_inverse(multiply(a,additive_identity))) = add(multiply(additive_identity,a),additive_inverse(multiply(a,additive_identity))),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
additive_inverse(multiply(a,additive_identity)) = add(additive_identity,additive_inverse(multiply(a,additive_identity))),
inference(symmetry,[status(thm)],[18]) ).
tff(106,plain,
additive_inverse(multiply(a,additive_identity)) = add(multiply(a,b),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity)))),
inference(transitivity,[status(thm)],[105,104,102,64]) ).
tff(107,plain,
add(additive_inverse(multiply(a,b)),additive_inverse(multiply(a,additive_identity))) = add(additive_inverse(multiply(a,b)),add(multiply(a,b),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity))))),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
add(additive_inverse(multiply(a,b)),add(multiply(a,b),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity))))) = add(additive_inverse(multiply(a,b)),additive_inverse(multiply(a,additive_identity))),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(additive_inverse(multiply(a,b)),add(multiply(a,b),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity))))) = add(add(additive_inverse(multiply(a,b)),multiply(a,b)),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
add(additive_inverse(multiply(a,b)),add(multiply(a,b),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity))))) = add(add(additive_inverse(multiply(a,b)),multiply(a,b)),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity)))),
inference(unit_resolution,[status(thm)],[109,61]) ).
tff(111,plain,
add(add(additive_inverse(multiply(a,b)),multiply(a,b)),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity)))) = add(additive_inverse(multiply(a,b)),add(multiply(a,b),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity))))),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(a,add(additive_inverse(b),b)) = add(multiply(a,additive_inverse(b)),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
multiply(a,add(additive_inverse(b),b)) = add(multiply(a,additive_inverse(b)),multiply(a,b)),
inference(unit_resolution,[status(thm)],[112,96]) ).
tff(114,plain,
multiply(a,additive_identity) = multiply(a,add(additive_inverse(b),b)),
inference(symmetry,[status(thm)],[77]) ).
tff(115,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(multiply(a,b)),multiply(a,b)) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
add(additive_inverse(multiply(a,b)),multiply(a,b)) = additive_identity,
inference(unit_resolution,[status(thm)],[115,48]) ).
tff(117,plain,
add(additive_inverse(multiply(a,b)),multiply(a,b)) = add(multiply(a,additive_inverse(b)),multiply(a,b)),
inference(transitivity,[status(thm)],[116,37,114,113]) ).
tff(118,plain,
add(add(additive_inverse(multiply(a,b)),multiply(a,b)),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity)))) = add(add(multiply(a,additive_inverse(b)),multiply(a,b)),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity)))),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
add(add(multiply(a,additive_inverse(b)),multiply(a,b)),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity)))) = add(add(additive_inverse(multiply(a,b)),multiply(a,b)),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity)))),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(multiply(a,additive_inverse(b)),add(multiply(a,b),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity))))) = add(add(multiply(a,additive_inverse(b)),multiply(a,b)),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
add(multiply(a,additive_inverse(b)),add(multiply(a,b),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity))))) = add(add(multiply(a,additive_inverse(b)),multiply(a,b)),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity)))),
inference(unit_resolution,[status(thm)],[120,61]) ).
tff(122,plain,
add(multiply(a,b),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity)))) = additive_inverse(multiply(a,additive_identity)),
inference(transitivity,[status(thm)],[63,101,103,18]) ).
tff(123,plain,
add(multiply(a,additive_inverse(b)),add(multiply(a,b),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity))))) = add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity))),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity))) = add(multiply(a,additive_inverse(b)),add(multiply(a,b),add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity))))),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
add(multiply(a,additive_inverse(b)),additive_identity) = add(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,additive_identity))),
inference(monotonicity,[status(thm)],[52]) ).
tff(126,plain,
( ~ ! [X: $i] : ( add(X,additive_identity) = X )
| ( add(multiply(a,additive_inverse(b)),additive_identity) = multiply(a,additive_inverse(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
add(multiply(a,additive_inverse(b)),additive_identity) = multiply(a,additive_inverse(b)),
inference(unit_resolution,[status(thm)],[126,7]) ).
tff(128,plain,
multiply(a,additive_inverse(b)) = add(multiply(a,additive_inverse(b)),additive_identity),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
multiply(a,additive_inverse(b)) = additive_inverse(multiply(a,b)),
inference(transitivity,[status(thm)],[128,125,124,121,119,111,108,54,9]) ).
tff(130,plain,
( ( multiply(a,additive_inverse(b)) != additive_inverse(multiply(a,b)) )
<=> ( multiply(a,additive_inverse(b)) != additive_inverse(multiply(a,b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(131,axiom,
multiply(a,additive_inverse(b)) != additive_inverse(multiply(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
tff(132,plain,
multiply(a,additive_inverse(b)) != additive_inverse(multiply(a,b)),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
$false,
inference(unit_resolution,[status(thm)],[132,129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG014-6 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n009.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 03:09:03 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.45 % SZS status Unsatisfiable
% 0.21/0.45 % SZS output start Proof
% See solution above
% 0.21/0.46 % E exiting
%------------------------------------------------------------------------------