%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG001-5 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:23:51 AM UTC 2025
% Result : Unsatisfiable 0.64s 0.80s
% Output : Proof 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 47
% Syntax : Number of formulae : 110 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 641 ( 0 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 961 ( 460 ~; 443 |; 0 &)
% ( 58 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 30 ( 30 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 493 ( 446 !; 0 ?; 493 :)
% Comments :
%------------------------------------------------------------------------------
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( product(X,Y,multiply(X,Y))
<=> product(X,Y,multiply(X,Y)) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
<=> ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
<=> ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
tff(5,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
| product(a,multiply(a,a),multiply(a,multiply(a,a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
product(a,multiply(a,a),multiply(a,multiply(a,a))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
| product(a,additive_identity,multiply(a,additive_identity)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(11,plain,
product(a,additive_identity,multiply(a,additive_identity)),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
^ [X: $i] :
refl(( sum(additive_identity,X,X)
<=> sum(additive_identity,X,X) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [X: $i] : sum(additive_identity,X,X)
<=> ! [X: $i] : sum(additive_identity,X,X) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [X: $i] : sum(additive_identity,X,X)
<=> ! [X: $i] : sum(additive_identity,X,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
! [X: $i] : sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
tff(16,plain,
! [X: $i] : sum(additive_identity,X,X),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] : sum(additive_identity,X,X),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [X: $i] : sum(additive_identity,X,X),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [X: $i] : sum(additive_identity,X,X)
| sum(additive_identity,multiply(a,a),multiply(a,a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
sum(additive_identity,multiply(a,a),multiply(a,a)),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
refl(( ( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
<=> ( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ product(X,V3,V4) ) )),
rewrite(( ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ product(X,V3,V4) )
<=> ( ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4) )
<=> ( ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) )
<=> ( ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| sum(V1,V2,V4) ) )),
rewrite(( ( ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| sum(V1,V2,V4) )
<=> ( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) )
<=> ( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
tff(27,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,multiply(a,a),multiply(a,multiply(a,a)))
| ~ sum(additive_identity,multiply(a,a),multiply(a,a))
| sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,multiply(a,a),multiply(a,multiply(a,a)))
| ~ sum(additive_identity,multiply(a,a),multiply(a,a))
| sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a)))
| ~ product(a,multiply(a,a),multiply(a,multiply(a,a)))
| ~ sum(additive_identity,multiply(a,a),multiply(a,a))
| ~ product(a,multiply(a,a),multiply(a,multiply(a,a)))
| ~ product(a,additive_identity,multiply(a,additive_identity)) )
<=> ( ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,multiply(a,a),multiply(a,multiply(a,a)))
| ~ sum(additive_identity,multiply(a,a),multiply(a,a))
| sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a)))
| ~ product(a,multiply(a,a),multiply(a,multiply(a,a)))
| ~ sum(additive_identity,multiply(a,a),multiply(a,a))
| ~ product(a,multiply(a,a),multiply(a,multiply(a,a)))
| ~ product(a,additive_identity,multiply(a,additive_identity)) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,multiply(a,a),multiply(a,multiply(a,a)))
| ~ sum(additive_identity,multiply(a,a),multiply(a,a))
| sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a)))
| ~ product(a,multiply(a,a),multiply(a,multiply(a,a)))
| ~ sum(additive_identity,multiply(a,a),multiply(a,a))
| ~ product(a,multiply(a,a),multiply(a,multiply(a,a)))
| ~ product(a,additive_identity,multiply(a,additive_identity)) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,multiply(a,a),multiply(a,multiply(a,a)))
| ~ sum(additive_identity,multiply(a,a),multiply(a,a))
| sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a)))
| ~ product(a,multiply(a,a),multiply(a,multiply(a,a)))
| ~ sum(additive_identity,multiply(a,a),multiply(a,a))
| ~ product(a,multiply(a,a),multiply(a,multiply(a,a)))
| ~ product(a,additive_identity,multiply(a,additive_identity)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,multiply(a,a),multiply(a,multiply(a,a)))
| ~ sum(additive_identity,multiply(a,a),multiply(a,a))
| sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))),
inference(unit_resolution,[status(thm)],[36,30,20,11,9]) ).
tff(38,plain,
^ [X: $i] :
refl(( sum(X,additive_inverse(X),additive_identity)
<=> sum(X,additive_inverse(X),additive_identity) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [X: $i] : sum(X,additive_inverse(X),additive_identity)
<=> ! [X: $i] : sum(X,additive_inverse(X),additive_identity) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X: $i] : sum(X,additive_inverse(X),additive_identity)
<=> ! [X: $i] : sum(X,additive_inverse(X),additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
! [X: $i] : sum(X,additive_inverse(X),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
tff(42,plain,
! [X: $i] : sum(X,additive_inverse(X),additive_identity),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X: $i] : sum(X,additive_inverse(X),additive_identity),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [X: $i] : sum(X,additive_inverse(X),additive_identity),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [X: $i] : sum(X,additive_inverse(X),additive_identity)
| sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
^ [X: $i] :
refl(( sum(X,additive_identity,X)
<=> sum(X,additive_identity,X) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [X: $i] : sum(X,additive_identity,X)
<=> ! [X: $i] : sum(X,additive_identity,X) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [X: $i] : sum(X,additive_identity,X)
<=> ! [X: $i] : sum(X,additive_identity,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
! [X: $i] : sum(X,additive_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
tff(51,plain,
! [X: $i] : sum(X,additive_identity,X),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [X: $i] : sum(X,additive_identity,X),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [X: $i] : sum(X,additive_identity,X),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [X: $i] : sum(X,additive_identity,X)
| sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity)),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
( ~ product(a,additive_identity,additive_identity)
<=> ~ product(a,additive_identity,additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_multiplicative_identity_axiom) ).
tff(58,plain,
~ product(a,additive_identity,additive_identity),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
refl(( ( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) )
<=> ( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
rewrite(( ( ~ equalish(X,Y)
| ~ product(W,Z,X)
| product(W,Z,Y) )
<=> ( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| ~ product(W,Z,X)
| product(W,Z,Y) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| ~ product(W,Z,X)
| product(W,Z,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
tff(65,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) )
| product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ equalish(multiply(a,additive_identity),additive_identity) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) )
| product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ equalish(multiply(a,additive_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ( ~ equalish(multiply(a,additive_identity),additive_identity)
| product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity)) )
<=> ( product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ equalish(multiply(a,additive_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) )
| ~ equalish(multiply(a,additive_identity),additive_identity)
| product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) )
| product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ equalish(multiply(a,additive_identity),additive_identity) ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) )
| ~ equalish(multiply(a,additive_identity),additive_identity)
| product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity)) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) )
| product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ equalish(multiply(a,additive_identity),additive_identity) ) ),
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) )
| ~ equalish(multiply(a,additive_identity),additive_identity)
| product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| product(W,Z,Y)
| ~ product(W,Z,X) )
| product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ equalish(multiply(a,additive_identity),additive_identity) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
~ equalish(multiply(a,additive_identity),additive_identity),
inference(unit_resolution,[status(thm)],[74,68,58,11]) ).
tff(76,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(( ( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) )
<=> ( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(77,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
rewrite(( ( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) )
<=> ( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
tff(82,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) ),
inference(modus_ponens,[status(thm)],[84,77]) ).
tff(86,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) )
| equalish(multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),additive_identity,additive_identity) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) )
| equalish(multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ( ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),additive_identity,additive_identity)
| equalish(multiply(a,additive_identity),additive_identity) )
<=> ( equalish(multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) )
| ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),additive_identity,additive_identity)
| equalish(multiply(a,additive_identity),additive_identity) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) )
| equalish(multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),additive_identity,additive_identity) ) ),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) )
| ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),additive_identity,additive_identity)
| equalish(multiply(a,additive_identity),additive_identity) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) )
| equalish(multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),additive_identity,additive_identity) ) ),
inference(transitivity,[status(thm)],[88,86]) ).
tff(90,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) )
| ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),additive_identity,additive_identity)
| equalish(multiply(a,additive_identity),additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) )
| equalish(multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),additive_identity,additive_identity) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
( ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),additive_identity,additive_identity) ),
inference(unit_resolution,[status(thm)],[91,85,75]) ).
tff(93,plain,
~ sum(multiply(a,additive_identity),additive_identity,additive_identity),
inference(unit_resolution,[status(thm)],[92,55]) ).
tff(94,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(( ( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) )
<=> ( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) )
<=> ( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) )),
( ( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W)
| sum(X,V,W) )
<=> ( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
rewrite(( ( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
<=> ( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) )),
( ( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W)
| sum(X,V,W) )
<=> ( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) )),
inference(bind,[status(th)],[]) ).
tff(98,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W)
| sum(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W)
| sum(X,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition1) ).
tff(100,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(modus_ponens,[status(thm)],[102,95]) ).
tff(104,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) )
| sum(multiply(a,additive_identity),additive_identity,additive_identity)
| ~ sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) )
| sum(multiply(a,additive_identity),additive_identity,additive_identity)
| ~ sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,plain,
( ( sum(multiply(a,additive_identity),additive_identity,additive_identity)
| ~ sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity)
| ~ sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) )
<=> ( sum(multiply(a,additive_identity),additive_identity,additive_identity)
| ~ sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) )
| sum(multiply(a,additive_identity),additive_identity,additive_identity)
| ~ sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity)
| ~ sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) )
| sum(multiply(a,additive_identity),additive_identity,additive_identity)
| ~ sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) ) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) )
| sum(multiply(a,additive_identity),additive_identity,additive_identity)
| ~ sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity)
| ~ sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) )
| sum(multiply(a,additive_identity),additive_identity,additive_identity)
| ~ sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) ) ),
inference(transitivity,[status(thm)],[106,104]) ).
tff(108,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) )
| sum(multiply(a,additive_identity),additive_identity,additive_identity)
| ~ sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity)
| ~ sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) )
| sum(multiply(a,additive_identity),additive_identity,additive_identity)
| ~ sum(multiply(a,multiply(a,a)),additive_inverse(multiply(a,multiply(a,a))),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
$false,
inference(unit_resolution,[status(thm)],[109,103,93,46,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG001-5 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 03:04:54 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.64/0.80 % SZS status Unsatisfiable
% 0.64/0.80 % SZS output start Proof
% See solution above
% 0.64/0.82 % E exiting
%------------------------------------------------------------------------------