TSTP Solution File: RNG039-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG039-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Tue Sep 20 03:17:51 EDT 2022
% Result : Unsatisfiable 0.18s 0.52s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 119
% Syntax : Number of formulae : 330 ( 163 unt; 9 typ; 0 def)
% Number of atoms : 947 ( 221 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 1107 ( 507 ~; 489 |; 0 &)
% ( 111 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 26 ( 26 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 4 >; 6 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 557 ( 521 !; 0 ?; 557 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(a_type,type,
a: $i ).
tff(c_type,type,
c: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(d_type,type,
d: $i ).
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(1,plain,
^ [A: $i] :
refl(
( ( multiply(A,A) = A )
<=> ( multiply(A,A) = A ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i] : ( multiply(A,A) = A )
<=> ! [A: $i] : ( multiply(A,A) = A ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( multiply(A,A) = A )
<=> ! [A: $i] : ( multiply(A,A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [A: $i] : ( multiply(A,A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
tff(5,plain,
! [A: $i] : ( multiply(A,A) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( multiply(A,A) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( multiply(A,A) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( multiply(A,A) = A )
| ( multiply(b,b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
multiply(b,b) = b,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
b = multiply(b,b),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( product(a,b,b)
<=> product(a,multiply(b,b),multiply(b,b)) ),
inference(monotonicity,[status(thm)],[10,10]) ).
tff(12,plain,
( product(a,multiply(b,b),multiply(b,b))
<=> product(a,b,b) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
^ [B: $i,A: $i] :
refl(
( product(a,multiply(b,A),multiply(B,A))
<=> product(a,multiply(b,A),multiply(B,A)) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A))
<=> ! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A)) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A))
<=> ! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A)) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
tff(17,plain,
! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A)),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A)),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A)),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ~ ! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A))
| product(a,multiply(b,b),multiply(b,b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
product(a,multiply(b,b),multiply(b,b)),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
product(a,b,b),
inference(modus_ponens,[status(thm)],[21,12]) ).
tff(23,plain,
( product(a,b,multiply(c,b))
<=> product(a,b,multiply(multiply(a,b),b)) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( product(a,b,multiply(c,b))
<=> product(a,b,multiply(c,b)) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
product(a,b,multiply(c,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause45) ).
tff(26,plain,
product(a,b,multiply(c,b)),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
product(a,b,multiply(multiply(a,b),b)),
inference(modus_ponens,[status(thm)],[26,23]) ).
tff(28,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
<=> ( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
rewrite(
( ( ~ product(X,Y,U)
| ~ product(X,Y,V)
| ( U = V ) )
<=> ( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| ( U = V ) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
tff(34,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,b,multiply(multiply(a,b),b))
| ~ product(a,b,b)
| ( b = multiply(multiply(a,b),b) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,b,multiply(multiply(a,b),b))
| ~ product(a,b,b)
| ( b = multiply(multiply(a,b),b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,b,multiply(multiply(a,b),b))
| ~ product(a,b,b)
| ( b = multiply(multiply(a,b),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,b,multiply(multiply(a,b),b))
| ~ product(a,b,b)
| ( b = multiply(multiply(a,b),b) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ~ product(a,b,b)
| ( b = multiply(multiply(a,b),b) ) ),
inference(unit_resolution,[status(thm)],[40,37,27]) ).
tff(42,plain,
b = multiply(multiply(a,b),b),
inference(unit_resolution,[status(thm)],[41,22]) ).
tff(43,plain,
multiply(multiply(a,b),b) = b,
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
multiply(additive_identity,multiply(multiply(a,b),b)) = multiply(additive_identity,b),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
multiply(additive_identity,b) = multiply(additive_identity,multiply(multiply(a,b),b)),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
( product(additive_identity,multiply(multiply(a,b),b),multiply(additive_identity,b))
<=> product(additive_identity,multiply(multiply(a,b),b),multiply(additive_identity,multiply(multiply(a,b),b))) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( product(additive_identity,multiply(multiply(a,b),b),multiply(additive_identity,multiply(multiply(a,b),b)))
<=> product(additive_identity,multiply(multiply(a,b),b),multiply(additive_identity,b)) ),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
^ [Y: $i,X: $i] :
refl(
( product(X,Y,multiply(X,Y))
<=> product(X,Y,multiply(X,Y)) )),
inference(bind,[status(th)],]) ).
tff(49,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)],[48]) ).
tff(50,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(51,axiom,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
tff(52,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
| product(additive_identity,multiply(multiply(a,b),b),multiply(additive_identity,multiply(multiply(a,b),b))) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
product(additive_identity,multiply(multiply(a,b),b),multiply(additive_identity,multiply(multiply(a,b),b))),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
product(additive_identity,multiply(multiply(a,b),b),multiply(additive_identity,b)),
inference(modus_ponens,[status(thm)],[56,47]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
| product(add(multiply(a,b),a),multiply(multiply(b,a),a),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
product(add(multiply(a,b),a),multiply(multiply(b,a),a),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a))),
inference(unit_resolution,[status(thm)],[58,54]) ).
tff(60,plain,
( product(b,a,multiply(b,d))
<=> product(b,a,multiply(b,multiply(b,a))) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( product(b,a,multiply(b,d))
<=> product(b,a,multiply(b,d)) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
product(b,a,multiply(b,d)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause58) ).
tff(63,plain,
product(b,a,multiply(b,d)),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
product(b,a,multiply(b,multiply(b,a))),
inference(modus_ponens,[status(thm)],[63,60]) ).
tff(65,plain,
( product(b,a,multiply(d,a))
<=> product(b,a,multiply(multiply(b,a),a)) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( product(b,a,multiply(d,a))
<=> product(b,a,multiply(d,a)) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
product(b,a,multiply(d,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause48) ).
tff(68,plain,
product(b,a,multiply(d,a)),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
product(b,a,multiply(multiply(b,a),a)),
inference(modus_ponens,[status(thm)],[68,65]) ).
tff(70,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(b,a,multiply(multiply(b,a),a))
| ~ product(b,a,multiply(b,multiply(b,a)))
| ( multiply(b,multiply(b,a)) = multiply(multiply(b,a),a) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(b,a,multiply(multiply(b,a),a))
| ~ product(b,a,multiply(b,multiply(b,a)))
| ( multiply(b,multiply(b,a)) = multiply(multiply(b,a),a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(b,a,multiply(multiply(b,a),a))
| ~ product(b,a,multiply(b,multiply(b,a)))
| ( multiply(b,multiply(b,a)) = multiply(multiply(b,a),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(b,a,multiply(multiply(b,a),a))
| ~ product(b,a,multiply(b,multiply(b,a)))
| ( multiply(b,multiply(b,a)) = multiply(multiply(b,a),a) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
multiply(b,multiply(b,a)) = multiply(multiply(b,a),a),
inference(unit_resolution,[status(thm)],[72,37,69,64]) ).
tff(74,plain,
multiply(multiply(b,a),a) = multiply(b,multiply(b,a)),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
( product(a,multiply(multiply(b,a),a),multiply(multiply(b,a),a))
<=> product(a,multiply(b,multiply(b,a)),multiply(b,multiply(b,a))) ),
inference(monotonicity,[status(thm)],[74,74]) ).
tff(76,plain,
( product(a,multiply(b,multiply(b,a)),multiply(b,multiply(b,a)))
<=> product(a,multiply(multiply(b,a),a),multiply(multiply(b,a),a)) ),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( ~ ! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A))
| product(a,multiply(b,multiply(b,a)),multiply(b,multiply(b,a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
product(a,multiply(b,multiply(b,a)),multiply(b,multiply(b,a))),
inference(unit_resolution,[status(thm)],[77,19]) ).
tff(79,plain,
product(a,multiply(multiply(b,a),a),multiply(multiply(b,a),a)),
inference(modus_ponens,[status(thm)],[78,76]) ).
tff(80,plain,
( product(a,multiply(multiply(b,a),a),multiply(a,multiply(b,a)))
<=> product(a,multiply(b,multiply(b,a)),multiply(a,multiply(b,a))) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(81,plain,
( product(a,multiply(b,multiply(b,a)),multiply(a,multiply(b,a)))
<=> product(a,multiply(multiply(b,a),a),multiply(a,multiply(b,a))) ),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A))
| product(a,multiply(b,multiply(b,a)),multiply(a,multiply(b,a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
product(a,multiply(b,multiply(b,a)),multiply(a,multiply(b,a))),
inference(unit_resolution,[status(thm)],[82,19]) ).
tff(84,plain,
product(a,multiply(multiply(b,a),a),multiply(a,multiply(b,a))),
inference(modus_ponens,[status(thm)],[83,81]) ).
tff(85,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,multiply(multiply(b,a),a),multiply(multiply(b,a),a))
| ~ product(a,multiply(multiply(b,a),a),multiply(a,multiply(b,a)))
| ( multiply(a,multiply(b,a)) = multiply(multiply(b,a),a) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,multiply(multiply(b,a),a),multiply(multiply(b,a),a))
| ~ product(a,multiply(multiply(b,a),a),multiply(a,multiply(b,a)))
| ( multiply(a,multiply(b,a)) = multiply(multiply(b,a),a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,multiply(multiply(b,a),a),multiply(multiply(b,a),a))
| ~ product(a,multiply(multiply(b,a),a),multiply(a,multiply(b,a)))
| ( multiply(a,multiply(b,a)) = multiply(multiply(b,a),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,multiply(multiply(b,a),a),multiply(multiply(b,a),a))
| ~ product(a,multiply(multiply(b,a),a),multiply(a,multiply(b,a)))
| ( multiply(a,multiply(b,a)) = multiply(multiply(b,a),a) ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
( ~ product(a,multiply(multiply(b,a),a),multiply(multiply(b,a),a))
| ~ product(a,multiply(multiply(b,a),a),multiply(a,multiply(b,a)))
| ( multiply(a,multiply(b,a)) = multiply(multiply(b,a),a) ) ),
inference(unit_resolution,[status(thm)],[87,37]) ).
tff(89,plain,
multiply(a,multiply(b,a)) = multiply(multiply(b,a),a),
inference(unit_resolution,[status(thm)],[88,84,79]) ).
tff(90,plain,
( product(a,b,c)
<=> product(a,b,multiply(a,b)) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( product(a,b,c)
<=> product(a,b,c) ),
inference(rewrite,[status(thm)],]) ).
tff(92,axiom,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
tff(93,plain,
product(a,b,c),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
product(a,b,multiply(a,b)),
inference(modus_ponens,[status(thm)],[93,90]) ).
tff(95,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,b,multiply(multiply(a,b),b))
| ~ product(a,b,multiply(a,b))
| ( multiply(a,b) = multiply(multiply(a,b),b) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,b,multiply(multiply(a,b),b))
| ~ product(a,b,multiply(a,b))
| ( multiply(a,b) = multiply(multiply(a,b),b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,b,multiply(multiply(a,b),b))
| ~ product(a,b,multiply(a,b))
| ( multiply(a,b) = multiply(multiply(a,b),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,b,multiply(multiply(a,b),b))
| ~ product(a,b,multiply(a,b))
| ( multiply(a,b) = multiply(multiply(a,b),b) ) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
multiply(a,b) = multiply(multiply(a,b),b),
inference(unit_resolution,[status(thm)],[97,37,27,94]) ).
tff(99,plain,
multiply(multiply(a,b),b) = multiply(a,b),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
( product(multiply(multiply(a,b),b),a,multiply(a,multiply(b,a)))
<=> product(multiply(a,b),a,multiply(a,multiply(b,a))) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( product(multiply(a,b),a,multiply(a,multiply(b,a)))
<=> product(multiply(multiply(a,b),b),a,multiply(a,multiply(b,a))) ),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
( product(c,a,multiply(a,d))
<=> product(multiply(a,b),a,multiply(a,multiply(b,a))) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( product(c,a,multiply(a,d))
<=> product(c,a,multiply(a,d)) ),
inference(rewrite,[status(thm)],]) ).
tff(104,axiom,
product(c,a,multiply(a,d)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause60) ).
tff(105,plain,
product(c,a,multiply(a,d)),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
product(multiply(a,b),a,multiply(a,multiply(b,a))),
inference(modus_ponens,[status(thm)],[105,102]) ).
tff(107,plain,
product(multiply(multiply(a,b),b),a,multiply(a,multiply(b,a))),
inference(modus_ponens,[status(thm)],[106,101]) ).
tff(108,plain,
^ [A: $i] :
refl(
( product(multiply(A,b),a,multiply(A,multiply(b,a)))
<=> product(multiply(A,b),a,multiply(A,multiply(b,a))) )),
inference(bind,[status(th)],]) ).
tff(109,plain,
( ! [A: $i] : product(multiply(A,b),a,multiply(A,multiply(b,a)))
<=> ! [A: $i] : product(multiply(A,b),a,multiply(A,multiply(b,a))) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,plain,
^ [A: $i] :
rewrite(
( product(multiply(A,b),a,multiply(A,d))
<=> product(multiply(A,b),a,multiply(A,multiply(b,a))) )),
inference(bind,[status(th)],]) ).
tff(111,plain,
( ! [A: $i] : product(multiply(A,b),a,multiply(A,d))
<=> ! [A: $i] : product(multiply(A,b),a,multiply(A,multiply(b,a))) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,plain,
( ! [A: $i] : product(multiply(A,b),a,multiply(A,d))
<=> ! [A: $i] : product(multiply(A,b),a,multiply(A,d)) ),
inference(rewrite,[status(thm)],]) ).
tff(113,axiom,
! [A: $i] : product(multiply(A,b),a,multiply(A,d)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
tff(114,plain,
! [A: $i] : product(multiply(A,b),a,multiply(A,d)),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [A: $i] : product(multiply(A,b),a,multiply(A,multiply(b,a))),
inference(modus_ponens,[status(thm)],[114,111]) ).
tff(116,plain,
! [A: $i] : product(multiply(A,b),a,multiply(A,multiply(b,a))),
inference(skolemize,[status(sab)],[115]) ).
tff(117,plain,
! [A: $i] : product(multiply(A,b),a,multiply(A,multiply(b,a))),
inference(modus_ponens,[status(thm)],[116,109]) ).
tff(118,plain,
( ~ ! [A: $i] : product(multiply(A,b),a,multiply(A,multiply(b,a)))
| product(multiply(multiply(a,b),b),a,multiply(multiply(a,b),multiply(b,a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
product(multiply(multiply(a,b),b),a,multiply(multiply(a,b),multiply(b,a))),
inference(unit_resolution,[status(thm)],[118,117]) ).
tff(120,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(multiply(multiply(a,b),b),a,multiply(a,multiply(b,a)))
| ~ product(multiply(multiply(a,b),b),a,multiply(multiply(a,b),multiply(b,a)))
| ( multiply(multiply(a,b),multiply(b,a)) = multiply(a,multiply(b,a)) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(multiply(multiply(a,b),b),a,multiply(a,multiply(b,a)))
| ~ product(multiply(multiply(a,b),b),a,multiply(multiply(a,b),multiply(b,a)))
| ( multiply(multiply(a,b),multiply(b,a)) = multiply(a,multiply(b,a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(multiply(multiply(a,b),b),a,multiply(a,multiply(b,a)))
| ~ product(multiply(multiply(a,b),b),a,multiply(multiply(a,b),multiply(b,a)))
| ( multiply(multiply(a,b),multiply(b,a)) = multiply(a,multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(multiply(multiply(a,b),b),a,multiply(a,multiply(b,a)))
| ~ product(multiply(multiply(a,b),b),a,multiply(multiply(a,b),multiply(b,a)))
| ( multiply(multiply(a,b),multiply(b,a)) = multiply(a,multiply(b,a)) ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
( ~ product(multiply(multiply(a,b),b),a,multiply(a,multiply(b,a)))
| ( multiply(multiply(a,b),multiply(b,a)) = multiply(a,multiply(b,a)) ) ),
inference(unit_resolution,[status(thm)],[122,37,119]) ).
tff(124,plain,
multiply(multiply(a,b),multiply(b,a)) = multiply(a,multiply(b,a)),
inference(unit_resolution,[status(thm)],[123,107]) ).
tff(125,plain,
( product(b,a,d)
<=> product(b,a,multiply(b,a)) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( product(b,a,d)
<=> product(b,a,d) ),
inference(rewrite,[status(thm)],]) ).
tff(127,axiom,
product(b,a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a) ).
tff(128,plain,
product(b,a,d),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
product(b,a,multiply(b,a)),
inference(modus_ponens,[status(thm)],[128,125]) ).
tff(130,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(b,a,multiply(multiply(b,a),a))
| ~ product(b,a,multiply(b,a))
| ( multiply(b,a) = multiply(multiply(b,a),a) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(b,a,multiply(multiply(b,a),a))
| ~ product(b,a,multiply(b,a))
| ( multiply(b,a) = multiply(multiply(b,a),a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(b,a,multiply(multiply(b,a),a))
| ~ product(b,a,multiply(b,a))
| ( multiply(b,a) = multiply(multiply(b,a),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(132,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(b,a,multiply(multiply(b,a),a))
| ~ product(b,a,multiply(b,a))
| ( multiply(b,a) = multiply(multiply(b,a),a) ) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
multiply(b,a) = multiply(multiply(b,a),a),
inference(unit_resolution,[status(thm)],[132,37,69,129]) ).
tff(134,plain,
multiply(multiply(b,a),a) = multiply(b,a),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
multiply(multiply(multiply(a,b),b),multiply(multiply(b,a),a)) = multiply(multiply(a,b),multiply(b,a)),
inference(monotonicity,[status(thm)],[99,134]) ).
tff(136,plain,
multiply(multiply(a,b),multiply(b,a)) = multiply(multiply(multiply(a,b),b),multiply(multiply(b,a),a)),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
multiply(b,multiply(multiply(b,a),a)) = multiply(b,multiply(b,a)),
inference(monotonicity,[status(thm)],[134]) ).
tff(138,plain,
multiply(b,multiply(b,a)) = multiply(b,multiply(multiply(b,a),a)),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
multiply(multiply(b,a),a) = multiply(b,multiply(multiply(b,a),a)),
inference(transitivity,[status(thm)],[74,138]) ).
tff(140,plain,
( product(a,multiply(multiply(b,a),a),multiply(multiply(a,b),multiply(b,a)))
<=> product(a,multiply(b,multiply(multiply(b,a),a)),multiply(multiply(multiply(a,b),b),multiply(multiply(b,a),a))) ),
inference(monotonicity,[status(thm)],[139,136]) ).
tff(141,plain,
( product(a,multiply(b,multiply(multiply(b,a),a)),multiply(multiply(multiply(a,b),b),multiply(multiply(b,a),a)))
<=> product(a,multiply(multiply(b,a),a),multiply(multiply(a,b),multiply(b,a))) ),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A))
| product(a,multiply(b,multiply(multiply(b,a),a)),multiply(multiply(multiply(a,b),b),multiply(multiply(b,a),a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
product(a,multiply(b,multiply(multiply(b,a),a)),multiply(multiply(multiply(a,b),b),multiply(multiply(b,a),a))),
inference(unit_resolution,[status(thm)],[142,19]) ).
tff(144,plain,
product(a,multiply(multiply(b,a),a),multiply(multiply(a,b),multiply(b,a))),
inference(modus_ponens,[status(thm)],[143,141]) ).
tff(145,plain,
( ~ ! [A: $i] : ( multiply(A,A) = A )
| ( multiply(a,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(146,plain,
multiply(a,a) = a,
inference(unit_resolution,[status(thm)],[145,7]) ).
tff(147,plain,
a = multiply(a,a),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
( product(a,multiply(multiply(b,a),a),a)
<=> product(a,multiply(b,a),multiply(a,a)) ),
inference(monotonicity,[status(thm)],[134,147]) ).
tff(149,plain,
( product(a,multiply(b,a),multiply(a,a))
<=> product(a,multiply(multiply(b,a),a),a) ),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
( ~ ! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A))
| product(a,multiply(b,a),multiply(a,a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(151,plain,
product(a,multiply(b,a),multiply(a,a)),
inference(unit_resolution,[status(thm)],[150,19]) ).
tff(152,plain,
product(a,multiply(multiply(b,a),a),a),
inference(modus_ponens,[status(thm)],[151,149]) ).
tff(153,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,multiply(multiply(b,a),a),a)
| ~ product(a,multiply(multiply(b,a),a),multiply(multiply(a,b),multiply(b,a)))
| ( multiply(multiply(a,b),multiply(b,a)) = a ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,multiply(multiply(b,a),a),a)
| ~ product(a,multiply(multiply(b,a),a),multiply(multiply(a,b),multiply(b,a)))
| ( multiply(multiply(a,b),multiply(b,a)) = a ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(154,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,multiply(multiply(b,a),a),a)
| ~ product(a,multiply(multiply(b,a),a),multiply(multiply(a,b),multiply(b,a)))
| ( multiply(multiply(a,b),multiply(b,a)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(155,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,multiply(multiply(b,a),a),a)
| ~ product(a,multiply(multiply(b,a),a),multiply(multiply(a,b),multiply(b,a)))
| ( multiply(multiply(a,b),multiply(b,a)) = a ) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
( ~ product(a,multiply(multiply(b,a),a),a)
| ~ product(a,multiply(multiply(b,a),a),multiply(multiply(a,b),multiply(b,a)))
| ( multiply(multiply(a,b),multiply(b,a)) = a ) ),
inference(unit_resolution,[status(thm)],[155,37]) ).
tff(157,plain,
multiply(multiply(a,b),multiply(b,a)) = a,
inference(unit_resolution,[status(thm)],[156,152,144]) ).
tff(158,plain,
a = multiply(multiply(a,b),multiply(b,a)),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
a = multiply(multiply(b,a),a),
inference(transitivity,[status(thm)],[158,124,89]) ).
tff(160,plain,
add(multiply(b,a),a) = add(multiply(multiply(b,a),a),multiply(multiply(b,a),a)),
inference(monotonicity,[status(thm)],[133,159]) ).
tff(161,plain,
add(multiply(multiply(b,a),a),multiply(multiply(b,a),a)) = add(multiply(b,a),a),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
^ [A: $i] :
refl(
( ( add(A,A) = additive_identity )
<=> ( add(A,A) = additive_identity ) )),
inference(bind,[status(th)],]) ).
tff(163,plain,
( ! [A: $i] : ( add(A,A) = additive_identity )
<=> ! [A: $i] : ( add(A,A) = additive_identity ) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,plain,
( ! [A: $i] : ( add(A,A) = additive_identity )
<=> ! [A: $i] : ( add(A,A) = additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(165,axiom,
! [A: $i] : ( add(A,A) = additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
tff(166,plain,
! [A: $i] : ( add(A,A) = additive_identity ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
! [A: $i] : ( add(A,A) = additive_identity ),
inference(skolemize,[status(sab)],[166]) ).
tff(168,plain,
! [A: $i] : ( add(A,A) = additive_identity ),
inference(modus_ponens,[status(thm)],[167,163]) ).
tff(169,plain,
( ~ ! [A: $i] : ( add(A,A) = additive_identity )
| ( add(multiply(multiply(b,a),a),multiply(multiply(b,a),a)) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(170,plain,
add(multiply(multiply(b,a),a),multiply(multiply(b,a),a)) = additive_identity,
inference(unit_resolution,[status(thm)],[169,168]) ).
tff(171,plain,
additive_identity = add(multiply(multiply(b,a),a),multiply(multiply(b,a),a)),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
additive_identity = add(multiply(b,a),a),
inference(transitivity,[status(thm)],[171,161]) ).
tff(173,plain,
multiply(a,multiply(b,a)) = multiply(multiply(a,b),multiply(b,a)),
inference(symmetry,[status(thm)],[124]) ).
tff(174,plain,
multiply(multiply(b,a),a) = multiply(a,multiply(b,a)),
inference(symmetry,[status(thm)],[89]) ).
tff(175,plain,
multiply(multiply(b,a),a) = a,
inference(transitivity,[status(thm)],[174,173,157]) ).
tff(176,plain,
b = multiply(a,b),
inference(transitivity,[status(thm)],[42,99]) ).
tff(177,plain,
add(b,a) = add(multiply(a,b),a),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
add(multiply(a,b),a) = add(b,a),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
( product(add(multiply(a,b),a),multiply(multiply(b,a),a),additive_identity)
<=> product(add(b,a),a,add(multiply(b,a),a)) ),
inference(monotonicity,[status(thm)],[178,175,172]) ).
tff(180,plain,
( product(add(b,a),a,add(multiply(b,a),a))
<=> product(add(multiply(a,b),a),multiply(multiply(b,a),a),additive_identity) ),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
( product(add(b,a),a,add(d,a))
<=> product(add(b,a),a,add(multiply(b,a),a)) ),
inference(rewrite,[status(thm)],]) ).
tff(182,plain,
( product(add(b,a),a,add(d,a))
<=> product(add(b,a),a,add(d,a)) ),
inference(rewrite,[status(thm)],]) ).
tff(183,axiom,
product(add(b,a),a,add(d,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
tff(184,plain,
product(add(b,a),a,add(d,a)),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
product(add(b,a),a,add(multiply(b,a),a)),
inference(modus_ponens,[status(thm)],[184,181]) ).
tff(186,plain,
product(add(multiply(a,b),a),multiply(multiply(b,a),a),additive_identity),
inference(modus_ponens,[status(thm)],[185,180]) ).
tff(187,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(add(multiply(a,b),a),multiply(multiply(b,a),a),additive_identity)
| ~ product(add(multiply(a,b),a),multiply(multiply(b,a),a),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)))
| ( multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)) = additive_identity ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(add(multiply(a,b),a),multiply(multiply(b,a),a),additive_identity)
| ~ product(add(multiply(a,b),a),multiply(multiply(b,a),a),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)))
| ( multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)) = additive_identity ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(188,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(add(multiply(a,b),a),multiply(multiply(b,a),a),additive_identity)
| ~ product(add(multiply(a,b),a),multiply(multiply(b,a),a),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)))
| ( multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(189,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(add(multiply(a,b),a),multiply(multiply(b,a),a),additive_identity)
| ~ product(add(multiply(a,b),a),multiply(multiply(b,a),a),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)))
| ( multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)) = additive_identity ) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)) = additive_identity,
inference(unit_resolution,[status(thm)],[189,37,186,59]) ).
tff(191,plain,
( product(multiply(multiply(b,a),a),multiply(multiply(b,a),a),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)))
<=> product(a,multiply(b,multiply(multiply(b,a),a)),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a))) ),
inference(monotonicity,[status(thm)],[175,139]) ).
tff(192,plain,
( product(a,multiply(b,multiply(multiply(b,a),a)),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)))
<=> product(multiply(multiply(b,a),a),multiply(multiply(b,a),a),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a))) ),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
( ~ ! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A))
| product(a,multiply(b,multiply(multiply(b,a),a)),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(194,plain,
product(a,multiply(b,multiply(multiply(b,a),a)),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a))),
inference(unit_resolution,[status(thm)],[193,19]) ).
tff(195,plain,
product(multiply(multiply(b,a),a),multiply(multiply(b,a),a),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a))),
inference(modus_ponens,[status(thm)],[194,192]) ).
tff(196,plain,
( product(multiply(multiply(b,a),a),multiply(multiply(b,a),a),multiply(multiply(b,a),a))
<=> product(multiply(b,a),multiply(multiply(b,a),a),multiply(multiply(b,a),a)) ),
inference(monotonicity,[status(thm)],[134]) ).
tff(197,plain,
( product(multiply(b,a),multiply(multiply(b,a),a),multiply(multiply(b,a),a))
<=> product(multiply(multiply(b,a),a),multiply(multiply(b,a),a),multiply(multiply(b,a),a)) ),
inference(symmetry,[status(thm)],[196]) ).
tff(198,plain,
^ [B: $i,A: $i] :
refl(
( product(A,multiply(A,B),multiply(A,B))
<=> product(A,multiply(A,B),multiply(A,B)) )),
inference(bind,[status(th)],]) ).
tff(199,plain,
( ! [B: $i,A: $i] : product(A,multiply(A,B),multiply(A,B))
<=> ! [B: $i,A: $i] : product(A,multiply(A,B),multiply(A,B)) ),
inference(quant_intro,[status(thm)],[198]) ).
tff(200,plain,
( ! [B: $i,A: $i] : product(A,multiply(A,B),multiply(A,B))
<=> ! [B: $i,A: $i] : product(A,multiply(A,B),multiply(A,B)) ),
inference(rewrite,[status(thm)],]) ).
tff(201,axiom,
! [B: $i,A: $i] : product(A,multiply(A,B),multiply(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
tff(202,plain,
! [B: $i,A: $i] : product(A,multiply(A,B),multiply(A,B)),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
! [B: $i,A: $i] : product(A,multiply(A,B),multiply(A,B)),
inference(skolemize,[status(sab)],[202]) ).
tff(204,plain,
! [B: $i,A: $i] : product(A,multiply(A,B),multiply(A,B)),
inference(modus_ponens,[status(thm)],[203,199]) ).
tff(205,plain,
( ~ ! [B: $i,A: $i] : product(A,multiply(A,B),multiply(A,B))
| product(multiply(b,a),multiply(multiply(b,a),a),multiply(multiply(b,a),a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(206,plain,
product(multiply(b,a),multiply(multiply(b,a),a),multiply(multiply(b,a),a)),
inference(unit_resolution,[status(thm)],[205,204]) ).
tff(207,plain,
product(multiply(multiply(b,a),a),multiply(multiply(b,a),a),multiply(multiply(b,a),a)),
inference(modus_ponens,[status(thm)],[206,197]) ).
tff(208,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(multiply(multiply(b,a),a),multiply(multiply(b,a),a),multiply(multiply(b,a),a))
| ~ product(multiply(multiply(b,a),a),multiply(multiply(b,a),a),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)))
| ( multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)) = multiply(multiply(b,a),a) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(multiply(multiply(b,a),a),multiply(multiply(b,a),a),multiply(multiply(b,a),a))
| ~ product(multiply(multiply(b,a),a),multiply(multiply(b,a),a),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)))
| ( multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)) = multiply(multiply(b,a),a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(209,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(multiply(multiply(b,a),a),multiply(multiply(b,a),a),multiply(multiply(b,a),a))
| ~ product(multiply(multiply(b,a),a),multiply(multiply(b,a),a),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)))
| ( multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)) = multiply(multiply(b,a),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(210,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(multiply(multiply(b,a),a),multiply(multiply(b,a),a),multiply(multiply(b,a),a))
| ~ product(multiply(multiply(b,a),a),multiply(multiply(b,a),a),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)))
| ( multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)) = multiply(multiply(b,a),a) ) ),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
( ~ product(multiply(multiply(b,a),a),multiply(multiply(b,a),a),multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)))
| ( multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)) = multiply(multiply(b,a),a) ) ),
inference(unit_resolution,[status(thm)],[210,37,207]) ).
tff(212,plain,
multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)) = multiply(multiply(b,a),a),
inference(unit_resolution,[status(thm)],[211,195]) ).
tff(213,plain,
multiply(multiply(b,a),a) = multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
multiply(b,a) = additive_identity,
inference(transitivity,[status(thm)],[133,213,190]) ).
tff(215,plain,
additive_identity = multiply(add(multiply(a,b),a),multiply(multiply(b,a),a)),
inference(symmetry,[status(thm)],[190]) ).
tff(216,plain,
additive_identity = multiply(b,a),
inference(transitivity,[status(thm)],[215,212,134]) ).
tff(217,plain,
multiply(additive_identity,b) = multiply(multiply(b,a),multiply(a,b)),
inference(monotonicity,[status(thm)],[216,176]) ).
tff(218,plain,
multiply(multiply(b,a),multiply(a,b)) = multiply(additive_identity,b),
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
( product(a,b,multiply(a,c))
<=> product(a,b,multiply(a,multiply(a,b))) ),
inference(rewrite,[status(thm)],]) ).
tff(220,plain,
( product(a,b,multiply(a,c))
<=> product(a,b,multiply(a,c)) ),
inference(rewrite,[status(thm)],]) ).
tff(221,axiom,
product(a,b,multiply(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
tff(222,plain,
product(a,b,multiply(a,c)),
inference(modus_ponens,[status(thm)],[221,220]) ).
tff(223,plain,
product(a,b,multiply(a,multiply(a,b))),
inference(modus_ponens,[status(thm)],[222,219]) ).
tff(224,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,b,multiply(multiply(a,b),b))
| ~ product(a,b,multiply(a,multiply(a,b)))
| ( multiply(a,multiply(a,b)) = multiply(multiply(a,b),b) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,b,multiply(multiply(a,b),b))
| ~ product(a,b,multiply(a,multiply(a,b)))
| ( multiply(a,multiply(a,b)) = multiply(multiply(a,b),b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(225,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,b,multiply(multiply(a,b),b))
| ~ product(a,b,multiply(a,multiply(a,b)))
| ( multiply(a,multiply(a,b)) = multiply(multiply(a,b),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(226,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,b,multiply(multiply(a,b),b))
| ~ product(a,b,multiply(a,multiply(a,b)))
| ( multiply(a,multiply(a,b)) = multiply(multiply(a,b),b) ) ),
inference(modus_ponens,[status(thm)],[225,224]) ).
tff(227,plain,
multiply(a,multiply(a,b)) = multiply(multiply(a,b),b),
inference(unit_resolution,[status(thm)],[226,37,27,223]) ).
tff(228,plain,
multiply(multiply(a,b),b) = multiply(a,multiply(a,b)),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
( product(b,multiply(multiply(a,b),b),multiply(multiply(b,a),multiply(a,b)))
<=> product(b,multiply(a,multiply(a,b)),multiply(multiply(b,a),multiply(a,b))) ),
inference(monotonicity,[status(thm)],[228]) ).
tff(230,plain,
( product(b,multiply(a,multiply(a,b)),multiply(multiply(b,a),multiply(a,b)))
<=> product(b,multiply(multiply(a,b),b),multiply(multiply(b,a),multiply(a,b))) ),
inference(symmetry,[status(thm)],[229]) ).
tff(231,plain,
^ [A: $i] :
refl(
( product(b,multiply(a,A),multiply(multiply(b,a),A))
<=> product(b,multiply(a,A),multiply(multiply(b,a),A)) )),
inference(bind,[status(th)],]) ).
tff(232,plain,
( ! [A: $i] : product(b,multiply(a,A),multiply(multiply(b,a),A))
<=> ! [A: $i] : product(b,multiply(a,A),multiply(multiply(b,a),A)) ),
inference(quant_intro,[status(thm)],[231]) ).
tff(233,plain,
^ [A: $i] :
rewrite(
( product(b,multiply(a,A),multiply(d,A))
<=> product(b,multiply(a,A),multiply(multiply(b,a),A)) )),
inference(bind,[status(th)],]) ).
tff(234,plain,
( ! [A: $i] : product(b,multiply(a,A),multiply(d,A))
<=> ! [A: $i] : product(b,multiply(a,A),multiply(multiply(b,a),A)) ),
inference(quant_intro,[status(thm)],[233]) ).
tff(235,plain,
( ! [A: $i] : product(b,multiply(a,A),multiply(d,A))
<=> ! [A: $i] : product(b,multiply(a,A),multiply(d,A)) ),
inference(rewrite,[status(thm)],]) ).
tff(236,axiom,
! [A: $i] : product(b,multiply(a,A),multiply(d,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause47) ).
tff(237,plain,
! [A: $i] : product(b,multiply(a,A),multiply(d,A)),
inference(modus_ponens,[status(thm)],[236,235]) ).
tff(238,plain,
! [A: $i] : product(b,multiply(a,A),multiply(multiply(b,a),A)),
inference(modus_ponens,[status(thm)],[237,234]) ).
tff(239,plain,
! [A: $i] : product(b,multiply(a,A),multiply(multiply(b,a),A)),
inference(skolemize,[status(sab)],[238]) ).
tff(240,plain,
! [A: $i] : product(b,multiply(a,A),multiply(multiply(b,a),A)),
inference(modus_ponens,[status(thm)],[239,232]) ).
tff(241,plain,
( ~ ! [A: $i] : product(b,multiply(a,A),multiply(multiply(b,a),A))
| product(b,multiply(a,multiply(a,b)),multiply(multiply(b,a),multiply(a,b))) ),
inference(quant_inst,[status(thm)],]) ).
tff(242,plain,
product(b,multiply(a,multiply(a,b)),multiply(multiply(b,a),multiply(a,b))),
inference(unit_resolution,[status(thm)],[241,240]) ).
tff(243,plain,
product(b,multiply(multiply(a,b),b),multiply(multiply(b,a),multiply(a,b))),
inference(modus_ponens,[status(thm)],[242,230]) ).
tff(244,plain,
( product(b,multiply(multiply(a,b),b),multiply(b,multiply(a,b)))
<=> product(b,multiply(a,b),multiply(b,multiply(a,b))) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(245,plain,
( product(b,multiply(a,b),multiply(b,multiply(a,b)))
<=> product(b,multiply(multiply(a,b),b),multiply(b,multiply(a,b))) ),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
( ~ ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
| product(b,multiply(a,b),multiply(b,multiply(a,b))) ),
inference(quant_inst,[status(thm)],]) ).
tff(247,plain,
product(b,multiply(a,b),multiply(b,multiply(a,b))),
inference(unit_resolution,[status(thm)],[246,54]) ).
tff(248,plain,
product(b,multiply(multiply(a,b),b),multiply(b,multiply(a,b))),
inference(modus_ponens,[status(thm)],[247,245]) ).
tff(249,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(b,multiply(multiply(a,b),b),multiply(multiply(b,a),multiply(a,b)))
| ~ product(b,multiply(multiply(a,b),b),multiply(b,multiply(a,b)))
| ( multiply(b,multiply(a,b)) = multiply(multiply(b,a),multiply(a,b)) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(b,multiply(multiply(a,b),b),multiply(multiply(b,a),multiply(a,b)))
| ~ product(b,multiply(multiply(a,b),b),multiply(b,multiply(a,b)))
| ( multiply(b,multiply(a,b)) = multiply(multiply(b,a),multiply(a,b)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(250,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(b,multiply(multiply(a,b),b),multiply(multiply(b,a),multiply(a,b)))
| ~ product(b,multiply(multiply(a,b),b),multiply(b,multiply(a,b)))
| ( multiply(b,multiply(a,b)) = multiply(multiply(b,a),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(251,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(b,multiply(multiply(a,b),b),multiply(multiply(b,a),multiply(a,b)))
| ~ product(b,multiply(multiply(a,b),b),multiply(b,multiply(a,b)))
| ( multiply(b,multiply(a,b)) = multiply(multiply(b,a),multiply(a,b)) ) ),
inference(modus_ponens,[status(thm)],[250,249]) ).
tff(252,plain,
( ~ product(b,multiply(multiply(a,b),b),multiply(multiply(b,a),multiply(a,b)))
| ~ product(b,multiply(multiply(a,b),b),multiply(b,multiply(a,b)))
| ( multiply(b,multiply(a,b)) = multiply(multiply(b,a),multiply(a,b)) ) ),
inference(unit_resolution,[status(thm)],[251,37]) ).
tff(253,plain,
multiply(b,multiply(a,b)) = multiply(multiply(b,a),multiply(a,b)),
inference(unit_resolution,[status(thm)],[252,248,243]) ).
tff(254,plain,
( product(a,multiply(b,multiply(a,b)),multiply(multiply(a,b),b))
<=> product(a,multiply(b,multiply(a,b)),multiply(a,multiply(a,b))) ),
inference(monotonicity,[status(thm)],[228]) ).
tff(255,plain,
( product(a,multiply(b,multiply(a,b)),multiply(a,multiply(a,b)))
<=> product(a,multiply(b,multiply(a,b)),multiply(multiply(a,b),b)) ),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
( ~ ! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A))
| product(a,multiply(b,multiply(a,b)),multiply(a,multiply(a,b))) ),
inference(quant_inst,[status(thm)],]) ).
tff(257,plain,
product(a,multiply(b,multiply(a,b)),multiply(a,multiply(a,b))),
inference(unit_resolution,[status(thm)],[256,19]) ).
tff(258,plain,
product(a,multiply(b,multiply(a,b)),multiply(multiply(a,b),b)),
inference(modus_ponens,[status(thm)],[257,255]) ).
tff(259,plain,
( ~ ! [B: $i,A: $i] : product(a,multiply(b,A),multiply(B,A))
| product(a,multiply(b,multiply(a,b)),multiply(b,multiply(a,b))) ),
inference(quant_inst,[status(thm)],]) ).
tff(260,plain,
product(a,multiply(b,multiply(a,b)),multiply(b,multiply(a,b))),
inference(unit_resolution,[status(thm)],[259,19]) ).
tff(261,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,multiply(b,multiply(a,b)),multiply(multiply(a,b),b))
| ~ product(a,multiply(b,multiply(a,b)),multiply(b,multiply(a,b)))
| ( multiply(b,multiply(a,b)) = multiply(multiply(a,b),b) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,multiply(b,multiply(a,b)),multiply(multiply(a,b),b))
| ~ product(a,multiply(b,multiply(a,b)),multiply(b,multiply(a,b)))
| ( multiply(b,multiply(a,b)) = multiply(multiply(a,b),b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(262,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,multiply(b,multiply(a,b)),multiply(multiply(a,b),b))
| ~ product(a,multiply(b,multiply(a,b)),multiply(b,multiply(a,b)))
| ( multiply(b,multiply(a,b)) = multiply(multiply(a,b),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(263,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(a,multiply(b,multiply(a,b)),multiply(multiply(a,b),b))
| ~ product(a,multiply(b,multiply(a,b)),multiply(b,multiply(a,b)))
| ( multiply(b,multiply(a,b)) = multiply(multiply(a,b),b) ) ),
inference(modus_ponens,[status(thm)],[262,261]) ).
tff(264,plain,
( ~ product(a,multiply(b,multiply(a,b)),multiply(multiply(a,b),b))
| ( multiply(b,multiply(a,b)) = multiply(multiply(a,b),b) ) ),
inference(unit_resolution,[status(thm)],[263,37,260]) ).
tff(265,plain,
multiply(b,multiply(a,b)) = multiply(multiply(a,b),b),
inference(unit_resolution,[status(thm)],[264,258]) ).
tff(266,plain,
multiply(multiply(a,b),b) = multiply(b,multiply(a,b)),
inference(symmetry,[status(thm)],[265]) ).
tff(267,plain,
multiply(a,b) = multiply(additive_identity,b),
inference(transitivity,[status(thm)],[98,266,253,218]) ).
tff(268,plain,
( ( multiply(a,b) = multiply(b,a) )
<=> ( multiply(additive_identity,b) = additive_identity ) ),
inference(monotonicity,[status(thm)],[267,214]) ).
tff(269,plain,
( ( multiply(a,b) != multiply(b,a) )
<=> ( multiply(additive_identity,b) != additive_identity ) ),
inference(monotonicity,[status(thm)],[268]) ).
tff(270,plain,
( ( c != d )
<=> ( multiply(a,b) != multiply(b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(271,plain,
( ( c != d )
<=> ( c != d ) ),
inference(rewrite,[status(thm)],]) ).
tff(272,axiom,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
tff(273,plain,
c != d,
inference(modus_ponens,[status(thm)],[272,271]) ).
tff(274,plain,
multiply(a,b) != multiply(b,a),
inference(modus_ponens,[status(thm)],[273,270]) ).
tff(275,plain,
multiply(additive_identity,b) != additive_identity,
inference(modus_ponens,[status(thm)],[274,269]) ).
tff(276,plain,
add(multiply(a,b),b) = add(multiply(multiply(a,b),b),multiply(multiply(a,b),b)),
inference(monotonicity,[status(thm)],[98,42]) ).
tff(277,plain,
add(multiply(multiply(a,b),b),multiply(multiply(a,b),b)) = add(multiply(a,b),b),
inference(symmetry,[status(thm)],[276]) ).
tff(278,plain,
( ~ ! [A: $i] : ( add(A,A) = additive_identity )
| ( add(multiply(multiply(a,b),b),multiply(multiply(a,b),b)) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(279,plain,
add(multiply(multiply(a,b),b),multiply(multiply(a,b),b)) = additive_identity,
inference(unit_resolution,[status(thm)],[278,168]) ).
tff(280,plain,
additive_identity = add(multiply(multiply(a,b),b),multiply(multiply(a,b),b)),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
additive_identity = add(multiply(a,b),b),
inference(transitivity,[status(thm)],[280,277]) ).
tff(282,plain,
( sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
<=> sum(b,multiply(a,b),add(multiply(a,b),b)) ),
inference(monotonicity,[status(thm)],[43,99,281]) ).
tff(283,plain,
( sum(b,multiply(a,b),add(multiply(a,b),b))
<=> sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity) ),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
^ [B: $i,A: $i] :
refl(
( sum(A,B,add(B,A))
<=> sum(A,B,add(B,A)) )),
inference(bind,[status(th)],]) ).
tff(285,plain,
( ! [B: $i,A: $i] : sum(A,B,add(B,A))
<=> ! [B: $i,A: $i] : sum(A,B,add(B,A)) ),
inference(quant_intro,[status(thm)],[284]) ).
tff(286,plain,
( ! [B: $i,A: $i] : sum(A,B,add(B,A))
<=> ! [B: $i,A: $i] : sum(A,B,add(B,A)) ),
inference(rewrite,[status(thm)],]) ).
tff(287,axiom,
! [B: $i,A: $i] : sum(A,B,add(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause38) ).
tff(288,plain,
! [B: $i,A: $i] : sum(A,B,add(B,A)),
inference(modus_ponens,[status(thm)],[287,286]) ).
tff(289,plain,
! [B: $i,A: $i] : sum(A,B,add(B,A)),
inference(skolemize,[status(sab)],[288]) ).
tff(290,plain,
! [B: $i,A: $i] : sum(A,B,add(B,A)),
inference(modus_ponens,[status(thm)],[289,285]) ).
tff(291,plain,
( ~ ! [B: $i,A: $i] : sum(A,B,add(B,A))
| sum(b,multiply(a,b),add(multiply(a,b),b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(292,plain,
sum(b,multiply(a,b),add(multiply(a,b),b)),
inference(unit_resolution,[status(thm)],[291,290]) ).
tff(293,plain,
sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity),
inference(modus_ponens,[status(thm)],[292,283]) ).
tff(294,plain,
( product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b))
<=> product(multiply(a,b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(295,plain,
( product(multiply(a,b),multiply(multiply(a,b),b),multiply(multiply(a,b),b))
<=> product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)) ),
inference(symmetry,[status(thm)],[294]) ).
tff(296,plain,
( ~ ! [B: $i,A: $i] : product(A,multiply(A,B),multiply(A,B))
| product(multiply(a,b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(297,plain,
product(multiply(a,b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)),
inference(unit_resolution,[status(thm)],[296,204]) ).
tff(298,plain,
product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)),
inference(modus_ponens,[status(thm)],[297,295]) ).
tff(299,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
refl(
( ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
<=> ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
inference(bind,[status(th)],]) ).
tff(300,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ),
inference(quant_intro,[status(thm)],[299]) ).
tff(301,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(302,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
( ( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1)
| ~ sum(V1,V2,V4) ) )),
rewrite(
( ( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1)
| ~ sum(V1,V2,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
( ( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
( ( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1)
| product(V3,X,V4) ) )),
rewrite(
( ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1)
| product(V3,X,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
( ( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
inference(bind,[status(th)],]) ).
tff(303,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ),
inference(quant_intro,[status(thm)],[302]) ).
tff(304,axiom,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity4) ).
tff(305,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(modus_ponens,[status(thm)],[304,303]) ).
tff(306,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(modus_ponens,[status(thm)],[305,301]) ).
tff(307,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(skolemize,[status(sab)],[306]) ).
tff(308,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(modus_ponens,[status(thm)],[307,300]) ).
tff(309,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
| product(additive_identity,multiply(multiply(a,b),b),additive_identity)
| ~ product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
| product(additive_identity,multiply(multiply(a,b),b),additive_identity)
| ~ product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(310,plain,
( ( ~ sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
| ~ sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
| product(additive_identity,multiply(multiply(a,b),b),additive_identity)
| ~ product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b))
| ~ product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)) )
<=> ( ~ sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
| product(additive_identity,multiply(multiply(a,b),b),additive_identity)
| ~ product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(311,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
| ~ sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
| product(additive_identity,multiply(multiply(a,b),b),additive_identity)
| ~ product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b))
| ~ product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
| product(additive_identity,multiply(multiply(a,b),b),additive_identity)
| ~ product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)) ) ),
inference(monotonicity,[status(thm)],[310]) ).
tff(312,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
| ~ sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
| product(additive_identity,multiply(multiply(a,b),b),additive_identity)
| ~ product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b))
| ~ product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
| product(additive_identity,multiply(multiply(a,b),b),additive_identity)
| ~ product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)) ) ),
inference(transitivity,[status(thm)],[311,309]) ).
tff(313,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
| ~ sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
| product(additive_identity,multiply(multiply(a,b),b),additive_identity)
| ~ product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b))
| ~ product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(314,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
| product(additive_identity,multiply(multiply(a,b),b),additive_identity)
| ~ product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)) ),
inference(modus_ponens,[status(thm)],[313,312]) ).
tff(315,plain,
( ~ sum(multiply(multiply(a,b),b),multiply(multiply(a,b),b),additive_identity)
| product(additive_identity,multiply(multiply(a,b),b),additive_identity)
| ~ product(multiply(multiply(a,b),b),multiply(multiply(a,b),b),multiply(multiply(a,b),b)) ),
inference(unit_resolution,[status(thm)],[314,308]) ).
tff(316,plain,
product(additive_identity,multiply(multiply(a,b),b),additive_identity),
inference(unit_resolution,[status(thm)],[315,298,293]) ).
tff(317,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(additive_identity,multiply(multiply(a,b),b),additive_identity)
| ~ product(additive_identity,multiply(multiply(a,b),b),multiply(additive_identity,b))
| ( multiply(additive_identity,b) = additive_identity ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(additive_identity,multiply(multiply(a,b),b),additive_identity)
| ~ product(additive_identity,multiply(multiply(a,b),b),multiply(additive_identity,b))
| ( multiply(additive_identity,b) = additive_identity ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(318,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(additive_identity,multiply(multiply(a,b),b),additive_identity)
| ~ product(additive_identity,multiply(multiply(a,b),b),multiply(additive_identity,b))
| ( multiply(additive_identity,b) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(319,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| ( U = V ) )
| ~ product(additive_identity,multiply(multiply(a,b),b),additive_identity)
| ~ product(additive_identity,multiply(multiply(a,b),b),multiply(additive_identity,b))
| ( multiply(additive_identity,b) = additive_identity ) ),
inference(modus_ponens,[status(thm)],[318,317]) ).
tff(320,plain,
( ~ product(additive_identity,multiply(multiply(a,b),b),multiply(additive_identity,b))
| ( multiply(additive_identity,b) = additive_identity ) ),
inference(unit_resolution,[status(thm)],[319,37,316]) ).
tff(321,plain,
$false,
inference(unit_resolution,[status(thm)],[320,275,57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : RNG039-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 22:04:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.52 % SZS status Unsatisfiable
% 0.18/0.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------