TSTP Solution File: RNG026-7 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG026-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 03:17:46 EDT 2022
% Result : Unsatisfiable 8.49s 5.69s
% Output : Proof 8.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 71
% Syntax : Number of formulae : 214 ( 154 unt; 9 typ; 0 def)
% Number of atoms : 276 ( 265 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 95 ( 34 ~; 30 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 285 ( 262 !; 0 ?; 285 :)
% Comments :
%------------------------------------------------------------------------------
tff(additive_identity_type,type,
additive_identity: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(d_type,type,
d: $i ).
tff(associator_type,type,
associator: ( $i * $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( add(X,additive_inverse(X)) = additive_identity )
<=> ( add(X,additive_inverse(X)) = additive_identity ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
<=> ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
<=> ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).
tff(5,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
| ( add(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
add(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = additive_identity,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(
( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
tff(14,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(multiply(associator(a,b,c),d),add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d)))) = add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
add(multiply(associator(a,b,c),d),add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d)))) = add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
<=> ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associator) ).
tff(23,plain,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
| ( associator(a,multiply(b,c),d) = add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
associator(a,multiply(b,c),d) = add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))) = associator(a,multiply(b,c),d),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,associator(b,c,d))) = add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
add(multiply(associator(a,b,c),d),add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,associator(b,c,d)))) = add(multiply(associator(a,b,c),d),add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d)))),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
<=> ( add(X,add(Y,Z)) = add(add(X,Y),Z) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(multiply(associator(a,b,c),d),add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,associator(b,c,d)))) = add(add(multiply(associator(a,b,c),d),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),multiply(a,associator(b,c,d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
add(multiply(associator(a,b,c),d),add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,associator(b,c,d)))) = add(add(multiply(associator(a,b,c),d),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),multiply(a,associator(b,c,d))),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
add(add(multiply(associator(a,b,c),d),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),multiply(a,associator(b,c,d))) = add(multiply(associator(a,b,c),d),add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,associator(b,c,d)))),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
| ( associator(b,c,d) = add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
associator(b,c,d) = add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d)))),
inference(unit_resolution,[status(thm)],[41,25]) ).
tff(43,plain,
multiply(a,associator(b,c,d)) = multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))) = multiply(a,associator(b,c,d)),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute1) ).
tff(49,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))) = add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))) = add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))) = multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))) = multiply(a,associator(b,c,d)),
inference(transitivity,[status(thm)],[54,44]) ).
tff(56,plain,
add(add(multiply(associator(a,b,c),d),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))) = add(add(multiply(associator(a,b,c),d),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),multiply(a,associator(b,c,d))),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
add(add(multiply(associator(a,b,c),d),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))) = add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)),
inference(transitivity,[status(thm)],[56,40,30,18]) ).
tff(58,plain,
add(add(add(multiply(associator(a,b,c),d),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = add(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(add(multiply(associator(a,b,c),d),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),add(add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(add(add(multiply(associator(a,b,c),d),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
add(add(multiply(associator(a,b,c),d),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),add(add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(add(add(multiply(associator(a,b,c),d),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(unit_resolution,[status(thm)],[59,37]) ).
tff(61,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute2) ).
tff(65,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d) = add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d) = add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),
inference(unit_resolution,[status(thm)],[68,67]) ).
tff(70,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
| ( associator(a,b,c) = add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
associator(a,b,c) = add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),
inference(unit_resolution,[status(thm)],[70,25]) ).
tff(72,plain,
multiply(associator(a,b,c),d) = multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
multiply(associator(a,b,c),d) = add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),
inference(transitivity,[status(thm)],[72,69]) ).
tff(74,plain,
add(multiply(associator(a,b,c),d),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))) = add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))) = add(multiply(associator(a,b,c),d),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))) = add(add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),additive_inverse(multiply(a,multiply(multiply(b,c),d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))) = add(add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),
inference(unit_resolution,[status(thm)],[76,37]) ).
tff(78,plain,
add(add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),additive_inverse(multiply(a,multiply(multiply(b,c),d)))) = add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
add(add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),additive_inverse(multiply(a,multiply(multiply(b,c),d)))) = add(multiply(associator(a,b,c),d),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),
inference(transitivity,[status(thm)],[78,75]) ).
tff(80,plain,
add(add(add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),add(add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(add(multiply(associator(a,b,c),d),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d))))),add(add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))))) = add(add(add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),add(add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
add(add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))))) = add(add(add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),add(add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))),
inference(unit_resolution,[status(thm)],[81,37]) ).
tff(83,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(unit_resolution,[status(thm)],[83,37]) ).
tff(85,plain,
add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
add(add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))))),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
multiply(a,associator(b,c,d)) = add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d))))),
inference(transitivity,[status(thm)],[43,53]) ).
tff(88,plain,
add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,associator(b,c,d))) = add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))) = add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,associator(b,c,d))),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,associator(b,c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,associator(b,c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))) = add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))) = add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),
inference(unit_resolution,[status(thm)],[92,37]) ).
tff(94,plain,
add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))) = add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
^ [X: $i] :
refl(
( ( add(additive_inverse(X),X) = additive_identity )
<=> ( add(additive_inverse(X),X) = additive_identity ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,axiom,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_additive_inverse) ).
tff(99,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,multiply(multiply(b,c),d))) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,multiply(multiply(b,c),d))) = additive_identity,
inference(unit_resolution,[status(thm)],[102,101]) ).
tff(104,plain,
additive_identity = add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,multiply(multiply(b,c),d))),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d))) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d))) = additive_identity,
inference(unit_resolution,[status(thm)],[105,101]) ).
tff(107,plain,
add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d))) = add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,multiply(multiply(b,c),d))),
inference(transitivity,[status(thm)],[106,104]) ).
tff(108,plain,
add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))) = add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,multiply(multiply(b,c),d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,multiply(multiply(b,c),d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))) = add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,multiply(multiply(b,c),d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))) = add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,multiply(multiply(b,c),d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,multiply(multiply(b,c),d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))) = add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,multiply(multiply(b,c),d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),
inference(unit_resolution,[status(thm)],[110,37]) ).
tff(112,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(X,add(Y,additive_inverse(Z))) = add(multiply(X,Y),additive_inverse(multiply(X,Z))) )
<=> ( multiply(X,add(Y,additive_inverse(Z))) = add(multiply(X,Y),additive_inverse(multiply(X,Z))) ) )),
inference(bind,[status(th)],]) ).
tff(113,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,additive_inverse(Z))) = add(multiply(X,Y),additive_inverse(multiply(X,Z))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,additive_inverse(Z))) = add(multiply(X,Y),additive_inverse(multiply(X,Z))) ) ),
inference(quant_intro,[status(thm)],[112]) ).
tff(114,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,additive_inverse(Z))) = add(multiply(X,Y),additive_inverse(multiply(X,Z))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,additive_inverse(Z))) = add(multiply(X,Y),additive_inverse(multiply(X,Z))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,additive_inverse(Z))) = add(multiply(X,Y),additive_inverse(multiply(X,Z))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_of_difference1) ).
tff(116,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,additive_inverse(Z))) = add(multiply(X,Y),additive_inverse(multiply(X,Z))) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,additive_inverse(Z))) = add(multiply(X,Y),additive_inverse(multiply(X,Z))) ),
inference(skolemize,[status(sab)],[116]) ).
tff(118,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,additive_inverse(Z))) = add(multiply(X,Y),additive_inverse(multiply(X,Z))) ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,additive_inverse(Z))) = add(multiply(X,Y),additive_inverse(multiply(X,Z))) )
| ( multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))) = add(multiply(a,multiply(multiply(b,c),d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))) = add(multiply(a,multiply(multiply(b,c),d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),
inference(unit_resolution,[status(thm)],[119,118]) ).
tff(121,plain,
add(multiply(a,multiply(multiply(b,c),d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))) = multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
add(multiply(a,multiply(multiply(b,c),d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))) = multiply(a,associator(b,c,d)),
inference(transitivity,[status(thm)],[121,44]) ).
tff(123,plain,
add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,multiply(multiply(b,c),d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))) = add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,associator(b,c,d))),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,associator(b,c,d))) = add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,multiply(multiply(b,c),d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,associator(b,c,d))) = add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),
inference(transitivity,[status(thm)],[124,111,109,94]) ).
tff(126,plain,
add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,associator(b,c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,associator(b,c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(unit_resolution,[status(thm)],[128,37]) ).
tff(130,plain,
add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(transitivity,[status(thm)],[129,127,91]) ).
tff(131,plain,
add(add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))))) = add(add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,multiply(multiply(b,c),d)),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
| ( associator(a,b,multiply(c,d)) = add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
associator(a,b,multiply(c,d)) = add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),
inference(unit_resolution,[status(thm)],[132,25]) ).
tff(134,plain,
add(associator(a,b,multiply(c,d)),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(associator(a,b,multiply(c,d)),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = add(associator(a,b,multiply(c,d)),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(symmetry,[status(thm)],[134]) ).
tff(137,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(unit_resolution,[status(thm)],[137,37]) ).
tff(139,plain,
add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(associator(a,b,multiply(c,d)),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(transitivity,[status(thm)],[138,136]) ).
tff(140,plain,
add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))))) = add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(associator(a,b,multiply(c,d)),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))))) = add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d))),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(142,plain,
add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))))) = add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d))),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))),
inference(unit_resolution,[status(thm)],[141,37]) ).
tff(143,plain,
add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d))),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
additive_identity = add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d))),
inference(symmetry,[status(thm)],[106]) ).
tff(145,plain,
add(additive_identity,add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d))),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
^ [X: $i] :
refl(
( ( add(additive_identity,X) = X )
<=> ( add(additive_identity,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(147,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,axiom,
! [X: $i] : ( add(additive_identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).
tff(150,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(skolemize,[status(sab)],[150]) ).
tff(152,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[151,147]) ).
tff(153,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
add(additive_identity,add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(unit_resolution,[status(thm)],[153,152]) ).
tff(155,plain,
add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = add(additive_identity,add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))),
inference(transitivity,[status(thm)],[155,145,143,140,135]) ).
tff(157,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(add(X,additive_inverse(Y)),Z) = add(multiply(X,Z),additive_inverse(multiply(Y,Z))) )
<=> ( multiply(add(X,additive_inverse(Y)),Z) = add(multiply(X,Z),additive_inverse(multiply(Y,Z))) ) )),
inference(bind,[status(th)],]) ).
tff(158,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,additive_inverse(Y)),Z) = add(multiply(X,Z),additive_inverse(multiply(Y,Z))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,additive_inverse(Y)),Z) = add(multiply(X,Z),additive_inverse(multiply(Y,Z))) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,additive_inverse(Y)),Z) = add(multiply(X,Z),additive_inverse(multiply(Y,Z))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,additive_inverse(Y)),Z) = add(multiply(X,Z),additive_inverse(multiply(Y,Z))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(160,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,additive_inverse(Y)),Z) = add(multiply(X,Z),additive_inverse(multiply(Y,Z))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_of_difference2) ).
tff(161,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,additive_inverse(Y)),Z) = add(multiply(X,Z),additive_inverse(multiply(Y,Z))) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,additive_inverse(Y)),Z) = add(multiply(X,Z),additive_inverse(multiply(Y,Z))) ),
inference(skolemize,[status(sab)],[161]) ).
tff(163,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,additive_inverse(Y)),Z) = add(multiply(X,Z),additive_inverse(multiply(Y,Z))) ),
inference(modus_ponens,[status(thm)],[162,158]) ).
tff(164,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,additive_inverse(Y)),Z) = add(multiply(X,Z),additive_inverse(multiply(Y,Z))) )
| ( multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d) = add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,multiply(b,c)),d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(165,plain,
multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d) = add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,multiply(b,c)),d))),
inference(unit_resolution,[status(thm)],[164,163]) ).
tff(166,plain,
add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)) = multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d),
inference(symmetry,[status(thm)],[69]) ).
tff(167,plain,
add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)) = add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,multiply(b,c)),d))),
inference(transitivity,[status(thm)],[166,165]) ).
tff(168,plain,
add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)) = add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,multiply(b,c)),d))),multiply(multiply(a,multiply(b,c)),d)),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,plain,
add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,multiply(b,c)),d))),multiply(multiply(a,multiply(b,c)),d)) = add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,multiply(b,c)),d)),multiply(multiply(a,multiply(b,c)),d))) = add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,multiply(b,c)),d))),multiply(multiply(a,multiply(b,c)),d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,multiply(b,c)),d)),multiply(multiply(a,multiply(b,c)),d))) = add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,multiply(b,c)),d))),multiply(multiply(a,multiply(b,c)),d)),
inference(unit_resolution,[status(thm)],[170,37]) ).
tff(172,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(multiply(multiply(a,multiply(b,c)),d)),multiply(multiply(a,multiply(b,c)),d)) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(173,plain,
add(additive_inverse(multiply(multiply(a,multiply(b,c)),d)),multiply(multiply(a,multiply(b,c)),d)) = additive_identity,
inference(unit_resolution,[status(thm)],[172,101]) ).
tff(174,plain,
add(additive_inverse(multiply(multiply(a,multiply(b,c)),d)),multiply(multiply(a,multiply(b,c)),d)) = add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d))),
inference(transitivity,[status(thm)],[173,144]) ).
tff(175,plain,
add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,multiply(b,c)),d)),multiply(multiply(a,multiply(b,c)),d))) = add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d)))),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d)))) = add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,multiply(b,c)),d)),multiply(multiply(a,multiply(b,c)),d))),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d)))) = add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(178,plain,
add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d)))) = add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))),
inference(unit_resolution,[status(thm)],[177,37]) ).
tff(179,plain,
add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))) = add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(a,b),multiply(c,d)))),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))) = add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),
inference(transitivity,[status(thm)],[179,176,171,169]) ).
tff(181,plain,
add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(add(add(multiply(multiply(multiply(a,b),c),d),multiply(additive_inverse(multiply(a,multiply(b,c))),d)),multiply(multiply(a,multiply(b,c)),d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))))),
inference(monotonicity,[status(thm)],[180,156]) ).
tff(182,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,plain,
add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))) = add(add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(unit_resolution,[status(thm)],[182,37]) ).
tff(184,plain,
add(add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d))))),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))) = add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(186,plain,
add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))) = add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),
inference(unit_resolution,[status(thm)],[185,37]) ).
tff(187,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
| ( associator(multiply(a,b),c,d) = add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
associator(multiply(a,b),c,d) = add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),
inference(unit_resolution,[status(thm)],[187,25]) ).
tff(189,plain,
add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))) = add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),
inference(monotonicity,[status(thm)],[188,133]) ).
tff(190,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(associator(a,b,multiply(c,d)),associator(multiply(a,b),c,d)) = add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(191,plain,
add(associator(a,b,multiply(c,d)),associator(multiply(a,b),c,d)) = add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),
inference(unit_resolution,[status(thm)],[190,16]) ).
tff(192,plain,
add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))) = associator(multiply(a,b),c,d),
inference(symmetry,[status(thm)],[188]) ).
tff(193,plain,
add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))) = associator(a,b,multiply(c,d)),
inference(symmetry,[status(thm)],[133]) ).
tff(194,plain,
add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d))))) = add(associator(a,b,multiply(c,d)),associator(multiply(a,b),c,d)),
inference(monotonicity,[status(thm)],[193,192]) ).
tff(195,plain,
add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d))))) = add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),
inference(transitivity,[status(thm)],[194,191,189,186]) ).
tff(196,plain,
add(add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = add(add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(monotonicity,[status(thm)],[195]) ).
tff(197,plain,
add(associator(a,b,multiply(c,d)),associator(multiply(a,b),c,d)) = add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d))))),
inference(symmetry,[status(thm)],[194]) ).
tff(198,plain,
add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))) = add(associator(a,b,multiply(c,d)),associator(multiply(a,b),c,d)),
inference(symmetry,[status(thm)],[191]) ).
tff(199,plain,
add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))) = add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d))))),
inference(transitivity,[status(thm)],[198,197]) ).
tff(200,plain,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = add(add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d))))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(monotonicity,[status(thm)],[199]) ).
tff(201,plain,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) = additive_identity,
inference(transitivity,[status(thm)],[200,196,184,181,131,86,82,80,60,58,9]) ).
tff(202,plain,
( ( add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity )
<=> ( add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(203,axiom,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_teichmuller_identity) ).
tff(204,plain,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
$false,
inference(unit_resolution,[status(thm)],[204,201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG026-7 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n006.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 21:31:09 EDT 2022
% 0.12/0.34 % 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.
% 8.49/5.69 % SZS status Unsatisfiable
% 8.49/5.69 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------