TSTP Solution File: GRP001-4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP001-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 : Fri Sep 16 22:25:19 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 48
% Syntax : Number of formulae : 204 ( 160 unt; 5 typ; 0 def)
% Number of atoms : 244 ( 240 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 80 ( 38 ~; 31 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 126 ( 121 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(identity_type,type,
identity: $i ).
tff(c_type,type,
c: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
tff(5,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
multiply(identity,a) = a,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
a = multiply(identity,a),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
multiply(a,b) = multiply(multiply(identity,a),b),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
multiply(multiply(identity,a),b) = multiply(a,b),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
tff(17,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(identity,a),b) = multiply(identity,multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
multiply(multiply(identity,a),b) = multiply(identity,multiply(a,b)),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
multiply(identity,multiply(a,b)) = multiply(multiply(identity,a),b),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
multiply(a,b) = multiply(identity,multiply(a,b)),
inference(transitivity,[status(thm)],[11,21]) ).
tff(24,plain,
^ [X: $i] :
refl(
( ( multiply(X,X) = identity )
<=> ( multiply(X,X) = identity ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [X: $i] : ( multiply(X,X) = identity )
<=> ! [X: $i] : ( multiply(X,X) = identity ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X: $i] : ( multiply(X,X) = identity )
<=> ! [X: $i] : ( multiply(X,X) = identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
! [X: $i] : ( multiply(X,X) = identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',squareness) ).
tff(28,plain,
! [X: $i] : ( multiply(X,X) = identity ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [X: $i] : ( multiply(X,X) = identity ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [X: $i] : ( multiply(X,X) = identity ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [X: $i] : ( multiply(X,X) = identity )
| ( multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),identity))) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),identity))) = identity,
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
identity = multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),identity))),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
multiply(identity,multiply(a,b)) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),identity))),multiply(identity,multiply(a,b))),
inference(monotonicity,[status(thm)],[33,23]) ).
tff(35,plain,
multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),identity))),multiply(identity,multiply(a,b))) = multiply(identity,multiply(a,b)),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),identity))),multiply(identity,multiply(a,b))) = multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),identity))),multiply(identity,multiply(a,b))) = multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(a,b)))),
inference(unit_resolution,[status(thm)],[36,19]) ).
tff(38,plain,
multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(a,b)))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),identity))),multiply(identity,multiply(a,b))),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
multiply(b,a) = multiply(b,multiply(identity,a)),
inference(monotonicity,[status(thm)],[10]) ).
tff(40,plain,
( ~ ! [X: $i] : ( multiply(X,X) = identity )
| ( multiply(a,a) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
multiply(a,a) = identity,
inference(unit_resolution,[status(thm)],[40,30]) ).
tff(42,plain,
identity = multiply(a,a),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
multiply(identity,a) = multiply(multiply(a,a),a),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
multiply(multiply(a,a),a) = multiply(identity,a),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),a) = multiply(a,multiply(a,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
multiply(multiply(a,a),a) = multiply(a,multiply(a,a)),
inference(unit_resolution,[status(thm)],[45,19]) ).
tff(47,plain,
multiply(a,multiply(a,a)) = multiply(multiply(a,a),a),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
multiply(a,multiply(a,a)) = multiply(a,identity),
inference(monotonicity,[status(thm)],[41]) ).
tff(49,plain,
multiply(a,identity) = multiply(a,multiply(a,a)),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
multiply(a,identity) = a,
inference(transitivity,[status(thm)],[49,47,44,9]) ).
tff(51,plain,
multiply(b,multiply(a,identity)) = multiply(b,a),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
multiply(a,identity) = multiply(multiply(identity,a),identity),
inference(monotonicity,[status(thm)],[10]) ).
tff(53,plain,
multiply(multiply(identity,a),identity) = multiply(a,identity),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(identity,a),identity) = multiply(identity,multiply(a,identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
multiply(multiply(identity,a),identity) = multiply(identity,multiply(a,identity)),
inference(unit_resolution,[status(thm)],[54,19]) ).
tff(56,plain,
multiply(identity,multiply(a,identity)) = multiply(multiply(identity,a),identity),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
multiply(identity,multiply(a,identity)) = multiply(a,identity),
inference(transitivity,[status(thm)],[56,53]) ).
tff(58,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
multiply(identity,b) = b,
inference(unit_resolution,[status(thm)],[58,7]) ).
tff(60,plain,
multiply(identity,b) = multiply(multiply(a,a),b),
inference(monotonicity,[status(thm)],[42]) ).
tff(61,plain,
multiply(multiply(a,a),b) = multiply(identity,b),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),b) = multiply(a,multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
multiply(multiply(a,a),b) = multiply(a,multiply(a,b)),
inference(unit_resolution,[status(thm)],[62,19]) ).
tff(64,plain,
multiply(a,multiply(a,b)) = multiply(multiply(a,a),b),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
multiply(multiply(identity,a),multiply(a,b)) = multiply(a,multiply(a,b)),
inference(monotonicity,[status(thm)],[9]) ).
tff(66,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(identity,a),multiply(a,b)) = multiply(identity,multiply(a,multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
multiply(multiply(identity,a),multiply(a,b)) = multiply(identity,multiply(a,multiply(a,b))),
inference(unit_resolution,[status(thm)],[66,19]) ).
tff(68,plain,
multiply(identity,multiply(a,multiply(a,b))) = multiply(multiply(identity,a),multiply(a,b)),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
multiply(identity,multiply(a,multiply(a,b))) = b,
inference(transitivity,[status(thm)],[68,65,64,61,59]) ).
tff(70,plain,
multiply(multiply(identity,multiply(a,multiply(a,b))),multiply(identity,multiply(a,identity))) = multiply(b,multiply(a,identity)),
inference(monotonicity,[status(thm)],[69,57]) ).
tff(71,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(identity,multiply(a,multiply(a,b))),multiply(identity,multiply(a,identity))) = multiply(identity,multiply(multiply(a,multiply(a,b)),multiply(identity,multiply(a,identity)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
multiply(multiply(identity,multiply(a,multiply(a,b))),multiply(identity,multiply(a,identity))) = multiply(identity,multiply(multiply(a,multiply(a,b)),multiply(identity,multiply(a,identity)))),
inference(unit_resolution,[status(thm)],[71,19]) ).
tff(73,plain,
multiply(identity,multiply(multiply(a,multiply(a,b)),multiply(identity,multiply(a,identity)))) = multiply(multiply(identity,multiply(a,multiply(a,b))),multiply(identity,multiply(a,identity))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
multiply(a,multiply(a,b)) = b,
inference(transitivity,[status(thm)],[64,61,59]) ).
tff(75,plain,
multiply(multiply(a,multiply(a,b)),multiply(identity,multiply(a,identity))) = multiply(b,multiply(a,identity)),
inference(monotonicity,[status(thm)],[74,57]) ).
tff(76,plain,
multiply(b,multiply(a,identity)) = multiply(multiply(a,multiply(a,b)),multiply(identity,multiply(a,identity))),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
multiply(b,a) = multiply(b,multiply(a,identity)),
inference(symmetry,[status(thm)],[51]) ).
tff(78,plain,
multiply(b,multiply(identity,a)) = multiply(b,a),
inference(symmetry,[status(thm)],[39]) ).
tff(79,plain,
multiply(b,multiply(identity,a)) = multiply(multiply(a,multiply(a,b)),multiply(identity,multiply(a,identity))),
inference(transitivity,[status(thm)],[78,77,76]) ).
tff(80,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(identity,multiply(identity,multiply(a,b))),identity) = multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
multiply(multiply(identity,multiply(identity,multiply(a,b))),identity) = multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),
inference(unit_resolution,[status(thm)],[80,19]) ).
tff(82,plain,
multiply(identity,multiply(a,b)) = multiply(a,b),
inference(transitivity,[status(thm)],[22,12]) ).
tff(83,plain,
multiply(identity,multiply(identity,multiply(a,b))) = multiply(identity,multiply(a,b)),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
multiply(multiply(identity,multiply(identity,multiply(a,b))),identity) = multiply(multiply(identity,multiply(a,b)),identity),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
multiply(multiply(identity,multiply(a,b)),identity) = multiply(multiply(identity,multiply(identity,multiply(a,b))),identity),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
multiply(multiply(identity,a),a) = multiply(a,a),
inference(monotonicity,[status(thm)],[9]) ).
tff(87,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(identity,a),a) = multiply(identity,multiply(a,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
multiply(multiply(identity,a),a) = multiply(identity,multiply(a,a)),
inference(unit_resolution,[status(thm)],[87,19]) ).
tff(89,plain,
multiply(identity,multiply(a,a)) = multiply(multiply(identity,a),a),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
multiply(identity,identity) = multiply(identity,multiply(a,a)),
inference(monotonicity,[status(thm)],[42]) ).
tff(91,plain,
multiply(a,multiply(identity,a)) = multiply(a,a),
inference(monotonicity,[status(thm)],[9]) ).
tff(92,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,identity),a) = multiply(a,multiply(identity,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
multiply(multiply(a,identity),a) = multiply(a,multiply(identity,a)),
inference(unit_resolution,[status(thm)],[92,19]) ).
tff(94,plain,
multiply(multiply(a,identity),a) = identity,
inference(transitivity,[status(thm)],[93,91,41]) ).
tff(95,plain,
multiply(multiply(multiply(a,identity),a),identity) = multiply(identity,identity),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,identity),a),identity) = multiply(multiply(a,identity),multiply(a,identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
multiply(multiply(multiply(a,identity),a),identity) = multiply(multiply(a,identity),multiply(a,identity)),
inference(unit_resolution,[status(thm)],[96,19]) ).
tff(98,plain,
multiply(multiply(a,identity),multiply(a,identity)) = multiply(multiply(multiply(a,identity),a),identity),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
multiply(multiply(identity,multiply(a,identity)),multiply(identity,multiply(a,identity))) = multiply(multiply(a,identity),multiply(a,identity)),
inference(monotonicity,[status(thm)],[57,57]) ).
tff(100,plain,
multiply(multiply(identity,multiply(a,identity)),multiply(identity,multiply(a,identity))) = identity,
inference(transitivity,[status(thm)],[99,98,95,90,89,86,41]) ).
tff(101,plain,
multiply(multiply(identity,multiply(a,b)),multiply(multiply(identity,multiply(a,identity)),multiply(identity,multiply(a,identity)))) = multiply(multiply(identity,multiply(a,b)),identity),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))),multiply(identity,multiply(a,identity))) = multiply(multiply(identity,multiply(a,b)),multiply(multiply(identity,multiply(a,identity)),multiply(identity,multiply(a,identity)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
multiply(multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))),multiply(identity,multiply(a,identity))) = multiply(multiply(identity,multiply(a,b)),multiply(multiply(identity,multiply(a,identity)),multiply(identity,multiply(a,identity)))),
inference(unit_resolution,[status(thm)],[102,19]) ).
tff(104,plain,
multiply(multiply(identity,multiply(identity,multiply(a,b))),multiply(identity,multiply(a,identity))) = multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))),
inference(monotonicity,[status(thm)],[83]) ).
tff(105,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(identity,multiply(identity,multiply(a,b))),multiply(identity,multiply(a,identity))) = multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
multiply(multiply(identity,multiply(identity,multiply(a,b))),multiply(identity,multiply(a,identity))) = multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))),
inference(unit_resolution,[status(thm)],[105,19]) ).
tff(107,plain,
multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))) = multiply(multiply(identity,multiply(identity,multiply(a,b))),multiply(identity,multiply(a,identity))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))) = multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))),
inference(transitivity,[status(thm)],[107,104]) ).
tff(109,plain,
multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))),multiply(identity,multiply(a,identity))) = multiply(multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))),multiply(identity,multiply(a,identity))),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))),multiply(identity,multiply(a,identity))) = multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),
inference(transitivity,[status(thm)],[109,103,101,85,81]) ).
tff(111,plain,
multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))),multiply(identity,multiply(a,identity)))) = multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),identity))),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),multiply(identity,multiply(a,identity))) = multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))),multiply(identity,multiply(a,identity)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),multiply(identity,multiply(a,identity))) = multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))),multiply(identity,multiply(a,identity)))),
inference(unit_resolution,[status(thm)],[112,19]) ).
tff(114,plain,
multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),multiply(identity,multiply(a,identity))) = identity,
inference(transitivity,[status(thm)],[113,111,32]) ).
tff(115,plain,
multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),multiply(identity,multiply(a,identity))),multiply(b,multiply(identity,a))) = multiply(identity,multiply(multiply(a,multiply(a,b)),multiply(identity,multiply(a,identity)))),
inference(monotonicity,[status(thm)],[114,79]) ).
tff(116,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),multiply(identity,multiply(a,identity))),multiply(b,multiply(identity,a))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),multiply(multiply(identity,multiply(a,identity)),multiply(b,multiply(identity,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),multiply(identity,multiply(a,identity))),multiply(b,multiply(identity,a))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),multiply(multiply(identity,multiply(a,identity)),multiply(b,multiply(identity,a)))),
inference(unit_resolution,[status(thm)],[116,19]) ).
tff(118,plain,
multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),multiply(multiply(identity,multiply(a,identity)),multiply(b,multiply(identity,a)))) = multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),multiply(identity,multiply(a,identity))),multiply(b,multiply(identity,a))),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
multiply(multiply(identity,multiply(a,identity)),multiply(b,multiply(identity,a))) = multiply(multiply(identity,multiply(a,identity)),multiply(multiply(a,multiply(a,b)),multiply(identity,multiply(a,identity)))),
inference(monotonicity,[status(thm)],[79]) ).
tff(120,plain,
multiply(multiply(identity,multiply(a,identity)),multiply(multiply(a,multiply(a,b)),multiply(identity,multiply(a,identity)))) = multiply(multiply(identity,multiply(a,identity)),multiply(b,multiply(identity,a))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(identity,multiply(a,identity)),multiply(a,multiply(a,b))),multiply(identity,multiply(a,identity))) = multiply(multiply(identity,multiply(a,identity)),multiply(multiply(a,multiply(a,b)),multiply(identity,multiply(a,identity)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
multiply(multiply(multiply(identity,multiply(a,identity)),multiply(a,multiply(a,b))),multiply(identity,multiply(a,identity))) = multiply(multiply(identity,multiply(a,identity)),multiply(multiply(a,multiply(a,b)),multiply(identity,multiply(a,identity)))),
inference(unit_resolution,[status(thm)],[121,19]) ).
tff(123,plain,
multiply(multiply(multiply(a,identity),a),multiply(identity,multiply(a,b))) = multiply(identity,multiply(a,b)),
inference(monotonicity,[status(thm)],[94,82]) ).
tff(124,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,identity),a),multiply(identity,multiply(a,b))) = multiply(multiply(a,identity),multiply(a,multiply(identity,multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
multiply(multiply(multiply(a,identity),a),multiply(identity,multiply(a,b))) = multiply(multiply(a,identity),multiply(a,multiply(identity,multiply(a,b)))),
inference(unit_resolution,[status(thm)],[124,19]) ).
tff(126,plain,
multiply(multiply(a,identity),multiply(a,multiply(identity,multiply(a,b)))) = multiply(multiply(multiply(a,identity),a),multiply(identity,multiply(a,b))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
multiply(a,multiply(identity,multiply(a,b))) = multiply(a,multiply(a,b)),
inference(monotonicity,[status(thm)],[82]) ).
tff(128,plain,
multiply(a,multiply(a,b)) = multiply(a,multiply(identity,multiply(a,b))),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
a = multiply(a,identity),
inference(transitivity,[status(thm)],[10,43,46,48]) ).
tff(130,plain,
multiply(a,multiply(a,multiply(a,b))) = multiply(multiply(a,identity),multiply(a,multiply(identity,multiply(a,b)))),
inference(monotonicity,[status(thm)],[129,128]) ).
tff(131,plain,
multiply(identity,multiply(a,identity)) = a,
inference(transitivity,[status(thm)],[56,53,49,47,44,9]) ).
tff(132,plain,
multiply(multiply(identity,multiply(a,identity)),multiply(a,multiply(a,b))) = multiply(a,multiply(a,multiply(a,b))),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
multiply(multiply(identity,multiply(a,identity)),multiply(a,multiply(a,b))) = multiply(identity,multiply(a,b)),
inference(transitivity,[status(thm)],[132,130,126,123]) ).
tff(134,plain,
multiply(multiply(multiply(identity,multiply(a,identity)),multiply(a,multiply(a,b))),multiply(identity,multiply(a,identity))) = multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))) = multiply(multiply(multiply(identity,multiply(a,identity)),multiply(a,multiply(a,b))),multiply(identity,multiply(a,identity))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))) = multiply(multiply(identity,multiply(a,identity)),multiply(b,multiply(identity,a))),
inference(transitivity,[status(thm)],[107,104,135,122,120]) ).
tff(137,plain,
multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),multiply(multiply(identity,multiply(a,identity)),multiply(b,multiply(identity,a)))),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(139,plain,
multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))) = multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))))),
inference(unit_resolution,[status(thm)],[138,19]) ).
tff(140,plain,
multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))))) = multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
( ~ ! [X: $i] : ( multiply(X,X) = identity )
| ( multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(142,plain,
multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))) = identity,
inference(unit_resolution,[status(thm)],[141,30]) ).
tff(143,plain,
identity = multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity))))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
multiply(multiply(identity,multiply(a,b)),identity) = multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),
inference(transitivity,[status(thm)],[85,81]) ).
tff(145,plain,
multiply(multiply(multiply(identity,multiply(a,b)),identity),identity) = multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))),multiply(identity,multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,identity)))))),
inference(monotonicity,[status(thm)],[144,143]) ).
tff(146,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(identity,multiply(a,b)),identity),identity) = multiply(multiply(identity,multiply(a,b)),multiply(identity,identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(147,plain,
multiply(multiply(multiply(identity,multiply(a,b)),identity),identity) = multiply(multiply(identity,multiply(a,b)),multiply(identity,identity)),
inference(unit_resolution,[status(thm)],[146,19]) ).
tff(148,plain,
multiply(multiply(identity,multiply(a,b)),multiply(identity,identity)) = multiply(multiply(multiply(identity,multiply(a,b)),identity),identity),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
multiply(identity,multiply(a,a)) = multiply(identity,identity),
inference(symmetry,[status(thm)],[90]) ).
tff(150,plain,
multiply(a,a) = multiply(multiply(identity,a),a),
inference(symmetry,[status(thm)],[86]) ).
tff(151,plain,
identity = multiply(identity,identity),
inference(transitivity,[status(thm)],[42,150,88,149]) ).
tff(152,plain,
multiply(multiply(identity,multiply(a,b)),identity) = multiply(multiply(identity,multiply(a,b)),multiply(identity,identity)),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)) = multiply(multiply(identity,multiply(identity,multiply(a,b))),identity),
inference(symmetry,[status(thm)],[81]) ).
tff(154,plain,
multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)) = multiply(b,multiply(identity,a)),
inference(transitivity,[status(thm)],[153,84,152,148,145,140,137,118,115,73,70,51,39]) ).
tff(155,plain,
multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(a,b)))) = multiply(multiply(b,multiply(identity,a)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(a,b)))),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
multiply(multiply(b,multiply(identity,a)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(a,b)))) = multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(a,b)))),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
( ~ ! [X: $i] : ( multiply(X,X) = identity )
| ( multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,b))) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(158,plain,
multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,b))) = identity,
inference(unit_resolution,[status(thm)],[157,30]) ).
tff(159,plain,
multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(identity,multiply(a,b)))) = multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(a,b))),
inference(monotonicity,[status(thm)],[83]) ).
tff(160,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(identity,multiply(a,b)),identity),multiply(identity,multiply(a,b))) = multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(identity,multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(161,plain,
multiply(multiply(multiply(identity,multiply(a,b)),identity),multiply(identity,multiply(a,b))) = multiply(multiply(identity,multiply(a,b)),multiply(identity,multiply(identity,multiply(a,b)))),
inference(unit_resolution,[status(thm)],[160,19]) ).
tff(162,plain,
multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)) = multiply(multiply(identity,multiply(a,b)),identity),
inference(transitivity,[status(thm)],[153,84]) ).
tff(163,plain,
multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(a,b))) = multiply(multiply(multiply(identity,multiply(a,b)),identity),multiply(identity,multiply(a,b))),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(a,b))) = identity,
inference(transitivity,[status(thm)],[163,161,159,158]) ).
tff(165,plain,
multiply(multiply(b,multiply(identity,a)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(a,b)))) = multiply(multiply(b,multiply(identity,a)),identity),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
multiply(multiply(b,multiply(identity,a)),identity) = multiply(multiply(b,multiply(identity,a)),multiply(multiply(identity,multiply(multiply(identity,multiply(a,b)),identity)),multiply(identity,multiply(a,b)))),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
multiply(multiply(a,identity),multiply(a,identity)) = multiply(multiply(identity,multiply(a,identity)),multiply(identity,multiply(a,identity))),
inference(symmetry,[status(thm)],[99]) ).
tff(168,plain,
multiply(identity,identity) = multiply(multiply(multiply(a,identity),a),identity),
inference(symmetry,[status(thm)],[95]) ).
tff(169,plain,
identity = multiply(multiply(identity,multiply(a,identity)),multiply(identity,multiply(a,identity))),
inference(transitivity,[status(thm)],[42,150,88,149,168,97,167]) ).
tff(170,plain,
multiply(multiply(b,multiply(identity,a)),identity) = multiply(multiply(b,multiply(identity,a)),multiply(multiply(identity,multiply(a,identity)),multiply(identity,multiply(a,identity)))),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
multiply(multiply(b,multiply(identity,a)),multiply(multiply(identity,multiply(a,identity)),multiply(identity,multiply(a,identity)))) = multiply(multiply(b,multiply(identity,a)),identity),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(identity,a)),multiply(identity,multiply(a,identity))),multiply(identity,multiply(a,identity))) = multiply(multiply(b,multiply(identity,a)),multiply(multiply(identity,multiply(a,identity)),multiply(identity,multiply(a,identity)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(173,plain,
multiply(multiply(multiply(b,multiply(identity,a)),multiply(identity,multiply(a,identity))),multiply(identity,multiply(a,identity))) = multiply(multiply(b,multiply(identity,a)),multiply(multiply(identity,multiply(a,identity)),multiply(identity,multiply(a,identity)))),
inference(unit_resolution,[status(thm)],[172,19]) ).
tff(174,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,identity),identity) = multiply(b,multiply(identity,identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(175,plain,
multiply(multiply(b,identity),identity) = multiply(b,multiply(identity,identity)),
inference(unit_resolution,[status(thm)],[174,19]) ).
tff(176,plain,
multiply(b,multiply(identity,identity)) = multiply(multiply(b,identity),identity),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
multiply(b,identity) = multiply(b,multiply(identity,identity)),
inference(monotonicity,[status(thm)],[151]) ).
tff(178,plain,
multiply(b,multiply(a,a)) = multiply(b,identity),
inference(monotonicity,[status(thm)],[41]) ).
tff(179,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,a),a) = multiply(b,multiply(a,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(180,plain,
multiply(multiply(b,a),a) = multiply(b,multiply(a,a)),
inference(unit_resolution,[status(thm)],[179,19]) ).
tff(181,plain,
multiply(multiply(b,multiply(identity,a)),multiply(identity,multiply(a,identity))) = multiply(multiply(b,a),a),
inference(monotonicity,[status(thm)],[78,131]) ).
tff(182,plain,
multiply(multiply(b,multiply(identity,a)),multiply(identity,multiply(a,identity))) = multiply(multiply(b,identity),identity),
inference(transitivity,[status(thm)],[181,180,178,177,176]) ).
tff(183,plain,
multiply(multiply(multiply(b,multiply(identity,a)),multiply(identity,multiply(a,identity))),multiply(identity,multiply(a,identity))) = multiply(multiply(multiply(b,identity),identity),a),
inference(monotonicity,[status(thm)],[182,131]) ).
tff(184,plain,
multiply(multiply(multiply(b,identity),identity),a) = multiply(multiply(multiply(b,multiply(identity,a)),multiply(identity,multiply(a,identity))),multiply(identity,multiply(a,identity))),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,identity),identity),a) = multiply(multiply(b,identity),multiply(identity,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(186,plain,
multiply(multiply(multiply(b,identity),identity),a) = multiply(multiply(b,identity),multiply(identity,a)),
inference(unit_resolution,[status(thm)],[185,19]) ).
tff(187,plain,
multiply(multiply(b,identity),multiply(identity,a)) = multiply(multiply(multiply(b,identity),identity),a),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
multiply(multiply(b,identity),multiply(identity,a)) = multiply(multiply(b,identity),a),
inference(monotonicity,[status(thm)],[9]) ).
tff(189,plain,
multiply(multiply(b,identity),a) = multiply(multiply(b,identity),multiply(identity,a)),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,identity),a) = multiply(b,multiply(identity,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(191,plain,
multiply(multiply(b,identity),a) = multiply(b,multiply(identity,a)),
inference(unit_resolution,[status(thm)],[190,19]) ).
tff(192,plain,
multiply(b,multiply(identity,a)) = multiply(multiply(b,identity),a),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
multiply(b,a) = multiply(a,b),
inference(transitivity,[status(thm)],[39,192,189,187,184,173,171,166,156,38,35,22,12]) ).
tff(194,plain,
( ( multiply(b,a) != c )
<=> ( multiply(b,a) != multiply(a,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(195,plain,
( ( multiply(b,a) != c )
<=> ( multiply(b,a) != c ) ),
inference(rewrite,[status(thm)],]) ).
tff(196,axiom,
multiply(b,a) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
tff(197,plain,
multiply(b,a) != c,
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
multiply(b,a) != multiply(a,b),
inference(modus_ponens,[status(thm)],[197,194]) ).
tff(199,plain,
$false,
inference(unit_resolution,[status(thm)],[198,193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP001-4 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 14:03:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.35 Usage: tptp [options] [-file:]file
% 0.20/0.35 -h, -? prints this message.
% 0.20/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.35 -m, -model generate model.
% 0.20/0.35 -p, -proof generate proof.
% 0.20/0.35 -c, -core generate unsat core of named formulas.
% 0.20/0.35 -st, -statistics display statistics.
% 0.20/0.35 -t:timeout set timeout (in second).
% 0.20/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.35 -<param>:<value> configuration parameter and value.
% 0.20/0.35 -o:<output-file> file to place output in.
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------