%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP002-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:48 AM UTC 2025
% Result : Unsatisfiable 18.98s 19.21s
% Output : Proof 19.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 101
% Syntax : Number of formulae : 439 ( 350 unt; 0 typ; 0 def)
% Number of atoms : 540 ( 533 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 170 ( 75 ~; 71 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 245 ( 237 !; 0 ?; 245 :)
% Comments :
%------------------------------------------------------------------------------
tff(identity_type,type,
identity: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(b_type,type,
b: $i ).
tff(k_type,type,
k: $i ).
tff(a_type,type,
a: $i ).
tff(c_type,type,
c: $i ).
tff(h_type,type,
h: $i ).
tff(d_type,type,
d: $i ).
tff(j_type,type,
j: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( multiply(X,inverse(X)) = identity )
<=> ( multiply(X,inverse(X)) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = identity ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
tff(5,plain,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = identity )
| ( multiply(a,inverse(a)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(a,inverse(a)) = identity,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( ( multiply(X,identity) = X )
<=> ( multiply(X,identity) = X ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : ( multiply(X,identity) = X )
<=> ! [X: $i] : ( multiply(X,identity) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( multiply(X,identity) = X )
<=> ! [X: $i] : ( multiply(X,identity) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : ( multiply(X,identity) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
tff(14,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(a,identity) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
multiply(a,identity) = a,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X: $i] :
refl(( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(23,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(b),b) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
multiply(inverse(b),b) = identity,
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
multiply(a,multiply(inverse(b),b)) = multiply(a,identity),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,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(30,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)],[29]) ).
tff(31,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(32,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
tff(33,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,inverse(b)),b) = multiply(a,multiply(inverse(b),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
multiply(multiply(a,inverse(b)),b) = multiply(a,multiply(inverse(b),b)),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(42,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
multiply(identity,b) = b,
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(h),h) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
multiply(inverse(h),h) = identity,
inference(unit_resolution,[status(thm)],[47,25]) ).
tff(49,plain,
identity = multiply(inverse(h),h),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
multiply(identity,b) = multiply(multiply(inverse(h),h),b),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
multiply(multiply(inverse(h),h),b) = multiply(identity,b),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(h),h),b) = multiply(inverse(h),multiply(h,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
multiply(multiply(inverse(h),h),b) = multiply(inverse(h),multiply(h,b)),
inference(unit_resolution,[status(thm)],[52,35]) ).
tff(54,plain,
multiply(inverse(h),multiply(h,b)) = multiply(multiply(inverse(h),h),b),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(d,identity) = d ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
multiply(d,identity) = d,
inference(unit_resolution,[status(thm)],[55,16]) ).
tff(57,plain,
multiply(d,multiply(inverse(b),b)) = multiply(d,identity),
inference(monotonicity,[status(thm)],[27]) ).
tff(58,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(d,inverse(b)),b) = multiply(d,multiply(inverse(b),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
multiply(multiply(d,inverse(b)),b) = multiply(d,multiply(inverse(b),b)),
inference(unit_resolution,[status(thm)],[58,35]) ).
tff(60,plain,
( ( multiply(d,inverse(b)) = h )
<=> ( multiply(d,inverse(b)) = h ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
multiply(d,inverse(b)) = h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_times_inverse_b_is_h) ).
tff(62,plain,
multiply(d,inverse(b)) = h,
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
h = multiply(d,inverse(b)),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
multiply(h,b) = multiply(multiply(d,inverse(b)),b),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
multiply(h,b) = d,
inference(transitivity,[status(thm)],[64,59,57,56]) ).
tff(66,plain,
multiply(inverse(h),multiply(h,b)) = multiply(inverse(h),d),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
multiply(inverse(h),d) = multiply(inverse(h),multiply(h,b)),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(c,multiply(inverse(a),inverse(b))),b) = multiply(c,multiply(multiply(inverse(a),inverse(b)),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
multiply(multiply(c,multiply(inverse(a),inverse(b))),b) = multiply(c,multiply(multiply(inverse(a),inverse(b)),b)),
inference(unit_resolution,[status(thm)],[68,35]) ).
tff(70,plain,
( ( multiply(c,inverse(a)) = d )
<=> ( multiply(c,inverse(a)) = d ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
multiply(c,inverse(a)) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_inverse_a_is_d) ).
tff(72,plain,
multiply(c,inverse(a)) = d,
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
multiply(multiply(c,inverse(a)),inverse(b)) = multiply(d,inverse(b)),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(c,inverse(a)),inverse(b)) = multiply(c,multiply(inverse(a),inverse(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
multiply(multiply(c,inverse(a)),inverse(b)) = multiply(c,multiply(inverse(a),inverse(b))),
inference(unit_resolution,[status(thm)],[74,35]) ).
tff(76,plain,
multiply(c,multiply(inverse(a),inverse(b))) = multiply(multiply(c,inverse(a)),inverse(b)),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
multiply(c,multiply(inverse(a),inverse(b))) = h,
inference(transitivity,[status(thm)],[76,73,62]) ).
tff(78,plain,
multiply(multiply(c,multiply(inverse(a),inverse(b))),b) = multiply(h,b),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
multiply(h,b) = multiply(multiply(c,multiply(inverse(a),inverse(b))),b),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
multiply(multiply(d,inverse(b)),b) = multiply(h,b),
inference(symmetry,[status(thm)],[64]) ).
tff(81,plain,
multiply(d,multiply(inverse(b),b)) = multiply(multiply(d,inverse(b)),b),
inference(symmetry,[status(thm)],[59]) ).
tff(82,plain,
multiply(d,identity) = multiply(d,multiply(inverse(b),b)),
inference(symmetry,[status(thm)],[57]) ).
tff(83,plain,
d = multiply(d,identity),
inference(symmetry,[status(thm)],[56]) ).
tff(84,plain,
d = multiply(c,multiply(multiply(inverse(a),inverse(b)),b)),
inference(transitivity,[status(thm)],[83,82,81,80,79,69]) ).
tff(85,plain,
multiply(inverse(h),d) = multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))) = multiply(inverse(h),d),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))) = b,
inference(transitivity,[status(thm)],[86,67,54,51,46]) ).
tff(88,plain,
multiply(multiply(a,inverse(b)),multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))) = multiply(multiply(a,inverse(b)),b),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
multiply(multiply(a,inverse(b)),multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))) = a,
inference(transitivity,[status(thm)],[88,37,28,18]) ).
tff(90,plain,
multiply(multiply(multiply(a,inverse(b)),multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))),inverse(a)) = multiply(a,inverse(a)),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,inverse(b)),multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))),inverse(a)) = multiply(multiply(a,inverse(b)),multiply(multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
multiply(multiply(multiply(a,inverse(b)),multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))),inverse(a)) = multiply(multiply(a,inverse(b)),multiply(multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),inverse(a))),
inference(unit_resolution,[status(thm)],[91,35]) ).
tff(93,plain,
multiply(multiply(a,inverse(b)),multiply(multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),inverse(a))) = multiply(multiply(multiply(a,inverse(b)),multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))),inverse(a)),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
multiply(multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),inverse(a)) = multiply(multiply(inverse(h),d),inverse(a)),
inference(monotonicity,[status(thm)],[86]) ).
tff(95,plain,
multiply(multiply(inverse(h),d),inverse(a)) = multiply(multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),inverse(a)),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
multiply(inverse(h),d) = b,
inference(transitivity,[status(thm)],[67,54,51,46]) ).
tff(97,plain,
multiply(multiply(inverse(h),d),inverse(a)) = multiply(b,inverse(a)),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
multiply(b,inverse(a)) = multiply(multiply(inverse(h),d),inverse(a)),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
multiply(b,inverse(a)) = multiply(multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),inverse(a)),
inference(transitivity,[status(thm)],[98,95]) ).
tff(100,plain,
multiply(multiply(a,inverse(b)),multiply(b,inverse(a))) = multiply(multiply(a,inverse(b)),multiply(multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),inverse(a))),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(h),d),inverse(a)) = multiply(inverse(h),multiply(d,inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
multiply(multiply(inverse(h),d),inverse(a)) = multiply(inverse(h),multiply(d,inverse(a))),
inference(unit_resolution,[status(thm)],[101,35]) ).
tff(103,plain,
multiply(inverse(h),multiply(d,inverse(a))) = multiply(multiply(inverse(h),d),inverse(a)),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
multiply(d,inverse(a)) = multiply(multiply(c,multiply(multiply(inverse(a),inverse(b)),b)),inverse(a)),
inference(monotonicity,[status(thm)],[84]) ).
tff(105,plain,
multiply(multiply(c,multiply(multiply(inverse(a),inverse(b)),b)),inverse(a)) = multiply(d,inverse(a)),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(c,multiply(multiply(inverse(a),inverse(b)),b)),inverse(a)) = multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
multiply(multiply(c,multiply(multiply(inverse(a),inverse(b)),b)),inverse(a)) = multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),
inference(unit_resolution,[status(thm)],[106,35]) ).
tff(108,plain,
multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))) = multiply(multiply(c,multiply(multiply(inverse(a),inverse(b)),b)),inverse(a)),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))) = multiply(d,inverse(a)),
inference(transitivity,[status(thm)],[108,105]) ).
tff(110,plain,
multiply(inverse(h),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))) = multiply(inverse(h),multiply(d,inverse(a))),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
multiply(inverse(h),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))) = multiply(b,inverse(a)),
inference(transitivity,[status(thm)],[110,103,97]) ).
tff(112,plain,
multiply(multiply(a,inverse(b)),multiply(inverse(h),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))))) = multiply(multiply(a,inverse(b)),multiply(b,inverse(a))),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,inverse(b)),inverse(h)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))) = multiply(multiply(a,inverse(b)),multiply(inverse(h),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
multiply(multiply(multiply(a,inverse(b)),inverse(h)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))) = multiply(multiply(a,inverse(b)),multiply(inverse(h),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))))),
inference(unit_resolution,[status(thm)],[113,35]) ).
tff(115,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,inverse(b)),inverse(h)) = multiply(a,multiply(inverse(b),inverse(h))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
multiply(multiply(a,inverse(b)),inverse(h)) = multiply(a,multiply(inverse(b),inverse(h))),
inference(unit_resolution,[status(thm)],[115,35]) ).
tff(117,plain,
multiply(a,multiply(inverse(b),inverse(h))) = multiply(multiply(a,inverse(b)),inverse(h)),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
multiply(multiply(a,multiply(inverse(b),inverse(h))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))) = multiply(multiply(multiply(a,inverse(b)),inverse(h)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,multiply(inverse(b),inverse(h))) = multiply(inverse(b),inverse(h)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
multiply(identity,multiply(inverse(b),inverse(h))) = multiply(inverse(b),inverse(h)),
inference(unit_resolution,[status(thm)],[119,44]) ).
tff(121,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = identity )
| ( multiply(b,inverse(b)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
multiply(b,inverse(b)) = identity,
inference(unit_resolution,[status(thm)],[121,7]) ).
tff(123,plain,
multiply(multiply(b,inverse(b)),multiply(inverse(b),inverse(h))) = multiply(identity,multiply(inverse(b),inverse(h))),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,inverse(b)),multiply(inverse(b),inverse(h))) = multiply(b,multiply(inverse(b),multiply(inverse(b),inverse(h)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
multiply(multiply(b,inverse(b)),multiply(inverse(b),inverse(h))) = multiply(b,multiply(inverse(b),multiply(inverse(b),inverse(h)))),
inference(unit_resolution,[status(thm)],[124,35]) ).
tff(126,plain,
multiply(b,multiply(inverse(b),multiply(inverse(b),inverse(h)))) = multiply(multiply(b,inverse(b)),multiply(inverse(b),inverse(h))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
multiply(multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),multiply(inverse(b),multiply(inverse(b),inverse(h)))) = multiply(b,multiply(inverse(b),multiply(inverse(b),inverse(h)))),
inference(monotonicity,[status(thm)],[87]) ).
tff(128,plain,
multiply(multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),multiply(inverse(b),multiply(inverse(b),inverse(h)))) = multiply(inverse(b),inverse(h)),
inference(transitivity,[status(thm)],[127,126,123,120]) ).
tff(129,plain,
multiply(a,multiply(multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),multiply(inverse(b),multiply(inverse(b),inverse(h))))) = multiply(a,multiply(inverse(b),inverse(h))),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))),multiply(inverse(b),multiply(inverse(b),inverse(h)))) = multiply(a,multiply(multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),multiply(inverse(b),multiply(inverse(b),inverse(h))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
multiply(multiply(a,multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))),multiply(inverse(b),multiply(inverse(b),inverse(h)))) = multiply(a,multiply(multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),multiply(inverse(b),multiply(inverse(b),inverse(h))))),
inference(unit_resolution,[status(thm)],[130,35]) ).
tff(132,plain,
multiply(a,multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))) = multiply(a,b),
inference(monotonicity,[status(thm)],[87]) ).
tff(133,plain,
multiply(a,b) = multiply(a,multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
( ( multiply(a,b) = c )
<=> ( multiply(a,b) = c ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,axiom,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
tff(136,plain,
multiply(a,b) = c,
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
c = multiply(a,b),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
c = multiply(a,multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))),
inference(transitivity,[status(thm)],[137,133]) ).
tff(139,plain,
multiply(c,multiply(inverse(b),multiply(inverse(b),inverse(h)))) = multiply(multiply(a,multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))),multiply(inverse(b),multiply(inverse(b),inverse(h)))),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
multiply(c,multiply(inverse(b),multiply(inverse(b),inverse(h)))) = multiply(a,multiply(inverse(b),inverse(h))),
inference(transitivity,[status(thm)],[139,131,129]) ).
tff(141,plain,
multiply(multiply(c,multiply(inverse(b),multiply(inverse(b),inverse(h)))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))) = multiply(multiply(a,multiply(inverse(b),inverse(h))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
multiply(multiply(a,multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))),multiply(inverse(b),multiply(inverse(b),inverse(h)))) = multiply(c,multiply(inverse(b),multiply(inverse(b),inverse(h)))),
inference(symmetry,[status(thm)],[139]) ).
tff(143,plain,
multiply(a,multiply(multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),multiply(inverse(b),multiply(inverse(b),inverse(h))))) = multiply(multiply(a,multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))),multiply(inverse(b),multiply(inverse(b),inverse(h)))),
inference(symmetry,[status(thm)],[131]) ).
tff(144,plain,
multiply(a,multiply(inverse(b),inverse(h))) = multiply(a,multiply(multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),multiply(inverse(b),multiply(inverse(b),inverse(h))))),
inference(symmetry,[status(thm)],[129]) ).
tff(145,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,multiply(a,multiply(inverse(b),inverse(h)))) = multiply(a,multiply(inverse(b),inverse(h))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(146,plain,
multiply(identity,multiply(a,multiply(inverse(b),inverse(h)))) = multiply(a,multiply(inverse(b),inverse(h))),
inference(unit_resolution,[status(thm)],[145,44]) ).
tff(147,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,inverse(a)),inverse(a)) = multiply(b,multiply(inverse(a),inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,plain,
multiply(multiply(b,inverse(a)),inverse(a)) = multiply(b,multiply(inverse(a),inverse(a))),
inference(unit_resolution,[status(thm)],[147,35]) ).
tff(149,plain,
multiply(b,multiply(inverse(a),inverse(a))) = multiply(multiply(b,inverse(a)),inverse(a)),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,plain,
multiply(identity,a) = a,
inference(unit_resolution,[status(thm)],[150,44]) ).
tff(152,plain,
^ [X: $i] :
refl(( ( multiply(X,multiply(X,X)) = identity )
<=> ( multiply(X,multiply(X,X)) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(153,plain,
( ! [X: $i] : ( multiply(X,multiply(X,X)) = identity )
<=> ! [X: $i] : ( multiply(X,multiply(X,X)) = identity ) ),
inference(quant_intro,[status(thm)],[152]) ).
tff(154,plain,
( ! [X: $i] : ( multiply(X,multiply(X,X)) = identity )
<=> ! [X: $i] : ( multiply(X,multiply(X,X)) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,axiom,
! [X: $i] : ( multiply(X,multiply(X,X)) = identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity) ).
tff(156,plain,
! [X: $i] : ( multiply(X,multiply(X,X)) = identity ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
! [X: $i] : ( multiply(X,multiply(X,X)) = identity ),
inference(skolemize,[status(sab)],[156]) ).
tff(158,plain,
! [X: $i] : ( multiply(X,multiply(X,X)) = identity ),
inference(modus_ponens,[status(thm)],[157,153]) ).
tff(159,plain,
( ~ ! [X: $i] : ( multiply(X,multiply(X,X)) = identity )
| ( multiply(inverse(a),multiply(inverse(a),inverse(a))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(160,plain,
multiply(inverse(a),multiply(inverse(a),inverse(a))) = identity,
inference(unit_resolution,[status(thm)],[159,158]) ).
tff(161,plain,
multiply(multiply(inverse(a),multiply(inverse(a),inverse(a))),a) = multiply(identity,a),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),multiply(inverse(a),inverse(a))),a) = multiply(inverse(a),multiply(multiply(inverse(a),inverse(a)),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
multiply(multiply(inverse(a),multiply(inverse(a),inverse(a))),a) = multiply(inverse(a),multiply(multiply(inverse(a),inverse(a)),a)),
inference(unit_resolution,[status(thm)],[162,35]) ).
tff(164,plain,
multiply(inverse(a),multiply(multiply(inverse(a),inverse(a)),a)) = multiply(multiply(inverse(a),multiply(inverse(a),inverse(a))),a),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),inverse(a)),a) = multiply(inverse(a),multiply(inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(166,plain,
multiply(multiply(inverse(a),inverse(a)),a) = multiply(inverse(a),multiply(inverse(a),a)),
inference(unit_resolution,[status(thm)],[165,35]) ).
tff(167,plain,
multiply(inverse(a),multiply(inverse(a),a)) = multiply(multiply(inverse(a),inverse(a)),a),
inference(symmetry,[status(thm)],[166]) ).
tff(168,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(a),a) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(169,plain,
multiply(inverse(a),a) = identity,
inference(unit_resolution,[status(thm)],[168,25]) ).
tff(170,plain,
multiply(inverse(a),multiply(inverse(a),a)) = multiply(inverse(a),identity),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
multiply(inverse(a),identity) = multiply(inverse(a),multiply(inverse(a),a)),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(inverse(a),identity) = inverse(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,plain,
multiply(inverse(a),identity) = inverse(a),
inference(unit_resolution,[status(thm)],[172,16]) ).
tff(174,plain,
inverse(a) = multiply(inverse(a),identity),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
inverse(a) = multiply(multiply(inverse(a),inverse(a)),a),
inference(transitivity,[status(thm)],[174,171,167]) ).
tff(176,plain,
multiply(inverse(a),inverse(a)) = multiply(inverse(a),multiply(multiply(inverse(a),inverse(a)),a)),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
multiply(inverse(a),inverse(a)) = a,
inference(transitivity,[status(thm)],[176,164,161,151]) ).
tff(178,plain,
b = multiply(identity,b),
inference(symmetry,[status(thm)],[46]) ).
tff(179,plain,
b = multiply(inverse(h),d),
inference(transitivity,[status(thm)],[178,50,53,66]) ).
tff(180,plain,
multiply(b,multiply(inverse(a),inverse(a))) = multiply(multiply(inverse(h),d),a),
inference(monotonicity,[status(thm)],[179,177]) ).
tff(181,plain,
multiply(multiply(inverse(h),d),a) = multiply(b,multiply(inverse(a),inverse(a))),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(h),d),a) = multiply(inverse(h),multiply(d,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(183,plain,
multiply(multiply(inverse(h),d),a) = multiply(inverse(h),multiply(d,a)),
inference(unit_resolution,[status(thm)],[182,35]) ).
tff(184,plain,
multiply(inverse(h),multiply(d,a)) = multiply(multiply(inverse(h),d),a),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
multiply(multiply(c,inverse(a)),a) = multiply(d,a),
inference(monotonicity,[status(thm)],[72]) ).
tff(186,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(c,inverse(a)),a) = multiply(c,multiply(inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(187,plain,
multiply(multiply(c,inverse(a)),a) = multiply(c,multiply(inverse(a),a)),
inference(unit_resolution,[status(thm)],[186,35]) ).
tff(188,plain,
multiply(c,multiply(inverse(a),a)) = multiply(multiply(c,inverse(a)),a),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
identity = multiply(inverse(a),a),
inference(symmetry,[status(thm)],[169]) ).
tff(190,plain,
multiply(c,identity) = multiply(c,multiply(inverse(a),a)),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(c,identity) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
multiply(c,identity) = c,
inference(unit_resolution,[status(thm)],[191,16]) ).
tff(193,plain,
c = multiply(c,identity),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
c = multiply(d,a),
inference(transitivity,[status(thm)],[193,190,188,185]) ).
tff(195,plain,
multiply(inverse(h),c) = multiply(inverse(h),multiply(d,a)),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
multiply(inverse(h),multiply(a,b)) = multiply(inverse(h),c),
inference(monotonicity,[status(thm)],[136]) ).
tff(197,plain,
multiply(inverse(h),multiply(a,b)) = multiply(multiply(b,inverse(a)),inverse(a)),
inference(transitivity,[status(thm)],[196,195,184,181,149]) ).
tff(198,plain,
multiply(a,multiply(inverse(h),multiply(a,b))) = multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
multiply(a,multiply(multiply(b,inverse(a)),inverse(a))) = multiply(a,multiply(inverse(h),multiply(a,b))),
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(b,inverse(a))),inverse(a)) = multiply(a,multiply(multiply(b,inverse(a)),inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(201,plain,
multiply(multiply(a,multiply(b,inverse(a))),inverse(a)) = multiply(a,multiply(multiply(b,inverse(a)),inverse(a))),
inference(unit_resolution,[status(thm)],[200,35]) ).
tff(202,plain,
multiply(multiply(a,b),inverse(a)) = multiply(c,inverse(a)),
inference(monotonicity,[status(thm)],[136]) ).
tff(203,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),inverse(a)) = multiply(a,multiply(b,inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(204,plain,
multiply(multiply(a,b),inverse(a)) = multiply(a,multiply(b,inverse(a))),
inference(unit_resolution,[status(thm)],[203,35]) ).
tff(205,plain,
multiply(a,multiply(b,inverse(a))) = multiply(multiply(a,b),inverse(a)),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
multiply(a,multiply(b,inverse(a))) = d,
inference(transitivity,[status(thm)],[205,202,72]) ).
tff(207,plain,
multiply(multiply(a,multiply(b,inverse(a))),inverse(a)) = multiply(d,inverse(a)),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
multiply(d,inverse(a)) = multiply(multiply(a,multiply(b,inverse(a))),inverse(a)),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))) = multiply(a,multiply(inverse(h),multiply(a,b))),
inference(transitivity,[status(thm)],[108,105,208,201,199]) ).
tff(210,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(a,multiply(inverse(h),multiply(a,b)))),
inference(monotonicity,[status(thm)],[209]) ).
tff(211,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(a,multiply(inverse(h),multiply(a,b)))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),a),multiply(inverse(h),multiply(a,b))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(a,multiply(inverse(h),multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(213,plain,
multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),a),multiply(inverse(h),multiply(a,b))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(a,multiply(inverse(h),multiply(a,b)))),
inference(unit_resolution,[status(thm)],[212,35]) ).
tff(214,plain,
identity = multiply(inverse(b),b),
inference(symmetry,[status(thm)],[27]) ).
tff(215,plain,
multiply(inverse(a),a) = multiply(inverse(b),b),
inference(transitivity,[status(thm)],[169,214]) ).
tff(216,plain,
multiply(d,multiply(inverse(a),a)) = multiply(d,multiply(inverse(b),b)),
inference(monotonicity,[status(thm)],[215]) ).
tff(217,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(d,inverse(a)),a) = multiply(d,multiply(inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(218,plain,
multiply(multiply(d,inverse(a)),a) = multiply(d,multiply(inverse(a),a)),
inference(unit_resolution,[status(thm)],[217,35]) ).
tff(219,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),a) = multiply(multiply(d,inverse(a)),a),
inference(monotonicity,[status(thm)],[109]) ).
tff(220,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),a) = d,
inference(transitivity,[status(thm)],[219,218,216,57,56]) ).
tff(221,plain,
multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),a),multiply(inverse(h),multiply(a,b))) = multiply(d,multiply(inverse(h),c)),
inference(monotonicity,[status(thm)],[220,196]) ).
tff(222,plain,
multiply(d,multiply(inverse(h),c)) = multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),a),multiply(inverse(h),multiply(a,b))),
inference(symmetry,[status(thm)],[221]) ).
tff(223,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(d,inverse(h)),c) = multiply(d,multiply(inverse(h),c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(224,plain,
multiply(multiply(d,inverse(h)),c) = multiply(d,multiply(inverse(h),c)),
inference(unit_resolution,[status(thm)],[223,35]) ).
tff(225,plain,
( ( multiply(j,inverse(h)) = k )
<=> ( multiply(j,inverse(h)) = k ) ),
inference(rewrite,[status(thm)],[]) ).
tff(226,axiom,
multiply(j,inverse(h)) = k,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',j_times_inverse_h_is_k) ).
tff(227,plain,
multiply(j,inverse(h)) = k,
inference(modus_ponens,[status(thm)],[226,225]) ).
tff(228,plain,
( ( multiply(h,b) = j )
<=> ( multiply(h,b) = j ) ),
inference(rewrite,[status(thm)],[]) ).
tff(229,axiom,
multiply(h,b) = j,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_times_b_is_j) ).
tff(230,plain,
multiply(h,b) = j,
inference(modus_ponens,[status(thm)],[229,228]) ).
tff(231,plain,
j = multiply(h,b),
inference(symmetry,[status(thm)],[230]) ).
tff(232,plain,
j = d,
inference(transitivity,[status(thm)],[231,64,59,57,56]) ).
tff(233,plain,
multiply(j,inverse(h)) = multiply(d,inverse(h)),
inference(monotonicity,[status(thm)],[232]) ).
tff(234,plain,
multiply(d,inverse(h)) = multiply(j,inverse(h)),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
multiply(d,inverse(h)) = k,
inference(transitivity,[status(thm)],[234,227]) ).
tff(236,plain,
multiply(multiply(d,inverse(h)),c) = multiply(k,c),
inference(monotonicity,[status(thm)],[235]) ).
tff(237,plain,
multiply(k,c) = multiply(multiply(d,inverse(h)),c),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
multiply(k,c) = multiply(k,multiply(a,b)),
inference(monotonicity,[status(thm)],[137]) ).
tff(239,plain,
multiply(k,multiply(a,b)) = multiply(k,c),
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
multiply(k,multiply(a,b)) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))),
inference(transitivity,[status(thm)],[239,237,224,222,213,211]) ).
tff(241,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(k,multiply(a,b))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))))),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(k,multiply(a,b))),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
( ~ ! [X: $i] : ( multiply(X,multiply(X,X)) = identity )
| ( multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(244,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))))) = identity,
inference(unit_resolution,[status(thm)],[243,158]) ).
tff(245,plain,
identity = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))))),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
identity = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(k,multiply(a,b))),
inference(transitivity,[status(thm)],[245,242]) ).
tff(247,plain,
multiply(identity,multiply(a,multiply(inverse(b),inverse(h)))) = multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(k,multiply(a,b))),multiply(a,multiply(inverse(b),inverse(h)))),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(k,multiply(a,b))),multiply(a,multiply(inverse(b),inverse(h)))) = multiply(identity,multiply(a,multiply(inverse(b),inverse(h)))),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(k,multiply(a,b))),multiply(a,multiply(inverse(b),inverse(h)))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(multiply(k,multiply(a,b)),multiply(a,multiply(inverse(b),inverse(h))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(250,plain,
multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(k,multiply(a,b))),multiply(a,multiply(inverse(b),inverse(h)))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(multiply(k,multiply(a,b)),multiply(a,multiply(inverse(b),inverse(h))))),
inference(unit_resolution,[status(thm)],[249,35]) ).
tff(251,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(multiply(k,multiply(a,b)),multiply(a,multiply(inverse(b),inverse(h))))) = multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(k,multiply(a,b))),multiply(a,multiply(inverse(b),inverse(h)))),
inference(symmetry,[status(thm)],[250]) ).
tff(252,plain,
multiply(multiply(d,inverse(a)),a) = d,
inference(transitivity,[status(thm)],[218,216,57,56]) ).
tff(253,plain,
multiply(multiply(multiply(d,inverse(a)),a),inverse(a)) = multiply(d,inverse(a)),
inference(monotonicity,[status(thm)],[252]) ).
tff(254,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(d,inverse(a)),a),inverse(a)) = multiply(multiply(d,inverse(a)),multiply(a,inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(255,plain,
multiply(multiply(multiply(d,inverse(a)),a),inverse(a)) = multiply(multiply(d,inverse(a)),multiply(a,inverse(a))),
inference(unit_resolution,[status(thm)],[254,35]) ).
tff(256,plain,
multiply(multiply(d,inverse(a)),multiply(a,inverse(a))) = multiply(multiply(multiply(d,inverse(a)),a),inverse(a)),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
identity = multiply(a,inverse(a)),
inference(symmetry,[status(thm)],[9]) ).
tff(258,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = identity )
| ( multiply(h,inverse(h)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(259,plain,
multiply(h,inverse(h)) = identity,
inference(unit_resolution,[status(thm)],[258,7]) ).
tff(260,plain,
multiply(multiply(d,inverse(b)),inverse(h)) = multiply(h,inverse(h)),
inference(monotonicity,[status(thm)],[62]) ).
tff(261,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(d,inverse(b)),inverse(h)) = multiply(d,multiply(inverse(b),inverse(h))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(262,plain,
multiply(multiply(d,inverse(b)),inverse(h)) = multiply(d,multiply(inverse(b),inverse(h))),
inference(unit_resolution,[status(thm)],[261,35]) ).
tff(263,plain,
multiply(d,multiply(inverse(b),inverse(h))) = multiply(multiply(d,inverse(b)),inverse(h)),
inference(symmetry,[status(thm)],[262]) ).
tff(264,plain,
multiply(multiply(multiply(d,inverse(a)),a),multiply(inverse(b),inverse(h))) = multiply(d,multiply(inverse(b),inverse(h))),
inference(monotonicity,[status(thm)],[252]) ).
tff(265,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(d,inverse(a)),a),multiply(inverse(b),inverse(h))) = multiply(multiply(d,inverse(a)),multiply(a,multiply(inverse(b),inverse(h)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(266,plain,
multiply(multiply(multiply(d,inverse(a)),a),multiply(inverse(b),inverse(h))) = multiply(multiply(d,inverse(a)),multiply(a,multiply(inverse(b),inverse(h)))),
inference(unit_resolution,[status(thm)],[265,35]) ).
tff(267,plain,
multiply(multiply(d,inverse(a)),multiply(a,multiply(inverse(b),inverse(h)))) = multiply(multiply(multiply(d,inverse(a)),a),multiply(inverse(b),inverse(h))),
inference(symmetry,[status(thm)],[266]) ).
tff(268,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(a,multiply(inverse(b),inverse(h)))) = multiply(multiply(d,inverse(a)),multiply(a,multiply(inverse(b),inverse(h)))),
inference(monotonicity,[status(thm)],[109]) ).
tff(269,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(a,multiply(inverse(b),inverse(h)))) = multiply(a,inverse(a)),
inference(transitivity,[status(thm)],[268,267,264,263,260,259,257]) ).
tff(270,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(a,multiply(inverse(b),inverse(h))))) = multiply(multiply(d,inverse(a)),multiply(a,inverse(a))),
inference(monotonicity,[status(thm)],[109,269]) ).
tff(271,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))),multiply(a,multiply(inverse(b),inverse(h)))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(a,multiply(inverse(b),inverse(h))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(272,plain,
multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))),multiply(a,multiply(inverse(b),inverse(h)))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(a,multiply(inverse(b),inverse(h))))),
inference(unit_resolution,[status(thm)],[271,35]) ).
tff(273,plain,
multiply(multiply(k,multiply(a,b)),multiply(a,multiply(inverse(b),inverse(h)))) = multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))),multiply(a,multiply(inverse(b),inverse(h)))),
inference(monotonicity,[status(thm)],[240]) ).
tff(274,plain,
multiply(multiply(k,multiply(a,b)),multiply(a,multiply(inverse(b),inverse(h)))) = multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),
inference(transitivity,[status(thm)],[273,272,270,256,253,104,107]) ).
tff(275,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(multiply(k,multiply(a,b)),multiply(a,multiply(inverse(b),inverse(h))))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))),
inference(monotonicity,[status(thm)],[274]) ).
tff(276,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),multiply(multiply(k,multiply(a,b)),multiply(a,multiply(inverse(b),inverse(h))))),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
multiply(k,multiply(a,b)) = multiply(c,multiply(inverse(b),multiply(inverse(b),inverse(h)))),
inference(transitivity,[status(thm)],[239,237,224,222,213,211,276,251,248,146,144,143,142]) ).
tff(278,plain,
multiply(multiply(k,multiply(a,b)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))) = multiply(multiply(c,multiply(inverse(b),multiply(inverse(b),inverse(h)))),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))),
inference(monotonicity,[status(thm)],[277]) ).
tff(279,plain,
multiply(a,inverse(a)) = multiply(inverse(b),b),
inference(transitivity,[status(thm)],[9,214]) ).
tff(280,plain,
multiply(d,multiply(a,inverse(a))) = multiply(d,multiply(inverse(b),b)),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(d,a),inverse(a)) = multiply(d,multiply(a,inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(282,plain,
multiply(multiply(d,a),inverse(a)) = multiply(d,multiply(a,inverse(a))),
inference(unit_resolution,[status(thm)],[281,35]) ).
tff(283,plain,
multiply(multiply(d,a),inverse(a)) = d,
inference(transitivity,[status(thm)],[282,280,57,56]) ).
tff(284,plain,
multiply(multiply(multiply(d,a),inverse(a)),inverse(a)) = multiply(d,inverse(a)),
inference(monotonicity,[status(thm)],[283]) ).
tff(285,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(d,a),inverse(a)),inverse(a)) = multiply(multiply(d,a),multiply(inverse(a),inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(286,plain,
multiply(multiply(multiply(d,a),inverse(a)),inverse(a)) = multiply(multiply(d,a),multiply(inverse(a),inverse(a))),
inference(unit_resolution,[status(thm)],[285,35]) ).
tff(287,plain,
multiply(multiply(d,a),multiply(inverse(a),inverse(a))) = multiply(multiply(multiply(d,a),inverse(a)),inverse(a)),
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
multiply(inverse(a),multiply(multiply(inverse(a),inverse(a)),a)) = multiply(inverse(a),inverse(a)),
inference(symmetry,[status(thm)],[176]) ).
tff(289,plain,
multiply(identity,a) = multiply(multiply(inverse(a),multiply(inverse(a),inverse(a))),a),
inference(symmetry,[status(thm)],[161]) ).
tff(290,plain,
a = multiply(identity,a),
inference(symmetry,[status(thm)],[151]) ).
tff(291,plain,
a = multiply(inverse(a),inverse(a)),
inference(transitivity,[status(thm)],[290,289,163,288]) ).
tff(292,plain,
multiply(d,a) = multiply(multiply(c,multiply(multiply(inverse(a),inverse(b)),b)),a),
inference(monotonicity,[status(thm)],[84]) ).
tff(293,plain,
multiply(multiply(c,multiply(multiply(inverse(a),inverse(b)),b)),a) = multiply(d,a),
inference(symmetry,[status(thm)],[292]) ).
tff(294,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(c,multiply(multiply(inverse(a),inverse(b)),b)),a) = multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(295,plain,
multiply(multiply(c,multiply(multiply(inverse(a),inverse(b)),b)),a) = multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),
inference(unit_resolution,[status(thm)],[294,35]) ).
tff(296,plain,
multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)) = multiply(multiply(c,multiply(multiply(inverse(a),inverse(b)),b)),a),
inference(symmetry,[status(thm)],[295]) ).
tff(297,plain,
multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)) = multiply(d,a),
inference(transitivity,[status(thm)],[296,293]) ).
tff(298,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),a) = multiply(multiply(d,a),multiply(inverse(a),inverse(a))),
inference(monotonicity,[status(thm)],[297,291]) ).
tff(299,plain,
multiply(multiply(multiply(d,a),inverse(a)),a) = multiply(d,a),
inference(monotonicity,[status(thm)],[283]) ).
tff(300,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(d,a),inverse(a)),a) = multiply(multiply(d,a),multiply(inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(301,plain,
multiply(multiply(multiply(d,a),inverse(a)),a) = multiply(multiply(d,a),multiply(inverse(a),a)),
inference(unit_resolution,[status(thm)],[300,35]) ).
tff(302,plain,
multiply(multiply(d,a),multiply(inverse(a),a)) = multiply(multiply(multiply(d,a),inverse(a)),a),
inference(symmetry,[status(thm)],[301]) ).
tff(303,plain,
multiply(multiply(multiply(d,a),inverse(a)),multiply(inverse(b),inverse(h))) = multiply(d,multiply(inverse(b),inverse(h))),
inference(monotonicity,[status(thm)],[283]) ).
tff(304,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(d,a),inverse(a)),multiply(inverse(b),inverse(h))) = multiply(multiply(d,a),multiply(inverse(a),multiply(inverse(b),inverse(h)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(305,plain,
multiply(multiply(multiply(d,a),inverse(a)),multiply(inverse(b),inverse(h))) = multiply(multiply(d,a),multiply(inverse(a),multiply(inverse(b),inverse(h)))),
inference(unit_resolution,[status(thm)],[304,35]) ).
tff(306,plain,
multiply(multiply(d,a),multiply(inverse(a),multiply(inverse(b),inverse(h)))) = multiply(multiply(multiply(d,a),inverse(a)),multiply(inverse(b),inverse(h))),
inference(symmetry,[status(thm)],[305]) ).
tff(307,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(inverse(a),multiply(inverse(b),inverse(h)))) = multiply(multiply(d,a),multiply(inverse(a),multiply(inverse(b),inverse(h)))),
inference(monotonicity,[status(thm)],[297]) ).
tff(308,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(inverse(a),multiply(inverse(b),inverse(h)))) = multiply(inverse(a),a),
inference(transitivity,[status(thm)],[307,306,303,263,260,259,189]) ).
tff(309,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(inverse(a),multiply(inverse(b),inverse(h))))) = multiply(multiply(d,a),multiply(inverse(a),a)),
inference(monotonicity,[status(thm)],[297,308]) ).
tff(310,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(inverse(a),multiply(inverse(b),inverse(h)))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(inverse(a),multiply(inverse(b),inverse(h))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(311,plain,
multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(inverse(a),multiply(inverse(b),inverse(h)))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(inverse(a),multiply(inverse(b),inverse(h))))),
inference(unit_resolution,[status(thm)],[310,35]) ).
tff(312,plain,
multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(inverse(a),multiply(inverse(b),inverse(h)))) = multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),
inference(transitivity,[status(thm)],[311,309,302,299,292,295]) ).
tff(313,plain,
multiply(multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(inverse(a),multiply(inverse(b),inverse(h)))),a) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),a),
inference(monotonicity,[status(thm)],[312]) ).
tff(314,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(inverse(a),multiply(inverse(b),inverse(h)))),a) = multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(multiply(inverse(a),multiply(inverse(b),inverse(h))),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(315,plain,
multiply(multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(inverse(a),multiply(inverse(b),inverse(h)))),a) = multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(multiply(inverse(a),multiply(inverse(b),inverse(h))),a)),
inference(unit_resolution,[status(thm)],[314,35]) ).
tff(316,plain,
multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(multiply(inverse(a),multiply(inverse(b),inverse(h))),a)) = multiply(multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(inverse(a),multiply(inverse(b),inverse(h)))),a),
inference(symmetry,[status(thm)],[315]) ).
tff(317,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),inverse(b)),inverse(h)) = multiply(inverse(a),multiply(inverse(b),inverse(h))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(318,plain,
multiply(multiply(inverse(a),inverse(b)),inverse(h)) = multiply(inverse(a),multiply(inverse(b),inverse(h))),
inference(unit_resolution,[status(thm)],[317,35]) ).
tff(319,plain,
multiply(inverse(a),multiply(inverse(b),inverse(h))) = multiply(multiply(inverse(a),inverse(b)),inverse(h)),
inference(symmetry,[status(thm)],[318]) ).
tff(320,plain,
multiply(multiply(inverse(a),c),multiply(inverse(a),multiply(inverse(b),inverse(h)))) = multiply(multiply(inverse(a),c),multiply(multiply(inverse(a),inverse(b)),inverse(h))),
inference(monotonicity,[status(thm)],[319]) ).
tff(321,plain,
multiply(multiply(inverse(a),c),multiply(multiply(inverse(a),inverse(b)),inverse(h))) = multiply(multiply(inverse(a),c),multiply(inverse(a),multiply(inverse(b),inverse(h)))),
inference(symmetry,[status(thm)],[320]) ).
tff(322,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),c),multiply(multiply(inverse(a),inverse(b)),inverse(h))) = multiply(inverse(a),multiply(c,multiply(multiply(inverse(a),inverse(b)),inverse(h)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(323,plain,
multiply(multiply(inverse(a),c),multiply(multiply(inverse(a),inverse(b)),inverse(h))) = multiply(inverse(a),multiply(c,multiply(multiply(inverse(a),inverse(b)),inverse(h)))),
inference(unit_resolution,[status(thm)],[322,35]) ).
tff(324,plain,
multiply(inverse(a),multiply(c,multiply(multiply(inverse(a),inverse(b)),inverse(h)))) = multiply(multiply(inverse(a),c),multiply(multiply(inverse(a),inverse(b)),inverse(h))),
inference(symmetry,[status(thm)],[323]) ).
tff(325,plain,
multiply(multiply(c,multiply(inverse(a),inverse(b))),inverse(h)) = multiply(h,inverse(h)),
inference(monotonicity,[status(thm)],[77]) ).
tff(326,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(c,multiply(inverse(a),inverse(b))),inverse(h)) = multiply(c,multiply(multiply(inverse(a),inverse(b)),inverse(h))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(327,plain,
multiply(multiply(c,multiply(inverse(a),inverse(b))),inverse(h)) = multiply(c,multiply(multiply(inverse(a),inverse(b)),inverse(h))),
inference(unit_resolution,[status(thm)],[326,35]) ).
tff(328,plain,
multiply(c,multiply(multiply(inverse(a),inverse(b)),inverse(h))) = multiply(multiply(c,multiply(inverse(a),inverse(b))),inverse(h)),
inference(symmetry,[status(thm)],[327]) ).
tff(329,plain,
multiply(c,multiply(multiply(inverse(a),inverse(b)),inverse(h))) = identity,
inference(transitivity,[status(thm)],[328,325,259]) ).
tff(330,plain,
multiply(inverse(a),multiply(c,multiply(multiply(inverse(a),inverse(b)),inverse(h)))) = multiply(inverse(a),identity),
inference(monotonicity,[status(thm)],[329]) ).
tff(331,plain,
multiply(inverse(a),identity) = multiply(inverse(a),multiply(c,multiply(multiply(inverse(a),inverse(b)),inverse(h)))),
inference(symmetry,[status(thm)],[330]) ).
tff(332,plain,
inverse(a) = multiply(multiply(inverse(a),c),multiply(inverse(a),multiply(inverse(b),inverse(h)))),
inference(transitivity,[status(thm)],[174,331,324,321]) ).
tff(333,plain,
multiply(inverse(b),inverse(a)) = multiply(inverse(b),multiply(multiply(inverse(a),c),multiply(inverse(a),multiply(inverse(b),inverse(h))))),
inference(monotonicity,[status(thm)],[332]) ).
tff(334,plain,
multiply(inverse(b),multiply(multiply(inverse(a),c),multiply(inverse(a),multiply(inverse(b),inverse(h))))) = multiply(inverse(b),inverse(a)),
inference(symmetry,[status(thm)],[333]) ).
tff(335,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(b),multiply(inverse(a),c)),multiply(inverse(a),multiply(inverse(b),inverse(h)))) = multiply(inverse(b),multiply(multiply(inverse(a),c),multiply(inverse(a),multiply(inverse(b),inverse(h))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(336,plain,
multiply(multiply(inverse(b),multiply(inverse(a),c)),multiply(inverse(a),multiply(inverse(b),inverse(h)))) = multiply(inverse(b),multiply(multiply(inverse(a),c),multiply(inverse(a),multiply(inverse(b),inverse(h))))),
inference(unit_resolution,[status(thm)],[335,35]) ).
tff(337,plain,
multiply(inverse(b),multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))) = multiply(inverse(b),b),
inference(monotonicity,[status(thm)],[87]) ).
tff(338,plain,
multiply(multiply(inverse(a),a),b) = multiply(identity,b),
inference(monotonicity,[status(thm)],[169]) ).
tff(339,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),a),b) = multiply(inverse(a),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(340,plain,
multiply(multiply(inverse(a),a),b) = multiply(inverse(a),multiply(a,b)),
inference(unit_resolution,[status(thm)],[339,35]) ).
tff(341,plain,
multiply(inverse(a),multiply(a,b)) = multiply(multiply(inverse(a),a),b),
inference(symmetry,[status(thm)],[340]) ).
tff(342,plain,
multiply(inverse(a),c) = multiply(inverse(a),multiply(a,b)),
inference(monotonicity,[status(thm)],[137]) ).
tff(343,plain,
multiply(inverse(a),c) = multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b))),
inference(transitivity,[status(thm)],[342,341,338,50,53,66,85]) ).
tff(344,plain,
multiply(inverse(b),multiply(inverse(a),c)) = multiply(inverse(b),multiply(inverse(h),multiply(c,multiply(multiply(inverse(a),inverse(b)),b)))),
inference(monotonicity,[status(thm)],[343]) ).
tff(345,plain,
multiply(inverse(b),multiply(inverse(a),c)) = identity,
inference(transitivity,[status(thm)],[344,337,27]) ).
tff(346,plain,
multiply(multiply(inverse(b),multiply(inverse(a),c)),multiply(inverse(a),multiply(inverse(b),inverse(h)))) = multiply(identity,multiply(inverse(a),multiply(inverse(b),inverse(h)))),
inference(monotonicity,[status(thm)],[345]) ).
tff(347,plain,
multiply(identity,multiply(inverse(a),multiply(inverse(b),inverse(h)))) = multiply(multiply(inverse(b),multiply(inverse(a),c)),multiply(inverse(a),multiply(inverse(b),inverse(h)))),
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(identity,inverse(a)),multiply(inverse(b),inverse(h))) = multiply(identity,multiply(inverse(a),multiply(inverse(b),inverse(h)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(349,plain,
multiply(multiply(identity,inverse(a)),multiply(inverse(b),inverse(h))) = multiply(identity,multiply(inverse(a),multiply(inverse(b),inverse(h)))),
inference(unit_resolution,[status(thm)],[348,35]) ).
tff(350,plain,
multiply(inverse(a),multiply(a,inverse(a))) = multiply(inverse(a),identity),
inference(monotonicity,[status(thm)],[9]) ).
tff(351,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),a),inverse(a)) = multiply(inverse(a),multiply(a,inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(352,plain,
multiply(multiply(inverse(a),a),inverse(a)) = multiply(inverse(a),multiply(a,inverse(a))),
inference(unit_resolution,[status(thm)],[351,35]) ).
tff(353,plain,
multiply(identity,inverse(a)) = multiply(multiply(inverse(a),a),inverse(a)),
inference(monotonicity,[status(thm)],[189]) ).
tff(354,plain,
multiply(identity,inverse(a)) = inverse(a),
inference(transitivity,[status(thm)],[353,352,350,173]) ).
tff(355,plain,
multiply(multiply(identity,inverse(a)),multiply(inverse(b),inverse(h))) = multiply(inverse(a),multiply(inverse(b),inverse(h))),
inference(monotonicity,[status(thm)],[354]) ).
tff(356,plain,
multiply(inverse(a),multiply(inverse(b),inverse(h))) = multiply(multiply(identity,inverse(a)),multiply(inverse(b),inverse(h))),
inference(symmetry,[status(thm)],[355]) ).
tff(357,plain,
multiply(inverse(a),multiply(inverse(b),inverse(h))) = multiply(inverse(b),inverse(a)),
inference(transitivity,[status(thm)],[356,349,347,336,334]) ).
tff(358,plain,
multiply(multiply(inverse(a),multiply(inverse(b),inverse(h))),a) = multiply(multiply(inverse(b),inverse(a)),a),
inference(monotonicity,[status(thm)],[357]) ).
tff(359,plain,
multiply(multiply(inverse(b),inverse(a)),a) = multiply(multiply(inverse(a),multiply(inverse(b),inverse(h))),a),
inference(symmetry,[status(thm)],[358]) ).
tff(360,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(b),inverse(a)),a) = multiply(inverse(b),multiply(inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(361,plain,
multiply(multiply(inverse(b),inverse(a)),a) = multiply(inverse(b),multiply(inverse(a),a)),
inference(unit_resolution,[status(thm)],[360,35]) ).
tff(362,plain,
multiply(inverse(b),multiply(inverse(a),a)) = multiply(multiply(inverse(b),inverse(a)),a),
inference(symmetry,[status(thm)],[361]) ).
tff(363,plain,
multiply(inverse(b),multiply(inverse(a),a)) = multiply(inverse(b),identity),
inference(monotonicity,[status(thm)],[169]) ).
tff(364,plain,
multiply(inverse(b),identity) = multiply(inverse(b),multiply(inverse(a),a)),
inference(symmetry,[status(thm)],[363]) ).
tff(365,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(inverse(b),identity) = inverse(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(366,plain,
multiply(inverse(b),identity) = inverse(b),
inference(unit_resolution,[status(thm)],[365,16]) ).
tff(367,plain,
inverse(b) = multiply(inverse(b),identity),
inference(symmetry,[status(thm)],[366]) ).
tff(368,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,inverse(b)) = inverse(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(369,plain,
multiply(identity,inverse(b)) = inverse(b),
inference(unit_resolution,[status(thm)],[368,44]) ).
tff(370,plain,
identity = multiply(h,inverse(h)),
inference(symmetry,[status(thm)],[259]) ).
tff(371,plain,
multiply(identity,inverse(b)) = multiply(multiply(h,inverse(h)),inverse(b)),
inference(monotonicity,[status(thm)],[370]) ).
tff(372,plain,
multiply(multiply(h,inverse(h)),inverse(b)) = multiply(identity,inverse(b)),
inference(symmetry,[status(thm)],[371]) ).
tff(373,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(h,inverse(h)),inverse(b)) = multiply(h,multiply(inverse(h),inverse(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(374,plain,
multiply(multiply(h,inverse(h)),inverse(b)) = multiply(h,multiply(inverse(h),inverse(b))),
inference(unit_resolution,[status(thm)],[373,35]) ).
tff(375,plain,
multiply(h,multiply(inverse(h),inverse(b))) = multiply(multiply(h,inverse(h)),inverse(b)),
inference(symmetry,[status(thm)],[374]) ).
tff(376,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,multiply(inverse(h),inverse(b))) = multiply(inverse(h),inverse(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(377,plain,
multiply(identity,multiply(inverse(h),inverse(b))) = multiply(inverse(h),inverse(b)),
inference(unit_resolution,[status(thm)],[376,44]) ).
tff(378,plain,
multiply(inverse(h),inverse(b)) = multiply(identity,multiply(inverse(h),inverse(b))),
inference(symmetry,[status(thm)],[377]) ).
tff(379,plain,
multiply(h,multiply(inverse(h),inverse(b))) = multiply(h,multiply(identity,multiply(inverse(h),inverse(b)))),
inference(monotonicity,[status(thm)],[378]) ).
tff(380,plain,
multiply(h,multiply(identity,multiply(inverse(h),inverse(b)))) = multiply(h,multiply(inverse(h),inverse(b))),
inference(symmetry,[status(thm)],[379]) ).
tff(381,plain,
multiply(h,multiply(identity,multiply(inverse(h),inverse(b)))) = multiply(multiply(inverse(a),multiply(inverse(b),inverse(h))),a),
inference(transitivity,[status(thm)],[380,375,372,369,367,364,362,359]) ).
tff(382,plain,
multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(h,multiply(identity,multiply(inverse(h),inverse(b))))) = multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(multiply(inverse(a),multiply(inverse(b),inverse(h))),a)),
inference(monotonicity,[status(thm)],[381]) ).
tff(383,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(inverse(a),multiply(inverse(b),inverse(h))))) = multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(inverse(a),multiply(inverse(b),inverse(h)))),
inference(symmetry,[status(thm)],[311]) ).
tff(384,plain,
multiply(multiply(d,a),multiply(inverse(a),a)) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(inverse(a),multiply(inverse(b),inverse(h))))),
inference(symmetry,[status(thm)],[309]) ).
tff(385,plain,
multiply(d,a) = multiply(multiply(multiply(d,a),inverse(a)),a),
inference(symmetry,[status(thm)],[299]) ).
tff(386,plain,
multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)) = multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(inverse(a),multiply(inverse(b),inverse(h)))),
inference(transitivity,[status(thm)],[296,293,385,301,384,383]) ).
tff(387,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(inverse(a),multiply(inverse(b),inverse(h))))),
inference(monotonicity,[status(thm)],[386]) ).
tff(388,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(inverse(a),multiply(inverse(b),inverse(h))))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),
inference(symmetry,[status(thm)],[387]) ).
tff(389,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)))),multiply(inverse(a),multiply(inverse(b),inverse(h)))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(inverse(a),multiply(inverse(b),inverse(h))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(390,plain,
multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)))),multiply(inverse(a),multiply(inverse(b),inverse(h)))) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(inverse(a),multiply(inverse(b),inverse(h))))),
inference(unit_resolution,[status(thm)],[389,35]) ).
tff(391,plain,
( ~ ! [X: $i] : ( multiply(X,multiply(X,X)) = identity )
| ( multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(392,plain,
multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)))) = identity,
inference(unit_resolution,[status(thm)],[391,158]) ).
tff(393,plain,
multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)))),multiply(inverse(a),multiply(inverse(b),inverse(h)))) = multiply(identity,multiply(inverse(a),multiply(inverse(b),inverse(h)))),
inference(monotonicity,[status(thm)],[392]) ).
tff(394,plain,
multiply(identity,multiply(inverse(a),multiply(inverse(b),inverse(h)))) = multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)))),multiply(inverse(a),multiply(inverse(b),inverse(h)))),
inference(symmetry,[status(thm)],[393]) ).
tff(395,plain,
multiply(multiply(inverse(a),inverse(b)),inverse(h)) = multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),
inference(transitivity,[status(thm)],[318,356,349,394,390,388]) ).
tff(396,plain,
multiply(multiply(multiply(inverse(a),inverse(b)),inverse(h)),multiply(h,multiply(identity,multiply(inverse(h),inverse(b))))) = multiply(multiply(multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),a))),multiply(h,multiply(identity,multiply(inverse(h),inverse(b))))),
inference(monotonicity,[status(thm)],[395]) ).
tff(397,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(inverse(a),inverse(b)),inverse(h)),multiply(h,multiply(identity,multiply(inverse(h),inverse(b))))) = multiply(multiply(inverse(a),inverse(b)),multiply(inverse(h),multiply(h,multiply(identity,multiply(inverse(h),inverse(b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(398,plain,
multiply(multiply(multiply(inverse(a),inverse(b)),inverse(h)),multiply(h,multiply(identity,multiply(inverse(h),inverse(b))))) = multiply(multiply(inverse(a),inverse(b)),multiply(inverse(h),multiply(h,multiply(identity,multiply(inverse(h),inverse(b)))))),
inference(unit_resolution,[status(thm)],[397,35]) ).
tff(399,plain,
multiply(multiply(inverse(a),inverse(b)),multiply(inverse(h),multiply(h,multiply(identity,multiply(inverse(h),inverse(b)))))) = multiply(multiply(multiply(inverse(a),inverse(b)),inverse(h)),multiply(h,multiply(identity,multiply(inverse(h),inverse(b))))),
inference(symmetry,[status(thm)],[398]) ).
tff(400,plain,
multiply(inverse(h),multiply(h,multiply(identity,multiply(inverse(h),inverse(b))))) = multiply(inverse(h),multiply(h,multiply(inverse(h),inverse(b)))),
inference(monotonicity,[status(thm)],[380]) ).
tff(401,plain,
multiply(inverse(h),multiply(h,multiply(inverse(h),inverse(b)))) = multiply(inverse(h),multiply(h,multiply(identity,multiply(inverse(h),inverse(b))))),
inference(symmetry,[status(thm)],[400]) ).
tff(402,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(h),h),multiply(inverse(h),inverse(b))) = multiply(inverse(h),multiply(h,multiply(inverse(h),inverse(b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(403,plain,
multiply(multiply(inverse(h),h),multiply(inverse(h),inverse(b))) = multiply(inverse(h),multiply(h,multiply(inverse(h),inverse(b)))),
inference(unit_resolution,[status(thm)],[402,35]) ).
tff(404,plain,
multiply(multiply(inverse(h),h),multiply(inverse(h),inverse(b))) = multiply(identity,multiply(inverse(h),inverse(b))),
inference(monotonicity,[status(thm)],[48]) ).
tff(405,plain,
multiply(identity,multiply(inverse(h),inverse(b))) = multiply(multiply(inverse(h),h),multiply(inverse(h),inverse(b))),
inference(symmetry,[status(thm)],[404]) ).
tff(406,plain,
multiply(inverse(h),inverse(b)) = multiply(inverse(h),multiply(h,multiply(identity,multiply(inverse(h),inverse(b))))),
inference(transitivity,[status(thm)],[378,405,403,401]) ).
tff(407,plain,
multiply(multiply(inverse(a),inverse(b)),multiply(inverse(h),inverse(b))) = multiply(multiply(inverse(a),inverse(b)),multiply(inverse(h),multiply(h,multiply(identity,multiply(inverse(h),inverse(b)))))),
inference(monotonicity,[status(thm)],[406]) ).
tff(408,plain,
multiply(multiply(inverse(a),inverse(b)),multiply(identity,multiply(inverse(h),inverse(b)))) = multiply(multiply(inverse(a),inverse(b)),multiply(inverse(h),inverse(b))),
inference(monotonicity,[status(thm)],[377]) ).
tff(409,plain,
multiply(multiply(inverse(a),inverse(b)),multiply(identity,multiply(inverse(h),inverse(b)))) = multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a))),
inference(transitivity,[status(thm)],[408,407,399,396,382,316,313,298,287,284,104,107]) ).
tff(410,plain,
multiply(multiply(k,c),multiply(multiply(inverse(a),inverse(b)),multiply(identity,multiply(inverse(h),inverse(b))))) = multiply(multiply(k,multiply(a,b)),multiply(c,multiply(multiply(multiply(inverse(a),inverse(b)),b),inverse(a)))),
inference(monotonicity,[status(thm)],[238,409]) ).
tff(411,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(k,c),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(h),inverse(b)))) = multiply(multiply(k,c),multiply(multiply(inverse(a),inverse(b)),multiply(identity,multiply(inverse(h),inverse(b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(412,plain,
multiply(multiply(multiply(k,c),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(h),inverse(b)))) = multiply(multiply(k,c),multiply(multiply(inverse(a),inverse(b)),multiply(identity,multiply(inverse(h),inverse(b))))),
inference(unit_resolution,[status(thm)],[411,35]) ).
tff(413,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(k,c),multiply(inverse(a),inverse(b))) = multiply(k,multiply(c,multiply(inverse(a),inverse(b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(414,plain,
multiply(multiply(k,c),multiply(inverse(a),inverse(b))) = multiply(k,multiply(c,multiply(inverse(a),inverse(b)))),
inference(unit_resolution,[status(thm)],[413,35]) ).
tff(415,plain,
multiply(k,multiply(c,multiply(inverse(a),inverse(b)))) = multiply(multiply(k,c),multiply(inverse(a),inverse(b))),
inference(symmetry,[status(thm)],[414]) ).
tff(416,plain,
k = multiply(j,inverse(h)),
inference(symmetry,[status(thm)],[227]) ).
tff(417,plain,
k = multiply(d,inverse(h)),
inference(transitivity,[status(thm)],[416,233]) ).
tff(418,plain,
multiply(k,multiply(c,multiply(inverse(a),inverse(b)))) = multiply(multiply(d,inverse(h)),h),
inference(monotonicity,[status(thm)],[417,77]) ).
tff(419,plain,
multiply(multiply(d,inverse(h)),h) = multiply(k,multiply(c,multiply(inverse(a),inverse(b)))),
inference(symmetry,[status(thm)],[418]) ).
tff(420,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(d,inverse(h)),h) = multiply(d,multiply(inverse(h),h)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(421,plain,
multiply(multiply(d,inverse(h)),h) = multiply(d,multiply(inverse(h),h)),
inference(unit_resolution,[status(thm)],[420,35]) ).
tff(422,plain,
multiply(d,multiply(inverse(h),h)) = multiply(multiply(d,inverse(h)),h),
inference(symmetry,[status(thm)],[421]) ).
tff(423,plain,
multiply(inverse(h),h) = multiply(inverse(b),b),
inference(transitivity,[status(thm)],[48,214]) ).
tff(424,plain,
multiply(d,multiply(inverse(h),h)) = multiply(d,multiply(inverse(b),b)),
inference(monotonicity,[status(thm)],[423]) ).
tff(425,plain,
multiply(d,multiply(inverse(b),b)) = multiply(d,multiply(inverse(h),h)),
inference(symmetry,[status(thm)],[424]) ).
tff(426,plain,
d = multiply(multiply(k,c),multiply(inverse(a),inverse(b))),
inference(transitivity,[status(thm)],[83,82,425,422,419,415]) ).
tff(427,plain,
multiply(d,multiply(identity,multiply(inverse(h),inverse(b)))) = multiply(multiply(multiply(k,c),multiply(inverse(a),inverse(b))),multiply(identity,multiply(inverse(h),inverse(b)))),
inference(monotonicity,[status(thm)],[426]) ).
tff(428,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(d,identity),multiply(inverse(h),inverse(b))) = multiply(d,multiply(identity,multiply(inverse(h),inverse(b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(429,plain,
multiply(multiply(d,identity),multiply(inverse(h),inverse(b))) = multiply(d,multiply(identity,multiply(inverse(h),inverse(b)))),
inference(unit_resolution,[status(thm)],[428,35]) ).
tff(430,plain,
j = multiply(d,identity),
inference(transitivity,[status(thm)],[231,64,59,57]) ).
tff(431,plain,
multiply(j,multiply(inverse(h),inverse(b))) = multiply(multiply(d,identity),multiply(inverse(h),inverse(b))),
inference(monotonicity,[status(thm)],[430]) ).
tff(432,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(j,inverse(h)),inverse(b)) = multiply(j,multiply(inverse(h),inverse(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(433,plain,
multiply(multiply(j,inverse(h)),inverse(b)) = multiply(j,multiply(inverse(h),inverse(b))),
inference(unit_resolution,[status(thm)],[432,35]) ).
tff(434,plain,
multiply(k,inverse(b)) = multiply(multiply(j,inverse(h)),inverse(b)),
inference(monotonicity,[status(thm)],[416]) ).
tff(435,plain,
multiply(k,inverse(b)) = identity,
inference(transitivity,[status(thm)],[434,433,431,429,427,412,410,278,141,118,114,112,100,93,90,9]) ).
tff(436,plain,
( ( multiply(k,inverse(b)) != identity )
<=> ( multiply(k,inverse(b)) != identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(437,axiom,
multiply(k,inverse(b)) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
tff(438,plain,
multiply(k,inverse(b)) != identity,
inference(modus_ponens,[status(thm)],[437,436]) ).
tff(439,plain,
$false,
inference(unit_resolution,[status(thm)],[438,435]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP002-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.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 : Thu Jun 19 15:27:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 18.98/19.21 % SZS status Unsatisfiable
% 18.98/19.21 % SZS output start Proof
% See solution above
% 19.04/19.25 % E exiting
%------------------------------------------------------------------------------