%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP114-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:07:01 AM UTC 2025
% Result : Unsatisfiable 9.77s 9.97s
% Output : Proof 9.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 97
% Syntax : Number of formulae : 324 ( 245 unt; 0 typ; 0 def)
% Number of atoms : 433 ( 417 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 143 ( 49 ~; 45 |; 0 &)
% ( 49 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 15 ( 15 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 : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 384 ( 352 !; 0 ?; 384 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_type,type,
a: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(negative_part_type,type,
negative_part: $i > $i ).
tff(positive_part_type,type,
positive_part: $i > $i ).
tff(identity_type,type,
identity: $i ).
tff(intersection_type,type,
intersection: ( $i * $i ) > $i ).
tff(union_type,type,
union: ( $i * $i ) > $i ).
tff(inverse_type,type,
inverse: $i > $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/sandbox2/benchmark/Axioms/GRP004-0.ax',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,
^ [Y: $i,X: $i] :
refl(( ( intersection(union(X,Y),Y) = Y )
<=> ( intersection(union(X,Y),Y) = Y ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( intersection(union(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( intersection(union(X,Y),Y) = Y ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( intersection(union(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( intersection(union(X,Y),Y) = Y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( intersection(union(X,Y),Y) = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_union_absorbtion) ).
tff(14,plain,
! [Y: $i,X: $i] : ( intersection(union(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( intersection(union(X,Y),Y) = Y ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( intersection(union(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( intersection(union(X,Y),Y) = Y )
| ( intersection(union(a,identity),identity) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
intersection(union(a,identity),identity) = identity,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Y: $i,X: $i] :
refl(( ( intersection(X,Y) = intersection(Y,X) )
<=> ( intersection(X,Y) = intersection(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [Y: $i,X: $i] : ( intersection(X,Y) = intersection(Y,X) )
<=> ! [Y: $i,X: $i] : ( intersection(X,Y) = intersection(Y,X) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [Y: $i,X: $i] : ( intersection(X,Y) = intersection(Y,X) )
<=> ! [Y: $i,X: $i] : ( intersection(X,Y) = intersection(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [Y: $i,X: $i] : ( intersection(X,Y) = intersection(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_commutative) ).
tff(23,plain,
! [Y: $i,X: $i] : ( intersection(X,Y) = intersection(Y,X) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Y: $i,X: $i] : ( intersection(X,Y) = intersection(Y,X) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( intersection(X,Y) = intersection(Y,X) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] : ( intersection(X,Y) = intersection(Y,X) )
| ( intersection(identity,union(a,identity)) = intersection(union(a,identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
intersection(identity,union(a,identity)) = intersection(union(a,identity),identity),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
intersection(identity,union(a,identity)) = identity,
inference(transitivity,[status(thm)],[27,18]) ).
tff(29,plain,
multiply(intersection(identity,union(a,identity)),a) = multiply(identity,a),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(intersection(Y,Z),X) = intersection(multiply(Y,X),multiply(Z,X)) )
<=> ( multiply(intersection(Y,Z),X) = intersection(multiply(Y,X),multiply(Z,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(intersection(Y,Z),X) = intersection(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(intersection(Y,Z),X) = intersection(multiply(Y,X),multiply(Z,X)) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(intersection(Y,Z),X) = intersection(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(intersection(Y,Z),X) = intersection(multiply(Y,X),multiply(Z,X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(intersection(Y,Z),X) = intersection(multiply(Y,X),multiply(Z,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_intersection2) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(intersection(Y,Z),X) = intersection(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(intersection(Y,Z),X) = intersection(multiply(Y,X),multiply(Z,X)) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(intersection(Y,Z),X) = intersection(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(intersection(Y,Z),X) = intersection(multiply(Y,X),multiply(Z,X)) )
| ( multiply(intersection(identity,union(a,identity)),a) = intersection(multiply(identity,a),multiply(union(a,identity),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
multiply(intersection(identity,union(a,identity)),a) = intersection(multiply(identity,a),multiply(union(a,identity),a)),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
intersection(multiply(identity,a),multiply(union(a,identity),a)) = multiply(intersection(identity,union(a,identity)),a),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(union(Y,Z),X) = union(multiply(Y,X),multiply(Z,X)) )
<=> ( multiply(union(Y,Z),X) = union(multiply(Y,X),multiply(Z,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(union(Y,Z),X) = union(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(union(Y,Z),X) = union(multiply(Y,X),multiply(Z,X)) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(union(Y,Z),X) = union(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(union(Y,Z),X) = union(multiply(Y,X),multiply(Z,X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(union(Y,Z),X) = union(multiply(Y,X),multiply(Z,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_union2) ).
tff(44,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(union(Y,Z),X) = union(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(union(Y,Z),X) = union(multiply(Y,X),multiply(Z,X)) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(union(Y,Z),X) = union(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(union(Y,Z),X) = union(multiply(Y,X),multiply(Z,X)) )
| ( multiply(union(a,identity),a) = union(multiply(a,a),multiply(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
multiply(union(a,identity),a) = union(multiply(a,a),multiply(identity,a)),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
union(multiply(a,a),multiply(identity,a)) = multiply(union(a,identity),a),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
a = multiply(identity,a),
inference(symmetry,[status(thm)],[9]) ).
tff(51,plain,
( ~ ! [Y: $i,X: $i] : ( intersection(union(X,Y),Y) = Y )
| ( intersection(union(identity,a),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
intersection(union(identity,a),a) = a,
inference(unit_resolution,[status(thm)],[51,16]) ).
tff(53,plain,
^ [Y: $i,X: $i] :
refl(( ( union(X,Y) = union(Y,X) )
<=> ( union(X,Y) = union(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [Y: $i,X: $i] : ( union(X,Y) = union(Y,X) )
<=> ! [Y: $i,X: $i] : ( union(X,Y) = union(Y,X) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [Y: $i,X: $i] : ( union(X,Y) = union(Y,X) )
<=> ! [Y: $i,X: $i] : ( union(X,Y) = union(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
! [Y: $i,X: $i] : ( union(X,Y) = union(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_commutative) ).
tff(57,plain,
! [Y: $i,X: $i] : ( union(X,Y) = union(Y,X) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [Y: $i,X: $i] : ( union(X,Y) = union(Y,X) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [Y: $i,X: $i] : ( union(X,Y) = union(Y,X) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( ~ ! [Y: $i,X: $i] : ( union(X,Y) = union(Y,X) )
| ( union(identity,a) = union(a,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
union(identity,a) = union(a,identity),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
union(a,identity) = union(identity,a),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
intersection(union(a,identity),a) = intersection(union(identity,a),a),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ~ ! [Y: $i,X: $i] : ( intersection(X,Y) = intersection(Y,X) )
| ( intersection(a,union(a,identity)) = intersection(union(a,identity),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
intersection(a,union(a,identity)) = intersection(union(a,identity),a),
inference(unit_resolution,[status(thm)],[64,25]) ).
tff(66,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,union(a,identity)) = union(a,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
multiply(identity,union(a,identity)) = union(a,identity),
inference(unit_resolution,[status(thm)],[66,7]) ).
tff(68,plain,
^ [X: $i] :
refl(( ( positive_part(X) = union(X,identity) )
<=> ( positive_part(X) = union(X,identity) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [X: $i] : ( positive_part(X) = union(X,identity) )
<=> ! [X: $i] : ( positive_part(X) = union(X,identity) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [X: $i] : ( positive_part(X) = union(X,identity) )
<=> ! [X: $i] : ( positive_part(X) = union(X,identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
! [X: $i] : ( positive_part(X) = union(X,identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',positive_part) ).
tff(72,plain,
! [X: $i] : ( positive_part(X) = union(X,identity) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [X: $i] : ( positive_part(X) = union(X,identity) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [X: $i] : ( positive_part(X) = union(X,identity) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
( ~ ! [X: $i] : ( positive_part(X) = union(X,identity) )
| ( positive_part(a) = union(a,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
positive_part(a) = union(a,identity),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
union(a,identity) = positive_part(a),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
inverse(union(a,identity)) = inverse(positive_part(a)),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
inverse(positive_part(a)) = inverse(union(a,identity)),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
inverse(inverse(positive_part(a))) = inverse(inverse(union(a,identity))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
inverse(inverse(union(a,identity))) = inverse(inverse(positive_part(a))),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
( ! [X: $i] : ( inverse(inverse(X)) = X )
<=> ! [X: $i] : ( inverse(inverse(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ! [X: $i] : ( inverse(inverse(X)) = X )
<=> ! [X: $i] : ( inverse(inverse(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,axiom,
! [X: $i] : ( inverse(inverse(X)) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_involution) ).
tff(85,plain,
! [X: $i] : ( inverse(inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [X: $i] : ( inverse(inverse(X)) = X ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [X: $i] : ( inverse(inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
( ~ ! [X: $i] : ( inverse(inverse(X)) = X )
| ( inverse(inverse(union(a,identity))) = union(a,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
inverse(inverse(union(a,identity))) = union(a,identity),
inference(unit_resolution,[status(thm)],[88,87]) ).
tff(90,plain,
union(a,identity) = inverse(inverse(union(a,identity))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
union(a,identity) = inverse(inverse(positive_part(a))),
inference(transitivity,[status(thm)],[90,81]) ).
tff(92,plain,
multiply(union(a,identity),inverse(positive_part(a))) = multiply(inverse(inverse(positive_part(a))),inverse(positive_part(a))),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
multiply(inverse(inverse(positive_part(a))),inverse(positive_part(a))) = multiply(union(a,identity),inverse(positive_part(a))),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
^ [X: $i] :
refl(( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(98,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(inverse(positive_part(a))),inverse(positive_part(a))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
multiply(inverse(inverse(positive_part(a))),inverse(positive_part(a))) = identity,
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
identity = multiply(inverse(inverse(positive_part(a))),inverse(positive_part(a))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
identity = multiply(union(a,identity),inverse(positive_part(a))),
inference(transitivity,[status(thm)],[103,93]) ).
tff(105,plain,
multiply(identity,union(a,identity)) = multiply(multiply(union(a,identity),inverse(positive_part(a))),union(a,identity)),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
multiply(multiply(union(a,identity),inverse(positive_part(a))),union(a,identity)) = multiply(identity,union(a,identity)),
inference(symmetry,[status(thm)],[105]) ).
tff(107,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(108,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)],[107]) ).
tff(109,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(110,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(111,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[111]) ).
tff(113,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(union(a,identity),inverse(positive_part(a))),union(a,identity)) = multiply(union(a,identity),multiply(inverse(positive_part(a)),union(a,identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
multiply(multiply(union(a,identity),inverse(positive_part(a))),union(a,identity)) = multiply(union(a,identity),multiply(inverse(positive_part(a)),union(a,identity))),
inference(unit_resolution,[status(thm)],[114,113]) ).
tff(116,plain,
multiply(union(a,identity),multiply(inverse(positive_part(a)),union(a,identity))) = multiply(multiply(union(a,identity),inverse(positive_part(a))),union(a,identity)),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(union(a,identity)),union(a,identity)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
multiply(inverse(union(a,identity)),union(a,identity)) = identity,
inference(unit_resolution,[status(thm)],[117,100]) ).
tff(119,plain,
multiply(inverse(positive_part(a)),union(a,identity)) = multiply(inverse(union(a,identity)),union(a,identity)),
inference(monotonicity,[status(thm)],[79]) ).
tff(120,plain,
multiply(inverse(positive_part(a)),union(a,identity)) = identity,
inference(transitivity,[status(thm)],[119,118]) ).
tff(121,plain,
multiply(union(a,identity),multiply(inverse(positive_part(a)),union(a,identity))) = multiply(union(a,identity),identity),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
multiply(union(a,identity),identity) = multiply(union(a,identity),multiply(inverse(positive_part(a)),union(a,identity))),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(union(Y,Z),X) = union(multiply(Y,X),multiply(Z,X)) )
| ( multiply(union(a,identity),identity) = union(multiply(a,identity),multiply(identity,identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
multiply(union(a,identity),identity) = union(multiply(a,identity),multiply(identity,identity)),
inference(unit_resolution,[status(thm)],[123,46]) ).
tff(125,plain,
union(multiply(a,identity),multiply(identity,identity)) = multiply(union(a,identity),identity),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
union(multiply(a,identity),multiply(identity,identity)) = union(a,identity),
inference(transitivity,[status(thm)],[125,122,116,106,67]) ).
tff(127,plain,
intersection(a,union(multiply(a,identity),multiply(identity,identity))) = intersection(a,union(a,identity)),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
intersection(a,union(multiply(a,identity),multiply(identity,identity))) = multiply(identity,a),
inference(transitivity,[status(thm)],[127,65,63,52,50]) ).
tff(129,plain,
intersection(intersection(a,union(multiply(a,identity),multiply(identity,identity))),union(multiply(a,a),multiply(identity,a))) = intersection(multiply(identity,a),multiply(union(a,identity),a)),
inference(monotonicity,[status(thm)],[128,49]) ).
tff(130,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( intersection(X,intersection(Y,Z)) = intersection(intersection(X,Y),Z) )
<=> ( intersection(X,intersection(Y,Z)) = intersection(intersection(X,Y),Z) ) )),
inference(bind,[status(th)],[]) ).
tff(131,plain,
( ! [Z: $i,Y: $i,X: $i] : ( intersection(X,intersection(Y,Z)) = intersection(intersection(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( intersection(X,intersection(Y,Z)) = intersection(intersection(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
( ! [Z: $i,Y: $i,X: $i] : ( intersection(X,intersection(Y,Z)) = intersection(intersection(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( intersection(X,intersection(Y,Z)) = intersection(intersection(X,Y),Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,axiom,
! [Z: $i,Y: $i,X: $i] : ( intersection(X,intersection(Y,Z)) = intersection(intersection(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_associative) ).
tff(134,plain,
! [Z: $i,Y: $i,X: $i] : ( intersection(X,intersection(Y,Z)) = intersection(intersection(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [Z: $i,Y: $i,X: $i] : ( intersection(X,intersection(Y,Z)) = intersection(intersection(X,Y),Z) ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [Z: $i,Y: $i,X: $i] : ( intersection(X,intersection(Y,Z)) = intersection(intersection(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( intersection(X,intersection(Y,Z)) = intersection(intersection(X,Y),Z) )
| ( intersection(a,intersection(union(multiply(a,identity),multiply(identity,identity)),union(multiply(a,a),multiply(identity,a)))) = intersection(intersection(a,union(multiply(a,identity),multiply(identity,identity))),union(multiply(a,a),multiply(identity,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
intersection(a,intersection(union(multiply(a,identity),multiply(identity,identity)),union(multiply(a,a),multiply(identity,a)))) = intersection(intersection(a,union(multiply(a,identity),multiply(identity,identity))),union(multiply(a,a),multiply(identity,a))),
inference(unit_resolution,[status(thm)],[137,136]) ).
tff(139,plain,
intersection(union(multiply(a,identity),multiply(identity,identity)),union(multiply(a,a),multiply(identity,a))) = intersection(multiply(union(a,identity),identity),multiply(union(a,identity),a)),
inference(monotonicity,[status(thm)],[125,49]) ).
tff(140,plain,
intersection(multiply(union(a,identity),identity),multiply(union(a,identity),a)) = intersection(union(multiply(a,identity),multiply(identity,identity)),union(multiply(a,a),multiply(identity,a))),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
( ~ ! [Y: $i,X: $i] : ( intersection(X,Y) = intersection(Y,X) )
| ( intersection(multiply(union(a,identity),identity),multiply(union(a,identity),a)) = intersection(multiply(union(a,identity),a),multiply(union(a,identity),identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
intersection(multiply(union(a,identity),identity),multiply(union(a,identity),a)) = intersection(multiply(union(a,identity),a),multiply(union(a,identity),identity)),
inference(unit_resolution,[status(thm)],[141,25]) ).
tff(143,plain,
intersection(multiply(union(a,identity),a),multiply(union(a,identity),identity)) = intersection(multiply(union(a,identity),identity),multiply(union(a,identity),a)),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(X,intersection(Y,Z)) = intersection(multiply(X,Y),multiply(X,Z)) )
<=> ( multiply(X,intersection(Y,Z)) = intersection(multiply(X,Y),multiply(X,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(145,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,intersection(Y,Z)) = intersection(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,intersection(Y,Z)) = intersection(multiply(X,Y),multiply(X,Z)) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,intersection(Y,Z)) = intersection(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,intersection(Y,Z)) = intersection(multiply(X,Y),multiply(X,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,intersection(Y,Z)) = intersection(multiply(X,Y),multiply(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_intersection1) ).
tff(148,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,intersection(Y,Z)) = intersection(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,intersection(Y,Z)) = intersection(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[148]) ).
tff(150,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,intersection(Y,Z)) = intersection(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[149,145]) ).
tff(151,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,intersection(Y,Z)) = intersection(multiply(X,Y),multiply(X,Z)) )
| ( multiply(union(a,identity),intersection(a,identity)) = intersection(multiply(union(a,identity),a),multiply(union(a,identity),identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(152,plain,
multiply(union(a,identity),intersection(a,identity)) = intersection(multiply(union(a,identity),a),multiply(union(a,identity),identity)),
inference(unit_resolution,[status(thm)],[151,150]) ).
tff(153,plain,
^ [X: $i] :
refl(( ( negative_part(X) = intersection(X,identity) )
<=> ( negative_part(X) = intersection(X,identity) ) )),
inference(bind,[status(th)],[]) ).
tff(154,plain,
( ! [X: $i] : ( negative_part(X) = intersection(X,identity) )
<=> ! [X: $i] : ( negative_part(X) = intersection(X,identity) ) ),
inference(quant_intro,[status(thm)],[153]) ).
tff(155,plain,
( ! [X: $i] : ( negative_part(X) = intersection(X,identity) )
<=> ! [X: $i] : ( negative_part(X) = intersection(X,identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,axiom,
! [X: $i] : ( negative_part(X) = intersection(X,identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',negative_part) ).
tff(157,plain,
! [X: $i] : ( negative_part(X) = intersection(X,identity) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
! [X: $i] : ( negative_part(X) = intersection(X,identity) ),
inference(skolemize,[status(sab)],[157]) ).
tff(159,plain,
! [X: $i] : ( negative_part(X) = intersection(X,identity) ),
inference(modus_ponens,[status(thm)],[158,154]) ).
tff(160,plain,
( ~ ! [X: $i] : ( negative_part(X) = intersection(X,identity) )
| ( negative_part(a) = intersection(a,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(161,plain,
negative_part(a) = intersection(a,identity),
inference(unit_resolution,[status(thm)],[160,159]) ).
tff(162,plain,
intersection(a,identity) = negative_part(a),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
multiply(union(a,identity),intersection(a,identity)) = multiply(positive_part(a),negative_part(a)),
inference(monotonicity,[status(thm)],[77,162]) ).
tff(164,plain,
multiply(positive_part(a),negative_part(a)) = multiply(union(a,identity),intersection(a,identity)),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
( ~ ! [X: $i] : ( inverse(inverse(X)) = X )
| ( inverse(inverse(multiply(positive_part(a),negative_part(a)))) = multiply(positive_part(a),negative_part(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(166,plain,
inverse(inverse(multiply(positive_part(a),negative_part(a)))) = multiply(positive_part(a),negative_part(a)),
inference(unit_resolution,[status(thm)],[165,87]) ).
tff(167,plain,
^ [Y: $i,X: $i] :
refl(( ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
<=> ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(168,plain,
( ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
<=> ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ) ),
inference(quant_intro,[status(thm)],[167]) ).
tff(169,plain,
( ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
<=> ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(170,axiom,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product_lemma) ).
tff(171,plain,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
inference(skolemize,[status(sab)],[171]) ).
tff(173,plain,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
inference(modus_ponens,[status(thm)],[172,168]) ).
tff(174,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
| ( inverse(multiply(positive_part(a),negative_part(a))) = multiply(inverse(negative_part(a)),inverse(positive_part(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
inverse(multiply(positive_part(a),negative_part(a))) = multiply(inverse(negative_part(a)),inverse(positive_part(a))),
inference(unit_resolution,[status(thm)],[174,173]) ).
tff(176,plain,
inverse(inverse(multiply(positive_part(a),negative_part(a)))) = inverse(multiply(inverse(negative_part(a)),inverse(positive_part(a)))),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
inverse(multiply(inverse(negative_part(a)),inverse(positive_part(a)))) = inverse(inverse(multiply(positive_part(a),negative_part(a)))),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,multiply(inverse(negative_part(a)),inverse(positive_part(a)))) = multiply(inverse(negative_part(a)),inverse(positive_part(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
multiply(identity,multiply(inverse(negative_part(a)),inverse(positive_part(a)))) = multiply(inverse(negative_part(a)),inverse(positive_part(a))),
inference(unit_resolution,[status(thm)],[178,7]) ).
tff(180,plain,
multiply(inverse(negative_part(a)),inverse(positive_part(a))) = multiply(identity,multiply(inverse(negative_part(a)),inverse(positive_part(a)))),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
inverse(multiply(inverse(negative_part(a)),inverse(positive_part(a)))) = inverse(multiply(identity,multiply(inverse(negative_part(a)),inverse(positive_part(a))))),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
inverse(multiply(identity,multiply(inverse(negative_part(a)),inverse(positive_part(a))))) = inverse(multiply(inverse(negative_part(a)),inverse(positive_part(a)))),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
| ( inverse(multiply(identity,multiply(inverse(negative_part(a)),inverse(positive_part(a))))) = multiply(inverse(multiply(inverse(negative_part(a)),inverse(positive_part(a)))),inverse(identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
inverse(multiply(identity,multiply(inverse(negative_part(a)),inverse(positive_part(a))))) = multiply(inverse(multiply(inverse(negative_part(a)),inverse(positive_part(a)))),inverse(identity)),
inference(unit_resolution,[status(thm)],[183,173]) ).
tff(185,plain,
multiply(inverse(multiply(inverse(negative_part(a)),inverse(positive_part(a)))),inverse(identity)) = inverse(multiply(identity,multiply(inverse(negative_part(a)),inverse(positive_part(a))))),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
( ( inverse(identity) = identity )
<=> ( inverse(identity) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_of_identity) ).
tff(188,plain,
inverse(identity) = identity,
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
| ( inverse(multiply(inverse(negative_part(a)),inverse(positive_part(a)))) = multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(190,plain,
inverse(multiply(inverse(negative_part(a)),inverse(positive_part(a)))) = multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),
inference(unit_resolution,[status(thm)],[189,173]) ).
tff(191,plain,
multiply(inverse(multiply(inverse(negative_part(a)),inverse(positive_part(a)))),inverse(identity)) = multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity),
inference(monotonicity,[status(thm)],[190,188]) ).
tff(192,plain,
multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity) = multiply(inverse(multiply(inverse(negative_part(a)),inverse(positive_part(a)))),inverse(identity)),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( intersection(X,intersection(Y,Z)) = intersection(intersection(X,Y),Z) )
| ( intersection(union(a,identity),intersection(union(a,identity),identity)) = intersection(intersection(union(a,identity),union(a,identity)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(194,plain,
intersection(union(a,identity),intersection(union(a,identity),identity)) = intersection(intersection(union(a,identity),union(a,identity)),identity),
inference(unit_resolution,[status(thm)],[193,136]) ).
tff(195,plain,
intersection(union(a,identity),intersection(union(a,identity),identity)) = intersection(union(a,identity),identity),
inference(monotonicity,[status(thm)],[18]) ).
tff(196,plain,
intersection(union(a,identity),identity) = intersection(union(a,identity),intersection(union(a,identity),identity)),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
identity = intersection(union(a,identity),identity),
inference(symmetry,[status(thm)],[18]) ).
tff(198,plain,
identity = intersection(intersection(union(a,identity),union(a,identity)),identity),
inference(transitivity,[status(thm)],[197,196,194]) ).
tff(199,plain,
multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity) = multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(intersection(union(a,identity),union(a,identity)),identity)),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(intersection(union(a,identity),union(a,identity)),identity)) = multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,intersection(Y,Z)) = intersection(multiply(X,Y),multiply(X,Z)) )
| ( multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(intersection(union(a,identity),union(a,identity)),identity)) = intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(202,plain,
multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(intersection(union(a,identity),union(a,identity)),identity)) = intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity)),
inference(unit_resolution,[status(thm)],[201,150]) ).
tff(203,plain,
intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity)) = multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(intersection(union(a,identity),union(a,identity)),identity)),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity)) = intersection(union(multiply(a,identity),multiply(identity,identity)),union(multiply(a,a),multiply(identity,a))),
inference(transitivity,[status(thm)],[203,200,192,185,182,177,166,164,152,143,140]) ).
tff(205,plain,
intersection(a,intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity))) = intersection(a,intersection(union(multiply(a,identity),multiply(identity,identity)),union(multiply(a,a),multiply(identity,a)))),
inference(monotonicity,[status(thm)],[204]) ).
tff(206,plain,
( ~ ! [X: $i] : ( inverse(inverse(X)) = X )
| ( inverse(inverse(a)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(207,plain,
inverse(inverse(a)) = a,
inference(unit_resolution,[status(thm)],[206,87]) ).
tff(208,plain,
inverse(a) = inverse(multiply(identity,a)),
inference(monotonicity,[status(thm)],[50]) ).
tff(209,plain,
inverse(multiply(identity,a)) = inverse(a),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
| ( inverse(multiply(identity,a)) = multiply(inverse(a),inverse(identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(211,plain,
inverse(multiply(identity,a)) = multiply(inverse(a),inverse(identity)),
inference(unit_resolution,[status(thm)],[210,173]) ).
tff(212,plain,
multiply(inverse(a),inverse(identity)) = inverse(multiply(identity,a)),
inference(symmetry,[status(thm)],[211]) ).
tff(213,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,multiply(inverse(a),inverse(identity))) = multiply(inverse(a),inverse(identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(214,plain,
multiply(identity,multiply(inverse(a),inverse(identity))) = multiply(inverse(a),inverse(identity)),
inference(unit_resolution,[status(thm)],[213,7]) ).
tff(215,plain,
multiply(identity,multiply(inverse(a),inverse(identity))) = inverse(a),
inference(transitivity,[status(thm)],[214,212,209]) ).
tff(216,plain,
inverse(multiply(identity,multiply(inverse(a),inverse(identity)))) = inverse(inverse(a)),
inference(monotonicity,[status(thm)],[215]) ).
tff(217,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
| ( inverse(multiply(identity,multiply(inverse(a),inverse(identity)))) = multiply(inverse(multiply(inverse(a),inverse(identity))),inverse(identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(218,plain,
inverse(multiply(identity,multiply(inverse(a),inverse(identity)))) = multiply(inverse(multiply(inverse(a),inverse(identity))),inverse(identity)),
inference(unit_resolution,[status(thm)],[217,173]) ).
tff(219,plain,
multiply(inverse(multiply(inverse(a),inverse(identity))),inverse(identity)) = inverse(multiply(identity,multiply(inverse(a),inverse(identity)))),
inference(symmetry,[status(thm)],[218]) ).
tff(220,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[188]) ).
tff(221,plain,
multiply(inverse(a),inverse(identity)) = inverse(a),
inference(transitivity,[status(thm)],[212,209]) ).
tff(222,plain,
inverse(multiply(inverse(a),inverse(identity))) = inverse(inverse(a)),
inference(monotonicity,[status(thm)],[221]) ).
tff(223,plain,
inverse(inverse(a)) = inverse(multiply(inverse(a),inverse(identity))),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
a = inverse(inverse(a)),
inference(symmetry,[status(thm)],[207]) ).
tff(225,plain,
a = inverse(multiply(inverse(a),inverse(identity))),
inference(transitivity,[status(thm)],[224,223]) ).
tff(226,plain,
multiply(a,identity) = multiply(inverse(multiply(inverse(a),inverse(identity))),inverse(identity)),
inference(monotonicity,[status(thm)],[225,220]) ).
tff(227,plain,
^ [Y: $i,X: $i] :
refl(( ( union(intersection(X,Y),Y) = Y )
<=> ( union(intersection(X,Y),Y) = Y ) )),
inference(bind,[status(th)],[]) ).
tff(228,plain,
( ! [Y: $i,X: $i] : ( union(intersection(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( union(intersection(X,Y),Y) = Y ) ),
inference(quant_intro,[status(thm)],[227]) ).
tff(229,plain,
( ! [Y: $i,X: $i] : ( union(intersection(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( union(intersection(X,Y),Y) = Y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(230,axiom,
! [Y: $i,X: $i] : ( union(intersection(X,Y),Y) = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_intersection_absorbtion) ).
tff(231,plain,
! [Y: $i,X: $i] : ( union(intersection(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[230,229]) ).
tff(232,plain,
! [Y: $i,X: $i] : ( union(intersection(X,Y),Y) = Y ),
inference(skolemize,[status(sab)],[231]) ).
tff(233,plain,
! [Y: $i,X: $i] : ( union(intersection(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[232,228]) ).
tff(234,plain,
( ~ ! [Y: $i,X: $i] : ( union(intersection(X,Y),Y) = Y )
| ( union(intersection(multiply(a,a),multiply(a,identity)),multiply(a,identity)) = multiply(a,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(235,plain,
union(intersection(multiply(a,a),multiply(a,identity)),multiply(a,identity)) = multiply(a,identity),
inference(unit_resolution,[status(thm)],[234,233]) ).
tff(236,plain,
( ~ ! [Y: $i,X: $i] : ( union(intersection(X,Y),Y) = Y )
| ( union(intersection(identity,a),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(237,plain,
union(intersection(identity,a),a) = a,
inference(unit_resolution,[status(thm)],[236,233]) ).
tff(238,plain,
( ~ ! [Y: $i,X: $i] : ( intersection(X,Y) = intersection(Y,X) )
| ( intersection(identity,a) = intersection(a,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(239,plain,
intersection(identity,a) = intersection(a,identity),
inference(unit_resolution,[status(thm)],[238,25]) ).
tff(240,plain,
intersection(a,identity) = intersection(identity,a),
inference(symmetry,[status(thm)],[239]) ).
tff(241,plain,
union(intersection(a,identity),a) = union(intersection(identity,a),a),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
union(intersection(a,identity),a) = a,
inference(transitivity,[status(thm)],[241,237]) ).
tff(243,plain,
multiply(union(intersection(a,identity),a),identity) = multiply(a,identity),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(union(Y,Z),X) = union(multiply(Y,X),multiply(Z,X)) )
| ( multiply(union(intersection(a,identity),a),identity) = union(multiply(intersection(a,identity),identity),multiply(a,identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(245,plain,
multiply(union(intersection(a,identity),a),identity) = union(multiply(intersection(a,identity),identity),multiply(a,identity)),
inference(unit_resolution,[status(thm)],[244,46]) ).
tff(246,plain,
union(multiply(intersection(a,identity),identity),multiply(a,identity)) = multiply(union(intersection(a,identity),a),identity),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
inverse(intersection(a,identity)) = inverse(negative_part(a)),
inference(monotonicity,[status(thm)],[162]) ).
tff(248,plain,
inverse(negative_part(a)) = inverse(intersection(a,identity)),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,intersection(a,identity)) = intersection(a,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(250,plain,
multiply(identity,intersection(a,identity)) = intersection(a,identity),
inference(unit_resolution,[status(thm)],[249,7]) ).
tff(251,plain,
intersection(a,identity) = multiply(identity,intersection(a,identity)),
inference(symmetry,[status(thm)],[250]) ).
tff(252,plain,
negative_part(a) = multiply(identity,intersection(a,identity)),
inference(transitivity,[status(thm)],[161,251]) ).
tff(253,plain,
inverse(negative_part(a)) = inverse(multiply(identity,intersection(a,identity))),
inference(monotonicity,[status(thm)],[252]) ).
tff(254,plain,
inverse(multiply(identity,intersection(a,identity))) = inverse(negative_part(a)),
inference(symmetry,[status(thm)],[253]) ).
tff(255,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
| ( inverse(multiply(identity,intersection(a,identity))) = multiply(inverse(intersection(a,identity)),inverse(identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(256,plain,
inverse(multiply(identity,intersection(a,identity))) = multiply(inverse(intersection(a,identity)),inverse(identity)),
inference(unit_resolution,[status(thm)],[255,173]) ).
tff(257,plain,
multiply(inverse(intersection(a,identity)),inverse(identity)) = inverse(multiply(identity,intersection(a,identity))),
inference(symmetry,[status(thm)],[256]) ).
tff(258,plain,
multiply(inverse(intersection(a,identity)),inverse(identity)) = inverse(intersection(a,identity)),
inference(transitivity,[status(thm)],[257,254,248]) ).
tff(259,plain,
multiply(multiply(inverse(intersection(a,identity)),inverse(identity)),intersection(a,identity)) = multiply(inverse(intersection(a,identity)),intersection(a,identity)),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
multiply(inverse(intersection(a,identity)),intersection(a,identity)) = multiply(multiply(inverse(intersection(a,identity)),inverse(identity)),intersection(a,identity)),
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(intersection(a,identity)),intersection(a,identity)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(262,plain,
multiply(inverse(intersection(a,identity)),intersection(a,identity)) = identity,
inference(unit_resolution,[status(thm)],[261,100]) ).
tff(263,plain,
identity = multiply(inverse(intersection(a,identity)),intersection(a,identity)),
inference(symmetry,[status(thm)],[262]) ).
tff(264,plain,
identity = multiply(multiply(inverse(intersection(a,identity)),inverse(identity)),intersection(a,identity)),
inference(transitivity,[status(thm)],[263,260]) ).
tff(265,plain,
multiply(intersection(a,identity),identity) = multiply(intersection(a,identity),multiply(multiply(inverse(intersection(a,identity)),inverse(identity)),intersection(a,identity))),
inference(monotonicity,[status(thm)],[264]) ).
tff(266,plain,
multiply(intersection(a,identity),multiply(multiply(inverse(intersection(a,identity)),inverse(identity)),intersection(a,identity))) = multiply(intersection(a,identity),identity),
inference(symmetry,[status(thm)],[265]) ).
tff(267,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(intersection(a,identity),multiply(inverse(intersection(a,identity)),inverse(identity))),intersection(a,identity)) = multiply(intersection(a,identity),multiply(multiply(inverse(intersection(a,identity)),inverse(identity)),intersection(a,identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(268,plain,
multiply(multiply(intersection(a,identity),multiply(inverse(intersection(a,identity)),inverse(identity))),intersection(a,identity)) = multiply(intersection(a,identity),multiply(multiply(inverse(intersection(a,identity)),inverse(identity)),intersection(a,identity))),
inference(unit_resolution,[status(thm)],[267,113]) ).
tff(269,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(inverse(negative_part(a))),inverse(negative_part(a))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(270,plain,
multiply(inverse(inverse(negative_part(a))),inverse(negative_part(a))) = identity,
inference(unit_resolution,[status(thm)],[269,100]) ).
tff(271,plain,
multiply(inverse(intersection(a,identity)),inverse(identity)) = inverse(negative_part(a)),
inference(transitivity,[status(thm)],[257,254]) ).
tff(272,plain,
inverse(inverse(negative_part(a))) = inverse(inverse(intersection(a,identity))),
inference(monotonicity,[status(thm)],[248]) ).
tff(273,plain,
inverse(inverse(intersection(a,identity))) = inverse(inverse(negative_part(a))),
inference(symmetry,[status(thm)],[272]) ).
tff(274,plain,
( ~ ! [X: $i] : ( inverse(inverse(X)) = X )
| ( inverse(inverse(intersection(a,identity))) = intersection(a,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(275,plain,
inverse(inverse(intersection(a,identity))) = intersection(a,identity),
inference(unit_resolution,[status(thm)],[274,87]) ).
tff(276,plain,
intersection(a,identity) = inverse(inverse(intersection(a,identity))),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
intersection(a,identity) = inverse(inverse(negative_part(a))),
inference(transitivity,[status(thm)],[276,273]) ).
tff(278,plain,
multiply(intersection(a,identity),multiply(inverse(intersection(a,identity)),inverse(identity))) = multiply(inverse(inverse(negative_part(a))),inverse(negative_part(a))),
inference(monotonicity,[status(thm)],[277,271]) ).
tff(279,plain,
multiply(intersection(a,identity),multiply(inverse(intersection(a,identity)),inverse(identity))) = identity,
inference(transitivity,[status(thm)],[278,270]) ).
tff(280,plain,
multiply(multiply(intersection(a,identity),multiply(inverse(intersection(a,identity)),inverse(identity))),intersection(a,identity)) = multiply(identity,intersection(a,identity)),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
multiply(identity,intersection(a,identity)) = multiply(multiply(intersection(a,identity),multiply(inverse(intersection(a,identity)),inverse(identity))),intersection(a,identity)),
inference(symmetry,[status(thm)],[280]) ).
tff(282,plain,
intersection(a,identity) = multiply(intersection(a,identity),identity),
inference(transitivity,[status(thm)],[251,281,268,266]) ).
tff(283,plain,
union(intersection(a,identity),multiply(a,identity)) = union(multiply(intersection(a,identity),identity),multiply(a,identity)),
inference(monotonicity,[status(thm)],[282]) ).
tff(284,plain,
union(intersection(a,identity),multiply(a,identity)) = multiply(a,identity),
inference(transitivity,[status(thm)],[283,246,243]) ).
tff(285,plain,
union(intersection(multiply(a,a),multiply(a,identity)),union(intersection(a,identity),multiply(a,identity))) = union(intersection(multiply(a,a),multiply(a,identity)),multiply(a,identity)),
inference(monotonicity,[status(thm)],[284]) ).
tff(286,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( union(X,union(Y,Z)) = union(union(X,Y),Z) )
<=> ( union(X,union(Y,Z)) = union(union(X,Y),Z) ) )),
inference(bind,[status(th)],[]) ).
tff(287,plain,
( ! [Z: $i,Y: $i,X: $i] : ( union(X,union(Y,Z)) = union(union(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( union(X,union(Y,Z)) = union(union(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[286]) ).
tff(288,plain,
( ! [Z: $i,Y: $i,X: $i] : ( union(X,union(Y,Z)) = union(union(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( union(X,union(Y,Z)) = union(union(X,Y),Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(289,axiom,
! [Z: $i,Y: $i,X: $i] : ( union(X,union(Y,Z)) = union(union(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_associative) ).
tff(290,plain,
! [Z: $i,Y: $i,X: $i] : ( union(X,union(Y,Z)) = union(union(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[289,288]) ).
tff(291,plain,
! [Z: $i,Y: $i,X: $i] : ( union(X,union(Y,Z)) = union(union(X,Y),Z) ),
inference(skolemize,[status(sab)],[290]) ).
tff(292,plain,
! [Z: $i,Y: $i,X: $i] : ( union(X,union(Y,Z)) = union(union(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[291,287]) ).
tff(293,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( union(X,union(Y,Z)) = union(union(X,Y),Z) )
| ( union(intersection(multiply(a,a),multiply(a,identity)),union(intersection(a,identity),multiply(a,identity))) = union(union(intersection(multiply(a,a),multiply(a,identity)),intersection(a,identity)),multiply(a,identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(294,plain,
union(intersection(multiply(a,a),multiply(a,identity)),union(intersection(a,identity),multiply(a,identity))) = union(union(intersection(multiply(a,a),multiply(a,identity)),intersection(a,identity)),multiply(a,identity)),
inference(unit_resolution,[status(thm)],[293,292]) ).
tff(295,plain,
union(union(intersection(multiply(a,a),multiply(a,identity)),intersection(a,identity)),multiply(a,identity)) = union(intersection(multiply(a,a),multiply(a,identity)),union(intersection(a,identity),multiply(a,identity))),
inference(symmetry,[status(thm)],[294]) ).
tff(296,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,intersection(Y,Z)) = intersection(multiply(X,Y),multiply(X,Z)) )
| ( multiply(a,intersection(a,identity)) = intersection(multiply(a,a),multiply(a,identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(297,plain,
multiply(a,intersection(a,identity)) = intersection(multiply(a,a),multiply(a,identity)),
inference(unit_resolution,[status(thm)],[296,150]) ).
tff(298,plain,
intersection(multiply(a,a),multiply(a,identity)) = multiply(a,intersection(a,identity)),
inference(symmetry,[status(thm)],[297]) ).
tff(299,plain,
union(intersection(multiply(a,a),multiply(a,identity)),intersection(a,identity)) = union(multiply(a,intersection(a,identity)),multiply(identity,intersection(a,identity))),
inference(monotonicity,[status(thm)],[298,251]) ).
tff(300,plain,
union(multiply(a,intersection(a,identity)),multiply(identity,intersection(a,identity))) = union(intersection(multiply(a,a),multiply(a,identity)),intersection(a,identity)),
inference(symmetry,[status(thm)],[299]) ).
tff(301,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(union(Y,Z),X) = union(multiply(Y,X),multiply(Z,X)) )
| ( multiply(union(a,identity),intersection(a,identity)) = union(multiply(a,intersection(a,identity)),multiply(identity,intersection(a,identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(302,plain,
multiply(union(a,identity),intersection(a,identity)) = union(multiply(a,intersection(a,identity)),multiply(identity,intersection(a,identity))),
inference(unit_resolution,[status(thm)],[301,46]) ).
tff(303,plain,
multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))) = inverse(multiply(inverse(negative_part(a)),inverse(positive_part(a)))),
inference(symmetry,[status(thm)],[190]) ).
tff(304,plain,
multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))) = union(intersection(multiply(a,a),multiply(a,identity)),intersection(a,identity)),
inference(transitivity,[status(thm)],[303,177,166,164,302,300]) ).
tff(305,plain,
union(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),multiply(a,identity)) = union(union(intersection(multiply(a,a),multiply(a,identity)),intersection(a,identity)),multiply(a,identity)),
inference(monotonicity,[status(thm)],[304]) ).
tff(306,plain,
intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity)) = multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),
inference(transitivity,[status(thm)],[203,200,192,185,182,190]) ).
tff(307,plain,
union(intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity)),multiply(a,identity)) = union(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),multiply(a,identity)),
inference(monotonicity,[status(thm)],[306]) ).
tff(308,plain,
( ~ ! [Y: $i,X: $i] : ( union(X,Y) = union(Y,X) )
| ( union(multiply(a,identity),intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity))) = union(intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity)),multiply(a,identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(309,plain,
union(multiply(a,identity),intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity))) = union(intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity)),multiply(a,identity)),
inference(unit_resolution,[status(thm)],[308,59]) ).
tff(310,plain,
multiply(inverse(multiply(inverse(a),inverse(identity))),inverse(identity)) = multiply(a,identity),
inference(symmetry,[status(thm)],[226]) ).
tff(311,plain,
inverse(inverse(a)) = inverse(multiply(identity,multiply(inverse(a),inverse(identity)))),
inference(symmetry,[status(thm)],[216]) ).
tff(312,plain,
a = multiply(a,identity),
inference(transitivity,[status(thm)],[224,311,218,310]) ).
tff(313,plain,
union(a,intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity))) = union(multiply(a,identity),intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity))),
inference(monotonicity,[status(thm)],[312]) ).
tff(314,plain,
union(a,intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity))) = a,
inference(transitivity,[status(thm)],[313,309,307,305,295,285,235,226,219,216,207]) ).
tff(315,plain,
intersection(union(a,intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity))),intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity))) = intersection(a,intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity))),
inference(monotonicity,[status(thm)],[314]) ).
tff(316,plain,
( ~ ! [Y: $i,X: $i] : ( intersection(union(X,Y),Y) = Y )
| ( intersection(union(a,intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity))),intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity))) = intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(317,plain,
intersection(union(a,intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity))),intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity))) = intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity)),
inference(unit_resolution,[status(thm)],[316,16]) ).
tff(318,plain,
intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity)) = intersection(union(a,intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity))),intersection(multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),intersection(union(a,identity),union(a,identity))),multiply(multiply(inverse(inverse(positive_part(a))),inverse(inverse(negative_part(a)))),identity))),
inference(symmetry,[status(thm)],[317]) ).
tff(319,plain,
multiply(positive_part(a),negative_part(a)) = inverse(inverse(multiply(positive_part(a),negative_part(a)))),
inference(symmetry,[status(thm)],[166]) ).
tff(320,plain,
multiply(positive_part(a),negative_part(a)) = a,
inference(transitivity,[status(thm)],[319,176,181,184,191,199,202,318,315,205,138,129,39,29,9]) ).
tff(321,plain,
( ( multiply(positive_part(a),negative_part(a)) != a )
<=> ( multiply(positive_part(a),negative_part(a)) != a ) ),
inference(rewrite,[status(thm)],[]) ).
tff(322,axiom,
multiply(positive_part(a),negative_part(a)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_product) ).
tff(323,plain,
multiply(positive_part(a),negative_part(a)) != a,
inference(modus_ponens,[status(thm)],[322,321]) ).
tff(324,plain,
$false,
inference(unit_resolution,[status(thm)],[323,320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP114-1 : TPTP v9.0.0. Released v1.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 15:42:10 EDT 2025
% 0.12/0.34 % CPUTime :
% 9.77/9.97 % SZS status Unsatisfiable
% 9.77/9.97 % SZS output start Proof
% See solution above
% 9.83/10.01 % E exiting
%------------------------------------------------------------------------------