TSTP Solution File: BOO005-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : BOO005-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 17:18:36 EDT 2022
% Result : Unsatisfiable 14.74s 9.74s
% Output : Proof 14.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 50
% Syntax : Number of formulae : 139 ( 99 unt; 5 typ; 0 def)
% Number of atoms : 187 ( 177 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 64 ( 20 ~; 16 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 207 ( 188 !; 0 ?; 207 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiplicative_identity_type,type,
multiplicative_identity: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( multiply(multiplicative_identity,X) = X )
<=> ( multiply(multiplicative_identity,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(multiplicative_identity,X) = X )
<=> ! [X: $i] : ( multiply(multiplicative_identity,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(multiplicative_identity,X) = X )
<=> ! [X: $i] : ( multiply(multiplicative_identity,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( multiply(multiplicative_identity,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
tff(5,plain,
! [X: $i] : ( multiply(multiplicative_identity,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(multiplicative_identity,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(multiplicative_identity,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(multiplicative_identity,X) = X )
| ( multiply(multiplicative_identity,multiplicative_identity) = multiplicative_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
multiply(multiplicative_identity,multiplicative_identity) = multiplicative_identity,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(
( ( add(inverse(X),X) = multiplicative_identity )
<=> ( add(inverse(X),X) = multiplicative_identity ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] : ( add(inverse(X),X) = multiplicative_identity )
<=> ! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( add(inverse(X),X) = multiplicative_identity )
<=> ! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_inverse2) ).
tff(14,plain,
! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( add(inverse(X),X) = multiplicative_identity )
| ( add(inverse(multiply(a,add(multiplicative_identity,a))),multiply(a,add(multiplicative_identity,a))) = multiplicative_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
add(inverse(multiply(a,add(multiplicative_identity,a))),multiply(a,add(multiplicative_identity,a))) = multiplicative_identity,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
multiplicative_identity = add(inverse(multiply(a,add(multiplicative_identity,a))),multiply(a,add(multiplicative_identity,a))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
multiply(multiplicative_identity,multiplicative_identity) = multiply(add(inverse(multiply(a,add(multiplicative_identity,a))),multiply(a,add(multiplicative_identity,a))),multiplicative_identity),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
multiply(add(inverse(multiply(a,add(multiplicative_identity,a))),multiply(a,add(multiplicative_identity,a))),multiplicative_identity) = multiply(multiplicative_identity,multiplicative_identity),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity3) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(inverse(multiply(a,add(multiplicative_identity,a))),multiply(a,add(multiplicative_identity,a))),multiplicative_identity) = add(multiply(inverse(multiply(a,add(multiplicative_identity,a))),multiplicative_identity),multiply(multiply(a,add(multiplicative_identity,a)),multiplicative_identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
multiply(add(inverse(multiply(a,add(multiplicative_identity,a))),multiply(a,add(multiplicative_identity,a))),multiplicative_identity) = add(multiply(inverse(multiply(a,add(multiplicative_identity,a))),multiplicative_identity),multiply(multiply(a,add(multiplicative_identity,a)),multiplicative_identity)),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
add(multiply(inverse(multiply(a,add(multiplicative_identity,a))),multiplicative_identity),multiply(multiply(a,add(multiplicative_identity,a)),multiplicative_identity)) = multiply(add(inverse(multiply(a,add(multiplicative_identity,a))),multiply(a,add(multiplicative_identity,a))),multiplicative_identity),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
^ [X: $i] :
refl(
( ( multiply(X,multiplicative_identity) = X )
<=> ( multiply(X,multiplicative_identity) = X ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
<=> ! [X: $i] : ( multiply(X,multiplicative_identity) = X ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
<=> ! [X: $i] : ( multiply(X,multiplicative_identity) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
tff(36,plain,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
| ( multiply(multiply(a,add(multiplicative_identity,a)),multiplicative_identity) = multiply(a,add(multiplicative_identity,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
multiply(multiply(a,add(multiplicative_identity,a)),multiplicative_identity) = multiply(a,add(multiplicative_identity,a)),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
add(multiply(inverse(multiply(a,add(multiplicative_identity,a))),multiplicative_identity),multiply(multiply(a,add(multiplicative_identity,a)),multiplicative_identity)) = add(multiply(inverse(multiply(a,add(multiplicative_identity,a))),multiplicative_identity),multiply(a,add(multiplicative_identity,a))),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
add(multiply(inverse(multiply(a,add(multiplicative_identity,a))),multiplicative_identity),multiply(a,add(multiplicative_identity,a))) = add(multiply(inverse(multiply(a,add(multiplicative_identity,a))),multiplicative_identity),multiply(multiply(a,add(multiplicative_identity,a)),multiplicative_identity)),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) )
<=> ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity1) ).
tff(47,plain,
! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) )
| ( add(multiply(inverse(multiply(a,add(multiplicative_identity,a))),multiplicative_identity),multiply(a,add(multiplicative_identity,a))) = multiply(add(inverse(multiply(a,add(multiplicative_identity,a))),multiply(a,add(multiplicative_identity,a))),add(multiplicative_identity,multiply(a,add(multiplicative_identity,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
add(multiply(inverse(multiply(a,add(multiplicative_identity,a))),multiplicative_identity),multiply(a,add(multiplicative_identity,a))) = multiply(add(inverse(multiply(a,add(multiplicative_identity,a))),multiply(a,add(multiplicative_identity,a))),add(multiplicative_identity,multiply(a,add(multiplicative_identity,a)))),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
multiply(add(inverse(multiply(a,add(multiplicative_identity,a))),multiply(a,add(multiplicative_identity,a))),add(multiplicative_identity,multiply(a,add(multiplicative_identity,a)))) = add(multiply(inverse(multiply(a,add(multiplicative_identity,a))),multiplicative_identity),multiply(a,add(multiplicative_identity,a))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
( ~ ! [X: $i] : ( multiply(multiplicative_identity,X) = X )
| ( multiply(multiplicative_identity,add(multiplicative_identity,a)) = add(multiplicative_identity,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
multiply(multiplicative_identity,add(multiplicative_identity,a)) = add(multiplicative_identity,a),
inference(unit_resolution,[status(thm)],[53,7]) ).
tff(55,plain,
add(multiply(multiplicative_identity,multiplicative_identity),a) = add(multiplicative_identity,a),
inference(monotonicity,[status(thm)],[9]) ).
tff(56,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) )
| ( add(multiply(multiplicative_identity,multiplicative_identity),a) = multiply(add(multiplicative_identity,a),add(multiplicative_identity,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
add(multiply(multiplicative_identity,multiplicative_identity),a) = multiply(add(multiplicative_identity,a),add(multiplicative_identity,a)),
inference(unit_resolution,[status(thm)],[56,49]) ).
tff(58,plain,
multiply(add(multiplicative_identity,a),add(multiplicative_identity,a)) = add(multiply(multiplicative_identity,multiplicative_identity),a),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity4) ).
tff(63,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(add(multiplicative_identity,a),add(multiplicative_identity,a)) = add(multiply(add(multiplicative_identity,a),multiplicative_identity),multiply(add(multiplicative_identity,a),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
multiply(add(multiplicative_identity,a),add(multiplicative_identity,a)) = add(multiply(add(multiplicative_identity,a),multiplicative_identity),multiply(add(multiplicative_identity,a),a)),
inference(unit_resolution,[status(thm)],[66,65]) ).
tff(68,plain,
add(multiply(add(multiplicative_identity,a),multiplicative_identity),multiply(add(multiplicative_identity,a),a)) = multiply(add(multiplicative_identity,a),add(multiplicative_identity,a)),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
^ [Y: $i,X: $i] :
refl(
( ( multiply(X,Y) = multiply(Y,X) )
<=> ( multiply(X,Y) = multiply(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
<=> ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
<=> ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,axiom,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).
tff(73,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(multiplicative_identity,add(multiplicative_identity,a)) = multiply(add(multiplicative_identity,a),multiplicative_identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
multiply(multiplicative_identity,add(multiplicative_identity,a)) = multiply(add(multiplicative_identity,a),multiplicative_identity),
inference(unit_resolution,[status(thm)],[76,75]) ).
tff(78,plain,
add(multiplicative_identity,a) = multiply(multiplicative_identity,add(multiplicative_identity,a)),
inference(symmetry,[status(thm)],[54]) ).
tff(79,plain,
add(multiplicative_identity,a) = multiply(add(multiplicative_identity,a),multiplicative_identity),
inference(transitivity,[status(thm)],[78,77]) ).
tff(80,plain,
add(add(multiplicative_identity,a),multiply(add(multiplicative_identity,a),a)) = add(multiply(add(multiplicative_identity,a),multiplicative_identity),multiply(add(multiplicative_identity,a),a)),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
add(add(multiplicative_identity,a),multiply(add(multiplicative_identity,a),a)) = add(multiplicative_identity,a),
inference(transitivity,[status(thm)],[80,68,58,55]) ).
tff(82,plain,
multiply(multiplicative_identity,add(add(multiplicative_identity,a),multiply(add(multiplicative_identity,a),a))) = multiply(multiplicative_identity,add(multiplicative_identity,a)),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(multiplicative_identity,add(add(multiplicative_identity,a),multiply(add(multiplicative_identity,a),a))) = add(multiply(multiplicative_identity,add(multiplicative_identity,a)),multiply(multiplicative_identity,multiply(add(multiplicative_identity,a),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
multiply(multiplicative_identity,add(add(multiplicative_identity,a),multiply(add(multiplicative_identity,a),a))) = add(multiply(multiplicative_identity,add(multiplicative_identity,a)),multiply(multiplicative_identity,multiply(add(multiplicative_identity,a),a))),
inference(unit_resolution,[status(thm)],[83,65]) ).
tff(85,plain,
add(multiply(multiplicative_identity,add(multiplicative_identity,a)),multiply(multiplicative_identity,multiply(add(multiplicative_identity,a),a))) = multiply(multiplicative_identity,add(add(multiplicative_identity,a),multiply(add(multiplicative_identity,a),a))),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
add(add(multiplicative_identity,a),multiply(multiplicative_identity,multiply(add(multiplicative_identity,a),a))) = add(multiply(multiplicative_identity,add(multiplicative_identity,a)),multiply(multiplicative_identity,multiply(add(multiplicative_identity,a),a))),
inference(monotonicity,[status(thm)],[78]) ).
tff(87,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) )
<=> ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity2) ).
tff(91,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) )
| ( add(add(multiplicative_identity,a),multiply(multiplicative_identity,multiply(add(multiplicative_identity,a),a))) = multiply(add(add(multiplicative_identity,a),multiplicative_identity),add(add(multiplicative_identity,a),multiply(add(multiplicative_identity,a),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
add(add(multiplicative_identity,a),multiply(multiplicative_identity,multiply(add(multiplicative_identity,a),a))) = multiply(add(add(multiplicative_identity,a),multiplicative_identity),add(add(multiplicative_identity,a),multiply(add(multiplicative_identity,a),a))),
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
multiply(add(add(multiplicative_identity,a),multiplicative_identity),add(add(multiplicative_identity,a),multiply(add(multiplicative_identity,a),a))) = add(add(multiplicative_identity,a),multiply(multiplicative_identity,multiply(add(multiplicative_identity,a),a))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
add(multiply(add(multiplicative_identity,a),multiplicative_identity),multiply(add(multiplicative_identity,a),a)) = add(add(multiplicative_identity,a),multiply(add(multiplicative_identity,a),a)),
inference(symmetry,[status(thm)],[80]) ).
tff(98,plain,
add(multiplicative_identity,a) = add(multiply(multiplicative_identity,multiplicative_identity),a),
inference(symmetry,[status(thm)],[55]) ).
tff(99,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(multiplicative_identity,add(multiplicative_identity,a)) = add(multiply(multiplicative_identity,multiplicative_identity),multiply(multiplicative_identity,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
multiply(multiplicative_identity,add(multiplicative_identity,a)) = add(multiply(multiplicative_identity,multiplicative_identity),multiply(multiplicative_identity,a)),
inference(unit_resolution,[status(thm)],[99,65]) ).
tff(101,plain,
add(multiply(multiplicative_identity,multiplicative_identity),multiply(multiplicative_identity,a)) = multiply(multiplicative_identity,add(multiplicative_identity,a)),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
multiplicative_identity = multiply(multiplicative_identity,multiplicative_identity),
inference(symmetry,[status(thm)],[9]) ).
tff(103,plain,
add(multiplicative_identity,multiply(multiplicative_identity,a)) = add(multiply(multiplicative_identity,multiplicative_identity),multiply(multiplicative_identity,a)),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
add(multiplicative_identity,multiply(multiplicative_identity,a)) = add(add(multiplicative_identity,a),multiply(add(multiplicative_identity,a),a)),
inference(transitivity,[status(thm)],[103,101,54,98,57,67,97]) ).
tff(105,plain,
^ [Y: $i,X: $i] :
refl(
( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).
tff(109,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[109]) ).
tff(111,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[110,106]) ).
tff(112,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(multiplicative_identity,a),multiplicative_identity) = add(multiplicative_identity,add(multiplicative_identity,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
add(add(multiplicative_identity,a),multiplicative_identity) = add(multiplicative_identity,add(multiplicative_identity,a)),
inference(unit_resolution,[status(thm)],[112,111]) ).
tff(114,plain,
add(multiplicative_identity,add(multiplicative_identity,a)) = add(add(multiplicative_identity,a),multiplicative_identity),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
multiply(add(multiplicative_identity,add(multiplicative_identity,a)),add(multiplicative_identity,multiply(multiplicative_identity,a))) = multiply(add(add(multiplicative_identity,a),multiplicative_identity),add(add(multiplicative_identity,a),multiply(add(multiplicative_identity,a),a))),
inference(monotonicity,[status(thm)],[114,104]) ).
tff(116,plain,
add(multiply(multiplicative_identity,multiplicative_identity),multiply(multiplicative_identity,a)) = add(multiplicative_identity,multiply(multiplicative_identity,a)),
inference(symmetry,[status(thm)],[103]) ).
tff(117,plain,
add(multiplicative_identity,a) = add(multiplicative_identity,multiply(multiplicative_identity,a)),
inference(transitivity,[status(thm)],[78,100,116]) ).
tff(118,plain,
multiply(add(multiplicative_identity,add(multiplicative_identity,a)),add(multiplicative_identity,a)) = multiply(add(multiplicative_identity,add(multiplicative_identity,a)),add(multiplicative_identity,multiply(multiplicative_identity,a))),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) )
| ( add(multiplicative_identity,multiply(add(multiplicative_identity,a),a)) = multiply(add(multiplicative_identity,add(multiplicative_identity,a)),add(multiplicative_identity,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
add(multiplicative_identity,multiply(add(multiplicative_identity,a),a)) = multiply(add(multiplicative_identity,add(multiplicative_identity,a)),add(multiplicative_identity,a)),
inference(unit_resolution,[status(thm)],[119,93]) ).
tff(121,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(add(multiplicative_identity,a),a) = multiply(a,add(multiplicative_identity,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
multiply(add(multiplicative_identity,a),a) = multiply(a,add(multiplicative_identity,a)),
inference(unit_resolution,[status(thm)],[121,75]) ).
tff(123,plain,
multiply(a,add(multiplicative_identity,a)) = multiply(add(multiplicative_identity,a),a),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
add(multiplicative_identity,multiply(a,add(multiplicative_identity,a))) = add(multiplicative_identity,multiply(add(multiplicative_identity,a),a)),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
add(multiplicative_identity,multiply(a,add(multiplicative_identity,a))) = add(multiplicative_identity,a),
inference(transitivity,[status(thm)],[124,120,118,115,96,86,85,82,54]) ).
tff(126,plain,
multiply(add(inverse(multiply(a,add(multiplicative_identity,a))),multiply(a,add(multiplicative_identity,a))),add(multiplicative_identity,multiply(a,add(multiplicative_identity,a)))) = multiply(multiplicative_identity,add(multiplicative_identity,a)),
inference(monotonicity,[status(thm)],[18,125]) ).
tff(127,plain,
multiply(multiplicative_identity,add(multiplicative_identity,a)) = multiply(add(inverse(multiply(a,add(multiplicative_identity,a))),multiply(a,add(multiplicative_identity,a))),add(multiplicative_identity,multiply(a,add(multiplicative_identity,a)))),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(a,multiplicative_identity) = add(multiplicative_identity,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
add(a,multiplicative_identity) = add(multiplicative_identity,a),
inference(unit_resolution,[status(thm)],[128,111]) ).
tff(130,plain,
add(a,multiplicative_identity) = multiplicative_identity,
inference(transitivity,[status(thm)],[129,78,127,52,42,31,21,9]) ).
tff(131,plain,
( ( add(a,multiplicative_identity) != multiplicative_identity )
<=> ( add(a,multiplicative_identity) != multiplicative_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,axiom,
add(a,multiplicative_identity) != multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_plus_1_is_a) ).
tff(133,plain,
add(a,multiplicative_identity) != multiplicative_identity,
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
$false,
inference(unit_resolution,[status(thm)],[133,130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : BOO005-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 02:47:50 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 14.74/9.74 % SZS status Unsatisfiable
% 14.74/9.74 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------