TSTP Solution File: FLD010-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : FLD010-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 14:55:32 EDT 2022
% Result : Unsatisfiable 0.14s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 46
% Syntax : Number of formulae : 93 ( 21 unt; 6 typ; 0 def)
% Number of atoms : 412 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 528 ( 223 ~; 264 |; 0 &)
% ( 41 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 153 ( 142 !; 0 ?; 153 :)
% Comments :
%------------------------------------------------------------------------------
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(multiplicative_inverse_type,type,
multiplicative_inverse: $i > $i ).
tff(multiplicative_identity_type,type,
multiplicative_identity: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(1,plain,
( ~ equalish(additive_identity,multiplicative_identity)
<=> ~ equalish(additive_identity,multiplicative_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ equalish(additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',different_identities) ).
tff(3,plain,
~ equalish(additive_identity,multiplicative_identity),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(
( ( equalish(X,Y)
| ~ equalish(Y,X) )
<=> ( equalish(X,Y)
| ~ equalish(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
<=> ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
<=> ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
tff(8,plain,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_identity,multiplicative_identity)
| ~ equalish(multiplicative_identity,additive_identity) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_identity,multiplicative_identity)
| ~ equalish(multiplicative_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_identity,multiplicative_identity)
| ~ equalish(multiplicative_identity,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_identity,multiplicative_identity)
| ~ equalish(multiplicative_identity,additive_identity) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ equalish(multiplicative_identity,additive_identity),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [X: $i] :
refl(
( ( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) )
<=> ( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) )
<=> ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) )
<=> ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
^ [X: $i] :
rewrite(
( ( defined(multiplicative_inverse(X))
| ~ defined(X)
| equalish(X,additive_identity) )
<=> ( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [X: $i] :
( defined(multiplicative_inverse(X))
| ~ defined(X)
| equalish(X,additive_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [X: $i] :
( defined(multiplicative_inverse(X))
| ~ defined(X)
| equalish(X,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
tff(21,plain,
! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( defined(multiplicative_identity)
<=> defined(multiplicative_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_identity) ).
tff(27,plain,
defined(multiplicative_identity),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) )
| ~ defined(multiplicative_identity)
| equalish(multiplicative_identity,additive_identity)
| defined(multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) )
| ~ defined(multiplicative_identity)
| equalish(multiplicative_identity,additive_identity)
| defined(multiplicative_inverse(multiplicative_identity)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) )
| ~ defined(multiplicative_identity)
| equalish(multiplicative_identity,additive_identity)
| defined(multiplicative_inverse(multiplicative_identity)) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| defined(multiplicative_inverse(X)) )
| ~ defined(multiplicative_identity)
| equalish(multiplicative_identity,additive_identity)
| defined(multiplicative_inverse(multiplicative_identity)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
defined(multiplicative_inverse(multiplicative_identity)),
inference(unit_resolution,[status(thm)],[30,27,24,14]) ).
tff(32,plain,
^ [X: $i] :
refl(
( ( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) )
<=> ( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) )
<=> ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) )
<=> ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
^ [X: $i] :
rewrite(
( ( equalish(multiply(multiplicative_identity,X),X)
| ~ defined(X) )
<=> ( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [X: $i] :
( equalish(multiply(multiplicative_identity,X),X)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [X: $i] :
( equalish(multiply(multiplicative_identity,X),X)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
tff(38,plain,
! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) )
| ~ defined(multiplicative_inverse(multiplicative_identity))
| equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) )
| ~ defined(multiplicative_inverse(multiplicative_identity))
| equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) )
| ~ defined(multiplicative_inverse(multiplicative_identity))
| equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity)) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) )
| ~ defined(multiplicative_inverse(multiplicative_identity))
| equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity)),
inference(unit_resolution,[status(thm)],[44,41,31]) ).
tff(46,plain,
^ [X: $i] :
refl(
( ( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) )
<=> ( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity)
| ~ defined(X) )
<=> ( ~ defined(X)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ) )),
( ( equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity)
| ~ defined(X)
| equalish(X,additive_identity) )
<=> ( ~ defined(X)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity)
| equalish(X,additive_identity) ) )),
rewrite(
( ( ~ defined(X)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity)
| equalish(X,additive_identity) )
<=> ( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ) )),
( ( equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity)
| ~ defined(X)
| equalish(X,additive_identity) )
<=> ( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [X: $i] :
( equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity)
| ~ defined(X)
| equalish(X,additive_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [X: $i] :
( equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity)
| ~ defined(X)
| equalish(X,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).
tff(52,plain,
! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) )
| ~ defined(multiplicative_identity)
| equalish(multiplicative_identity,additive_identity)
| equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) )
| ~ defined(multiplicative_identity)
| equalish(multiplicative_identity,additive_identity)
| equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) )
| ~ defined(multiplicative_identity)
| equalish(multiplicative_identity,additive_identity)
| equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| equalish(X,additive_identity)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) )
| ~ defined(multiplicative_identity)
| equalish(multiplicative_identity,additive_identity)
| equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
( equalish(multiplicative_identity,additive_identity)
| equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity) ),
inference(unit_resolution,[status(thm)],[58,55,27]) ).
tff(60,plain,
equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity),
inference(unit_resolution,[status(thm)],[59,14]) ).
tff(61,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity))),
inference(unit_resolution,[status(thm)],[63,10,60]) ).
tff(65,plain,
( ~ equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity)
<=> ~ equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(66,axiom,
~ equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inv_not_equal_to_multiplicative_id_2) ).
tff(67,plain,
~ equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity)) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity)) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
~ equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(unit_resolution,[status(thm)],[70,10,67]) ).
tff(72,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( equalish(X,Z)
| ~ equalish(X,Y) )
<=> ( ~ equalish(X,Y)
| equalish(X,Z) ) )),
( ( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) )
<=> ( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ) )),
rewrite(
( ( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
<=> ( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ) )),
( ( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) )
<=> ( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [Z: $i,Y: $i,X: $i] :
( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [Z: $i,Y: $i,X: $i] :
( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
tff(77,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ( ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity))
| ~ equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity)) )
<=> ( equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity))
| ~ equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity)) ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity))
| ~ equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity)) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
tff(85,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity))
| ~ equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity)) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity)) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
$false,
inference(unit_resolution,[status(thm)],[86,80,71,64,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD010-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 02:13:16 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Unsatisfiable
% 0.14/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------