%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : FLD010-5 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:04:52 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 70
% Syntax : Number of formulae : 156 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 972 ( 0 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 1388 ( 624 ~; 677 |; 0 &)
% ( 87 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 52 ( 52 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 547 ( 501 !; 0 ?; 547 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(multiplicative_inverse_type,type,
multiplicative_inverse: $i > $i ).
tff(multiplicative_identity_type,type,
multiplicative_identity: $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(1,plain,
( ~ sum(additive_identity,multiplicative_identity,additive_identity)
<=> ~ sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ sum(additive_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_1) ).
tff(3,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i] :
refl(( ( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
<=> ( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [X: $i] :
rewrite(( ( defined(multiplicative_inverse(X))
| ~ defined(X)
| sum(additive_identity,X,additive_identity) )
<=> ( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [X: $i] :
( defined(multiplicative_inverse(X))
| ~ defined(X)
| sum(additive_identity,X,additive_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [X: $i] :
( defined(multiplicative_inverse(X))
| ~ defined(X)
| sum(additive_identity,X,additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
tff(10,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( defined(multiplicative_identity)
<=> defined(multiplicative_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
tff(16,plain,
defined(multiplicative_identity),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity)
| defined(multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity)
| defined(multiplicative_inverse(multiplicative_identity)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| defined(multiplicative_inverse(multiplicative_identity)) )
<=> ( sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity)
| defined(multiplicative_inverse(multiplicative_identity)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| defined(multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity)
| defined(multiplicative_inverse(multiplicative_identity)) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| defined(multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity)
| defined(multiplicative_inverse(multiplicative_identity)) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| defined(multiplicative_inverse(multiplicative_identity)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity)
| defined(multiplicative_inverse(multiplicative_identity)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
defined(multiplicative_inverse(multiplicative_identity)),
inference(unit_resolution,[status(thm)],[22,16,13,3]) ).
tff(24,plain,
^ [X: $i] :
refl(( ( ~ defined(X)
| product(multiplicative_identity,X,X) )
<=> ( ~ defined(X)
| product(multiplicative_identity,X,X) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [X: $i] :
rewrite(( ( product(multiplicative_identity,X,X)
| ~ defined(X) )
<=> ( ~ defined(X)
| product(multiplicative_identity,X,X) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [X: $i] :
( product(multiplicative_identity,X,X)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [X: $i] :
( product(multiplicative_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
tff(30,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(multiplicative_inverse(multiplicative_identity))
| product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(multiplicative_inverse(multiplicative_identity))
| product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(multiplicative_inverse(multiplicative_identity))
| product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(multiplicative_inverse(multiplicative_identity))
| product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)),
inference(unit_resolution,[status(thm)],[36,33,23]) ).
tff(38,plain,
^ [X: $i] :
refl(( ( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
<=> ( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity) )
<=> ( sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ) )),
( ( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity)
| ~ defined(X) )
<=> ( sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity)
| ~ defined(X) ) )),
rewrite(( ( sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity)
| ~ defined(X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ) )),
( ( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity)
| ~ defined(X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [X: $i] :
( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [X: $i] :
( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
tff(44,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(unit_resolution,[status(thm)],[50,47,16,3]) ).
tff(52,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(( ( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
<=> ( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( product(X,V,W)
| ~ product(X,Y,U) )
<=> ( ~ product(X,Y,U)
| product(X,V,W) ) )),
( ( product(X,V,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V) )
<=> ( ~ product(X,Y,U)
| product(X,V,W)
| ~ product(Y,Z,V) ) )),
rewrite(( ( ~ product(X,Y,U)
| product(X,V,W)
| ~ product(Y,Z,V) )
<=> ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) )),
( ( product(X,V,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V) )
<=> ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) )),
( ( product(X,V,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W) )
<=> ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W)
| ~ product(U,Z,W) ) )),
rewrite(( ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W)
| ~ product(U,Z,W) )
<=> ( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) )),
( ( product(X,V,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W) )
<=> ( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
tff(58,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)),
inference(unit_resolution,[status(thm)],[67,61,51,37]) ).
tff(69,plain,
( defined(additive_identity)
<=> defined(additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
tff(71,plain,
defined(additive_identity),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(additive_identity)
| product(multiplicative_identity,additive_identity,additive_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(additive_identity)
| product(multiplicative_identity,additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(additive_identity)
| product(multiplicative_identity,additive_identity,additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(additive_identity)
| product(multiplicative_identity,additive_identity,additive_identity) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(unit_resolution,[status(thm)],[74,33,71]) ).
tff(76,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ( ~ product(multiplicative_identity,additive_identity,additive_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity) )
<=> ( ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity) ) ),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity) ) ),
inference(transitivity,[status(thm)],[78,76]) ).
tff(80,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity),
inference(unit_resolution,[status(thm)],[81,61,51,75]) ).
tff(83,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ product(X,Y,Z)
| product(Y,X,Z) )
<=> ( ~ product(X,Y,Z)
| product(Y,X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(( ( product(Y,X,Z)
| ~ product(X,Y,Z) )
<=> ( ~ product(X,Y,Z)
| product(Y,X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(87,plain,
( ! [Z: $i,Y: $i,X: $i] :
( product(Y,X,Z)
| ~ product(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,axiom,
! [Z: $i,Y: $i,X: $i] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
tff(89,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity)
| product(additive_identity,multiplicative_inverse(multiplicative_identity),additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity)
| product(additive_identity,multiplicative_inverse(multiplicative_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity)
| product(additive_identity,multiplicative_inverse(multiplicative_identity),additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity)
| product(additive_identity,multiplicative_inverse(multiplicative_identity),additive_identity) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
product(additive_identity,multiplicative_inverse(multiplicative_identity),additive_identity),
inference(unit_resolution,[status(thm)],[95,92,82]) ).
tff(97,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(unit_resolution,[status(thm)],[99,92,51]) ).
tff(101,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(unit_resolution,[status(thm)],[103,61,51,100,37]) ).
tff(105,plain,
^ [X: $i] :
refl(( ( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,X) ) )),
inference(bind,[status(th)],[]) ).
tff(106,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
^ [X: $i] :
rewrite(( ( sum(additive_identity,X,X)
| ~ defined(X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,X) ) )),
inference(bind,[status(th)],[]) ).
tff(109,plain,
( ! [X: $i] :
( sum(additive_identity,X,X)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,axiom,
! [X: $i] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
tff(111,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[113,106]) ).
tff(115,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(multiplicative_inverse(multiplicative_identity))
| sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(multiplicative_inverse(multiplicative_identity))
| sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(multiplicative_inverse(multiplicative_identity))
| sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(multiplicative_inverse(multiplicative_identity))
| sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)),
inference(unit_resolution,[status(thm)],[117,114,23]) ).
tff(119,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
<=> ( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(120,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(( ( sum(Y,X,Z)
| ~ sum(X,Y,Z) )
<=> ( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(123,plain,
( ! [Z: $i,Y: $i,X: $i] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,axiom,
! [Z: $i,Y: $i,X: $i] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
tff(125,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[127,120]) ).
tff(129,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_inverse(multiplicative_identity)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_inverse(multiplicative_identity)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_inverse(multiplicative_identity)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_inverse(multiplicative_identity)) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_inverse(multiplicative_identity)),
inference(unit_resolution,[status(thm)],[131,128,118]) ).
tff(133,plain,
( ~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity)
<=> ~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,axiom,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_2) ).
tff(135,plain,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity)
| sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity)
| sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity)
| sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity)
| sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity),
inference(unit_resolution,[status(thm)],[138,128,135]) ).
tff(140,plain,
^ [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
refl(( ( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
<=> ( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) )),
inference(bind,[status(th)],[]) ).
tff(141,plain,
( ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
<=> ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,plain,
( ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
<=> ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,plain,
^ [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( sum(C,D,B)
| ~ sum(X,Y,A) )
<=> ( ~ sum(X,Y,A)
| sum(C,D,B) ) )),
( ( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B) )
<=> ( ~ sum(X,Y,A)
| sum(C,D,B)
| ~ product(A,Z,B) ) )),
rewrite(( ( ~ sum(X,Y,A)
| sum(C,D,B)
| ~ product(A,Z,B) )
<=> ( ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) )),
( ( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B) )
<=> ( ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) )),
( ( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B)
| ~ product(X,Z,C) )
<=> ( ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B)
| ~ product(X,Z,C) ) )),
rewrite(( ( ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B)
| ~ product(X,Z,C) )
<=> ( ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) )),
( ( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B)
| ~ product(X,Z,C) )
<=> ( ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) )),
( ( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B)
| ~ product(X,Z,C)
| ~ product(Y,Z,D) )
<=> ( ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B)
| ~ product(Y,Z,D) ) )),
rewrite(( ( ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B)
| ~ product(Y,Z,D) )
<=> ( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) )),
( ( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B)
| ~ product(X,Z,C)
| ~ product(Y,Z,D) )
<=> ( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) )),
inference(bind,[status(th)],[]) ).
tff(144,plain,
( ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B)
| ~ product(X,Z,C)
| ~ product(Y,Z,D) )
<=> ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,axiom,
! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B)
| ~ product(X,Z,C)
| ~ product(Y,Z,D) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
tff(146,plain,
! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ),
inference(modus_ponens,[status(thm)],[146,142]) ).
tff(148,plain,
! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ),
inference(skolemize,[status(sab)],[147]) ).
tff(149,plain,
! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ),
inference(modus_ponens,[status(thm)],[148,141]) ).
tff(150,plain,
( ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity)
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(additive_identity,multiplicative_inverse(multiplicative_identity),additive_identity) )
<=> ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity)
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(additive_identity,multiplicative_inverse(multiplicative_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(151,plain,
( ( ~ product(additive_identity,multiplicative_inverse(multiplicative_identity),additive_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_inverse(multiplicative_identity))
| sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity) )
<=> ( sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity)
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(additive_identity,multiplicative_inverse(multiplicative_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
( ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| ~ product(additive_identity,multiplicative_inverse(multiplicative_identity),additive_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_inverse(multiplicative_identity))
| sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity) )
<=> ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity)
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(additive_identity,multiplicative_inverse(multiplicative_identity),additive_identity) ) ),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
( ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| ~ product(additive_identity,multiplicative_inverse(multiplicative_identity),additive_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_inverse(multiplicative_identity))
| sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity) )
<=> ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity)
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(additive_identity,multiplicative_inverse(multiplicative_identity),additive_identity) ) ),
inference(transitivity,[status(thm)],[152,150]) ).
tff(154,plain,
( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| ~ product(additive_identity,multiplicative_inverse(multiplicative_identity),additive_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_inverse(multiplicative_identity))
| sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity)
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| ~ product(additive_identity,multiplicative_inverse(multiplicative_identity),additive_identity) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
$false,
inference(unit_resolution,[status(thm)],[155,149,139,132,104,96,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : FLD010-5 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.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 : Thu Jun 19 13:32:32 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41 % SZS output start Proof
% See solution above
% 0.21/0.44 % E exiting
%------------------------------------------------------------------------------