%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : FLD006-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:04:51 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 34 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 127 ( 59 ~; 54 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 68 ( 60 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(1,plain,
( ~ sum(additive_identity,additive_inverse(additive_identity),additive_identity)
<=> ~ sum(additive_identity,additive_inverse(additive_identity),additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ sum(additive_identity,additive_inverse(additive_identity),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_1) ).
tff(3,plain,
~ sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(5,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)],[4]) ).
tff(6,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(7,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(8,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)],[7]) ).
tff(9,axiom,
! [Z: $i,Y: $i,X: $i] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
tff(10,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(additive_identity),additive_identity,additive_identity)
| sum(additive_identity,additive_inverse(additive_identity),additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(additive_identity),additive_identity,additive_identity)
| sum(additive_identity,additive_inverse(additive_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(additive_identity),additive_identity,additive_identity)
| sum(additive_identity,additive_inverse(additive_identity),additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(additive_identity),additive_identity,additive_identity)
| sum(additive_identity,additive_inverse(additive_identity),additive_identity) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( defined(additive_identity)
<=> defined(additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
tff(20,plain,
defined(additive_identity),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [X: $i] :
refl(( ( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
<=> ( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [X: $i] :
rewrite(( ( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) )
<=> ( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [X: $i] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [X: $i] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
tff(27,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(additive_identity)
| sum(additive_inverse(additive_identity),additive_identity,additive_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(additive_identity)
| sum(additive_inverse(additive_identity),additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(additive_identity)
| sum(additive_inverse(additive_identity),additive_identity,additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(additive_identity)
| sum(additive_inverse(additive_identity),additive_identity,additive_identity) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,30,20,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD006-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 13:33:46 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------