%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : FLD039-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:05:00 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 36
% Syntax : Number of formulae : 78 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 489 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 716 ( 337 ~; 332 |; 0 &)
% ( 47 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 32 ( 32 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 324 ( 292 !; 0 ?; 324 :)
% Comments :
%------------------------------------------------------------------------------
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(multiplicative_identity_type,type,
multiplicative_identity: $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(1,plain,
( defined(additive_identity)
<=> defined(additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
tff(3,plain,
defined(additive_identity),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i] :
refl(( ( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,X) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [X: $i] :
rewrite(( ( sum(additive_identity,X,X)
| ~ defined(X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,X) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [X: $i] :
( sum(additive_identity,X,X)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [X: $i] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
tff(10,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( sum(additive_identity,multiplicative_identity,additive_identity)
<=> sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
sum(additive_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).
tff(20,plain,
sum(additive_identity,multiplicative_identity,additive_identity),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,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(22,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)],[21]) ).
tff(23,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(24,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(25,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)],[24]) ).
tff(26,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(27,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,multiplicative_identity,additive_identity)
| sum(multiplicative_identity,additive_identity,additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,multiplicative_identity,additive_identity)
| sum(multiplicative_identity,additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,multiplicative_identity,additive_identity)
| sum(multiplicative_identity,additive_identity,additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,multiplicative_identity,additive_identity)
| sum(multiplicative_identity,additive_identity,additive_identity) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
sum(multiplicative_identity,additive_identity,additive_identity),
inference(unit_resolution,[status(thm)],[33,30,20]) ).
tff(35,plain,
( ~ sum(additive_identity,additive_identity,multiplicative_identity)
<=> ~ sum(additive_identity,additive_identity,multiplicative_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',different_identities) ).
tff(37,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(( ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
<=> ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( sum(U,Z,W)
| ~ sum(X,Y,U) )
<=> ( sum(U,Z,W)
| ~ sum(X,Y,U) ) )),
( ( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V) )
<=> ( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V) ) )),
rewrite(( ( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V) )
<=> ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) )),
( ( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V) )
<=> ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) )),
( ( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W) )
<=> ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ) )),
rewrite(( ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
<=> ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ) )),
( ( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W) )
<=> ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
tff(44,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ( sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity) )
<=> ( sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
~ sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(unit_resolution,[status(thm)],[53,47,37,34,17]) ).
tff(55,plain,
( defined(multiplicative_identity)
<=> defined(multiplicative_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
tff(57,plain,
defined(multiplicative_identity),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,multiplicative_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,multiplicative_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(unit_resolution,[status(thm)],[60,13,57]) ).
tff(62,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(( ( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
<=> ( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( sum(X,V,W)
| ~ sum(X,Y,U) )
<=> ( ~ sum(X,Y,U)
| sum(X,V,W) ) )),
( ( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V) )
<=> ( ~ sum(X,Y,U)
| sum(X,V,W)
| ~ sum(Y,Z,V) ) )),
rewrite(( ( ~ sum(X,Y,U)
| sum(X,V,W)
| ~ sum(Y,Z,V) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
( ( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
( ( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W)
| ~ sum(U,Z,W) ) )),
rewrite(( ( ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W)
| ~ sum(U,Z,W) )
<=> ( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
( ( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) )
<=> ( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
tff(68,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| sum(multiplicative_identity,additive_identity,multiplicative_identity) )
<=> ( ~ sum(additive_identity,multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| sum(multiplicative_identity,additive_identity,multiplicative_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| sum(multiplicative_identity,additive_identity,multiplicative_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| sum(multiplicative_identity,additive_identity,multiplicative_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity)
| sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
$false,
inference(unit_resolution,[status(thm)],[77,71,20,34,61,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : FLD039-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n013.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 13:32:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% See solution above
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------