%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : FLD017-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:04:54 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 43 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 244 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 350 ( 165 ~; 160 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 16 ( 16 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 : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 143 ( 129 !; 0 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(b_type,type,
b: $i ).
tff(x_type,type,
x: $i ).
tff(a_type,type,
a: $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(1,plain,
( ~ sum(x,b,c)
<=> ~ sum(x,b,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ sum(x,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_7) ).
tff(3,plain,
~ sum(x,b,c),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( sum(a,b,c)
<=> sum(a,b,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
sum(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_6) ).
tff(6,plain,
sum(a,b,c),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( sum(additive_identity,a,x)
<=> sum(additive_identity,a,x) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
sum(additive_identity,a,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_5) ).
tff(9,plain,
sum(additive_identity,a,x),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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(14,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)],[13]) ).
tff(15,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(16,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)],[15,14]) ).
tff(17,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)],[16,12]) ).
tff(18,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)],[17]) ).
tff(19,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)],[18,11]) ).
tff(20,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(x,b,c)
| ~ sum(additive_identity,a,x)
| ~ sum(a,b,c)
| ~ sum(additive_identity,c,c) )
<=> ( ~ ! [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(x,b,c)
| ~ sum(additive_identity,a,x)
| ~ sum(a,b,c)
| ~ sum(additive_identity,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( sum(x,b,c)
| ~ sum(a,b,c)
| ~ sum(additive_identity,a,x)
| ~ sum(additive_identity,c,c) )
<=> ( sum(x,b,c)
| ~ sum(additive_identity,a,x)
| ~ sum(a,b,c)
| ~ sum(additive_identity,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,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(x,b,c)
| ~ sum(a,b,c)
| ~ sum(additive_identity,a,x)
| ~ sum(additive_identity,c,c) )
<=> ( ~ ! [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(x,b,c)
| ~ sum(additive_identity,a,x)
| ~ sum(a,b,c)
| ~ sum(additive_identity,c,c) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,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(x,b,c)
| ~ sum(a,b,c)
| ~ sum(additive_identity,a,x)
| ~ sum(additive_identity,c,c) )
<=> ( ~ ! [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(x,b,c)
| ~ sum(additive_identity,a,x)
| ~ sum(a,b,c)
| ~ sum(additive_identity,c,c) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,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(x,b,c)
| ~ sum(a,b,c)
| ~ sum(additive_identity,a,x)
| ~ sum(additive_identity,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,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(x,b,c)
| ~ sum(additive_identity,a,x)
| ~ sum(a,b,c)
| ~ sum(additive_identity,c,c) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ sum(additive_identity,c,c),
inference(unit_resolution,[status(thm)],[25,19,9,6,3]) ).
tff(27,plain,
( defined(c)
<=> defined(c) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
tff(29,plain,
defined(c),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
^ [X: $i] :
refl(( ( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,X) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
^ [X: $i] :
rewrite(( ( sum(additive_identity,X,X)
| ~ defined(X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,X) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [X: $i] :
( sum(additive_identity,X,X)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [X: $i] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
tff(36,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(c)
| sum(additive_identity,c,c) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(c)
| sum(additive_identity,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(c)
| sum(additive_identity,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(c)
| sum(additive_identity,c,c) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
$false,
inference(unit_resolution,[status(thm)],[42,39,29,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD017-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 13:32:09 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------