%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : FLD069-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:05:08 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 29
% Syntax : Number of formulae : 60 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 339 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 480 ( 225 ~; 220 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 24 ( 24 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; 3 con; 0-0 aty)
% Number of variables : 156 ( 140 !; 0 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(less_or_equal_type,type,
less_or_equal: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( defined(b)
<=> defined(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
tff(3,plain,
defined(b),
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/sandbox/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(b)
| sum(additive_identity,b,b) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(b)
| sum(additive_identity,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(b)
| sum(additive_identity,b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(b)
| sum(additive_identity,b,b) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
sum(additive_identity,b,b),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( ~ sum(additive_identity,b,additive_identity)
<=> ~ sum(additive_identity,b,additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_5) ).
tff(20,plain,
~ sum(additive_identity,b,additive_identity),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( less_or_equal(additive_identity,b)
<=> less_or_equal(additive_identity,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
tff(23,plain,
less_or_equal(additive_identity,b),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
<=> ( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( sum(additive_identity,X,Y)
| ~ less_or_equal(X,Y) )
<=> ( ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ) )),
( ( sum(additive_identity,X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,X) )
<=> ( ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y)
| ~ less_or_equal(Y,X) ) )),
rewrite(( ( ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y)
| ~ less_or_equal(Y,X) )
<=> ( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ) )),
( ( sum(additive_identity,X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,X) )
<=> ( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [Y: $i,X: $i] :
( sum(additive_identity,X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [Y: $i,X: $i] :
( sum(additive_identity,X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
tff(30,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(b,additive_identity)
| sum(additive_identity,b,additive_identity) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(b,additive_identity)
| sum(additive_identity,b,additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(b,additive_identity)
| sum(additive_identity,b,additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) )
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(b,additive_identity)
| sum(additive_identity,b,additive_identity) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
~ less_or_equal(b,additive_identity),
inference(unit_resolution,[status(thm)],[36,33,23,20]) ).
tff(38,plain,
( sum(a,b,additive_identity)
<=> sum(a,b,additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
sum(a,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_6) ).
tff(40,plain,
sum(a,b,additive_identity),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( less_or_equal(additive_identity,a)
<=> less_or_equal(additive_identity,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
tff(43,plain,
less_or_equal(additive_identity,a),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
^ [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(( ( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
<=> ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
<=> ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
^ [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( less_or_equal(U,V)
| ~ less_or_equal(X,Y) )
<=> ( ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) )),
( ( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U) )
<=> ( ~ less_or_equal(X,Y)
| less_or_equal(U,V)
| ~ sum(X,Z,U) ) )),
rewrite(( ( ~ less_or_equal(X,Y)
| less_or_equal(U,V)
| ~ sum(X,Z,U) )
<=> ( ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) )),
( ( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U) )
<=> ( ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) )),
( ( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U)
| ~ sum(Y,Z,V) )
<=> ( ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V)
| ~ sum(Y,Z,V) ) )),
rewrite(( ( ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V)
| ~ sum(Y,Z,V) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) )),
( ( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U)
| ~ sum(Y,Z,V) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U)
| ~ sum(Y,Z,V) )
<=> ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U)
| ~ sum(Y,Z,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
tff(50,plain,
! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| less_or_equal(b,additive_identity)
| ~ sum(a,b,additive_identity)
| ~ less_or_equal(additive_identity,a)
| ~ sum(additive_identity,b,b) )
<=> ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| less_or_equal(b,additive_identity)
| ~ sum(a,b,additive_identity)
| ~ less_or_equal(additive_identity,a)
| ~ sum(additive_identity,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( ~ sum(a,b,additive_identity)
| ~ sum(additive_identity,b,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(b,additive_identity) )
<=> ( less_or_equal(b,additive_identity)
| ~ sum(a,b,additive_identity)
| ~ less_or_equal(additive_identity,a)
| ~ sum(additive_identity,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| ~ sum(a,b,additive_identity)
| ~ sum(additive_identity,b,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(b,additive_identity) )
<=> ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| less_or_equal(b,additive_identity)
| ~ sum(a,b,additive_identity)
| ~ less_or_equal(additive_identity,a)
| ~ sum(additive_identity,b,b) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| ~ sum(a,b,additive_identity)
| ~ sum(additive_identity,b,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(b,additive_identity) )
<=> ( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| less_or_equal(b,additive_identity)
| ~ sum(a,b,additive_identity)
| ~ less_or_equal(additive_identity,a)
| ~ sum(additive_identity,b,b) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| ~ sum(a,b,additive_identity)
| ~ sum(additive_identity,b,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(b,additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) )
| less_or_equal(b,additive_identity)
| ~ sum(a,b,additive_identity)
| ~ less_or_equal(additive_identity,a)
| ~ sum(additive_identity,b,b) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
$false,
inference(unit_resolution,[status(thm)],[59,53,43,40,37,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD069-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.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 13:45:11 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.12/0.39 % E exiting
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