%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV008-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:31:19 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 25
% Syntax : Number of formulae : 62 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 347 ( 26 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 437 ( 170 ~; 233 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 72 ( 64 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_than_type,type,
less_than: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i > $i ).
tff(predecessor_type,type,
predecessor: $i > $i ).
tff(n_type,type,
n: $i ).
tff(l_type,type,
l: $i ).
tff(one_type,type,
one: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) )
<=> ( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) )
<=> ! [X: $i] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) )
<=> ! [X: $i] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [X: $i] :
rewrite(( ( ~ less_than(one,X)
| ~ less_than(X,n)
| ~ less_than(a(X),a(predecessor(X))) )
<=> ( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X: $i] :
( ~ less_than(one,X)
| ~ less_than(X,n)
| ~ less_than(a(X),a(predecessor(X))) )
<=> ! [X: $i] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [X: $i] :
( ~ less_than(one,X)
| ~ less_than(X,n)
| ~ less_than(a(X),a(predecessor(X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
tff(7,plain,
! [X: $i] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [X: $i] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( less_than(a(l),a(predecessor(l)))
<=> less_than(a(l),a(predecessor(l))) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
less_than(a(l),a(predecessor(l))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
tff(13,plain,
less_than(a(l),a(predecessor(l))),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( less_than(one,l)
<=> less_than(one,l) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
less_than(one,l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
tff(16,plain,
less_than(one,l),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) )
| ~ less_than(a(l),a(predecessor(l)))
| ~ less_than(l,n)
| ~ less_than(one,l) )
<=> ( ~ ! [X: $i] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) )
| ~ less_than(a(l),a(predecessor(l)))
| ~ less_than(l,n)
| ~ less_than(one,l) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [X: $i] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) )
| ~ less_than(a(l),a(predecessor(l)))
| ~ less_than(l,n)
| ~ less_than(one,l) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [X: $i] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) )
| ~ less_than(a(l),a(predecessor(l)))
| ~ less_than(l,n)
| ~ less_than(one,l) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ less_than(l,n),
inference(unit_resolution,[status(thm)],[19,16,13,10]) ).
tff(21,plain,
( ~ less_than(n,l)
<=> ~ less_than(n,l) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
~ less_than(n,l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
tff(23,plain,
~ less_than(n,l),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [Y: $i,X: $i] :
refl(( ( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
<=> ( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
<=> ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
<=> ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [Y: $i,X: $i] :
rewrite(( ( less_than(X,Y)
| less_than(Y,X)
| ( X = Y ) )
<=> ( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [Y: $i,X: $i] :
( less_than(X,Y)
| less_than(Y,X)
| ( X = Y ) )
<=> ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [Y: $i,X: $i] :
( less_than(X,Y)
| less_than(Y,X)
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV001-0.ax',all_related) ).
tff(30,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| ( n = l )
| less_than(l,n)
| less_than(n,l) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| ( n = l )
| less_than(l,n)
| less_than(n,l) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| ( n = l )
| less_than(l,n)
| less_than(n,l) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| ( n = l )
| less_than(l,n)
| less_than(n,l) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
n = l,
inference(unit_resolution,[status(thm)],[36,33,23,20]) ).
tff(38,plain,
predecessor(n) = predecessor(l),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
a(predecessor(n)) = a(predecessor(l)),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( less_than(a(l),a(predecessor(n)))
<=> less_than(a(l),a(predecessor(l))) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( less_than(a(l),a(predecessor(l)))
<=> less_than(a(l),a(predecessor(n))) ),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
less_than(a(l),a(predecessor(n))),
inference(modus_ponens,[status(thm)],[13,41]) ).
tff(43,plain,
( less_than(one,n)
<=> less_than(one,l) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(44,plain,
( less_than(one,l)
<=> less_than(one,n) ),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
less_than(one,n),
inference(modus_ponens,[status(thm)],[16,44]) ).
tff(46,plain,
^ [X: $i] :
refl(( ( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) )
<=> ( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) )
<=> ! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) )
<=> ! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
^ [X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( less_than(X,n)
| less_than(n,X) )
<=> ( less_than(n,X)
| less_than(X,n) ) )),
( ( less_than(X,n)
| less_than(n,X)
| ~ less_than(one,n) )
<=> ( less_than(n,X)
| less_than(X,n)
| ~ less_than(one,n) ) )),
rewrite(( ( less_than(n,X)
| less_than(X,n)
| ~ less_than(one,n) )
<=> ( ~ less_than(one,n)
| less_than(n,X)
| less_than(X,n) ) )),
( ( less_than(X,n)
| less_than(n,X)
| ~ less_than(one,n) )
<=> ( ~ less_than(one,n)
| less_than(n,X)
| less_than(X,n) ) )),
( ( less_than(X,n)
| less_than(n,X)
| ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n))) )
<=> ( ~ less_than(one,n)
| less_than(n,X)
| less_than(X,n)
| ~ less_than(a(X),a(predecessor(n))) ) )),
rewrite(( ( ~ less_than(one,n)
| less_than(n,X)
| less_than(X,n)
| ~ less_than(a(X),a(predecessor(n))) )
<=> ( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) ) )),
( ( less_than(X,n)
| less_than(n,X)
| ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n))) )
<=> ( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X: $i] :
( less_than(X,n)
| less_than(n,X)
| ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n))) )
<=> ! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [X: $i] :
( less_than(X,n)
| less_than(n,X)
| ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
tff(52,plain,
! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) )
| less_than(n,l)
| ~ less_than(one,n)
| less_than(l,n)
| ~ less_than(a(l),a(predecessor(n))) )
<=> ( ~ ! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) )
| less_than(n,l)
| ~ less_than(one,n)
| less_than(l,n)
| ~ less_than(a(l),a(predecessor(n))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ( ~ less_than(one,n)
| ~ less_than(a(l),a(predecessor(n)))
| less_than(n,l)
| less_than(l,n) )
<=> ( less_than(n,l)
| ~ less_than(one,n)
| less_than(l,n)
| ~ less_than(a(l),a(predecessor(n))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ( ~ ! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) )
| ~ less_than(one,n)
| ~ less_than(a(l),a(predecessor(n)))
| less_than(n,l)
| less_than(l,n) )
<=> ( ~ ! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) )
| less_than(n,l)
| ~ less_than(one,n)
| less_than(l,n)
| ~ less_than(a(l),a(predecessor(n))) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( ~ ! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) )
| ~ less_than(one,n)
| ~ less_than(a(l),a(predecessor(n)))
| less_than(n,l)
| less_than(l,n) )
<=> ( ~ ! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) )
| less_than(n,l)
| ~ less_than(one,n)
| less_than(l,n)
| ~ less_than(a(l),a(predecessor(n))) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
( ~ ! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) )
| ~ less_than(one,n)
| ~ less_than(a(l),a(predecessor(n)))
| less_than(n,l)
| less_than(l,n) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [X: $i] :
( ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n)))
| less_than(n,X)
| less_than(X,n) )
| less_than(n,l)
| ~ less_than(one,n)
| less_than(l,n)
| ~ less_than(a(l),a(predecessor(n))) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
$false,
inference(unit_resolution,[status(thm)],[61,23,55,20,45,42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV008-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n004.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 09:20:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Unsatisfiable
% 0.12/0.36 % SZS output start Proof
% See solution above
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------