%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV005-1 : TPTP v9.0.0. Released v1.0.0.
% 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 05:31:19 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 29 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 195 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 248 ( 96 ~; 133 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 21 ( 19 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_than_type,type,
less_than: ( $i * $i ) > $o ).
tff(n_type,type,
n: $i ).
tff(a_type,type,
a: $i > $i ).
tff(predecessor_type,type,
predecessor: $i > $i ).
tff(l_type,type,
l: $i ).
tff(one_type,type,
one: $i ).
tff(k_type,type,
k: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) )
<=> ( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) )
<=> ! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) )
<=> ! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( less_than(X,l)
| less_than(n,X) )
<=> ( less_than(X,l)
| less_than(n,X) ) )),
( ( less_than(X,l)
| less_than(n,X)
| ~ less_than(one,l) )
<=> ( less_than(X,l)
| less_than(n,X)
| ~ less_than(one,l) ) )),
rewrite(( ( less_than(X,l)
| less_than(n,X)
| ~ less_than(one,l) )
<=> ( ~ less_than(one,l)
| less_than(X,l)
| less_than(n,X) ) )),
( ( less_than(X,l)
| less_than(n,X)
| ~ less_than(one,l) )
<=> ( ~ less_than(one,l)
| less_than(X,l)
| less_than(n,X) ) )),
( ( less_than(X,l)
| less_than(n,X)
| ~ less_than(one,l)
| ~ less_than(a(X),a(predecessor(l))) )
<=> ( ~ less_than(one,l)
| less_than(X,l)
| less_than(n,X)
| ~ less_than(a(X),a(predecessor(l))) ) )),
rewrite(( ( ~ less_than(one,l)
| less_than(X,l)
| less_than(n,X)
| ~ less_than(a(X),a(predecessor(l))) )
<=> ( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) ) )),
( ( less_than(X,l)
| less_than(n,X)
| ~ less_than(one,l)
| ~ less_than(a(X),a(predecessor(l))) )
<=> ( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X: $i] :
( less_than(X,l)
| less_than(n,X)
| ~ less_than(one,l)
| ~ less_than(a(X),a(predecessor(l))) )
<=> ! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [X: $i] :
( less_than(X,l)
| less_than(n,X)
| ~ less_than(one,l)
| ~ less_than(a(X),a(predecessor(l))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
tff(7,plain,
! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( less_than(a(k),a(predecessor(l)))
<=> less_than(a(k),a(predecessor(l))) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
less_than(a(k),a(predecessor(l))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
tff(13,plain,
less_than(a(k),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/sandbox/benchmark/theBenchmark.p',clause_5) ).
tff(16,plain,
less_than(one,l),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ~ less_than(k,l)
<=> ~ less_than(k,l) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
~ less_than(k,l),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
tff(19,plain,
~ less_than(k,l),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ less_than(n,k)
<=> ~ less_than(n,k) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
~ less_than(n,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
tff(22,plain,
~ less_than(n,k),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) )
| less_than(n,k)
| less_than(k,l)
| ~ less_than(one,l)
| ~ less_than(a(k),a(predecessor(l))) )
<=> ( ~ ! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) )
| less_than(n,k)
| less_than(k,l)
| ~ less_than(one,l)
| ~ less_than(a(k),a(predecessor(l))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( ~ less_than(one,l)
| less_than(k,l)
| ~ less_than(a(k),a(predecessor(l)))
| less_than(n,k) )
<=> ( less_than(n,k)
| less_than(k,l)
| ~ less_than(one,l)
| ~ less_than(a(k),a(predecessor(l))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) )
| ~ less_than(one,l)
| less_than(k,l)
| ~ less_than(a(k),a(predecessor(l)))
| less_than(n,k) )
<=> ( ~ ! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) )
| less_than(n,k)
| less_than(k,l)
| ~ less_than(one,l)
| ~ less_than(a(k),a(predecessor(l))) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) )
| ~ less_than(one,l)
| less_than(k,l)
| ~ less_than(a(k),a(predecessor(l)))
| less_than(n,k) )
<=> ( ~ ! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) )
| less_than(n,k)
| less_than(k,l)
| ~ less_than(one,l)
| ~ less_than(a(k),a(predecessor(l))) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) )
| ~ less_than(one,l)
| less_than(k,l)
| ~ less_than(a(k),a(predecessor(l)))
| less_than(n,k) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [X: $i] :
( ~ less_than(one,l)
| less_than(X,l)
| ~ less_than(a(X),a(predecessor(l)))
| less_than(n,X) )
| less_than(n,k)
| less_than(k,l)
| ~ less_than(one,l)
| ~ less_than(a(k),a(predecessor(l))) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,22,19,16,13,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SWV005-1 : TPTP v9.0.0. Released v1.0.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.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 : Fri Jun 20 09:21:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% See solution above
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------