%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV003-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 22 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 96 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 127 ( 60 ~; 56 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 48 ( 45 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_than_type,type,
less_than: ( $i * $i ) > $o ).
tff(i_type,type,
i: $i ).
tff(j_type,type,
j: $i ).
tff(k_type,type,
k: $i ).
tff(1,plain,
( less_than(j,i)
<=> less_than(j,i) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
less_than(j,i),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
tff(3,plain,
less_than(j,i),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ~ less_than(k,i)
<=> ~ less_than(k,i) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
~ less_than(k,i),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
tff(6,plain,
~ less_than(k,i),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( less_than(k,j)
<=> less_than(k,j) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
less_than(k,j),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
tff(9,plain,
less_than(k,j),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( less_than(X,Z)
| ~ less_than(X,Y) )
<=> ( ~ less_than(X,Y)
| less_than(X,Z) ) )),
( ( less_than(X,Z)
| ~ less_than(X,Y)
| ~ less_than(Y,Z) )
<=> ( ~ less_than(X,Y)
| less_than(X,Z)
| ~ less_than(Y,Z) ) )),
rewrite(( ( ~ less_than(X,Y)
| less_than(X,Z)
| ~ less_than(Y,Z) )
<=> ( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ) )),
( ( less_than(X,Z)
| ~ less_than(X,Y)
| ~ less_than(Y,Z) )
<=> ( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [Z: $i,Y: $i,X: $i] :
( less_than(X,Z)
| ~ less_than(X,Y)
| ~ less_than(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,axiom,
! [Z: $i,Y: $i,X: $i] :
( less_than(X,Z)
| ~ less_than(X,Y)
| ~ less_than(Y,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV001-0.ax',transitivity_of_less_than) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
inference(modus_ponens,[status(thm)],[17,10]) ).
tff(19,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
| ~ less_than(j,i)
| ~ less_than(k,j)
| less_than(k,i) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
| ~ less_than(j,i)
| ~ less_than(k,j)
| less_than(k,i) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
| ~ less_than(j,i)
| ~ less_than(k,j)
| less_than(k,i) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
| ~ less_than(j,i)
| ~ less_than(k,j)
| less_than(k,i) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
$false,
inference(unit_resolution,[status(thm)],[21,18,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV003-1 : TPTP v9.0.0. Released v1.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 09:21:25 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38 % SZS output start Proof
% See solution above
% 0.13/0.38 % E exiting
%------------------------------------------------------------------------------