%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO038-2 : TPTP v9.0.0. Released v1.0.0.
% 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 05:05:24 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 21 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 1 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-4 aty)
% Number of variables : 40 ( 36 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(extension_type,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(x_type,type,
x: $i ).
tff(w_type,type,
w: $i ).
tff(v_type,type,
v: $i ).
tff(u_type,type,
u: $i ).
tff(y_type,type,
y: $i ).
tff(1,plain,
( ( y = extension(u,v,w,x) )
<=> ( y = extension(u,v,w,x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
y = extension(u,v,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',y_is_extension) ).
tff(3,plain,
y = extension(u,v,w,x),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
extension(u,v,w,x) = y,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( between(u,v,extension(u,v,w,x))
<=> between(u,v,y) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( between(u,v,y)
<=> between(u,v,extension(u,v,w,x)) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ~ between(u,v,y)
<=> ~ between(u,v,extension(u,v,w,x)) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ~ between(u,v,y)
<=> ~ between(u,v,y) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
~ between(u,v,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary) ).
tff(10,plain,
~ between(u,v,y),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
~ between(u,v,extension(u,v,w,x)),
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
^ [W: $i,V: $i,Y: $i,X: $i] :
refl(( between(X,Y,extension(X,Y,W,V))
<=> between(X,Y,extension(X,Y,W,V)) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V))
<=> ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V))
<=> ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
tff(16,plain,
! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V))
| between(u,v,extension(u,v,w,x)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
between(u,v,extension(u,v,w,x)),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
$false,
inference(unit_resolution,[status(thm)],[20,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO038-2 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:07:39 EDT 2025
% 0.11/0.33 % 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
%------------------------------------------------------------------------------