%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO039-3 : 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 05:05:24 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 39 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 25 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 70 ( 31 ~; 24 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 2 ( 2 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 46 ( 42 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(x_type,type,
x: $i ).
tff(v_type,type,
v: $i ).
tff(w_type,type,
w: $i ).
tff(u_type,type,
u: $i ).
tff(1,plain,
( ( u = x )
<=> ( u = x ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
u = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_x) ).
tff(3,plain,
u = x,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
x = u,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( between(x,w,x)
<=> between(u,w,x) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( between(u,w,x)
<=> between(x,w,x) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( between(u,w,x)
<=> between(u,w,x) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
between(u,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_between_u_and_x) ).
tff(9,plain,
between(u,w,x),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
between(x,w,x),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ between(X,Y,X)
| ( X = Y ) )
<=> ( ~ between(X,Y,X)
| ( X = Y ) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
<=> ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
<=> ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
tff(15,plain,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(x,w,x)
| ( x = w ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(x,w,x)
| ( x = w ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(x,w,x)
| ( x = w ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(x,w,x)
| ( x = w ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ~ between(x,w,x)
| ( x = w ) ),
inference(unit_resolution,[status(thm)],[20,17]) ).
tff(22,plain,
x = w,
inference(unit_resolution,[status(thm)],[21,10]) ).
tff(23,plain,
( between(v,x,x)
<=> between(v,w,x) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( between(v,w,x)
<=> between(v,x,x) ),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( ~ between(v,w,x)
<=> ~ between(v,x,x) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ~ between(v,w,x)
<=> ~ between(v,w,x) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
~ between(v,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary) ).
tff(28,plain,
~ between(v,w,x),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ between(v,x,x),
inference(modus_ponens,[status(thm)],[28,25]) ).
tff(30,plain,
^ [V: $i,U: $i] :
refl(( between(U,V,V)
<=> between(U,V,V) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [V: $i,U: $i] : between(U,V,V)
<=> ! [V: $i,U: $i] : between(U,V,V) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [V: $i,U: $i] : between(U,V,V)
<=> ! [V: $i,U: $i] : between(U,V,V) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [V: $i,U: $i] : between(U,V,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
tff(34,plain,
! [V: $i,U: $i] : between(U,V,V),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [V: $i,U: $i] : between(U,V,V),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [V: $i,U: $i] : between(U,V,V),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [V: $i,U: $i] : between(U,V,V)
| between(v,x,x) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
between(v,x,x),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
$false,
inference(unit_resolution,[status(thm)],[38,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO039-3 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.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 14:07:08 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Unsatisfiable
% 0.11/0.38 % SZS output start Proof
% See solution above
% 0.11/0.38 % E exiting
%------------------------------------------------------------------------------