%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO040-2 : 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 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 25
% Syntax : Number of formulae : 55 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 214 ( 34 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 292 ( 138 ~; 134 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-5 aty)
% Number of variables : 204 ( 182 !; 0 ?; 204 :)
% Comments :
%------------------------------------------------------------------------------
tff(v_type,type,
v: $i ).
tff(u_type,type,
u: $i ).
tff(inner_pasch_type,type,
inner_pasch: ( $i * $i * $i * $i * $i ) > $i ).
tff(w_type,type,
w: $i ).
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(1,plain,
( between(v,u,w)
<=> between(v,u,w) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
between(v,u,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_between_v_and_w) ).
tff(3,plain,
between(v,u,w),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( between(u,v,w)
<=> between(u,v,w) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
tff(6,plain,
between(u,v,w),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
refl(( ( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) )
<=> ( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
rewrite(( ( ~ between(U,V,W)
| ~ between(Y,X,W)
| between(X,inner_pasch(U,V,W,X,Y),U) )
<=> ( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(Y,X,W)
| between(X,inner_pasch(U,V,W,X,Y),U) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(Y,X,W)
| between(X,inner_pasch(U,V,W,X,Y),U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).
tff(13,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) )
| ~ between(u,v,w)
| ~ between(v,u,w)
| between(v,inner_pasch(v,u,w,v,u),v) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) )
| ~ between(u,v,w)
| ~ between(v,u,w)
| between(v,inner_pasch(v,u,w,v,u),v) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) )
| ~ between(u,v,w)
| ~ between(v,u,w)
| between(v,inner_pasch(v,u,w,v,u),v) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(X,inner_pasch(U,V,W,X,Y),U) )
| ~ between(u,v,w)
| ~ between(v,u,w)
| between(v,inner_pasch(v,u,w,v,u),v) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
between(v,inner_pasch(v,u,w,v,u),v),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ between(X,Y,X)
| ( X = Y ) )
<=> ( ~ between(X,Y,X)
| ( X = Y ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,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)],[21]) ).
tff(23,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(24,axiom,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
tff(25,plain,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(v,inner_pasch(v,u,w,v,u),v)
| ( v = inner_pasch(v,u,w,v,u) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(v,inner_pasch(v,u,w,v,u),v)
| ( v = inner_pasch(v,u,w,v,u) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(v,inner_pasch(v,u,w,v,u),v)
| ( v = inner_pasch(v,u,w,v,u) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(v,inner_pasch(v,u,w,v,u),v)
| ( v = inner_pasch(v,u,w,v,u) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
v = inner_pasch(v,u,w,v,u),
inference(unit_resolution,[status(thm)],[30,27,20]) ).
tff(32,plain,
inner_pasch(v,u,w,v,u) = v,
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
refl(( ( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) )
<=> ( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
rewrite(( ( ~ between(U,V,W)
| ~ between(Y,X,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) )
<=> ( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(Y,X,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(Y,X,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).
tff(39,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) )
| ~ between(u,v,w)
| ~ between(v,u,w)
| between(u,inner_pasch(v,u,w,v,u),u) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) )
| ~ between(u,v,w)
| ~ between(v,u,w)
| between(u,inner_pasch(v,u,w,v,u),u) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) )
| ~ between(u,v,w)
| ~ between(v,u,w)
| between(u,inner_pasch(v,u,w,v,u),u) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ between(Y,X,W)
| ~ between(U,V,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) )
| ~ between(u,v,w)
| ~ between(v,u,w)
| between(u,inner_pasch(v,u,w,v,u),u) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
between(u,inner_pasch(v,u,w,v,u),u),
inference(unit_resolution,[status(thm)],[45,42,6,3]) ).
tff(47,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(u,inner_pasch(v,u,w,v,u),u)
| ( u = inner_pasch(v,u,w,v,u) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(u,inner_pasch(v,u,w,v,u),u)
| ( u = inner_pasch(v,u,w,v,u) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(u,inner_pasch(v,u,w,v,u),u)
| ( u = inner_pasch(v,u,w,v,u) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(u,inner_pasch(v,u,w,v,u),u)
| ( u = inner_pasch(v,u,w,v,u) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
u = inner_pasch(v,u,w,v,u),
inference(unit_resolution,[status(thm)],[49,27,46]) ).
tff(51,plain,
u = v,
inference(transitivity,[status(thm)],[50,32]) ).
tff(52,plain,
( ( u != v )
<=> ( u != v ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_u_is_v) ).
tff(54,plain,
u != v,
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
$false,
inference(unit_resolution,[status(thm)],[54,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO040-2 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n003.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 : Thu Jun 19 14:08:09 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38 % SZS output start Proof
% See solution above
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------