%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO043-3 : 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 05:05:25 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 32
% Syntax : Number of formulae : 73 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 315 ( 19 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 444 ( 208 ~; 204 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 6 ( 6 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 : 5 ( 5 usr; 4 con; 0-5 aty)
% Number of variables : 287 ( 262 !; 0 ?; 287 :)
% Comments :
%------------------------------------------------------------------------------
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(x_type,type,
x: $i ).
tff(w_type,type,
w: $i ).
tff(v_type,type,
v: $i ).
tff(inner_pasch_type,type,
inner_pasch: ( $i * $i * $i * $i * $i ) > $i ).
tff(u_type,type,
u: $i ).
tff(1,plain,
( between(u,w,x)
<=> between(u,w,x) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
between(u,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_between_u_and_x) ).
tff(3,plain,
between(u,w,x),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ between(U,V,W)
| between(W,V,U) )
<=> ( ~ between(U,V,W)
| between(W,V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
tff(8,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,w,x)
| between(x,w,u) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,w,x)
| between(x,w,u) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,w,x)
| between(x,w,u) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,w,x)
| between(x,w,u) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
between(x,w,u),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( between(u,v,w)
<=> between(u,v,w) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
tff(17,plain,
between(u,v,w),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
between(w,v,u),
inference(unit_resolution,[status(thm)],[20,10,17]) ).
tff(22,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(23,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)],[22]) ).
tff(24,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(25,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(26,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)],[25]) ).
tff(27,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(28,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)],[27,26]) ).
tff(29,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)],[28,24]) ).
tff(30,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)],[29]) ).
tff(31,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)],[30,23]) ).
tff(32,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(w,v,u)
| ~ between(x,w,u)
| between(w,inner_pasch(w,v,u,w,x),w) )
<=> ( ~ ! [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(w,v,u)
| ~ between(x,w,u)
| between(w,inner_pasch(w,v,u,w,x),w) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ between(x,w,u)
| ~ between(w,v,u)
| between(w,inner_pasch(w,v,u,w,x),w) )
<=> ( ~ between(w,v,u)
| ~ between(x,w,u)
| between(w,inner_pasch(w,v,u,w,x),w) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,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(x,w,u)
| ~ between(w,v,u)
| between(w,inner_pasch(w,v,u,w,x),w) )
<=> ( ~ ! [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(w,v,u)
| ~ between(x,w,u)
| between(w,inner_pasch(w,v,u,w,x),w) ) ),
inference(monotonicity,[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(X,inner_pasch(U,V,W,X,Y),U) )
| ~ between(x,w,u)
| ~ between(w,v,u)
| between(w,inner_pasch(w,v,u,w,x),w) )
<=> ( ~ ! [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(w,v,u)
| ~ between(x,w,u)
| between(w,inner_pasch(w,v,u,w,x),w) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,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(x,w,u)
| ~ between(w,v,u)
| between(w,inner_pasch(w,v,u,w,x),w) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,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(w,v,u)
| ~ between(x,w,u)
| between(w,inner_pasch(w,v,u,w,x),w) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
between(w,inner_pasch(w,v,u,w,x),w),
inference(unit_resolution,[status(thm)],[37,31,21,14]) ).
tff(39,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ between(X,Y,X)
| ( X = Y ) )
<=> ( ~ between(X,Y,X)
| ( X = Y ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,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)],[39]) ).
tff(41,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(42,axiom,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
tff(43,plain,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(w,inner_pasch(w,v,u,w,x),w)
| ( w = inner_pasch(w,v,u,w,x) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(w,inner_pasch(w,v,u,w,x),w)
| ( w = inner_pasch(w,v,u,w,x) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(w,inner_pasch(w,v,u,w,x),w)
| ( w = inner_pasch(w,v,u,w,x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(w,inner_pasch(w,v,u,w,x),w)
| ( w = inner_pasch(w,v,u,w,x) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
w = inner_pasch(w,v,u,w,x),
inference(unit_resolution,[status(thm)],[48,45,38]) ).
tff(50,plain,
( between(v,w,x)
<=> between(v,inner_pasch(w,v,u,w,x),x) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( between(v,inner_pasch(w,v,u,w,x),x)
<=> between(v,w,x) ),
inference(symmetry,[status(thm)],[50]) ).
tff(52,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(53,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)],[52]) ).
tff(54,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(55,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(56,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)],[55]) ).
tff(57,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(58,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)],[57,56]) ).
tff(59,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)],[58,54]) ).
tff(60,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)],[59]) ).
tff(61,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)],[60,53]) ).
tff(62,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(w,v,u)
| ~ between(x,w,u)
| between(v,inner_pasch(w,v,u,w,x),x) )
<=> ( ~ ! [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(w,v,u)
| ~ between(x,w,u)
| between(v,inner_pasch(w,v,u,w,x),x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( ~ between(x,w,u)
| ~ between(w,v,u)
| between(v,inner_pasch(w,v,u,w,x),x) )
<=> ( ~ between(w,v,u)
| ~ between(x,w,u)
| between(v,inner_pasch(w,v,u,w,x),x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,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(x,w,u)
| ~ between(w,v,u)
| between(v,inner_pasch(w,v,u,w,x),x) )
<=> ( ~ ! [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(w,v,u)
| ~ between(x,w,u)
| between(v,inner_pasch(w,v,u,w,x),x) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,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(x,w,u)
| ~ between(w,v,u)
| between(v,inner_pasch(w,v,u,w,x),x) )
<=> ( ~ ! [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(w,v,u)
| ~ between(x,w,u)
| between(v,inner_pasch(w,v,u,w,x),x) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,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(x,w,u)
| ~ between(w,v,u)
| between(v,inner_pasch(w,v,u,w,x),x) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,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(w,v,u)
| ~ between(x,w,u)
| between(v,inner_pasch(w,v,u,w,x),x) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
between(v,inner_pasch(w,v,u,w,x),x),
inference(unit_resolution,[status(thm)],[67,61,21,14]) ).
tff(69,plain,
between(v,w,x),
inference(modus_ponens,[status(thm)],[68,51]) ).
tff(70,plain,
( ~ between(v,w,x)
<=> ~ between(v,w,x) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
~ between(v,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_w_between_v_and_x) ).
tff(72,plain,
~ between(v,w,x),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
$false,
inference(unit_resolution,[status(thm)],[72,69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO043-3 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:08:24 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start Proof
% See solution above
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------