%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO048-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:05:26 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 24
% Syntax : Number of formulae : 48 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 198 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 279 ( 132 ~; 128 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-5 aty)
% Number of variables : 176 ( 163 !; 0 ?; 176 :)
% Comments :
%------------------------------------------------------------------------------
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
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(v1_type,type,
v1: $i ).
tff(u1_type,type,
u1: $i ).
tff(x_type,type,
x: $i ).
tff(v_type,type,
v: $i ).
tff(1,plain,
( between(u1,v1,w)
<=> between(u1,v1,w) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
between(u1,v1,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v1_between_u1_and_w) ).
tff(3,plain,
between(u1,v1,w),
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(u1,v1,w)
| between(w,v1,u1) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u1,v1,w)
| between(w,v1,u1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u1,v1,w)
| between(w,v1,u1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u1,v1,w)
| between(w,v1,u1) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
between(w,v1,u1),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( between(u,x,u1)
<=> between(u,x,u1) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
between(u,x,u1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_between_u_and_u1) ).
tff(17,plain,
between(u,x,u1),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,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(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) )
<=> ! [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)],[18]) ).
tff(20,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(21,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(22,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)],[21]) ).
tff(23,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(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) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,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)],[24,20]) ).
tff(26,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)],[25]) ).
tff(27,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)],[26,19]) ).
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) )
| ~ between(u,x,u1)
| ~ between(w,v1,u1)
| between(v1,inner_pasch(u,x,u1,v1,w),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) )
| ~ between(u,x,u1)
| ~ between(w,v1,u1)
| between(v1,inner_pasch(u,x,u1,v1,w),u) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( ~ between(w,v1,u1)
| ~ between(u,x,u1)
| between(v1,inner_pasch(u,x,u1,v1,w),u) )
<=> ( ~ between(u,x,u1)
| ~ between(w,v1,u1)
| between(v1,inner_pasch(u,x,u1,v1,w),u) ) ),
inference(rewrite,[status(thm)],[]) ).
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) )
| ~ between(w,v1,u1)
| ~ between(u,x,u1)
| between(v1,inner_pasch(u,x,u1,v1,w),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) )
| ~ between(u,x,u1)
| ~ between(w,v1,u1)
| between(v1,inner_pasch(u,x,u1,v1,w),u) ) ),
inference(monotonicity,[status(thm)],[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) )
| ~ between(w,v1,u1)
| ~ between(u,x,u1)
| between(v1,inner_pasch(u,x,u1,v1,w),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) )
| ~ between(u,x,u1)
| ~ between(w,v1,u1)
| between(v1,inner_pasch(u,x,u1,v1,w),u) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
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,v1,u1)
| ~ between(u,x,u1)
| between(v1,inner_pasch(u,x,u1,v1,w),u) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,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,x,u1)
| ~ between(w,v1,u1)
| between(v1,inner_pasch(u,x,u1,v1,w),u) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
between(v1,inner_pasch(u,x,u1,v1,w),u),
inference(unit_resolution,[status(thm)],[33,27,17,14]) ).
tff(35,plain,
( between(u,v,w)
<=> between(u,v,w) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
tff(37,plain,
between(u,v,w),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,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(39,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(40,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)],[39,38]) ).
tff(41,plain,
between(w,v,u),
inference(unit_resolution,[status(thm)],[40,10,37]) ).
tff(42,plain,
( ~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1)
<=> ~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_conclusion2) ).
tff(44,plain,
~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,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(v1,inner_pasch(u,x,u1,v1,w),u)
| between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1) )
<=> ( ~ ! [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(v1,inner_pasch(u,x,u1,v1,w),u)
| between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,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(v1,inner_pasch(u,x,u1,v1,w),u)
| between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,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(v1,inner_pasch(u,x,u1,v1,w),u)
| between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[47,27,44,41,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO048-3 : TPTP v9.0.0. Released v1.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.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 14:11:31 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39 % SZS output start Proof
% See solution above
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------