%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO051-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 27
% Syntax : Number of formulae : 56 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 420 ( 53 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 583 ( 241 ~; 306 |; 0 &)
% ( 36 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 22 ( 22 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 200 ( 184 !; 0 ?; 200 :)
% Comments :
%------------------------------------------------------------------------------
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(w_type,type,
w: $i ).
tff(x_type,type,
x: $i ).
tff(u_type,type,
u: $i ).
tff(v_type,type,
v: $i ).
tff(1,plain,
( ~ between(v,w,x)
<=> ~ between(v,w,x) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ between(v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_not_between_v_and_x) ).
tff(3,plain,
~ between(v,w,x),
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/sandbox/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,U: $i,X: $i] :
refl(( ( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
<=> ( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
rewrite(( ( ~ between(U,V,W)
| ~ between(U,W,X)
| between(V,W,X) )
<=> ( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(U,W,X)
| between(V,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(U,W,X)
| between(V,W,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b5) ).
tff(13,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| between(v,w,x)
| ~ between(u,v,w)
| ~ between(u,w,x) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| between(v,w,x)
| ~ between(u,v,w)
| ~ between(u,w,x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ between(u,v,w)
| between(v,w,x)
| ~ between(u,w,x) )
<=> ( between(v,w,x)
| ~ between(u,v,w)
| ~ between(u,w,x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| ~ between(u,v,w)
| between(v,w,x)
| ~ between(u,w,x) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| between(v,w,x)
| ~ between(u,v,w)
| ~ between(u,w,x) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| ~ between(u,v,w)
| between(v,w,x)
| ~ between(u,w,x) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| between(v,w,x)
| ~ between(u,v,w)
| ~ between(u,w,x) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| ~ between(u,v,w)
| between(v,w,x)
| ~ between(u,w,x) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| between(v,w,x)
| ~ between(u,v,w)
| ~ between(u,w,x) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ between(u,w,x),
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
tff(24,plain,
( ( u != v )
<=> ( u != v ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
tff(26,plain,
u != v,
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
( between(u,v,x)
<=> between(u,v,x) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
between(u,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_x) ).
tff(29,plain,
between(u,v,x),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ between(U,V,W)
| ~ between(U,V,X) )
<=> ( ~ between(U,V,X)
| ~ between(U,V,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V ) )
<=> ( ~ between(U,V,X)
| ~ between(U,V,W)
| ( U = V ) ) )),
rewrite(( ( ~ between(U,V,X)
| ~ between(U,V,W)
| ( U = V ) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V ) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(U,W,X) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X) ) )),
rewrite(( ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(U,W,X) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(U,W,X)
| between(U,X,W) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) ) )),
rewrite(( ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(U,W,X)
| between(U,X,W) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(U,W,X)
| between(U,X,W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(U,W,X)
| between(U,X,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b12) ).
tff(36,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) )
| ( u = v )
| ~ between(u,v,w)
| ~ between(u,v,x)
| between(u,x,w)
| between(u,w,x) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) )
| ( u = v )
| ~ between(u,v,w)
| ~ between(u,v,x)
| between(u,x,w)
| between(u,w,x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ( u = v )
| ~ between(u,v,x)
| ~ between(u,v,w)
| between(u,w,x)
| between(u,x,w) )
<=> ( ( u = v )
| ~ between(u,v,w)
| ~ between(u,v,x)
| between(u,x,w)
| between(u,w,x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) )
| ( u = v )
| ~ between(u,v,x)
| ~ between(u,v,w)
| between(u,w,x)
| between(u,x,w) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) )
| ( u = v )
| ~ between(u,v,w)
| ~ between(u,v,x)
| between(u,x,w)
| between(u,w,x) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) )
| ( u = v )
| ~ between(u,v,x)
| ~ between(u,v,w)
| between(u,w,x)
| between(u,x,w) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) )
| ( u = v )
| ~ between(u,v,w)
| ~ between(u,v,x)
| between(u,x,w)
| between(u,w,x) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) )
| ( u = v )
| ~ between(u,v,x)
| ~ between(u,v,w)
| between(u,w,x)
| between(u,x,w) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(U,W,X)
| between(U,X,W) )
| ( u = v )
| ~ between(u,v,w)
| ~ between(u,v,x)
| between(u,x,w)
| between(u,w,x) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
between(u,x,w),
inference(unit_resolution,[status(thm)],[45,39,6,29,26,23]) ).
tff(47,plain,
( ~ between(v,x,w)
<=> ~ between(v,x,w) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
~ between(v,x,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_between_v_and_w) ).
tff(49,plain,
~ between(v,x,w),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| between(v,x,w)
| ~ between(u,v,x)
| ~ between(u,x,w) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| between(v,x,w)
| ~ between(u,v,x)
| ~ between(u,x,w) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( ~ between(u,v,x)
| between(v,x,w)
| ~ between(u,x,w) )
<=> ( between(v,x,w)
| ~ between(u,v,x)
| ~ between(u,x,w) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| ~ between(u,v,x)
| between(v,x,w)
| ~ between(u,x,w) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| between(v,x,w)
| ~ between(u,v,x)
| ~ between(u,x,w) ) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| ~ between(u,v,x)
| between(v,x,w)
| ~ between(u,x,w) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| between(v,x,w)
| ~ between(u,v,x)
| ~ between(u,x,w) ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| ~ between(u,v,x)
| between(v,x,w)
| ~ between(u,x,w) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(V,W,X)
| ~ between(U,W,X) )
| between(v,x,w)
| ~ between(u,v,x)
| ~ between(u,x,w) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
$false,
inference(unit_resolution,[status(thm)],[55,16,29,49,46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO051-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:10:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% See solution above
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------