%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO008-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:05:18 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 47
% Syntax : Number of formulae : 127 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 585 ( 40 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 806 ( 362 ~; 384 |; 0 &)
% ( 60 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 14 ( 14 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 : 6 ( 6 usr; 5 con; 0-4 aty)
% Number of variables : 386 ( 356 !; 0 ?; 386 :)
% Comments :
%------------------------------------------------------------------------------
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(insertion_type,type,
insertion: ( $i * $i * $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(d_type,type,
d: $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
( between(a,c,e)
<=> between(a,c,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
between(a,c,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_between_a_and_e) ).
tff(3,plain,
between(a,c,e),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
<=> ( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i3) ).
tff(8,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,c,e)
| ( c = insertion(a,e,a,c) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,c,e)
| ( c = insertion(a,e,a,c) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,c,e)
| ( c = insertion(a,e,a,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,c,e)
| ( c = insertion(a,e,a,c) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c = insertion(a,e,a,c),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
insertion(a,e,a,c) = c,
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( between(a,insertion(a,e,a,c),e)
<=> between(a,c,e) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( between(a,c,e)
<=> between(a,insertion(a,e,a,c),e) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
between(a,insertion(a,e,a,c),e),
inference(modus_ponens,[status(thm)],[3,17]) ).
tff(19,plain,
( between(a,d,e)
<=> between(a,d,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
between(a,d,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_between_a_and_e) ).
tff(21,plain,
between(a,d,e),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,d,e)
| ( d = insertion(a,e,a,d) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,d,e)
| ( d = insertion(a,e,a,d) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,d,e)
| ( d = insertion(a,e,a,d) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,d,e)
| ( d = insertion(a,e,a,d) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
d = insertion(a,e,a,d),
inference(unit_resolution,[status(thm)],[24,10,21]) ).
tff(26,plain,
insertion(a,e,a,d) = d,
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
( between(a,insertion(a,e,a,d),e)
<=> between(a,d,e) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( between(a,d,e)
<=> between(a,insertion(a,e,a,d),e) ),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
between(a,insertion(a,e,a,d),e),
inference(modus_ponens,[status(thm)],[21,28]) ).
tff(30,plain,
( between(c,b,d)
<=> between(c,b,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
between(c,b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_between_c_and_d) ).
tff(32,plain,
between(c,b,d),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(c,b,d)
| ( b = insertion(c,d,c,b) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(c,b,d)
| ( b = insertion(c,d,c,b) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(c,b,d)
| ( b = insertion(c,d,c,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(c,b,d)
| ( b = insertion(c,d,c,b) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
b = insertion(c,d,c,b),
inference(unit_resolution,[status(thm)],[35,10,32]) ).
tff(37,plain,
insertion(c,d,c,b) = b,
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
( between(insertion(a,e,a,d),insertion(c,d,c,b),e)
<=> between(d,b,e) ),
inference(monotonicity,[status(thm)],[26,37]) ).
tff(39,plain,
( between(d,b,e)
<=> between(insertion(a,e,a,d),insertion(c,d,c,b),e) ),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( ~ between(d,b,e)
<=> ~ between(insertion(a,e,a,d),insertion(c,d,c,b),e) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ~ between(a,b,e)
<=> ~ between(a,b,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
~ between(a,b,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_betweenness) ).
tff(43,plain,
~ between(a,b,e),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
<=> ( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
rewrite(( ( ~ between(U,V,X)
| ~ between(V,W,X)
| between(U,W,X) )
<=> ( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| ~ between(V,W,X)
| between(U,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| ~ between(V,W,X)
| between(U,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b8) ).
tff(50,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| between(a,b,e)
| ~ between(a,d,e)
| ~ between(d,b,e) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| between(a,b,e)
| ~ between(a,d,e)
| ~ between(d,b,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( ~ between(a,d,e)
| between(a,b,e)
| ~ between(d,b,e) )
<=> ( between(a,b,e)
| ~ between(a,d,e)
| ~ between(d,b,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| ~ between(a,d,e)
| between(a,b,e)
| ~ between(d,b,e) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| between(a,b,e)
| ~ between(a,d,e)
| ~ between(d,b,e) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| ~ between(a,d,e)
| between(a,b,e)
| ~ between(d,b,e) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| between(a,b,e)
| ~ between(a,d,e)
| ~ between(d,b,e) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| ~ between(a,d,e)
| between(a,b,e)
| ~ between(d,b,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| between(a,b,e)
| ~ between(a,d,e)
| ~ between(d,b,e) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
~ between(d,b,e),
inference(unit_resolution,[status(thm)],[59,53,21,43]) ).
tff(61,plain,
~ between(insertion(a,e,a,d),insertion(c,d,c,b),e),
inference(modus_ponens,[status(thm)],[60,40]) ).
tff(62,plain,
( between(insertion(a,e,a,d),insertion(c,d,c,b),insertion(a,e,a,c))
<=> between(d,b,c) ),
inference(monotonicity,[status(thm)],[26,37,15]) ).
tff(63,plain,
( between(d,b,c)
<=> between(insertion(a,e,a,d),insertion(c,d,c,b),insertion(a,e,a,c)) ),
inference(symmetry,[status(thm)],[62]) ).
tff(64,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(65,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)],[64]) ).
tff(66,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(67,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
tff(68,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(c,b,d)
| between(d,b,c) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(c,b,d)
| between(d,b,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(c,b,d)
| between(d,b,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(c,b,d)
| between(d,b,c) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
between(d,b,c),
inference(unit_resolution,[status(thm)],[73,70,32]) ).
tff(75,plain,
between(insertion(a,e,a,d),insertion(c,d,c,b),insertion(a,e,a,c)),
inference(modus_ponens,[status(thm)],[74,63]) ).
tff(76,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) )
<=> ( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) ) )),
inference(bind,[status(th)],[]) ).
tff(77,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
rewrite(( ( ~ between(U,V,W)
| ~ between(U,W,X)
| between(U,V,X) )
<=> ( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(U,W,X)
| between(U,V,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(U,W,X)
| between(U,V,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b9) ).
tff(82,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) ),
inference(modus_ponens,[status(thm)],[84,77]) ).
tff(86,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) )
| between(insertion(a,e,a,d),insertion(c,d,c,b),e)
| ~ between(insertion(a,e,a,d),insertion(c,d,c,b),insertion(a,e,a,c))
| ~ between(insertion(a,e,a,d),insertion(a,e,a,c),e) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) )
| between(insertion(a,e,a,d),insertion(c,d,c,b),e)
| ~ between(insertion(a,e,a,d),insertion(c,d,c,b),insertion(a,e,a,c))
| ~ between(insertion(a,e,a,d),insertion(a,e,a,c),e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) )
| between(insertion(a,e,a,d),insertion(c,d,c,b),e)
| ~ between(insertion(a,e,a,d),insertion(c,d,c,b),insertion(a,e,a,c))
| ~ between(insertion(a,e,a,d),insertion(a,e,a,c),e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) )
| between(insertion(a,e,a,d),insertion(c,d,c,b),e)
| ~ between(insertion(a,e,a,d),insertion(c,d,c,b),insertion(a,e,a,c))
| ~ between(insertion(a,e,a,d),insertion(a,e,a,c),e) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
( between(insertion(a,e,a,d),insertion(c,d,c,b),e)
| ~ between(insertion(a,e,a,d),insertion(c,d,c,b),insertion(a,e,a,c))
| ~ between(insertion(a,e,a,d),insertion(a,e,a,c),e) ),
inference(unit_resolution,[status(thm)],[88,85]) ).
tff(90,plain,
~ between(insertion(a,e,a,d),insertion(a,e,a,c),e),
inference(unit_resolution,[status(thm)],[89,75,61]) ).
tff(91,plain,
( between(insertion(a,e,a,c),insertion(c,d,c,b),e)
<=> between(c,b,e) ),
inference(monotonicity,[status(thm)],[15,37]) ).
tff(92,plain,
( between(c,b,e)
<=> between(insertion(a,e,a,c),insertion(c,d,c,b),e) ),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
( ~ between(c,b,e)
<=> ~ between(insertion(a,e,a,c),insertion(c,d,c,b),e) ),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| between(a,b,e)
| ~ between(a,c,e)
| ~ between(c,b,e) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| between(a,b,e)
| ~ between(a,c,e)
| ~ between(c,b,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ( ~ between(a,c,e)
| between(a,b,e)
| ~ between(c,b,e) )
<=> ( between(a,b,e)
| ~ between(a,c,e)
| ~ between(c,b,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| ~ between(a,c,e)
| between(a,b,e)
| ~ between(c,b,e) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| between(a,b,e)
| ~ between(a,c,e)
| ~ between(c,b,e) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| ~ between(a,c,e)
| between(a,b,e)
| ~ between(c,b,e) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| between(a,b,e)
| ~ between(a,c,e)
| ~ between(c,b,e) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| ~ between(a,c,e)
| between(a,b,e)
| ~ between(c,b,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| between(a,b,e)
| ~ between(a,c,e)
| ~ between(c,b,e) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
~ between(c,b,e),
inference(unit_resolution,[status(thm)],[99,53,3,43]) ).
tff(101,plain,
~ between(insertion(a,e,a,c),insertion(c,d,c,b),e),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
( between(insertion(a,e,a,c),insertion(c,d,c,b),insertion(a,e,a,d))
<=> between(c,b,d) ),
inference(monotonicity,[status(thm)],[15,37,26]) ).
tff(103,plain,
( between(c,b,d)
<=> between(insertion(a,e,a,c),insertion(c,d,c,b),insertion(a,e,a,d)) ),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
between(insertion(a,e,a,c),insertion(c,d,c,b),insertion(a,e,a,d)),
inference(modus_ponens,[status(thm)],[32,103]) ).
tff(105,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) )
| between(insertion(a,e,a,c),insertion(c,d,c,b),e)
| ~ between(insertion(a,e,a,c),insertion(c,d,c,b),insertion(a,e,a,d))
| ~ between(insertion(a,e,a,c),insertion(a,e,a,d),e) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) )
| between(insertion(a,e,a,c),insertion(c,d,c,b),e)
| ~ between(insertion(a,e,a,c),insertion(c,d,c,b),insertion(a,e,a,d))
| ~ between(insertion(a,e,a,c),insertion(a,e,a,d),e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) )
| between(insertion(a,e,a,c),insertion(c,d,c,b),e)
| ~ between(insertion(a,e,a,c),insertion(c,d,c,b),insertion(a,e,a,d))
| ~ between(insertion(a,e,a,c),insertion(a,e,a,d),e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( between(U,V,X)
| ~ between(U,V,W)
| ~ between(U,W,X) )
| between(insertion(a,e,a,c),insertion(c,d,c,b),e)
| ~ between(insertion(a,e,a,c),insertion(c,d,c,b),insertion(a,e,a,d))
| ~ between(insertion(a,e,a,c),insertion(a,e,a,d),e) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
( between(insertion(a,e,a,c),insertion(c,d,c,b),e)
| ~ between(insertion(a,e,a,c),insertion(c,d,c,b),insertion(a,e,a,d))
| ~ between(insertion(a,e,a,c),insertion(a,e,a,d),e) ),
inference(unit_resolution,[status(thm)],[107,85]) ).
tff(109,plain,
~ between(insertion(a,e,a,c),insertion(a,e,a,d),e),
inference(unit_resolution,[status(thm)],[108,104,101]) ).
tff(110,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) )
<=> ( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) ) )),
inference(bind,[status(th)],[]) ).
tff(111,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ between(U,V,X)
| ~ between(U,W,X)
| between(V,W,X) )
<=> ( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X) ) )),
( ( ~ between(U,V,X)
| ~ between(U,W,X)
| between(V,W,X)
| between(W,V,X) )
<=> ( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) ) )),
rewrite(( ( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) )
<=> ( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) ) )),
( ( ~ between(U,V,X)
| ~ between(U,W,X)
| between(V,W,X)
| between(W,V,X) )
<=> ( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| ~ between(U,W,X)
| between(V,W,X)
| between(W,V,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| ~ between(U,W,X)
| between(V,W,X)
| between(W,V,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b14) ).
tff(116,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) ),
inference(modus_ponens,[status(thm)],[116,112]) ).
tff(118,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) ),
inference(modus_ponens,[status(thm)],[118,111]) ).
tff(120,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) )
| between(insertion(a,e,a,c),insertion(a,e,a,d),e)
| between(insertion(a,e,a,d),insertion(a,e,a,c),e)
| ~ between(a,insertion(a,e,a,c),e)
| ~ between(a,insertion(a,e,a,d),e) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) )
| between(insertion(a,e,a,c),insertion(a,e,a,d),e)
| between(insertion(a,e,a,d),insertion(a,e,a,c),e)
| ~ between(a,insertion(a,e,a,c),e)
| ~ between(a,insertion(a,e,a,d),e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
( ( ~ between(a,insertion(a,e,a,c),e)
| between(insertion(a,e,a,c),insertion(a,e,a,d),e)
| ~ between(a,insertion(a,e,a,d),e)
| between(insertion(a,e,a,d),insertion(a,e,a,c),e) )
<=> ( between(insertion(a,e,a,c),insertion(a,e,a,d),e)
| between(insertion(a,e,a,d),insertion(a,e,a,c),e)
| ~ between(a,insertion(a,e,a,c),e)
| ~ between(a,insertion(a,e,a,d),e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) )
| ~ between(a,insertion(a,e,a,c),e)
| between(insertion(a,e,a,c),insertion(a,e,a,d),e)
| ~ between(a,insertion(a,e,a,d),e)
| between(insertion(a,e,a,d),insertion(a,e,a,c),e) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) )
| between(insertion(a,e,a,c),insertion(a,e,a,d),e)
| between(insertion(a,e,a,d),insertion(a,e,a,c),e)
| ~ between(a,insertion(a,e,a,c),e)
| ~ between(a,insertion(a,e,a,d),e) ) ),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) )
| ~ between(a,insertion(a,e,a,c),e)
| between(insertion(a,e,a,c),insertion(a,e,a,d),e)
| ~ between(a,insertion(a,e,a,d),e)
| between(insertion(a,e,a,d),insertion(a,e,a,c),e) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) )
| between(insertion(a,e,a,c),insertion(a,e,a,d),e)
| between(insertion(a,e,a,d),insertion(a,e,a,c),e)
| ~ between(a,insertion(a,e,a,c),e)
| ~ between(a,insertion(a,e,a,d),e) ) ),
inference(transitivity,[status(thm)],[122,120]) ).
tff(124,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) )
| ~ between(a,insertion(a,e,a,c),e)
| between(insertion(a,e,a,c),insertion(a,e,a,d),e)
| ~ between(a,insertion(a,e,a,d),e)
| between(insertion(a,e,a,d),insertion(a,e,a,c),e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(V,W,X)
| ~ between(U,W,X)
| between(W,V,X) )
| between(insertion(a,e,a,c),insertion(a,e,a,d),e)
| between(insertion(a,e,a,d),insertion(a,e,a,c),e)
| ~ between(a,insertion(a,e,a,c),e)
| ~ between(a,insertion(a,e,a,d),e) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
( ~ between(a,insertion(a,e,a,c),e)
| ~ between(a,insertion(a,e,a,d),e) ),
inference(unit_resolution,[status(thm)],[125,119,109,90]) ).
tff(127,plain,
$false,
inference(unit_resolution,[status(thm)],[126,29,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO008-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 14:01:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% See solution above
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------