TSTP Solution File: GEO040-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO040-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : Fri Sep 16 20:34:28 EDT 2022
% Result : Unsatisfiable 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 37
% Syntax : Number of formulae : 83 ( 24 unt; 6 typ; 0 def)
% Number of atoms : 300 ( 82 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 383 ( 167 ~; 186 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 3 >; 9 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 255 ( 227 !; 0 ?; 255 :)
% 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(extension_type,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(w_type,type,
w: $i ).
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(1,plain,
( ( u != v )
<=> ( u != v ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_u_is_v) ).
tff(3,plain,
u != v,
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] :
refl(
( ( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
<=> ( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [W: $i,V: $i,U: $i] :
rewrite(
( ( ~ between(U,V,W)
| ( U = V )
| ( W = extension(U,V,V,W) ) )
<=> ( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( U = V )
| ( W = extension(U,V,V,W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( U = V )
| ( W = extension(U,V,V,W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_1) ).
tff(13,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( u = v )
| ~ between(u,v,w)
| ( w = extension(u,v,v,w) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( u = v )
| ~ between(u,v,w)
| ( w = extension(u,v,v,w) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( u = v )
| ~ between(u,v,w)
| ( w = extension(u,v,v,w) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( u = v )
| ~ between(u,v,w)
| ( w = extension(u,v,v,w) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
w = extension(u,v,v,w),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
extension(u,v,v,w) = w,
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( between(v,u,extension(u,v,v,w))
<=> between(v,u,w) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( between(v,u,w)
<=> between(v,u,extension(u,v,v,w)) ),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( between(v,u,w)
<=> between(v,u,w) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
between(v,u,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_between_v_and_w) ).
tff(26,plain,
between(v,u,w),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
between(v,u,extension(u,v,v,w)),
inference(modus_ponens,[status(thm)],[26,23]) ).
tff(28,plain,
( between(u,v,extension(u,v,v,w))
<=> between(u,v,w) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(29,plain,
( between(u,v,w)
<=> between(u,v,extension(u,v,v,w)) ),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
between(u,v,extension(u,v,v,w)),
inference(modus_ponens,[status(thm)],[6,29]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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(34,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(35,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)],[34]) ).
tff(36,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/sandbox/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).
tff(37,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)],[36,35]) ).
tff(38,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)],[37,33]) ).
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(skolemize,[status(sab)],[38]) ).
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)],[39,32]) ).
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) )
| ~ between(v,u,extension(u,v,v,w))
| ~ between(u,v,extension(u,v,v,w))
| between(v,inner_pasch(u,v,extension(u,v,v,w),u,v),v) )
<=> ( ~ ! [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(v,u,extension(u,v,v,w))
| ~ between(u,v,extension(u,v,v,w))
| between(v,inner_pasch(u,v,extension(u,v,v,w),u,v),v) ) ),
inference(rewrite,[status(thm)],]) ).
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) )
| ~ between(v,u,extension(u,v,v,w))
| ~ between(u,v,extension(u,v,v,w))
| between(v,inner_pasch(u,v,extension(u,v,v,w),u,v),v) ),
inference(quant_inst,[status(thm)],]) ).
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(v,u,extension(u,v,v,w))
| ~ between(u,v,extension(u,v,v,w))
| between(v,inner_pasch(u,v,extension(u,v,v,w),u,v),v) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ between(v,u,extension(u,v,v,w))
| ~ between(u,v,extension(u,v,v,w))
| between(v,inner_pasch(u,v,extension(u,v,v,w),u,v),v) ),
inference(unit_resolution,[status(thm)],[43,40]) ).
tff(45,plain,
between(v,inner_pasch(u,v,extension(u,v,v,w),u,v),v),
inference(unit_resolution,[status(thm)],[44,30,27]) ).
tff(46,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ between(X,Y,X)
| ( X = Y ) )
<=> ( ~ between(X,Y,X)
| ( X = Y ) ) )),
inference(bind,[status(th)],]) ).
tff(47,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)],[46]) ).
tff(48,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(49,axiom,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
tff(50,plain,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(v,inner_pasch(u,v,extension(u,v,v,w),u,v),v)
| ( v = inner_pasch(u,v,extension(u,v,v,w),u,v) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(v,inner_pasch(u,v,extension(u,v,v,w),u,v),v)
| ( v = inner_pasch(u,v,extension(u,v,v,w),u,v) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(v,inner_pasch(u,v,extension(u,v,v,w),u,v),v)
| ( v = inner_pasch(u,v,extension(u,v,v,w),u,v) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(v,inner_pasch(u,v,extension(u,v,v,w),u,v),v)
| ( v = inner_pasch(u,v,extension(u,v,v,w),u,v) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
v = inner_pasch(u,v,extension(u,v,v,w),u,v),
inference(unit_resolution,[status(thm)],[55,52,45]) ).
tff(57,plain,
inner_pasch(u,v,extension(u,v,v,w),u,v) = v,
inference(symmetry,[status(thm)],[56]) ).
tff(58,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(59,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)],[58]) ).
tff(60,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(61,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(62,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)],[61]) ).
tff(63,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/sandbox/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).
tff(64,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)],[63,62]) ).
tff(65,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)],[64,60]) ).
tff(66,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)],[65]) ).
tff(67,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)],[66,59]) ).
tff(68,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(v,u,extension(u,v,v,w))
| ~ between(u,v,extension(u,v,v,w))
| between(u,inner_pasch(u,v,extension(u,v,v,w),u,v),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(v,u,extension(u,v,v,w))
| ~ between(u,v,extension(u,v,v,w))
| between(u,inner_pasch(u,v,extension(u,v,v,w),u,v),u) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,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(v,u,extension(u,v,v,w))
| ~ between(u,v,extension(u,v,v,w))
| between(u,inner_pasch(u,v,extension(u,v,v,w),u,v),u) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,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(v,u,extension(u,v,v,w))
| ~ between(u,v,extension(u,v,v,w))
| between(u,inner_pasch(u,v,extension(u,v,v,w),u,v),u) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
between(u,inner_pasch(u,v,extension(u,v,v,w),u,v),u),
inference(unit_resolution,[status(thm)],[70,67,27,30]) ).
tff(72,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(u,inner_pasch(u,v,extension(u,v,v,w),u,v),u)
| ( u = inner_pasch(u,v,extension(u,v,v,w),u,v) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(u,inner_pasch(u,v,extension(u,v,v,w),u,v),u)
| ( u = inner_pasch(u,v,extension(u,v,v,w),u,v) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(u,inner_pasch(u,v,extension(u,v,v,w),u,v),u)
| ( u = inner_pasch(u,v,extension(u,v,v,w),u,v) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
( ~ ! [Y: $i,X: $i] :
( ~ between(X,Y,X)
| ( X = Y ) )
| ~ between(u,inner_pasch(u,v,extension(u,v,v,w),u,v),u)
| ( u = inner_pasch(u,v,extension(u,v,v,w),u,v) ) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
u = inner_pasch(u,v,extension(u,v,v,w),u,v),
inference(unit_resolution,[status(thm)],[74,52,71]) ).
tff(76,plain,
u = v,
inference(transitivity,[status(thm)],[75,57]) ).
tff(77,plain,
$false,
inference(unit_resolution,[status(thm)],[3,76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO040-3 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 04:54:15 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.20/0.53 % SZS status Unsatisfiable
% 0.20/0.53 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------