%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO024-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:05:21 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 48 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 115 ( 42 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 122 ( 57 ~; 50 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-4 aty)
% Number of variables : 111 ( 104 !; 0 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
tff(equidistant_type,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(v_type,type,
v: $i ).
tff(extension_type,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(lower_dimension_point_2_type,type,
lower_dimension_point_2: $i ).
tff(u_type,type,
u: $i ).
tff(lower_dimension_point_1_type,type,
lower_dimension_point_1: $i ).
tff(lower_dimension_point_3_type,type,
lower_dimension_point_3: $i ).
tff(1,plain,
^ [W: $i,V: $i,Y: $i,X: $i] :
refl(( equidistant(Y,extension(X,Y,W,V),W,V)
<=> equidistant(Y,extension(X,Y,W,V),W,V) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V)
<=> ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V)
<=> ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
tff(5,plain,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V)
| equidistant(lower_dimension_point_2,extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2),lower_dimension_point_2,lower_dimension_point_2) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
equidistant(lower_dimension_point_2,extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2),lower_dimension_point_2,lower_dimension_point_2),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
<=> ( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(lower_dimension_point_2,extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2),lower_dimension_point_2,lower_dimension_point_2)
| ( lower_dimension_point_2 = extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(lower_dimension_point_2,extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2),lower_dimension_point_2,lower_dimension_point_2)
| ( lower_dimension_point_2 = extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(lower_dimension_point_2,extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2),lower_dimension_point_2,lower_dimension_point_2)
| ( lower_dimension_point_2 = extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(lower_dimension_point_2,extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2),lower_dimension_point_2,lower_dimension_point_2)
| ( lower_dimension_point_2 = extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
lower_dimension_point_2 = extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2),
inference(unit_resolution,[status(thm)],[19,16,9]) ).
tff(21,plain,
extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2) = lower_dimension_point_2,
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( equidistant(u,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2))
<=> equidistant(u,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),lower_dimension_point_2,lower_dimension_point_2) ),
inference(monotonicity,[status(thm)],[21,21]) ).
tff(23,plain,
( equidistant(u,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),lower_dimension_point_2,lower_dimension_point_2)
<=> equidistant(u,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2)) ),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( ~ ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V)
| equidistant(u,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),lower_dimension_point_2,lower_dimension_point_2) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
equidistant(u,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),lower_dimension_point_2,lower_dimension_point_2),
inference(unit_resolution,[status(thm)],[24,7]) ).
tff(26,plain,
equidistant(u,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2)),
inference(modus_ponens,[status(thm)],[25,23]) ).
tff(27,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(u,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2))
| ( u = extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(u,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2))
| ( u = extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(u,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2))
| ( u = extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(u,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2))
| ( u = extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ equidistant(u,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_2))
| ( u = extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2) ) ),
inference(unit_resolution,[status(thm)],[29,16]) ).
tff(31,plain,
u = extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),
inference(unit_resolution,[status(thm)],[30,26]) ).
tff(32,plain,
extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2) = u,
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ~ ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V)
| equidistant(extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v),v,v) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
equidistant(extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v),v,v),
inference(unit_resolution,[status(thm)],[33,7]) ).
tff(35,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v),v,v)
| ( extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2) = extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v),v,v)
| ( extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2) = extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v),v,v)
| ( extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2) = extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v),v,v)
| ( extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2) = extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2) = extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v),
inference(unit_resolution,[status(thm)],[37,16,34]) ).
tff(39,plain,
extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v) = extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v) = u,
inference(transitivity,[status(thm)],[39,32]) ).
tff(41,plain,
( equidistant(extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v),v,v)
<=> equidistant(u,u,v,v) ),
inference(monotonicity,[status(thm)],[32,40]) ).
tff(42,plain,
( equidistant(u,u,v,v)
<=> equidistant(extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v),v,v) ),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
( ~ equidistant(u,u,v,v)
<=> ~ equidistant(extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v),v,v) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ~ equidistant(u,u,v,v)
<=> ~ equidistant(u,u,v,v) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
~ equidistant(u,u,v,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_congruence) ).
tff(46,plain,
~ equidistant(u,u,v,v),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
~ equidistant(extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),extension(lower_dimension_point_1,extension(lower_dimension_point_1,u,lower_dimension_point_2,lower_dimension_point_2),v,v),v,v),
inference(modus_ponens,[status(thm)],[46,43]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[34,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO024-2 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.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 14:05:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% See solution above
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------