%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO058-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:05:28 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 47 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 111 ( 32 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 111 ( 50 ~; 46 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 111 ( 102 !; 0 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
tff(v_type,type,
v: $i ).
tff(u_type,type,
u: $i ).
tff(reflection_type,type,
reflection: ( $i * $i ) > $i ).
tff(equidistant_type,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(1,plain,
( ( v = reflection(u,v) )
<=> ( v = reflection(u,v) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
v = reflection(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_equals_reflection) ).
tff(3,plain,
v = reflection(u,v),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
reflection(u,v) = v,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
reflection(u,reflection(u,v)) = reflection(u,v),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
reflection(u,v) = reflection(u,reflection(u,v)),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( equidistant(reflection(u,v),reflection(u,v),u,reflection(u,v))
<=> equidistant(reflection(u,v),reflection(u,reflection(u,v)),u,reflection(u,v)) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( equidistant(reflection(u,v),reflection(u,reflection(u,v)),u,reflection(u,v))
<=> equidistant(reflection(u,v),reflection(u,v),u,reflection(u,v)) ),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
^ [V: $i,U: $i] :
refl(( equidistant(V,reflection(U,V),U,V)
<=> equidistant(V,reflection(U,V),U,V) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V)
<=> ! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V)
<=> ! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
tff(13,plain,
! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
( ~ ! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V)
| equidistant(reflection(u,v),reflection(u,reflection(u,v)),u,reflection(u,v)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
equidistant(reflection(u,v),reflection(u,reflection(u,v)),u,reflection(u,v)),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
equidistant(reflection(u,v),reflection(u,v),u,reflection(u,v)),
inference(modus_ponens,[status(thm)],[17,8]) ).
tff(19,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
<=> ( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_5) ).
tff(23,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
| ~ equidistant(reflection(u,v),reflection(u,v),u,reflection(u,v))
| equidistant(reflection(u,v),u,reflection(u,v),reflection(u,v)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
| ~ equidistant(reflection(u,v),reflection(u,v),u,reflection(u,v))
| equidistant(reflection(u,v),u,reflection(u,v),reflection(u,v)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
| ~ equidistant(reflection(u,v),reflection(u,v),u,reflection(u,v))
| equidistant(reflection(u,v),u,reflection(u,v),reflection(u,v)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
| ~ equidistant(reflection(u,v),reflection(u,v),u,reflection(u,v))
| equidistant(reflection(u,v),u,reflection(u,v),reflection(u,v)) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ~ equidistant(reflection(u,v),reflection(u,v),u,reflection(u,v))
| equidistant(reflection(u,v),u,reflection(u,v),reflection(u,v)) ),
inference(unit_resolution,[status(thm)],[28,25]) ).
tff(30,plain,
equidistant(reflection(u,v),u,reflection(u,v),reflection(u,v)),
inference(unit_resolution,[status(thm)],[29,18]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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(34,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(35,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(reflection(u,v),u,reflection(u,v),reflection(u,v))
| ( reflection(u,v) = u ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(reflection(u,v),u,reflection(u,v),reflection(u,v))
| ( reflection(u,v) = u ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(reflection(u,v),u,reflection(u,v),reflection(u,v))
| ( reflection(u,v) = u ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) )
| ~ equidistant(reflection(u,v),u,reflection(u,v),reflection(u,v))
| ( reflection(u,v) = u ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
reflection(u,v) = u,
inference(unit_resolution,[status(thm)],[40,37,30]) ).
tff(42,plain,
u = reflection(u,v),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
u = v,
inference(transitivity,[status(thm)],[42,4]) ).
tff(44,plain,
( ( u != v )
<=> ( u != v ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_u_equals_v) ).
tff(46,plain,
u != v,
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
$false,
inference(unit_resolution,[status(thm)],[46,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO058-3 : TPTP v9.0.0. Released v1.0.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:11:56 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% See solution above
% 0.11/0.38 % E exiting
%------------------------------------------------------------------------------