TSTP Solution File: GEO058-3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO058-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 20:34:35 EDT 2022
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 22
% Syntax : Number of formulae : 51 ( 21 unt; 4 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 : 6 ( 2 >; 4 *; 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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
% 0.07/0.13 % Problem : GEO058-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 05:07:56 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------