TSTP Solution File: GEO054-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO054-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Fri Sep 16 20:34:33 EDT 2022
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 17 unt; 5 typ; 0 def)
% Number of atoms : 41 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 9 ~; 2 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 3 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 60 ( 54 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(extension_type,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(v_type,type,
v: $i ).
tff(u_type,type,
u: $i ).
tff(reflection_type,type,
reflection: ( $i * $i ) > $i ).
tff(1,plain,
^ [V: $i,U: $i] :
refl(
( ( reflection(U,V) = extension(U,V,U,V) )
<=> ( reflection(U,V) = extension(U,V,U,V) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) )
<=> ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) )
<=> ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-2.ax',reflection) ).
tff(5,plain,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) )
| ( reflection(u,v) = extension(u,v,u,v) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
reflection(u,v) = extension(u,v,u,v),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
extension(u,v,u,v) = reflection(u,v),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( between(u,v,extension(u,v,u,v))
<=> between(u,v,reflection(u,v)) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( between(u,v,reflection(u,v))
<=> between(u,v,extension(u,v,u,v)) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ~ between(u,v,reflection(u,v))
<=> ~ between(u,v,extension(u,v,u,v)) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ~ between(u,v,reflection(u,v))
<=> ~ between(u,v,reflection(u,v)) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
~ between(u,v,reflection(u,v)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_between_u_and_reflection) ).
tff(16,plain,
~ between(u,v,reflection(u,v)),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ between(u,v,extension(u,v,u,v)),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
^ [W: $i,V: $i,Y: $i,X: $i] :
refl(
( between(X,Y,extension(X,Y,W,V))
<=> between(X,Y,extension(X,Y,W,V)) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V))
<=> ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V))
<=> ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
tff(22,plain,
! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V))
| between(u,v,extension(u,v,u,v)) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
between(u,v,extension(u,v,u,v)),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
$false,
inference(unit_resolution,[status(thm)],[26,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO054-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 05:03:17 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------