TSTP Solution File: SYN278-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN278-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 : Thu Sep 29 23:54:30 EDT 2022
% Result : Unsatisfiable 0.21s 0.50s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 15
% Syntax : Number of formulae : 27 ( 10 unt; 4 typ; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 66 ( 35 ~; 23 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 2 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 46 ( 42 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
tff(q1_type,type,
q1: ( $i * $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ~ q1(X,Y,e)
<=> ~ q1(X,Y,e) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ~ q1(X,Y,e)
<=> ! [Y: $i,X: $i] : ~ q1(X,Y,e) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ~ q1(X,Y,e)
<=> ! [Y: $i,X: $i] : ~ q1(X,Y,e) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ~ q1(X,Y,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(5,plain,
! [Y: $i,X: $i] : ~ q1(X,Y,e),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ~ q1(X,Y,e),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ~ q1(X,Y,e),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
^ [H: $i,G: $i] :
refl(
( ( q1(G,G,G)
| ~ m0(G,H,G) )
<=> ( q1(G,G,G)
| ~ m0(G,H,G) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [H: $i,G: $i] :
( q1(G,G,G)
| ~ m0(G,H,G) )
<=> ! [H: $i,G: $i] :
( q1(G,G,G)
| ~ m0(G,H,G) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [H: $i,G: $i] :
( q1(G,G,G)
| ~ m0(G,H,G) )
<=> ! [H: $i,G: $i] :
( q1(G,G,G)
| ~ m0(G,H,G) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
! [H: $i,G: $i] :
( q1(G,G,G)
| ~ m0(G,H,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_122) ).
tff(12,plain,
! [H: $i,G: $i] :
( q1(G,G,G)
| ~ m0(G,H,G) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [H: $i,G: $i] :
( q1(G,G,G)
| ~ m0(G,H,G) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [H: $i,G: $i] :
( q1(G,G,G)
| ~ m0(G,H,G) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( m0(e,d,e)
<=> m0(e,d,e) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
m0(e,d,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_8) ).
tff(17,plain,
m0(e,d,e),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ( ~ ! [H: $i,G: $i] :
( q1(G,G,G)
| ~ m0(G,H,G) )
| q1(e,e,e)
| ~ m0(e,d,e) )
<=> ( ~ ! [H: $i,G: $i] :
( q1(G,G,G)
| ~ m0(G,H,G) )
| q1(e,e,e)
| ~ m0(e,d,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ~ ! [H: $i,G: $i] :
( q1(G,G,G)
| ~ m0(G,H,G) )
| q1(e,e,e)
| ~ m0(e,d,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
( ~ ! [H: $i,G: $i] :
( q1(G,G,G)
| ~ m0(G,H,G) )
| q1(e,e,e)
| ~ m0(e,d,e) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
q1(e,e,e),
inference(unit_resolution,[status(thm)],[20,17,14]) ).
tff(22,plain,
( ~ ! [Y: $i,X: $i] : ~ q1(X,Y,e)
| ~ q1(e,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,21,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN278-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n010.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 : Mon Sep 5 02:13:12 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.50 % SZS status Unsatisfiable
% 0.21/0.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------