TSTP Solution File: SWV278-2 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV278-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 15:10:48 EDT 2022
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 38 ( 14 unt; 8 typ; 0 def)
% Number of atoms : 64 ( 12 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 60 ( 27 ~; 23 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 5 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-1 aty)
% Number of variables : 35 ( 33 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(v_H_type,type,
v_H: $i ).
tff(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i > $i ).
tff(c_Message_OinvKey_type,type,
c_Message_OinvKey: $i > $i ).
tff(v_K_H_type,type,
v_K_H: $i ).
tff(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
tff(1,plain,
( ! [V_y: $i] : ( c_Message_OinvKey(c_Message_OinvKey(V_y)) = V_y )
<=> ! [V_y: $i] : ( c_Message_OinvKey(c_Message_OinvKey(V_y)) = V_y ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ! [V_y: $i] : ( c_Message_OinvKey(c_Message_OinvKey(V_y)) = V_y )
<=> ! [V_y: $i] : ( c_Message_OinvKey(c_Message_OinvKey(V_y)) = V_y ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
! [V_y: $i] : ( c_Message_OinvKey(c_Message_OinvKey(V_y)) = V_y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
tff(4,plain,
! [V_y: $i] : ( c_Message_OinvKey(c_Message_OinvKey(V_y)) = V_y ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
! [V_y: $i] : ( c_Message_OinvKey(c_Message_OinvKey(V_y)) = V_y ),
inference(skolemize,[status(sab)],[4]) ).
tff(6,plain,
! [V_y: $i] : ( c_Message_OinvKey(c_Message_OinvKey(V_y)) = V_y ),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( ~ ! [V_y: $i] : ( c_Message_OinvKey(c_Message_OinvKey(V_y)) = V_y )
| ( c_Message_OinvKey(c_Message_OinvKey(v_K_H)) = v_K_H ) ),
inference(quant_inst,[status(thm)],]) ).
tff(8,plain,
c_Message_OinvKey(c_Message_OinvKey(v_K_H)) = v_K_H,
inference(unit_resolution,[status(thm)],[7,6]) ).
tff(9,plain,
c_Message_Omsg_OKey(c_Message_OinvKey(c_Message_OinvKey(v_K_H))) = c_Message_Omsg_OKey(v_K_H),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Message_OinvKey(v_K_H))),c_Message_Oparts(v_H),tc_Message_Omsg)
<=> c_in(c_Message_Omsg_OKey(v_K_H),c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( c_in(c_Message_Omsg_OKey(v_K_H),c_Message_Oparts(v_H),tc_Message_Omsg)
<=> c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Message_OinvKey(v_K_H))),c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
^ [V_H: $i,V_X: $i] :
refl(
( ( ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ( ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__conj__parts_0) ).
tff(16,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( c_in(c_Message_Omsg_OKey(v_K_H),c_Message_Oanalz(v_H),tc_Message_Omsg)
<=> c_in(c_Message_Omsg_OKey(v_K_H),c_Message_Oanalz(v_H),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
c_in(c_Message_Omsg_OKey(v_K_H),c_Message_Oanalz(v_H),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(21,plain,
c_in(c_Message_Omsg_OKey(v_K_H),c_Message_Oanalz(v_H),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( ( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OKey(v_K_H),c_Message_Oanalz(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(v_K_H),c_Message_Oparts(v_H),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OKey(v_K_H),c_Message_Oanalz(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(v_K_H),c_Message_Oparts(v_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OKey(v_K_H),c_Message_Oanalz(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(v_K_H),c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OKey(v_K_H),c_Message_Oanalz(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(v_K_H),c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
c_in(c_Message_Omsg_OKey(v_K_H),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[24,21,18]) ).
tff(26,plain,
c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Message_OinvKey(v_K_H))),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[25,11]) ).
tff(27,plain,
( ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Message_OinvKey(v_K_H))),c_Message_Oparts(v_H),tc_Message_Omsg)
<=> ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Message_OinvKey(v_K_H))),c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Message_OinvKey(v_K_H))),c_Message_Oparts(v_H),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(29,plain,
~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Message_OinvKey(v_K_H))),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
$false,
inference(unit_resolution,[status(thm)],[29,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV278-2 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.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 : Sun Sep 4 02:08:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------