TSTP Solution File: SWV263-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV263-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 15:10:41 EDT 2022
% Result : Unsatisfiable 0.51s 0.62s
% Output : Proof 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 26
% Syntax : Number of formulae : 45 ( 11 unt; 8 typ; 0 def)
% Number of atoms : 152 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 213 ( 101 ~; 96 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 110 ( 100 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(v_H_type,type,
v_H: $i ).
tff(v_X_type,type,
v_X: $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(v_G_type,type,
v_G: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(1,plain,
( ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg)
<=> ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(3,plain,
~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_H: $i,V_X: $i] :
refl(
( ( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,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,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,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,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,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_Oparts_OInj_0) ).
tff(8,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(v_X,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,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(v_X,v_H,tc_Message_Omsg)
| c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(v_X,v_H,tc_Message_Omsg)
| c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(v_X,v_H,tc_Message_Omsg)
| c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ c_in(v_X,v_H,tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( c_in(v_X,v_G,tc_Message_Omsg)
<=> c_in(v_X,v_G,tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
c_in(v_X,v_G,tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(17,plain,
c_in(v_X,v_G,tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg))
<=> c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(20,plain,
c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) )
<=> ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
rewrite(
( ( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) )
<=> ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetD_0) ).
tff(27,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) )
| ~ c_in(v_X,v_G,tc_Message_Omsg)
| c_in(v_X,v_H,tc_Message_Omsg)
| ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) )
| ~ c_in(v_X,v_G,tc_Message_Omsg)
| c_in(v_X,v_H,tc_Message_Omsg)
| ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg))
| c_in(v_X,v_H,tc_Message_Omsg)
| ~ c_in(v_X,v_G,tc_Message_Omsg) )
<=> ( ~ c_in(v_X,v_G,tc_Message_Omsg)
| c_in(v_X,v_H,tc_Message_Omsg)
| ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) )
| ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg))
| c_in(v_X,v_H,tc_Message_Omsg)
| ~ c_in(v_X,v_G,tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) )
| ~ c_in(v_X,v_G,tc_Message_Omsg)
| c_in(v_X,v_H,tc_Message_Omsg)
| ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) )
| ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg))
| c_in(v_X,v_H,tc_Message_Omsg)
| ~ c_in(v_X,v_G,tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) )
| ~ c_in(v_X,v_G,tc_Message_Omsg)
| c_in(v_X,v_H,tc_Message_Omsg)
| ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) )
| ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg))
| c_in(v_X,v_H,tc_Message_Omsg)
| ~ c_in(v_X,v_G,tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) )
| ~ c_in(v_X,v_G,tc_Message_Omsg)
| c_in(v_X,v_H,tc_Message_Omsg)
| ~ c_lessequals(v_G,v_H,tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,30,20,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWV263-1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 01:25:09 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.
% 0.51/0.62 % SZS status Unsatisfiable
% 0.51/0.62 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------