TSTP Solution File: SET828-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET828-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : Tue Sep 20 05:08:12 EDT 2022
% Result : Unsatisfiable 0.20s 0.72s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 19
% Syntax : Number of formulae : 30 ( 9 unt; 7 typ; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 113 ( 54 ~; 50 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 7 ( 3 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 68 ( 60 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(t_a_type,type,
t_a: $i ).
tff(v_Y_type,type,
v_Y: $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_X_type,type,
v_X: $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,v_Y,t_a)
<=> ~ c_in(v_x,v_Y,t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ c_in(v_x,v_Y,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(3,plain,
~ c_in(v_x,v_Y,t_a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_in(v_x,v_X,t_a)
<=> c_in(v_x,v_X,t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
c_in(v_x,v_X,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(6,plain,
c_in(v_x,v_X,t_a),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( c_lessequals(v_X,v_Y,tc_set(t_a))
<=> c_lessequals(v_X,v_Y,tc_set(t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
c_lessequals(v_X,v_Y,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(9,plain,
c_lessequals(v_X,v_Y,tc_set(t_a)),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,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_A,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,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_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(14,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_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
tff(16,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
| c_in(v_x,v_Y,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_in(v_x,v_X,t_a) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
| c_in(v_x,v_Y,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_in(v_x,v_X,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
| c_in(v_x,v_Y,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_in(v_x,v_X,t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
| c_in(v_x,v_Y,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_in(v_x,v_X,t_a) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,19,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.45 % Problem : SET828-2 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.46 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.16/0.67 % Computer : n020.cluster.edu
% 0.16/0.67 % Model : x86_64 x86_64
% 0.16/0.67 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.67 % Memory : 8042.1875MB
% 0.16/0.67 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.67 % CPULimit : 300
% 0.16/0.67 % WCLimit : 300
% 0.16/0.67 % DateTime : Sat Sep 3 08:11:29 EDT 2022
% 0.16/0.67 % CPUTime :
% 0.16/0.67 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.67 Usage: tptp [options] [-file:]file
% 0.16/0.67 -h, -? prints this message.
% 0.16/0.67 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.67 -m, -model generate model.
% 0.16/0.67 -p, -proof generate proof.
% 0.16/0.67 -c, -core generate unsat core of named formulas.
% 0.16/0.67 -st, -statistics display statistics.
% 0.16/0.67 -t:timeout set timeout (in second).
% 0.16/0.67 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.67 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.67 -<param>:<value> configuration parameter and value.
% 0.16/0.67 -o:<output-file> file to place output in.
% 0.20/0.72 % SZS status Unsatisfiable
% 0.20/0.72 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------