TSTP Solution File: SET855-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET855-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 05:08:23 EDT 2022
% Result : Unsatisfiable 0.51s 0.61s
% Output : Proof 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 19
% Syntax : Number of formulae : 32 ( 9 unt; 6 typ; 0 def)
% Number of atoms : 133 ( 41 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 189 ( 90 ~; 84 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 57 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Union_type,type,
c_Union: ( $i * $i ) > $i ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_Y_type,type,
v_Y: $i ).
tff(v_n_type,type,
v_n: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(1,plain,
( ( v_n != c_Union(v_Y,tc_set(t_a)) )
<=> ( v_n != c_Union(v_Y,tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
v_n != c_Union(v_Y,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(3,plain,
v_n != c_Union(v_Y,tc_set(t_a)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a)))
<=> c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(6,plain,
c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
<=> c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(9,plain,
c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
trans(
monotonicity(
rewrite(
( ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ) )),
( ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) )
<=> ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) ) )),
rewrite(
( ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) )
<=> ( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ) )),
( ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) )
<=> ( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Set_Osubset__antisym_0) ).
tff(16,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| ( v_n = c_Union(v_Y,tc_set(t_a)) )
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| ( v_n = c_Union(v_Y,tc_set(t_a)) )
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ( ( v_n = c_Union(v_Y,tc_set(t_a)) )
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) )
<=> ( ( v_n = c_Union(v_Y,tc_set(t_a)) )
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| ( v_n = c_Union(v_Y,tc_set(t_a)) )
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| ( v_n = c_Union(v_Y,tc_set(t_a)) )
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| ( v_n = c_Union(v_Y,tc_set(t_a)) )
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| ( v_n = c_Union(v_Y,tc_set(t_a)) )
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| ( v_n = c_Union(v_Y,tc_set(t_a)) )
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| ( v_n = c_Union(v_Y,tc_set(t_a)) )
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,19,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET855-1 : TPTP v8.1.0. Released v3.2.0.
% 0.09/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n022.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 : Sat Sep 3 08:20:54 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.
% 0.51/0.61 % SZS status Unsatisfiable
% 0.51/0.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------