TSTP Solution File: PUZ063-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ063-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 : Sun Sep 18 14:11:12 EDT 2022
% Result : Unsatisfiable 0.94s 0.98s
% Output : Proof 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 23
% Syntax : Number of formulae : 37 ( 15 unt; 13 typ; 0 def)
% Number of atoms : 37 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 8 ~; 1 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 6 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 28 ( 24 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Mutil_Otiling_type,type,
c_Mutil_Otiling: ( $i * $i ) > $i ).
tff(v_A_type,type,
v_A: $i ).
tff(c_union_type,type,
c_union: ( $i * $i * $i ) > $i ).
tff(v_u_type,type,
v_u: $i ).
tff(c_SetInterval_OlessThan_type,type,
c_SetInterval_OlessThan: ( $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Nat_Osize_type,type,
c_Nat_Osize: ( $i * $i ) > $i ).
tff(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
tff(c_Product__Type_OUnity_type,type,
c_Product__Type_OUnity: $i ).
tff(c_emptyset_type,type,
c_emptyset: $i ).
tff(1,plain,
^ [T_a: $i,V_y: $i] :
refl(
( ( c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),V_y,T_a) = V_y )
<=> ( c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),V_y,T_a) = V_y ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [T_a: $i,V_y: $i] : ( c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),V_y,T_a) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),V_y,T_a) = V_y ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [T_a: $i,V_y: $i] :
rewrite(
( ( c_union(c_emptyset,V_y,T_a) = V_y )
<=> ( c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),V_y,T_a) = V_y ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),V_y,T_a) = V_y ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Set_OUn__empty__left_0) ).
tff(7,plain,
! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [T_a: $i,V_y: $i] : ( c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),V_y,T_a) = V_y ),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
! [T_a: $i,V_y: $i] : ( c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),V_y,T_a) = V_y ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T_a: $i,V_y: $i] : ( c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),V_y,T_a) = V_y ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),V_y,T_a) = V_y )
| ( c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),v_u,t_a) = v_u ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),v_u,t_a) = v_u,
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( c_in(c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
<=> c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
<=> c_in(c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
<=> c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(17,plain,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
c_in(c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[17,14]) ).
tff(19,plain,
( ~ c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
<=> ~ c_in(c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ~ c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
<=> ~ c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
~ c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(22,plain,
~ c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ c_in(c_union(c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[22,19]) ).
tff(24,plain,
$false,
inference(unit_resolution,[status(thm)],[23,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ063-1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.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 : Fri Sep 2 19:05:09 EDT 2022
% 0.13/0.34 % 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.
% 0.94/0.98 % SZS status Unsatisfiable
% 0.94/0.98 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------