TSTP Solution File: ALG417-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG417-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 6 16:10:10 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 16
% Syntax : Number of formulae : 25 ( 7 unt; 6 typ; 0 def)
% Number of atoms : 49 ( 25 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 58 ( 29 ~; 22 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 13 ( 12 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
tff(class_HOL_Ozero_type,type,
class_HOL_Ozero: $i > $o ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(v_s_____type,type,
v_s____: $i ).
tff(1,plain,
( class_HOL_Ozero(tc_Complex_Ocomplex)
<=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
tff(3,plain,
class_HOL_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sne_0) ).
tff(7,plain,
v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
^ [T_a: $i] :
refl(
( ( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).
tff(13,plain,
! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
( ( ~ ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
<=> ( ~ ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( ~ ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
( ~ ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
$false,
inference(unit_resolution,[status(thm)],[18,15,8,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG417-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.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 : Mon Aug 29 17:21:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------