TSTP Solution File: LCL760-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL760-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 04:58:11 EDT 2022
% Result : Unsatisfiable 0.48s 0.58s
% Output : Proof 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 25
% Syntax : Number of formulae : 31 ( 8 unt; 19 typ; 0 def)
% Number of atoms : 18 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 1 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 9 >; 13 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-5 aty)
% Number of variables : 20 ( 18 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_List_Ofoldl_type,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(tc_Lambda_OdB_type,type,
tc_Lambda_OdB: $i ).
tff(c_List_Omap_type,type,
c_List_Omap: ( $i * $i * $i * $i ) > $i ).
tff(v_ss_type,type,
v_ss: $i ).
tff(c_COMBC_type,type,
c_COMBC: ( $i * $i * $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(v_ja_type,type,
v_ja: $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(v_ia_type,type,
v_ia: $i ).
tff(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(v_s_type,type,
v_s: $i ).
tff(c_Suc_type,type,
c_Suc: $i > $i ).
tff(v_ra_type,type,
v_ra: $i ).
tff(c_Lambda_OdB_OApp_type,type,
c_Lambda_OdB_OApp: $i ).
tff(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i ).
tff(1,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
<=> ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(3,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_i: $i,V_j: $i] :
refl(
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(V_i))),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(V_i)),V_j)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_j,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
<=> hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(V_i))),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(V_i)),V_j)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_j,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_i: $i,V_j: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(V_i))),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(V_i)),V_j)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_j,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
<=> ! [V_i: $i,V_j: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(V_i))),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(V_i)),V_j)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_j,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_i: $i,V_j: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(V_i))),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(V_i)),V_j)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_j,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
<=> ! [V_i: $i,V_j: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(V_i))),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(V_i)),V_j)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_j,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [V_i: $i,V_j: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(V_i))),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(V_i)),V_j)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_j,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(8,plain,
! [V_i: $i,V_j: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(V_i))),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(V_i)),V_j)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_j,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_i: $i,V_j: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(V_i))),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(V_i)),V_j)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_j,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_i: $i,V_j: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(V_i))),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(V_i)),V_j)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_j,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [V_i: $i,V_j: $i] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(V_i))),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(V_i)),V_j)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_j,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
$false,
inference(unit_resolution,[status(thm)],[11,10,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL760-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 01:00:01 EDT 2022
% 0.12/0.34 % 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.
% 0.48/0.58 % SZS status Unsatisfiable
% 0.48/0.58 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------