TSTP Solution File: LCL858-1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL858-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 04:58:44 EDT 2022
% Result : Unsatisfiable 0.23s 0.50s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 28 ( 7 unt; 8 typ; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 66 ( 31 ~; 27 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 17 ( 15 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_t_type,type,
v_t: $i ).
tff(c_Wellfounded_Oaccp_type,type,
c_Wellfounded_Oaccp: ( $i * $i ) > $i ).
tff(tc_Lambda_OdB_type,type,
tc_Lambda_OdB: $i ).
tff(c_Predicate_Oconversep_type,type,
c_Predicate_Oconversep: ( $i * $i * $i ) > $i ).
tff(c_Lambda_Obeta_type,type,
c_Lambda_Obeta: $i ).
tff(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i ).
tff(1,plain,
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t))
<=> ~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( hBOOL(hAPP(c_InductTermi_OIT,v_t))
<=> hBOOL(hAPP(c_InductTermi_OIT,v_t)) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(6,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_t)),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_t: $i] :
refl(
( ( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) )
<=> ( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) )
<=> ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) )
<=> ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [V_t: $i] :
rewrite(
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) )
<=> ( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [V_t: $i] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) )
<=> ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_t: $i] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).
tff(13,plain,
! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) )
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)) )
<=> ( ~ ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) )
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) )
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) )
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
$false,
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : LCL858-1 : TPTP v8.1.0. Released v4.1.0.
% 0.15/0.16 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.16/0.37 % Computer : n029.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri Sep 2 01:32:59 EDT 2022
% 0.16/0.37 % CPUTime :
% 0.16/0.38 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.38 Usage: tptp [options] [-file:]file
% 0.16/0.38 -h, -? prints this message.
% 0.16/0.38 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.38 -m, -model generate model.
% 0.16/0.38 -p, -proof generate proof.
% 0.16/0.38 -c, -core generate unsat core of named formulas.
% 0.16/0.38 -st, -statistics display statistics.
% 0.16/0.38 -t:timeout set timeout (in second).
% 0.16/0.38 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.38 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.38 -<param>:<value> configuration parameter and value.
% 0.16/0.38 -o:<output-file> file to place output in.
% 0.23/0.50 % SZS status Unsatisfiable
% 0.23/0.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------