TSTP Solution File: LCL856-1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL856-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 26
% Syntax : Number of formulae : 42 ( 9 unt; 11 typ; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 114 ( 53 ~; 49 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 5 >; 7 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 56 ( 51 !; 0 ?; 56 :)
% 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_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i ).
tff(c_Type_Otyping_type,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(v_T_type,type,
v_T: $i ).
tff(v_e_type,type,
v_e: $i ).
tff(c_Wellfounded_Oaccp_type,type,
c_Wellfounded_Oaccp: ( $i * $i * $i ) > $o ).
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(1,plain,
( c_Type_Otyping(v_e,v_t,v_T)
<=> c_Type_Otyping(v_e,v_t,v_T) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
c_Type_Otyping(v_e,v_t,v_T),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
c_Type_Otyping(v_e,v_t,v_T),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_T: $i,V_t: $i,V_e: $i] :
refl(
( ( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
<=> ( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
<=> ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
<=> ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__implies__IT_0) ).
tff(8,plain,
! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
| hBOOL(hAPP(c_InductTermi_OIT,v_t))
| ~ c_Type_Otyping(v_e,v_t,v_T) )
<=> ( ~ ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
| hBOOL(hAPP(c_InductTermi_OIT,v_t))
| ~ c_Type_Otyping(v_e,v_t,v_T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
| hBOOL(hAPP(c_InductTermi_OIT,v_t))
| ~ c_Type_Otyping(v_e,v_t,v_T) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
| hBOOL(hAPP(c_InductTermi_OIT,v_t))
| ~ c_Type_Otyping(v_e,v_t,v_T) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_t)),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB)
<=> ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(17,plain,
~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [V_t: $i] :
refl(
( ( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) )
<=> ( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) )
<=> ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) )
<=> ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [V_t: $i] :
rewrite(
( ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) )
<=> ( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [V_t: $i] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) )
<=> ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [V_t: $i] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).
tff(24,plain,
! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) )
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB) )
<=> ( ~ ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) )
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) )
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) )
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
$false,
inference(unit_resolution,[status(thm)],[30,27,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL856-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Sep 2 01:21:05 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.47 % SZS status Unsatisfiable
% 0.21/0.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------