TSTP Solution File: LCL817-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL817-1 : 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 : Sun Sep 18 04:58:31 EDT 2022
% Result : Unsatisfiable 0.15s 0.42s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 29
% Syntax : Number of formulae : 42 ( 11 unt; 15 typ; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 115 ( 54 ~; 50 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 5 >; 12 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-5 aty)
% Number of variables : 102 ( 90 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Type_Otyping_type,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(v_T_H_H_____type,type,
v_T_H_H____: $i ).
tff(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: ( $i * $i * $i ) > $i ).
tff(v_i_____type,type,
v_i____: $i ).
tff(v_u_____type,type,
v_u____: $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(v_e_____type,type,
v_e____: $i ).
tff(c_Type_Oshift_type,type,
c_Type_Oshift: ( $i * $i * $i * $i ) > $i ).
tff(tc_Type_Otype_type,type,
tc_Type_Otype: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_List_Ofoldr_type,type,
c_List_Ofoldr: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_T_H_____type,type,
v_T_H____: $i ).
tff(v_Ts_____type,type,
v_Ts____: $i ).
tff(c_Type_Otype_OFun_type,type,
c_Type_Otype_OFun: $i ).
tff(v_T_____type,type,
v_T____: $i ).
tff(1,plain,
( ~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____)
<=> ~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
refl(
( ( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) )
<=> ( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) )
<=> ! [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) )
<=> ! [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
rewrite(
( ( ~ c_Type_Otyping(V_e_H,V_u,V_U)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T) )
<=> ( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
( ~ c_Type_Otyping(V_e_H,V_u,V_U)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T) )
<=> ! [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
( ~ c_Type_Otyping(V_e_H,V_u,V_U)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
tff(10,plain,
! [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____)
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),tc_Type_Otype),v_a____,v_T_H_H____) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____)
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_argT_0) ).
tff(17,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),tc_Type_Otype),v_a____,v_T_H_H____),
inference(modus_ponens,[status(thm)],[17,14]) ).
tff(19,plain,
( c_Type_Otyping(v_e____,v_u____,v_T____)
<=> c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( c_Type_Otyping(v_e____,v_u____,v_T____)
<=> c_Type_Otyping(v_e____,v_u____,v_T____) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_0) ).
tff(22,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(modus_ponens,[status(thm)],[22,19]) ).
tff(24,plain,
( ( ~ ! [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) )
| c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____)
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),tc_Type_Otype),v_a____,v_T_H_H____)
| ~ c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) )
<=> ( ~ ! [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) )
| c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____)
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),tc_Type_Otype),v_a____,v_T_H_H____)
| ~ c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ~ ! [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) )
| c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____)
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),tc_Type_Otype),v_a____,v_T_H_H____)
| ~ c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
( ~ ! [V_e_H: $i,V_i: $i,V_U: $i,V_T: $i,V_u: $i,V_t: $i] :
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) )
| c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____)
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),tc_Type_Otype),v_a____,v_T_H_H____)
| ~ c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
$false,
inference(unit_resolution,[status(thm)],[26,23,18,13,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LCL817-1 : TPTP v8.1.0. Released v4.1.0.
% 0.00/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.29 % Computer : n015.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Fri Sep 2 01:21:23 EDT 2022
% 0.14/0.29 % CPUTime :
% 0.14/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.30 Usage: tptp [options] [-file:]file
% 0.14/0.30 -h, -? prints this message.
% 0.14/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.30 -m, -model generate model.
% 0.14/0.30 -p, -proof generate proof.
% 0.14/0.30 -c, -core generate unsat core of named formulas.
% 0.14/0.30 -st, -statistics display statistics.
% 0.14/0.30 -t:timeout set timeout (in second).
% 0.14/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.30 -<param>:<value> configuration parameter and value.
% 0.14/0.30 -o:<output-file> file to place output in.
% 0.15/0.42 % SZS status Unsatisfiable
% 0.15/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------