TSTP Solution File: LCL800-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL800-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 04:58:23 EDT 2022
% Result : Unsatisfiable 0.20s 0.54s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of formulae : 58 ( 27 unt; 11 typ; 0 def)
% Number of atoms : 89 ( 50 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 53 ( 14 ~; 24 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 7 >; 6 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 96 ( 87 !; 0 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i > $o ).
tff(c_Lambda_OdB_OApp_type,type,
c_Lambda_OdB_OApp: ( $i * $i ) > $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(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(c_Lambda_Olift_type,type,
c_Lambda_Olift: ( $i * $i ) > $i ).
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(1,plain,
^ [V_u: $i,V_t: $i,V_k: $i,V_s: $i] :
refl(
( ( c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) )
<=> ( c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_u: $i,V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) )
<=> ! [V_u: $i,V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_u: $i,V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) )
<=> ! [V_u: $i,V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V_u: $i,V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).
tff(5,plain,
! [V_u: $i,V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_u: $i,V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_u: $i,V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_u: $i,V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) )
| ( c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_OdB_OApp(c_Lambda_Osubst(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_OdB_OApp(c_Lambda_Osubst(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_Lambda_OdB_OApp(c_Lambda_Osubst(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [V_x: $i,V_s: $i] :
refl(
( ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) )
<=> ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [V_x: $i,V_s: $i] :
( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) )
<=> ! [V_x: $i,V_s: $i] :
( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [V_x: $i,V_s: $i] :
( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) )
<=> ! [V_x: $i,V_s: $i] :
( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [V_x: $i,V_s: $i] :
( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_1) ).
tff(15,plain,
! [V_x: $i,V_s: $i] :
( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [V_x: $i,V_s: $i] :
( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [V_x: $i,V_s: $i] :
( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
<=> ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
tff(20,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ( ~ ! [V_x: $i,V_s: $i] :
( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) )
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(v_a____,v_u____,v_i____) ) )
<=> ( ~ ! [V_x: $i,V_s: $i] :
( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) )
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(v_a____,v_u____,v_i____) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ~ ! [V_x: $i,V_s: $i] :
( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) )
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(v_a____,v_u____,v_i____) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
( ~ ! [V_x: $i,V_s: $i] :
( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) )
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ( c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(v_a____,v_u____,v_i____) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(v_a____,v_u____,v_i____),
inference(unit_resolution,[status(thm)],[23,20,17]) ).
tff(25,plain,
c_Lambda_Osubst(v_a____,v_u____,v_i____) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
^ [V_t: $i,V_k: $i,V_s: $i] :
refl(
( ( c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t )
<=> ( c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t )
<=> ! [V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t )
<=> ! [V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
! [V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
tff(30,plain,
! [V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [V_t: $i,V_k: $i,V_s: $i] : ( c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t )
| ( c_Lambda_Osubst(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)) = v_u____ ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
c_Lambda_Osubst(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)) = v_u____,
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
v_u____ = c_Lambda_Osubst(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____)) = c_Lambda_OdB_OApp(c_Lambda_Osubst(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(monotonicity,[status(thm)],[35,25]) ).
tff(37,plain,
c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____)) = c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(transitivity,[status(thm)],[36,10]) ).
tff(38,plain,
( c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____)))
<=> c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)))
<=> c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))) ),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)))
<=> c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(42,plain,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))),
inference(modus_ponens,[status(thm)],[42,39]) ).
tff(44,plain,
( ~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____)))
<=> ~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(46,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
$false,
inference(unit_resolution,[status(thm)],[46,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL800-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 01:25:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.54 % SZS status Unsatisfiable
% 0.20/0.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------