TSTP Solution File: LCL811-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL811-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 04:58:29 EDT 2022
% Result : Unsatisfiable 0.44s 0.55s
% Output : Proof 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 31
% Syntax : Number of formulae : 64 ( 35 unt; 16 typ; 0 def)
% Number of atoms : 65 ( 49 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 9 ~; 5 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 7 >; 13 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-5 aty)
% Number of variables : 127 ( 116 !; 0 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_List_Olistsp_type,type,
c_List_Olistsp: ( $i * $i * $i ) > $o ).
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(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(v_bs_____type,type,
v_bs____: $i ).
tff(v_b_____type,type,
v_b____: $i ).
tff(c_COMBC_type,type,
c_COMBC: ( $i * $i * $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(v_i_____type,type,
v_i____: $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(v_u_____type,type,
v_u____: $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(c_Lambda_Olift_type,type,
c_Lambda_Olift: $i ).
tff(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(1,plain,
^ [T_b: $i,V_Q: $i,V_R: $i,T_a: $i,T_c: $i,V_P: $i] :
refl(
( ( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) )
<=> ( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [T_b: $i,V_Q: $i,V_R: $i,T_a: $i,T_c: $i,V_P: $i] : ( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) )
<=> ! [T_b: $i,V_Q: $i,V_R: $i,T_a: $i,T_c: $i,V_P: $i] : ( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_b: $i,V_Q: $i,V_R: $i,T_a: $i,T_c: $i,V_P: $i] : ( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) )
<=> ! [T_b: $i,V_Q: $i,V_R: $i,T_a: $i,T_c: $i,V_P: $i] : ( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [T_b: $i,V_Q: $i,V_R: $i,T_a: $i,T_c: $i,V_P: $i] : ( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
tff(5,plain,
! [T_b: $i,V_Q: $i,V_R: $i,T_a: $i,T_c: $i,V_P: $i] : ( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_b: $i,V_Q: $i,V_R: $i,T_a: $i,T_c: $i,V_P: $i] : ( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_b: $i,V_Q: $i,V_R: $i,T_a: $i,T_c: $i,V_P: $i] : ( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [T_b: $i,V_Q: $i,V_R: $i,T_a: $i,T_c: $i,V_P: $i] : ( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) )
| ( hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____) = hAPP(hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____),v_i____) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____) = hAPP(hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____),v_i____),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
hAPP(hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____),v_i____) = hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
hAPP(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____),v_i____)) = hAPP(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____)),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ~ ! [T_b: $i,V_Q: $i,V_R: $i,T_a: $i,T_c: $i,V_P: $i] : ( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) )
| ( hAPP(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____),v_i____)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
hAPP(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____),v_i____)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(unit_resolution,[status(thm)],[12,7]) ).
tff(14,plain,
hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____),v_i____)),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( ~ ! [T_b: $i,V_Q: $i,V_R: $i,T_a: $i,T_c: $i,V_P: $i] : ( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) )
| ( hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____) = hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____) = hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),
inference(unit_resolution,[status(thm)],[15,7]) ).
tff(17,plain,
hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____) = hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____) = hAPP(hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____),v_i____),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____)) = hAPP(c_Lambda_Olift,hAPP(hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____),v_i____)),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_b____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____)),
inference(transitivity,[status(thm)],[20,14,11]) ).
tff(22,plain,
c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_OCons(hAPP(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
c_List_Olist_OCons(hAPP(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
^ [T_b: $i,V_x: $i,V_xs: $i,V_f: $i,T_a: $i] :
refl(
( ( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) )
<=> ( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [T_b: $i,V_x: $i,V_xs: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) )
<=> ! [T_b: $i,V_x: $i,V_xs: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [T_b: $i,V_x: $i,V_xs: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) )
<=> ! [T_b: $i,V_x: $i,V_xs: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
! [T_b: $i,V_x: $i,V_xs: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
tff(28,plain,
! [T_b: $i,V_x: $i,V_xs: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [T_b: $i,V_x: $i,V_xs: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [T_b: $i,V_x: $i,V_xs: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [T_b: $i,V_x: $i,V_xs: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) )
| ( c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_List_Olist_OCons(hAPP(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_List_Olist_OCons(hAPP(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
( ~ ! [T_b: $i,V_x: $i,V_xs: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) )
| ( c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_b____,v_bs____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_List_Olist_OCons(hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_b____,v_bs____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_List_Olist_OCons(hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(unit_resolution,[status(thm)],[33,30]) ).
tff(35,plain,
c_List_Olist_OCons(hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_b____,v_bs____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_b____,v_bs____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_b____,v_bs____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_b____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_b____,v_bs____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(transitivity,[status(thm)],[37,32,23]) ).
tff(39,plain,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_b____,v_bs____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
<=> c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)
<=> c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_b____,v_bs____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)
<=> c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(43,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_b____,v_bs____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(modus_ponens,[status(thm)],[43,40]) ).
tff(45,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_b____,v_bs____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
<=> ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_b____,v_bs____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_b____,v_bs____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(47,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_b____,v_bs____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[47,44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : LCL811-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n005.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Sep 2 01:07:33 EDT 2022
% 0.16/0.31 % CPUTime :
% 0.16/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.32 Usage: tptp [options] [-file:]file
% 0.16/0.32 -h, -? prints this message.
% 0.16/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.32 -m, -model generate model.
% 0.16/0.32 -p, -proof generate proof.
% 0.16/0.32 -c, -core generate unsat core of named formulas.
% 0.16/0.32 -st, -statistics display statistics.
% 0.16/0.32 -t:timeout set timeout (in second).
% 0.16/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.32 -<param>:<value> configuration parameter and value.
% 0.16/0.32 -o:<output-file> file to place output in.
% 0.44/0.55 % SZS status Unsatisfiable
% 0.44/0.55 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------