TSTP Solution File: LCL828-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL828-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n006.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 : Wed Jul 27 13:05:33 EDT 2022
% Result : Unsatisfiable 2.29s 2.48s
% Output : Refutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of clauses : 7 ( 6 unt; 0 nHn; 7 RR)
% Number of literals : 10 ( 0 equ; 4 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 4 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(47,axiom,
( c_InductTermi_OIT(c_Lambda_Osubst(v_a____,A,B))
| ~ c_Type_Otyping(C,A,v_T____)
| ~ c_InductTermi_OIT(A)
| ~ c_Type_Otyping(c_Type_Oshift(C,B,v_T____,tc_Type_Otype),v_a____,D) ),
file('LCL828-1.p',unknown),
[] ).
cnf(48,axiom,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),
file('LCL828-1.p',unknown),
[] ).
cnf(66,axiom,
c_InductTermi_OIT(v_u____),
file('LCL828-1.p',unknown),
[] ).
cnf(69,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_Ua____),
file('LCL828-1.p',unknown),
[] ).
cnf(70,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('LCL828-1.p',unknown),
[] ).
cnf(1121,plain,
c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),
inference(hyper,[status(thm)],[69,47,70,66]),
[iquote('hyper,69,47,70,66')] ).
cnf(1122,plain,
$false,
inference(binary,[status(thm)],[1121,48]),
[iquote('binary,1121.1,48.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL828-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 09:22:46 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.23/2.39 ----- Otter 3.3f, August 2004 -----
% 2.23/2.39 The process was started by sandbox on n006.cluster.edu,
% 2.23/2.39 Wed Jul 27 09:22:47 2022
% 2.23/2.39 The command was "./otter". The process ID is 16387.
% 2.23/2.39
% 2.23/2.39 set(prolog_style_variables).
% 2.23/2.39 set(auto).
% 2.23/2.39 dependent: set(auto1).
% 2.23/2.39 dependent: set(process_input).
% 2.23/2.39 dependent: clear(print_kept).
% 2.23/2.39 dependent: clear(print_new_demod).
% 2.23/2.39 dependent: clear(print_back_demod).
% 2.23/2.39 dependent: clear(print_back_sub).
% 2.23/2.39 dependent: set(control_memory).
% 2.23/2.39 dependent: assign(max_mem, 12000).
% 2.23/2.39 dependent: assign(pick_given_ratio, 4).
% 2.23/2.39 dependent: assign(stats_level, 1).
% 2.23/2.39 dependent: assign(max_seconds, 10800).
% 2.23/2.39 clear(print_given).
% 2.23/2.39
% 2.23/2.39 list(usable).
% 2.23/2.39 0 [] A=A.
% 2.23/2.39 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 2.23/2.39 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 2.23/2.39 0 [] -class_Nat_Osemiring__char__0(T_a)|c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)!=c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)|V_m=V_n.
% 2.23/2.39 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 2.23/2.39 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 2.23/2.39 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 2.23/2.39 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 2.23/2.39 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 2.23/2.39 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a).
% 2.23/2.39 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 2.23/2.39 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 2.23/2.39 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 2.23/2.39 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 2.23/2.39 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 2.23/2.39 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 2.23/2.39 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y.
% 2.23/2.39 0 [] c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)|c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)|V_x=V_y.
% 2.23/2.39 0 [] c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)|V_m=V_n.
% 2.23/2.39 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 2.23/2.39 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y.
% 2.23/2.39 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 2.23/2.39 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 2.23/2.39 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 2.23/2.39 0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat).
% 2.23/2.39 0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat).
% 2.23/2.39 0 [] -class_Orderings_Opreorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_z,T_a)| -c_HOL_Oord__class_Oless(V_y,V_z,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 2.23/2.39 0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_z,V_x,T_a)| -c_HOL_Oord__class_Oless(V_z,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 2.23/2.39 0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 2.23/2.39 0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 2.23/2.39 0 [] c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 2.23/2.39 0 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t))| -c_Lambda_Obeta(V_s,V_t).
% 2.23/2.39 0 [] V_s=c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))| -c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s).
% 2.23/2.39 0 [] c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i)))| -c_InductTermi_OIT(V_t).
% 2.23/2.39 0 [] c_Lambda_Obeta(c_Lambda_Olift(V_r,V_i),c_Lambda_Olift(V_s,V_i))| -c_Lambda_Obeta(V_r,V_s).
% 2.23/2.39 0 [] c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k)=c_Lambda_OdB_OVar(V_i)| -c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 2.23/2.39 0 [] c_Lambda_Obeta(c_Lambda_OdB_OApp(V_s,V_u),c_Lambda_OdB_OApp(V_t,V_u))| -c_Lambda_Obeta(V_s,V_t).
% 2.23/2.39 0 [] c_Lambda_Obeta(c_Lambda_OdB_OApp(V_u,V_s),c_Lambda_OdB_OApp(V_u,V_t))| -c_Lambda_Obeta(V_s,V_t).
% 2.23/2.39 0 [] 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.
% 2.23/2.39 0 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k)=c_Lambda_OdB_OVar(V_i)|V_i=V_k|c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 2.23/2.39 0 [] c_Lambda_Olift(c_Lambda_OdB_OApp(V_s,V_t),V_k)=c_Lambda_OdB_OApp(c_Lambda_Olift(V_s,V_k),c_Lambda_Olift(V_t,V_k)).
% 2.23/2.39 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 2.23/2.39 0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 2.23/2.39 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H).
% 2.23/2.39 0 [] c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(V_s),V_t),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat))).
% 2.23/2.39 0 [] c_Lambda_OdB_OApp(V_dB1,V_dB2)!=c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)|V_dB2=V_dB2_H.
% 2.23/2.39 0 [] c_Lambda_OdB_OApp(V_dB1,V_dB2)!=c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)|V_dB1=V_dB1_H.
% 2.23/2.39 0 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t).
% 2.23/2.39 0 [] c_Lambda_Obeta(V_r,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))| -c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s).
% 2.23/2.39 0 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i)=c_Lambda_OdB_OVar(V_j)| -c_HOL_Oord__class_Oless(V_j,V_i,tc_nat).
% 2.23/2.39 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OApp(V_dB1,V_dB2).
% 2.23/2.39 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 2.23/2.39 0 [] c_Lambda_OdB_OApp(V_dB1,V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 2.23/2.39 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 2.23/2.39 0 [] 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)).
% 2.23/2.39 0 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k)=V_u.
% 2.23/2.39 0 [] c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j))| -c_InductTermi_OIT(V_r).
% 2.23/2.39 0 [] c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))| -c_InductTermi_OIT(V_t).
% 2.23/2.39 0 [] c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)).
% 2.23/2.39 0 [] v_n____!=v_i____.
% 2.23/2.39 0 [] c_Lambda_Obeta(c_Lambda_Osubst(V_r,V_t,V_i),c_Lambda_Osubst(V_s,V_t,V_i))| -c_Lambda_Obeta(V_r,V_s).
% 2.23/2.39 0 [] c_InductTermi_OIT(v_ua______).
% 2.23/2.39 0 [] c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))| -c_InductTermi_OIT(V_r).
% 2.23/2.39 0 [] c_InductTermi_OIT(v_u____).
% 2.23/2.39 0 [] c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k)=V_t.
% 2.23/2.39 0 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_Ua____).
% 2.23/2.39 0 [] c_InductTermi_OIT(c_Lambda_Osubst(v_a____,V_ua,V_ia))| -c_Type_Otyping(V_ea,V_ua,v_T____)| -c_InductTermi_OIT(V_ua)| -c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_a____,V_T_H).
% 2.23/2.39 0 [] c_InductTermi_OIT(v_u____).
% 2.23/2.39 0 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 2.23/2.39 0 [] -c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)).
% 2.23/2.39 0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 2.23/2.39 0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 2.23/2.39 0 [] class_Nat_Osemiring__char__0(tc_nat).
% 2.23/2.39 0 [] class_Orderings_Opreorder(tc_nat).
% 2.23/2.39 0 [] class_Orderings_Olinorder(tc_nat).
% 2.23/2.39 0 [] class_Orderings_Oorder(tc_nat).
% 2.23/2.39 end_of_list.
% 2.23/2.39
% 2.23/2.39 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.23/2.39
% 2.23/2.39 This ia a non-Horn set with equality. The strategy will be
% 2.23/2.39 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.23/2.39 deletion, with positive clauses in sos and nonpositive
% 2.23/2.39 clauses in usable.
% 2.23/2.39
% 2.23/2.39 dependent: set(knuth_bendix).
% 2.23/2.39 dependent: set(anl_eq).
% 2.23/2.39 dependent: set(para_from).
% 2.23/2.39 dependent: set(para_into).
% 2.23/2.39 dependent: clear(para_from_right).
% 2.23/2.39 dependent: clear(para_into_right).
% 2.23/2.39 dependent: set(para_from_vars).
% 2.23/2.39 dependent: set(eq_units_both_ways).
% 2.23/2.39 dependent: set(dynamic_demod_all).
% 2.23/2.39 dependent: set(dynamic_demod).
% 2.23/2.39 dependent: set(order_eq).
% 2.23/2.39 dependent: set(back_demod).
% 2.23/2.39 dependent: set(lrpo).
% 2.23/2.39 dependent: set(hyper_res).
% 2.23/2.39 dependent: set(unit_deletion).
% 2.23/2.39 dependent: set(factor).
% 2.23/2.39
% 2.23/2.39 ------------> process usable:
% 2.23/2.39 ** KEPT (pick-wt=9): 1 [] -class_Ring__and__Field_Oordered__semidom(A)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_HOL_Ozero__class_Ozero(A),A).
% 2.23/2.39 ** KEPT (pick-wt=9): 2 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Ozero__class_Ozero(A).
% 2.23/2.39 ** KEPT (pick-wt=12): 3 [] -class_Nat_Osemiring__char__0(A)|c_Nat_Osemiring__1__class_Oof__nat(B,A)!=c_Nat_Osemiring__1__class_Oof__nat(C,A)|B=C.
% 2.23/2.39 ** KEPT (pick-wt=14): 4 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 2.23/2.39 ** KEPT (pick-wt=14): 5 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A).
% 2.23/2.39 ** KEPT (pick-wt=10): 6 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 2.23/2.39 Following clause subsumed by 6 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 2.23/2.39 ** KEPT (pick-wt=10): 7 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 2.23/2.39 ** KEPT (pick-wt=10): 8 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 2.23/2.39 ** KEPT (pick-wt=6): 9 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 2.23/2.39 ** KEPT (pick-wt=14): 10 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A).
% 2.23/2.39 ** KEPT (pick-wt=14): 11 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 2.23/2.39 ** KEPT (pick-wt=13): 12 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A).
% 2.23/2.39 Following clause subsumed by 12 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B|c_HOL_Oord__class_Oless(C,B,A).
% 2.23/2.39 Following clause subsumed by 12 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)|C=B.
% 2.23/2.39 Following clause subsumed by 12 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 2.23/2.39 ** KEPT (pick-wt=13): 13 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)|C=B.
% 2.23/2.39 ** KEPT (pick-wt=6): 14 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 2.23/2.39 ** KEPT (pick-wt=6): 15 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 2.23/2.39 ** KEPT (pick-wt=6): 16 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 2.23/2.39 ** KEPT (pick-wt=4): 17 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 2.23/2.39 Following clause subsumed by 17 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 2.23/2.39 ** KEPT (pick-wt=14): 18 [] -class_Orderings_Opreorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 2.23/2.39 ** KEPT (pick-wt=14): 19 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(D,C,A).
% 2.23/2.39 ** KEPT (pick-wt=5): 20 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 2.23/2.39 Following clause subsumed by 20 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 2.23/2.39 ** KEPT (pick-wt=6): 21 [] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OVar(C).
% 2.23/2.39 ** KEPT (pick-wt=8): 22 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(A),c_Lambda_OdB_OAbs(B))| -c_Lambda_Obeta(A,B).
% 2.23/2.39 ** KEPT (pick-wt=10): 24 [copy,23,flip.1] c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(A,B))=B| -c_Lambda_Obeta(c_Lambda_OdB_OAbs(A),B).
% 2.23/2.39 ** KEPT (pick-wt=7): 25 [] c_InductTermi_OIT(c_Lambda_OdB_OApp(A,c_Lambda_OdB_OVar(B)))| -c_InductTermi_OIT(A).
% 2.23/2.39 ** KEPT (pick-wt=10): 26 [] c_Lambda_Obeta(c_Lambda_Olift(A,B),c_Lambda_Olift(C,B))| -c_Lambda_Obeta(A,C).
% 2.23/2.39 ** KEPT (pick-wt=11): 27 [] c_Lambda_Olift(c_Lambda_OdB_OVar(A),B)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 2.23/2.39 ** KEPT (pick-wt=10): 28 [] c_Lambda_Obeta(c_Lambda_OdB_OApp(A,B),c_Lambda_OdB_OApp(C,B))| -c_Lambda_Obeta(A,C).
% 2.23/2.39 ** KEPT (pick-wt=10): 29 [] c_Lambda_Obeta(c_Lambda_OdB_OApp(A,B),c_Lambda_OdB_OApp(A,C))| -c_Lambda_Obeta(B,C).
% 2.23/2.39 ** KEPT (pick-wt=5): 30 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 2.23/2.39 ** KEPT (pick-wt=8): 31 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 2.23/2.39 ** KEPT (pick-wt=6): 32 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OApp(B,C).
% 2.23/2.39 ** KEPT (pick-wt=10): 33 [] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OApp(C,D)|B=D.
% 2.23/2.39 ** KEPT (pick-wt=10): 34 [] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OApp(C,D)|A=C.
% 2.23/2.39 ** KEPT (pick-wt=4): 35 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(A),B).
% 2.23/2.39 ** KEPT (pick-wt=9): 36 [] c_Lambda_Obeta(A,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(A,B))| -c_Lambda_Obeta(c_Lambda_OdB_OAbs(A),B).
% 2.23/2.39 ** KEPT (pick-wt=12): 37 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,C)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 2.23/2.39 ** KEPT (pick-wt=6): 38 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OApp(B,C).
% 2.23/2.39 ** KEPT (pick-wt=8): 39 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 2.23/2.39 ** KEPT (pick-wt=6): 40 [] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OAbs(C).
% 2.23/2.39 ** KEPT (pick-wt=5): 41 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 2.23/2.39 ** KEPT (pick-wt=8): 42 [] c_InductTermi_OIT(c_Lambda_Osubst(A,c_Lambda_OdB_OVar(B),C))| -c_InductTermi_OIT(A).
% 2.23/2.39 ** KEPT (pick-wt=6): 43 [] c_InductTermi_OIT(c_Lambda_Olift(A,B))| -c_InductTermi_OIT(A).
% 2.23/2.39 ** KEPT (pick-wt=3): 44 [] v_n____!=v_i____.
% 2.23/2.39 ** KEPT (pick-wt=12): 45 [] c_Lambda_Obeta(c_Lambda_Osubst(A,B,C),c_Lambda_Osubst(D,B,C))| -c_Lambda_Obeta(A,D).
% 2.23/2.39 ** KEPT (pick-wt=5): 46 [] c_InductTermi_OIT(c_Lambda_OdB_OAbs(A))| -c_InductTermi_OIT(A).
% 2.23/2.39 ** KEPT (pick-wt=19): 47 [] c_InductTermi_OIT(c_Lambda_Osubst(v_a____,A,B))| -c_Type_Otyping(C,A,v_T____)| -c_InductTermi_OIT(A)| -c_Type_Otyping(c_Type_Oshift(C,B,v_T____,tc_Type_Otype),v_a____,D).
% 2.23/2.39 ** KEPT (pick-wt=5): 48 [] -c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)).
% 2.23/2.39 17 back subsumes 9.
% 2.23/2.39 Following clause subsumed by 32 during input processing: 0 [copy,21,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OApp(B,C).
% 2.23/2.39 Following clause subsumed by 41 during input processing: 0 [copy,30,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 2.23/2.39 Following clause subsumed by 21 during input processing: 0 [copy,32,flip.1] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OVar(C).
% 2.23/2.39 Following clause subsumed by 40 during input processing: 0 [copy,38,flip.1] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OAbs(C).
% 2.23/2.39 Following clause subsumed by 38 during input processing: 0 [copy,40,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OApp(B,C).
% 2.23/2.39 Following clause subsumed by 30 during input processing: 0 [copy,41,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 2.23/2.39
% 2.23/2.39 ------------> process sos:
% 2.23/2.39 ** KEPT (pick-wt=3): 51 [] A=A.
% 2.23/2.39 ** KEPT (pick-wt=9): 52 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 2.23/2.39 ** KEPT (pick-wt=11): 53 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 2.23/2.39 Following clause subsumed by 53 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 2.23/2.39 ** KEPT (pick-wt=7): 55 [copy,54,unit_del,17] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A)=B.
% 2.29/2.48 ---> New Demodulator: 56 [new_demod,55] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A)=B.
% 2.29/2.48 ** KEPT (pick-wt=15): 57 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,C)=c_Lambda_OdB_OVar(A)|A=C|c_HOL_Oord__class_Oless(C,A,tc_nat).
% 2.29/2.48 ** KEPT (pick-wt=13): 58 [] c_Lambda_Olift(c_Lambda_OdB_OApp(A,B),C)=c_Lambda_OdB_OApp(c_Lambda_Olift(A,C),c_Lambda_Olift(B,C)).
% 2.29/2.48 ---> New Demodulator: 59 [new_demod,58] c_Lambda_Olift(c_Lambda_OdB_OApp(A,B),C)=c_Lambda_OdB_OApp(c_Lambda_Olift(A,C),c_Lambda_Olift(B,C)).
% 2.29/2.48 ** KEPT (pick-wt=10): 60 [] c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(A),B),c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat))).
% 2.29/2.48 ** KEPT (pick-wt=16): 62 [copy,61,flip.1] c_Lambda_OdB_OApp(c_Lambda_Osubst(A,B,C),c_Lambda_Osubst(D,B,C))=c_Lambda_Osubst(c_Lambda_OdB_OApp(A,D),B,C).
% 2.29/2.48 ---> New Demodulator: 63 [new_demod,62] c_Lambda_OdB_OApp(c_Lambda_Osubst(A,B,C),c_Lambda_Osubst(D,B,C))=c_Lambda_Osubst(c_Lambda_OdB_OApp(A,D),B,C).
% 2.29/2.48 Following clause subsumed by 51 during input processing: 0 [demod,56] B=B.
% 2.29/2.48 ** KEPT (pick-wt=3): 64 [] c_InductTermi_OIT(c_Lambda_OdB_OVar(A)).
% 2.29/2.48 ** KEPT (pick-wt=2): 65 [] c_InductTermi_OIT(v_ua______).
% 2.29/2.48 ** KEPT (pick-wt=2): 66 [] c_InductTermi_OIT(v_u____).
% 2.29/2.48 ** KEPT (pick-wt=8): 67 [] c_Lambda_Osubst(c_Lambda_Olift(A,B),C,B)=A.
% 2.29/2.48 ---> New Demodulator: 68 [new_demod,67] c_Lambda_Osubst(c_Lambda_Olift(A,B),C,B)=A.
% 2.29/2.48 ** KEPT (pick-wt=8): 69 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_Ua____).
% 2.29/2.48 Following clause subsumed by 66 during input processing: 0 [] c_InductTermi_OIT(v_u____).
% 2.29/2.48 ** KEPT (pick-wt=4): 70 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 2.29/2.48 ** KEPT (pick-wt=2): 71 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 2.29/2.48 ** KEPT (pick-wt=2): 72 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 2.29/2.48 ** KEPT (pick-wt=2): 73 [] class_Nat_Osemiring__char__0(tc_nat).
% 2.29/2.48 ** KEPT (pick-wt=2): 74 [] class_Orderings_Opreorder(tc_nat).
% 2.29/2.48 ** KEPT (pick-wt=2): 75 [] class_Orderings_Olinorder(tc_nat).
% 2.29/2.48 ** KEPT (pick-wt=2): 76 [] class_Orderings_Oorder(tc_nat).
% 2.29/2.48 Following clause subsumed by 51 during input processing: 0 [copy,51,flip.1] A=A.
% 2.29/2.48 51 back subsumes 50.
% 2.29/2.48 51 back subsumes 49.
% 2.29/2.48 >>>> Starting back demodulation with 56.
% 2.29/2.48 >>>> Starting back demodulation with 59.
% 2.29/2.48 >>>> Starting back demodulation with 63.
% 2.29/2.48 >>>> Starting back demodulation with 68.
% 2.29/2.48
% 2.29/2.48 ======= end of input processing =======
% 2.29/2.48
% 2.29/2.48 =========== start of search ===========
% 2.29/2.48
% 2.29/2.48
% 2.29/2.48 Resetting weight limit to 8.
% 2.29/2.48
% 2.29/2.48
% 2.29/2.48 Resetting weight limit to 8.
% 2.29/2.48
% 2.29/2.48 sos_size=1007
% 2.29/2.48
% 2.29/2.48 -------- PROOF --------
% 2.29/2.48
% 2.29/2.48 ----> UNIT CONFLICT at 0.09 sec ----> 1122 [binary,1121.1,48.1] $F.
% 2.29/2.48
% 2.29/2.48 Length of proof is 1. Level of proof is 1.
% 2.29/2.48
% 2.29/2.48 ---------------- PROOF ----------------
% 2.29/2.48 % SZS status Unsatisfiable
% 2.29/2.48 % SZS output start Refutation
% See solution above
% 2.29/2.48 ------------ end of proof -------------
% 2.29/2.48
% 2.29/2.48
% 2.29/2.48 Search stopped by max_proofs option.
% 2.29/2.48
% 2.29/2.48
% 2.29/2.48 Search stopped by max_proofs option.
% 2.29/2.48
% 2.29/2.48 ============ end of search ============
% 2.29/2.48
% 2.29/2.48 -------------- statistics -------------
% 2.29/2.48 clauses given 46
% 2.29/2.48 clauses generated 1935
% 2.29/2.48 clauses kept 1113
% 2.29/2.48 clauses forward subsumed 428
% 2.29/2.48 clauses back subsumed 4
% 2.29/2.48 Kbytes malloced 4882
% 2.29/2.48
% 2.29/2.48 ----------- times (seconds) -----------
% 2.29/2.48 user CPU time 0.09 (0 hr, 0 min, 0 sec)
% 2.29/2.48 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.29/2.48 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.29/2.48
% 2.29/2.48 That finishes the proof of the theorem.
% 2.29/2.48
% 2.29/2.48 Process 16387 finished Wed Jul 27 09:22:49 2022
% 2.29/2.48 Otter interrupted
% 2.29/2.48 PROOF FOUND
%------------------------------------------------------------------------------