TSTP Solution File: LCL828-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : LCL828-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n020.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  : 600s
% DateTime : Sun Jul 17 13:50:36 EDT 2022

% Result   : Unsatisfiable 0.73s 1.02s
% Output   : Refutation 0.73s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL828-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.34  % Computer : n020.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jul  4 02:03:30 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.73/1.01  ============================== Prover9 ===============================
% 0.73/1.01  Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.01  Process 825 was started by sandbox2 on n020.cluster.edu,
% 0.73/1.01  Mon Jul  4 02:03:30 2022
% 0.73/1.01  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_662_n020.cluster.edu".
% 0.73/1.01  ============================== end of head ===========================
% 0.73/1.01  
% 0.73/1.01  ============================== INPUT =================================
% 0.73/1.01  
% 0.73/1.01  % Reading from file /tmp/Prover9_662_n020.cluster.edu
% 0.73/1.01  
% 0.73/1.01  set(prolog_style_variables).
% 0.73/1.01  set(auto2).
% 0.73/1.01      % set(auto2) -> set(auto).
% 0.73/1.01      % set(auto) -> set(auto_inference).
% 0.73/1.01      % set(auto) -> set(auto_setup).
% 0.73/1.01      % set(auto_setup) -> set(predicate_elim).
% 0.73/1.01      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.01      % set(auto) -> set(auto_limits).
% 0.73/1.01      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.01      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.01      % set(auto) -> set(auto_denials).
% 0.73/1.01      % set(auto) -> set(auto_process).
% 0.73/1.01      % set(auto2) -> assign(new_constants, 1).
% 0.73/1.01      % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.01      % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.01      % set(auto2) -> assign(max_hours, 1).
% 0.73/1.01      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.01      % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.01      % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.01      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.01      % set(auto2) -> set(sort_initial_sos).
% 0.73/1.01      % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.01      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.01      % set(auto2) -> assign(max_megs, 400).
% 0.73/1.01      % set(auto2) -> assign(stats, some).
% 0.73/1.01      % set(auto2) -> clear(echo_input).
% 0.73/1.01      % set(auto2) -> set(quiet).
% 0.73/1.01      % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.01      % set(auto2) -> clear(print_given).
% 0.73/1.01  assign(lrs_ticks,-1).
% 0.73/1.01  assign(sos_limit,10000).
% 0.73/1.01  assign(order,kbo).
% 0.73/1.01  set(lex_order_vars).
% 0.73/1.01  clear(print_given).
% 0.73/1.01  
% 0.73/1.01  % formulas(sos).  % not echoed (75 formulas)
% 0.73/1.01  
% 0.73/1.01  ============================== end of input ==========================
% 0.73/1.01  
% 0.73/1.01  % From the command line: assign(max_seconds, 300).
% 0.73/1.01  
% 0.73/1.01  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.01  
% 0.73/1.01  % Formulas that are not ordinary clauses:
% 0.73/1.01  
% 0.73/1.01  ============================== end of process non-clausal formulas ===
% 0.73/1.01  
% 0.73/1.01  ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.01  
% 0.73/1.01  ============================== PREDICATE ELIMINATION =================
% 0.73/1.01  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) # label(cls_of__nat__less__0__iff_0) # label(axiom).  [assumption].
% 0.73/1.01  2 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom).  [assumption].
% 0.73/1.01  Derived: -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).  [resolve(1,a,2,a)].
% 0.73/1.01  3 -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) # label(cls_of__nat__less__iff_1) # label(axiom).  [assumption].
% 0.73/1.01  Derived: c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat).  [resolve(3,a,2,a)].
% 0.73/1.01  4 -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) # label(cls_of__nat__less__iff_0) # label(axiom).  [assumption].
% 0.73/1.01  Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat).  [resolve(4,a,2,a)].
% 0.73/1.01  5 -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) # label(cls_of__nat__0__less__iff_0) # label(axiom).  [assumption].
% 0.73/1.01  Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat).  [resolve(5,a,2,a)].
% 0.73/1.01  6 -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) # label(cls_of__nat__0__less__iff_1) # label(axiom).  [assumption].
% 0.73/1.01  Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).  [resolve(6,a,2,a)].
% 0.73/1.01  7 -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) # label(cls_of__nat__0_0) # label(axiom).  [assumption].
% 0.73/1.01  8 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom).  [assumption].
% 0.73/1.01  Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(7,a,8,a)].
% 0.73/1.01  9 -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 # label(cls_of__nat__eq__iff_0) # label(axiom).  [assumption].
% 0.73/1.01  10 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom).  [assumption].
% 0.73/1.01  Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B.  [resolve(9,a,10,a)].
% 0.73/1.01  11 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__irrefl_0) # label(axiom).  [assumption].
% 0.73/1.01  12 class_Orderings_Opreorder(tc_nat) # label(clsarity_nat__Orderings_Opreorder) # label(axiom).  [assumption].
% 0.73/1.01  Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat).  [resolve(11,a,12,a)].
% 0.73/1.01  13 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_order__less__asym_H_0) # label(axiom).  [assumption].
% 0.73/1.01  Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat).  [resolve(13,a,12,a)].
% 0.73/1.01  14 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_order__less__asym_0) # label(axiom).  [assumption].
% 0.73/1.01  15 -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) # label(cls_order__less__trans_0) # label(axiom).  [assumption].
% 0.73/1.01  Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat).  [resolve(15,a,12,a)].
% 0.73/1.01  16 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom).  [assumption].
% 0.73/1.01  17 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom).  [assumption].
% 0.73/1.01  18 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom).  [assumption].
% 0.73/1.01  19 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom).  [assumption].
% 0.73/1.01  Derived: A = B | c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(B,A,tc_nat).  [resolve(19,a,17,a)].
% 0.73/1.01  20 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom).  [assumption].
% 0.73/1.01  21 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom).  [assumption].
% 0.73/1.01  22 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom).  [assumption].
% 0.73/1.01  23 -class_Orderings_Oorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__le_1) # label(axiom).  [assumption].
% 0.73/1.01  24 class_Orderings_Oorder(tc_nat) # label(clsarity_nat__Orderings_Oorder) # label(axiom).  [assumption].
% 0.73/1.02  25 -class_Orderings_Oorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_xt1_I9_J_0) # label(axiom).  [assumption].
% 0.73/1.02  26 -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) # label(cls_xt1_I10_J_0) # label(axiom).  [assumption].
% 0.73/1.02  
% 0.73/1.02  ============================== end predicate elimination =============
% 0.73/1.02  
% 0.73/1.02  Auto_denials:  (non-Horn, no changes).
% 0.73/1.02  
% 0.73/1.02  Term ordering decisions:
% 0.73/1.02  Function symbol KB weights:  tc_nat=1. v_T____=1. v_a____=1. v_u____=1. tc_Type_Otype=1. v_e____=1. v_Ua____=1. v_i____=1. v_ua______=1. v_n____=1. c_Lambda_OdB_OApp=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_Lambda_Olift=1. c_Lambda_Osko__Lambda__Xbeta__cases__2__1=1. c_Lambda_OdB_OVar=1. c_HOL_Ozero__class_Ozero=1. c_Lambda_OdB_OAbs=1. c_Lambda_Osubst=1. c_Type_Oshift=1.
% 0.73/1.02  
% 0.73/1.02  ============================== end of process initial clauses ========
% 0.73/1.02  
% 0.73/1.02  ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.02  
% 0.73/1.02  ============================== end of clauses for search =============
% 0.73/1.02  
% 0.73/1.02  ============================== SEARCH ================================
% 0.73/1.02  
% 0.73/1.02  % Starting search at 0.02 seconds.
% 0.73/1.02  
% 0.73/1.02  ============================== PROOF =================================
% 0.73/1.02  % SZS status Unsatisfiable
% 0.73/1.02  % SZS output start Refutation
% 0.73/1.02  
% 0.73/1.02  % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.73/1.02  % Length of proof is 6.
% 0.73/1.02  % Level of proof is 1.
% 0.73/1.02  % Maximum clause weight is 19.000.
% 0.73/1.02  % Given clauses 39.
% 0.73/1.02  
% 0.73/1.02  28 c_InductTermi_OIT(v_u____) # label(cls_uIT_0) # label(axiom).  [assumption].
% 0.73/1.02  30 c_Type_Otyping(v_e____,v_u____,v_T____) # label(cls_CHAINED_0_03) # label(axiom).  [assumption].
% 0.73/1.02  33 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_Ua____) # label(cls_CHAINED_0) # label(axiom).  [assumption].
% 0.73/1.02  50 -c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)) # label(cls_conjecture_0) # label(negated_conjecture).  [assumption].
% 0.73/1.02  73 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) # label(cls_CHAINED_0_01) # label(axiom).  [assumption].
% 0.73/1.02  141 $F.  [ur(73,a,50,a,c,28,a,d,33,a),unit_del(a,30)].
% 0.73/1.02  
% 0.73/1.02  % SZS output end Refutation
% 0.73/1.02  ============================== end of proof ==========================
% 0.73/1.02  
% 0.73/1.02  ============================== STATISTICS ============================
% 0.73/1.02  
% 0.73/1.02  Given=39. Generated=166. Kept=106. proofs=1.
% 0.73/1.02  Usable=39. Sos=65. Demods=7. Limbo=2, Disabled=86. Hints=0.
% 0.73/1.02  Megabytes=0.17.
% 0.73/1.02  User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.73/1.02  
% 0.73/1.02  ============================== end of statistics =====================
% 0.73/1.02  
% 0.73/1.02  ============================== end of search =========================
% 0.73/1.02  
% 0.73/1.02  THEOREM PROVED
% 0.73/1.02  % SZS status Unsatisfiable
% 0.73/1.02  
% 0.73/1.02  Exiting with 1 proof.
% 0.73/1.02  
% 0.73/1.02  Process 825 exit (max_proofs) Mon Jul  4 02:03:30 2022
% 0.73/1.02  Prover9 interrupted
%------------------------------------------------------------------------------