TSTP Solution File: LCL155-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : LCL155-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n021.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 13:44:25 EDT 2022

% Result   : Unsatisfiable 0.70s 0.98s
% Output   : Refutation 0.70s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : LCL155-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul  3 23:13:46 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.70/0.98  ============================== Prover9 ===============================
% 0.70/0.98  Prover9 (32) version 2009-11A, November 2009.
% 0.70/0.98  Process 13942 was started by sandbox2 on n021.cluster.edu,
% 0.70/0.98  Sun Jul  3 23:13:47 2022
% 0.70/0.98  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_13789_n021.cluster.edu".
% 0.70/0.98  ============================== end of head ===========================
% 0.70/0.98  
% 0.70/0.98  ============================== INPUT =================================
% 0.70/0.98  
% 0.70/0.98  % Reading from file /tmp/Prover9_13789_n021.cluster.edu
% 0.70/0.98  
% 0.70/0.98  set(prolog_style_variables).
% 0.70/0.98  set(auto2).
% 0.70/0.98      % set(auto2) -> set(auto).
% 0.70/0.98      % set(auto) -> set(auto_inference).
% 0.70/0.98      % set(auto) -> set(auto_setup).
% 0.70/0.98      % set(auto_setup) -> set(predicate_elim).
% 0.70/0.98      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/0.98      % set(auto) -> set(auto_limits).
% 0.70/0.98      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/0.98      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/0.98      % set(auto) -> set(auto_denials).
% 0.70/0.98      % set(auto) -> set(auto_process).
% 0.70/0.98      % set(auto2) -> assign(new_constants, 1).
% 0.70/0.98      % set(auto2) -> assign(fold_denial_max, 3).
% 0.70/0.98      % set(auto2) -> assign(max_weight, "200.000").
% 0.70/0.98      % set(auto2) -> assign(max_hours, 1).
% 0.70/0.98      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.70/0.98      % set(auto2) -> assign(max_seconds, 0).
% 0.70/0.98      % set(auto2) -> assign(max_minutes, 5).
% 0.70/0.98      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.70/0.98      % set(auto2) -> set(sort_initial_sos).
% 0.70/0.98      % set(auto2) -> assign(sos_limit, -1).
% 0.70/0.98      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.70/0.98      % set(auto2) -> assign(max_megs, 400).
% 0.70/0.98      % set(auto2) -> assign(stats, some).
% 0.70/0.98      % set(auto2) -> clear(echo_input).
% 0.70/0.98      % set(auto2) -> set(quiet).
% 0.70/0.98      % set(auto2) -> clear(print_initial_clauses).
% 0.70/0.98      % set(auto2) -> clear(print_given).
% 0.70/0.98  assign(lrs_ticks,-1).
% 0.70/0.98  assign(sos_limit,10000).
% 0.70/0.98  assign(order,kbo).
% 0.70/0.98  set(lex_order_vars).
% 0.70/0.98  clear(print_given).
% 0.70/0.98  
% 0.70/0.98  % formulas(sos).  % not echoed (17 formulas)
% 0.70/0.98  
% 0.70/0.98  ============================== end of input ==========================
% 0.70/0.98  
% 0.70/0.98  % From the command line: assign(max_seconds, 300).
% 0.70/0.98  
% 0.70/0.98  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.70/0.98  
% 0.70/0.98  % Formulas that are not ordinary clauses:
% 0.70/0.98  
% 0.70/0.98  ============================== end of process non-clausal formulas ===
% 0.70/0.98  
% 0.70/0.98  ============================== PROCESS INITIAL CLAUSES ===============
% 0.70/0.98  
% 0.70/0.98  ============================== PREDICATE ELIMINATION =================
% 0.70/0.98  
% 0.70/0.98  ============================== end predicate elimination =============
% 0.70/0.98  
% 0.70/0.98  Auto_denials:
% 0.70/0.98    % copying label prove_alternative_wajsberg_axiom to answer in negative clause
% 0.70/0.98  
% 0.70/0.98  Term ordering decisions:
% 0.70/0.98  
% 0.70/0.98  % Assigning unary symbol not kb_weight 0 and highest precedence (10).
% 0.70/0.98  Function symbol KB weights:  truth=1. falsehood=1. x=1. implies=1. or=1. and=1. and_star=1. xor=1. not=0.
% 0.70/0.98  
% 0.70/0.98  ============================== end of process initial clauses ========
% 0.70/0.98  
% 0.70/0.98  ============================== CLAUSES FOR SEARCH ====================
% 0.70/0.98  
% 0.70/0.98  ============================== end of clauses for search =============
% 0.70/0.98  
% 0.70/0.98  ============================== SEARCH ================================
% 0.70/0.98  
% 0.70/0.98  % Starting search at 0.01 seconds.
% 0.70/0.98  
% 0.70/0.98  ============================== PROOF =================================
% 0.70/0.98  % SZS status Unsatisfiable
% 0.70/0.98  % SZS output start Refutation
% 0.70/0.98  
% 0.70/0.98  % Proof 1 at 0.04 (+ 0.00) seconds: prove_alternative_wajsberg_axiom.
% 0.70/0.98  % Length of proof is 28.
% 0.70/0.98  % Level of proof is 7.
% 0.70/0.98  % Maximum clause weight is 22.000.
% 0.70/0.98  % Given clauses 27.
% 0.70/0.98  
% 0.70/0.98  1 not(truth) = falsehood # label(false_definition) # label(axiom).  [assumption].
% 0.70/0.98  2 falsehood = not(truth).  [copy(1),flip(a)].
% 0.70/0.98  3 implies(truth,A) = A # label(wajsberg_1) # label(axiom).  [assumption].
% 0.70/0.98  4 or(A,B) = or(B,A) # label(or_commutativity) # label(axiom).  [assumption].
% 0.70/0.98  5 and(A,B) = and(B,A) # label(and_commutativity) # label(axiom).  [assumption].
% 0.70/0.98  8 or(A,B) = implies(not(A),B) # label(or_definition) # label(axiom).  [assumption].
% 0.70/0.98  9 and(A,B) = not(or(not(A),not(B))) # label(and_definition) # label(axiom).  [assumption].
% 0.70/0.98  10 and(A,B) = not(implies(not(not(A)),not(B))).  [copy(9),rewrite([8(4)])].
% 0.70/0.98  13 implies(implies(A,B),B) = implies(implies(B,A),A) # label(wajsberg_3) # label(axiom).  [assumption].
% 0.70/0.98  14 implies(implies(not(A),not(B)),implies(B,A)) = truth # label(wajsberg_4) # label(axiom).  [assumption].
% 0.70/0.98  20 implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth # label(wajsberg_2) # label(axiom).  [assumption].
% 0.70/0.98  21 xor(A,B) = or(and(A,not(B)),and(not(A),B)) # label(xor_definition) # label(axiom).  [assumption].
% 0.70/0.98  22 xor(A,B) = implies(not(not(implies(not(not(A)),not(not(B))))),not(implies(not(not(B)),not(not(A))))).  [copy(21),rewrite([10(3),5(9),10(9),8(14)])].
% 0.70/0.98  23 xor(x,x) != falsehood # label(prove_alternative_wajsberg_axiom) # label(negated_conjecture) # answer(prove_alternative_wajsberg_axiom).  [assumption].
% 0.70/0.98  24 implies(not(not(implies(not(not(x)),not(not(x))))),not(implies(not(not(x)),not(not(x))))) != not(truth) # answer(prove_alternative_wajsberg_axiom).  [copy(23),rewrite([22(3),2(19)])].
% 0.70/0.98  25 implies(not(A),B) = implies(not(B),A).  [back_rewrite(4),rewrite([8(1),8(3)])].
% 0.70/0.98  26 implies(implies(A,truth),truth) = implies(A,A).  [para(3(a,1),13(a,1,1)),flip(a)].
% 0.70/0.98  29 implies(implies(implies(A,B),implies(not(B),not(A))),implies(not(B),not(A))) = implies(A,B).  [para(14(a,1),13(a,1,1)),rewrite([3(3)]),flip(a)].
% 0.70/0.98  67 implies(A,implies(implies(A,B),B)) = truth.  [para(3(a,1),20(a,1,1)),rewrite([3(3)])].
% 0.70/0.98  68 implies(implies(A,truth),implies(B,implies(A,B))) = truth.  [para(3(a,1),20(a,1,2,1))].
% 0.70/0.98  122 implies(not(not(implies(not(not(x)),not(not(x))))),not(implies(implies(not(truth),not(x)),truth))) != not(truth) # answer(prove_alternative_wajsberg_axiom).  [para(26(a,2),24(a,1,1,1,1)),rewrite([25(5),25(18)])].
% 0.70/0.98  133 implies(A,A) = truth.  [para(67(a,1),3(a,1)),rewrite([3(3)]),flip(a)].
% 0.70/0.98  145 implies(A,truth) = truth.  [para(26(a,1),67(a,1,2)),rewrite([133(1)])].
% 0.70/0.98  146 implies(not(not(truth)),not(truth)) != not(truth) # answer(prove_alternative_wajsberg_axiom).  [back_rewrite(122),rewrite([133(7),145(10)])].
% 0.70/0.98  154 implies(A,implies(B,A)) = truth.  [back_rewrite(68),rewrite([145(2),3(4)])].
% 0.70/0.98  189 implies(A,implies(not(A),B)) = truth.  [para(25(a,1),154(a,1,2))].
% 0.70/0.98  204 implies(not(A),not(truth)) = A.  [para(3(a,1),29(a,1,1,1)),rewrite([189(5),3(6),3(6)])].
% 0.70/0.98  205 $F # answer(prove_alternative_wajsberg_axiom).  [resolve(204,a,146,a)].
% 0.70/0.98  
% 0.70/0.98  % SZS output end Refutation
% 0.70/0.98  ============================== end of proof ==========================
% 0.70/0.98  
% 0.70/0.98  ============================== STATISTICS ============================
% 0.70/0.98  
% 0.70/0.98  Given=27. Generated=578. Kept=196. proofs=1.
% 0.70/0.98  Usable=22. Sos=112. Demods=91. Limbo=0, Disabled=78. Hints=0.
% 0.70/0.98  Megabytes=0.26.
% 0.70/0.98  User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.70/0.98  
% 0.70/0.98  ============================== end of statistics =====================
% 0.70/0.98  
% 0.70/0.98  ============================== end of search =========================
% 0.70/0.98  
% 0.70/0.98  THEOREM PROVED
% 0.70/0.98  % SZS status Unsatisfiable
% 0.70/0.98  
% 0.70/0.98  Exiting with 1 proof.
% 0.70/0.98  
% 0.70/0.98  Process 13942 exit (max_proofs) Sun Jul  3 23:13:47 2022
% 0.70/0.98  Prover9 interrupted
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