TSTP Solution File: RNG006-3 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : RNG006-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n029.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 : Mon Jul 18 20:39:09 EDT 2022

% Result   : Unsatisfiable 0.89s 1.14s
% Output   : Refutation 0.89s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : RNG006-3 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.35  % Computer : n029.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon May 30 19:07:59 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.89/1.14  ============================== Prover9 ===============================
% 0.89/1.14  Prover9 (32) version 2009-11A, November 2009.
% 0.89/1.14  Process 12964 was started by sandbox on n029.cluster.edu,
% 0.89/1.14  Mon May 30 19:08:00 2022
% 0.89/1.14  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12811_n029.cluster.edu".
% 0.89/1.14  ============================== end of head ===========================
% 0.89/1.14  
% 0.89/1.14  ============================== INPUT =================================
% 0.89/1.14  
% 0.89/1.14  % Reading from file /tmp/Prover9_12811_n029.cluster.edu
% 0.89/1.14  
% 0.89/1.14  set(prolog_style_variables).
% 0.89/1.14  set(auto2).
% 0.89/1.14      % set(auto2) -> set(auto).
% 0.89/1.14      % set(auto) -> set(auto_inference).
% 0.89/1.14      % set(auto) -> set(auto_setup).
% 0.89/1.14      % set(auto_setup) -> set(predicate_elim).
% 0.89/1.14      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.89/1.14      % set(auto) -> set(auto_limits).
% 0.89/1.14      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.89/1.14      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.89/1.14      % set(auto) -> set(auto_denials).
% 0.89/1.14      % set(auto) -> set(auto_process).
% 0.89/1.14      % set(auto2) -> assign(new_constants, 1).
% 0.89/1.14      % set(auto2) -> assign(fold_denial_max, 3).
% 0.89/1.14      % set(auto2) -> assign(max_weight, "200.000").
% 0.89/1.14      % set(auto2) -> assign(max_hours, 1).
% 0.89/1.14      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.89/1.14      % set(auto2) -> assign(max_seconds, 0).
% 0.89/1.14      % set(auto2) -> assign(max_minutes, 5).
% 0.89/1.14      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.89/1.14      % set(auto2) -> set(sort_initial_sos).
% 0.89/1.14      % set(auto2) -> assign(sos_limit, -1).
% 0.89/1.14      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.89/1.14      % set(auto2) -> assign(max_megs, 400).
% 0.89/1.14      % set(auto2) -> assign(stats, some).
% 0.89/1.14      % set(auto2) -> clear(echo_input).
% 0.89/1.14      % set(auto2) -> set(quiet).
% 0.89/1.14      % set(auto2) -> clear(print_initial_clauses).
% 0.89/1.14      % set(auto2) -> clear(print_given).
% 0.89/1.14  assign(lrs_ticks,-1).
% 0.89/1.14  assign(sos_limit,10000).
% 0.89/1.14  assign(order,kbo).
% 0.89/1.14  set(lex_order_vars).
% 0.89/1.14  clear(print_given).
% 0.89/1.14  
% 0.89/1.14  % formulas(sos).  % not echoed (22 formulas)
% 0.89/1.14  
% 0.89/1.14  ============================== end of input ==========================
% 0.89/1.14  
% 0.89/1.14  % From the command line: assign(max_seconds, 300).
% 0.89/1.14  
% 0.89/1.14  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.89/1.14  
% 0.89/1.14  % Formulas that are not ordinary clauses:
% 0.89/1.14  
% 0.89/1.14  ============================== end of process non-clausal formulas ===
% 0.89/1.14  
% 0.89/1.14  ============================== PROCESS INITIAL CLAUSES ===============
% 0.89/1.14  
% 0.89/1.14  ============================== PREDICATE ELIMINATION =================
% 0.89/1.14  
% 0.89/1.14  ============================== end predicate elimination =============
% 0.89/1.14  
% 0.89/1.14  Auto_denials:
% 0.89/1.14    % copying label prove_a_times_bS_Ic_is_aPb_S__IaPc to answer in negative clause
% 0.89/1.14  
% 0.89/1.14  Term ordering decisions:
% 0.89/1.14  
% 0.89/1.14  % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (14).
% 0.89/1.14  Function symbol KB weights:  additive_identity=1. a=1. aPb=1. aPc=1. b=1. c=1. aPb_S_IaPc=1. bS_Ic=1. add=1. multiply=1. additive_inverse=0.
% 0.89/1.14  
% 0.89/1.14  ============================== end of process initial clauses ========
% 0.89/1.14  
% 0.89/1.14  ============================== CLAUSES FOR SEARCH ====================
% 0.89/1.14  
% 0.89/1.14  ============================== end of clauses for search =============
% 0.89/1.14  
% 0.89/1.14  ============================== SEARCH ================================
% 0.89/1.14  
% 0.89/1.14  % Starting search at 0.01 seconds.
% 0.89/1.14  
% 0.89/1.14  ============================== PROOF =================================
% 0.89/1.14  % SZS status Unsatisfiable
% 0.89/1.14  % SZS output start Refutation
% 0.89/1.14  
% 0.89/1.14  % Proof 1 at 0.13 (+ 0.01) seconds: prove_a_times_bS_Ic_is_aPb_S__IaPc.
% 0.89/1.14  % Length of proof is 33.
% 0.89/1.14  % Level of proof is 5.
% 0.89/1.14  % Maximum clause weight is 20.000.
% 0.89/1.14  % Given clauses 78.
% 0.89/1.14  
% 0.89/1.14  1 sum(additive_identity,A,A) # label(additive_identity1) # label(axiom).  [assumption].
% 0.89/1.14  2 sum(A,additive_identity,A) # label(additive_identity2) # label(axiom).  [assumption].
% 0.89/1.14  3 product(a,b,aPb) # label(a_times_b) # label(hypothesis).  [assumption].
% 0.89/1.14  4 product(a,c,aPc) # label(a_times_c) # label(hypothesis).  [assumption].
% 0.89/1.14  5 sum(additive_inverse(A),A,additive_identity) # label(left_inverse) # label(axiom).  [assumption].
% 0.89/1.14  6 sum(A,additive_inverse(A),additive_identity) # label(right_inverse) # label(axiom).  [assumption].
% 0.89/1.14  7 sum(b,additive_inverse(c),bS_Ic) # label(b_plus_inverse_c) # label(hypothesis).  [assumption].
% 0.89/1.14  8 sum(aPb,additive_inverse(aPc),aPb_S_IaPc) # label(aPb_plus_IaPc) # label(hypothesis).  [assumption].
% 0.89/1.14  9 product(A,B,multiply(A,B)) # label(closure_of_multiplication) # label(axiom).  [assumption].
% 0.89/1.14  10 sum(A,B,add(A,B)) # label(closure_of_addition) # label(axiom).  [assumption].
% 0.89/1.14  11 -product(a,bS_Ic,aPb_S_IaPc) # label(prove_a_times_bS_Ic_is_aPb_S__IaPc) # label(negated_conjecture) # answer(prove_a_times_bS_Ic_is_aPb_S__IaPc).  [assumption].
% 0.89/1.14  12 -sum(A,B,C) | sum(B,A,C) # label(commutativity_of_addition) # label(axiom).  [assumption].
% 0.89/1.14  13 -sum(A,B,C) | -sum(A,B,D) | C = D # label(addition_is_well_defined) # label(axiom).  [assumption].
% 0.89/1.14  14 -product(A,B,C) | -product(A,B,D) | C = D # label(multiplication_is_well_defined) # label(axiom).  [assumption].
% 0.89/1.14  15 -sum(A,B,C) | -sum(B,D,E) | -sum(C,D,F) | sum(A,E,F) # label(associativity_of_addition1) # label(axiom).  [assumption].
% 0.89/1.14  16 -sum(A,B,C) | -sum(B,D,E) | -sum(A,E,F) | sum(C,D,F) # label(associativity_of_addition2) # label(axiom).  [assumption].
% 0.89/1.14  19 -product(A,B,C) | -product(A,D,E) | -sum(B,D,F) | -product(A,F,V6) | sum(C,E,V6) # label(distributivity1) # label(axiom).  [assumption].
% 0.89/1.14  20 -product(A,B,C) | -product(A,D,E) | -sum(B,D,F) | -sum(C,E,V6) | product(A,F,V6) # label(distributivity2) # label(axiom).  [assumption].
% 0.89/1.14  24 sum(additive_inverse(aPc),aPb,aPb_S_IaPc).  [hyper(12,a,8,a)].
% 0.89/1.14  30 add(A,additive_identity) = A.  [hyper(13,a,10,a,b,2,a)].
% 0.89/1.14  31 add(additive_identity,A) = A.  [hyper(13,a,10,a,b,1,a)].
% 0.89/1.14  33 multiply(a,c) = aPc.  [hyper(14,a,9,a,b,4,a)].
% 0.89/1.14  34 multiply(a,b) = aPb.  [hyper(14,a,9,a,b,3,a)].
% 0.89/1.14  50 sum(A,additive_identity,additive_inverse(additive_inverse(A))).  [hyper(15,a,6,a,b,6,a,c,10,a),rewrite([31(5)])].
% 0.89/1.14  68 sum(bS_Ic,c,b).  [hyper(16,a,7,a,b,5,a,c,10,a),rewrite([30(5)])].
% 0.89/1.14  92 sum(aPb,multiply(a,additive_identity),aPb).  [hyper(19,a,9,a,b,9,a,c,2,a,d,3,a),rewrite([34(3)])].
% 0.89/1.14  135 -sum(multiply(a,bS_Ic),multiply(a,additive_identity),aPb_S_IaPc) # answer(prove_a_times_bS_Ic_is_aPb_S__IaPc).  [ur(20,a,9,a,b,9,a,c,2,a,e,11,a)].
% 0.89/1.14  364 sum(c,bS_Ic,b).  [hyper(12,a,68,a)].
% 0.89/1.14  437 sum(aPc,multiply(a,bS_Ic),aPb).  [hyper(19,a,9,a,b,9,a,c,364,a,d,3,a),rewrite([33(3)])].
% 0.89/1.14  909 additive_inverse(additive_inverse(A)) = A.  [hyper(13,a,10,a,b,50,a),rewrite([30(2)]),flip(a)].
% 0.89/1.14  1101 -sum(additive_inverse(aPc),aPb,multiply(a,bS_Ic)) # answer(prove_a_times_bS_Ic_is_aPb_S__IaPc).  [ur(16,b,92,a,c,24,a,d,135,a)].
% 0.89/1.14  1222 -sum(aPc,multiply(a,bS_Ic),aPb) # answer(prove_a_times_bS_Ic_is_aPb_S__IaPc).  [ur(15,a,6,a,c,1,a,d,1101,a),rewrite([909(3)])].
% 0.89/1.14  1223 $F # answer(prove_a_times_bS_Ic_is_aPb_S__IaPc).  [resolve(1222,a,437,a)].
% 0.89/1.14  
% 0.89/1.14  % SZS output end Refutation
% 0.89/1.14  ============================== end of proof ==========================
% 0.89/1.14  
% 0.89/1.14  ============================== STATISTICS ============================
% 0.89/1.14  
% 0.89/1.14  Given=78. Generated=3292. Kept=1222. proofs=1.
% 0.89/1.14  Usable=76. Sos=798. Demods=20. Limbo=5, Disabled=364. Hints=0.
% 0.89/1.14  Megabytes=0.82.
% 0.89/1.14  User_CPU=0.13, System_CPU=0.01, Wall_clock=0.
% 0.89/1.14  
% 0.89/1.14  ============================== end of statistics =====================
% 0.89/1.14  
% 0.89/1.14  ============================== end of search =========================
% 0.89/1.14  
% 0.89/1.14  THEOREM PROVED
% 0.89/1.14  % SZS status Unsatisfiable
% 0.89/1.14  
% 0.89/1.14  Exiting with 1 proof.
% 0.89/1.14  
% 0.89/1.14  Process 12964 exit (max_proofs) Mon May 30 19:08:00 2022
% 0.89/1.14  Prover9 interrupted
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