TSTP Solution File: ALG004-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : ALG004-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n028.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 : Thu Jul 14 17:53:34 EDT 2022

% Result   : Unsatisfiable 2.34s 2.68s
% Output   : Refutation 2.34s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ALG004-1 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.33  % Computer : n028.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 : Wed Jun  8 19:57:16 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 2.34/2.68  ============================== Prover9 ===============================
% 2.34/2.68  Prover9 (32) version 2009-11A, November 2009.
% 2.34/2.68  Process 4397 was started by sandbox2 on n028.cluster.edu,
% 2.34/2.68  Wed Jun  8 19:57:17 2022
% 2.34/2.68  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4244_n028.cluster.edu".
% 2.34/2.68  ============================== end of head ===========================
% 2.34/2.68  
% 2.34/2.68  ============================== INPUT =================================
% 2.34/2.68  
% 2.34/2.68  % Reading from file /tmp/Prover9_4244_n028.cluster.edu
% 2.34/2.68  
% 2.34/2.68  set(prolog_style_variables).
% 2.34/2.68  set(auto2).
% 2.34/2.68      % set(auto2) -> set(auto).
% 2.34/2.68      % set(auto) -> set(auto_inference).
% 2.34/2.68      % set(auto) -> set(auto_setup).
% 2.34/2.68      % set(auto_setup) -> set(predicate_elim).
% 2.34/2.68      % set(auto_setup) -> assign(eq_defs, unfold).
% 2.34/2.68      % set(auto) -> set(auto_limits).
% 2.34/2.68      % set(auto_limits) -> assign(max_weight, "100.000").
% 2.34/2.68      % set(auto_limits) -> assign(sos_limit, 20000).
% 2.34/2.68      % set(auto) -> set(auto_denials).
% 2.34/2.68      % set(auto) -> set(auto_process).
% 2.34/2.68      % set(auto2) -> assign(new_constants, 1).
% 2.34/2.68      % set(auto2) -> assign(fold_denial_max, 3).
% 2.34/2.68      % set(auto2) -> assign(max_weight, "200.000").
% 2.34/2.68      % set(auto2) -> assign(max_hours, 1).
% 2.34/2.68      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.34/2.68      % set(auto2) -> assign(max_seconds, 0).
% 2.34/2.68      % set(auto2) -> assign(max_minutes, 5).
% 2.34/2.68      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.34/2.68      % set(auto2) -> set(sort_initial_sos).
% 2.34/2.68      % set(auto2) -> assign(sos_limit, -1).
% 2.34/2.68      % set(auto2) -> assign(lrs_ticks, 3000).
% 2.34/2.68      % set(auto2) -> assign(max_megs, 400).
% 2.34/2.68      % set(auto2) -> assign(stats, some).
% 2.34/2.68      % set(auto2) -> clear(echo_input).
% 2.34/2.68      % set(auto2) -> set(quiet).
% 2.34/2.68      % set(auto2) -> clear(print_initial_clauses).
% 2.34/2.68      % set(auto2) -> clear(print_given).
% 2.34/2.68  assign(lrs_ticks,-1).
% 2.34/2.68  assign(sos_limit,10000).
% 2.34/2.68  assign(order,kbo).
% 2.34/2.68  set(lex_order_vars).
% 2.34/2.68  clear(print_given).
% 2.34/2.68  
% 2.34/2.68  % formulas(sos).  % not echoed (7 formulas)
% 2.34/2.68  
% 2.34/2.68  ============================== end of input ==========================
% 2.34/2.68  
% 2.34/2.68  % From the command line: assign(max_seconds, 300).
% 2.34/2.68  
% 2.34/2.68  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.34/2.68  
% 2.34/2.68  % Formulas that are not ordinary clauses:
% 2.34/2.68  
% 2.34/2.68  ============================== end of process non-clausal formulas ===
% 2.34/2.68  
% 2.34/2.68  ============================== PROCESS INITIAL CLAUSES ===============
% 2.34/2.68  
% 2.34/2.68  ============================== PREDICATE ELIMINATION =================
% 2.34/2.68  
% 2.34/2.68  ============================== end predicate elimination =============
% 2.34/2.68  
% 2.34/2.68  Auto_denials:
% 2.34/2.68    % copying label prove_quotient_condition4 to answer in negative clause
% 2.34/2.68  
% 2.34/2.68  Term ordering decisions:
% 2.34/2.68  Function symbol KB weights:  a=1. a0=1. b=1. b0=1. c=1. c0=1. d=1. d0=1. multiply=1.
% 2.34/2.68  
% 2.34/2.68  ============================== end of process initial clauses ========
% 2.34/2.68  
% 2.34/2.68  ============================== CLAUSES FOR SEARCH ====================
% 2.34/2.68  
% 2.34/2.68  ============================== end of clauses for search =============
% 2.34/2.68  
% 2.34/2.68  ============================== SEARCH ================================
% 2.34/2.68  
% 2.34/2.68  % Starting search at 0.01 seconds.
% 2.34/2.68  
% 2.34/2.68  ============================== PROOF =================================
% 2.34/2.68  % SZS status Unsatisfiable
% 2.34/2.68  % SZS output start Refutation
% 2.34/2.68  
% 2.34/2.68  % Proof 1 at 1.71 (+ 0.01) seconds: prove_quotient_condition4.
% 2.34/2.68  % Length of proof is 21.
% 2.34/2.68  % Level of proof is 6.
% 2.34/2.68  % Maximum clause weight is 29.000.
% 2.34/2.68  % Given clauses 108.
% 2.34/2.68  
% 2.34/2.68  1 multiply(b,b0) = multiply(a,a0) # label(prove_quotient_condition1) # label(negated_conjecture).  [assumption].
% 2.34/2.68  2 multiply(d,b0) = multiply(c,a0) # label(prove_quotient_condition2) # label(negated_conjecture).  [assumption].
% 2.34/2.68  3 multiply(b,d0) = multiply(a,c0) # label(prove_quotient_condition3) # label(negated_conjecture).  [assumption].
% 2.34/2.68  4 multiply(multiply(A,B),multiply(C,D)) = multiply(multiply(A,C),multiply(B,D)) # label(medial_law) # label(axiom).  [assumption].
% 2.34/2.68  5 multiply(d,d0) != multiply(c,c0) # label(prove_quotient_condition4) # label(negated_conjecture) # answer(prove_quotient_condition4).  [assumption].
% 2.34/2.68  6 multiply(A,B) != C | multiply(D,B) != C | A = D # label(left_cancellation) # label(axiom).  [assumption].
% 2.34/2.68  7 multiply(A,B) != C | multiply(A,D) != C | B = D # label(right_cancelaation) # label(axiom).  [assumption].
% 2.34/2.68  8 multiply(d,d0) = c_0.  [new_symbol(5)].
% 2.34/2.68  9 multiply(c,c0) != c_0 # answer(prove_quotient_condition4).  [back_rewrite(5),rewrite([8(3)]),flip(a)].
% 2.34/2.68  10 multiply(multiply(a,a0),multiply(A,B)) = multiply(multiply(b,A),multiply(b0,B)).  [para(1(a,1),4(a,1,1))].
% 2.34/2.68  12 multiply(multiply(c,a0),multiply(A,B)) = multiply(multiply(d,A),multiply(b0,B)).  [para(2(a,1),4(a,1,1))].
% 2.34/2.68  27 multiply(multiply(A,d),multiply(B,d0)) = multiply(multiply(A,B),c_0).  [para(8(a,1),4(a,1,2)),flip(a)].
% 2.34/2.68  30 multiply(A,multiply(c,c0)) != multiply(A,c_0) # answer(prove_quotient_condition4).  [ur(7,b,xx,c,9,a)].
% 2.34/2.68  44 multiply(multiply(A,multiply(b,B)),multiply(C,multiply(b0,D))) = multiply(multiply(A,C),multiply(multiply(a,a0),multiply(B,D))).  [para(10(a,2),4(a,1,2)),flip(a)].
% 2.34/2.68  51 multiply(multiply(A,B),multiply(multiply(c,c0),C)) != multiply(multiply(A,c_0),multiply(B,C)) # answer(prove_quotient_condition4).  [ur(6,a,4,a,c,30,a),flip(a)].
% 2.34/2.68  137 multiply(multiply(d,A),multiply(b0,B)) = multiply(multiply(c,A),multiply(a0,B)).  [para(12(a,1),4(a,1))].
% 2.34/2.68  179 multiply(multiply(A,d),multiply(a,c0)) = multiply(multiply(A,b),c_0).  [para(3(a,1),27(a,1,2))].
% 2.34/2.68  245 multiply(multiply(multiply(A,B),multiply(C,D)),multiply(multiply(c,c0),E)) != multiply(multiply(multiply(A,C),c_0),multiply(multiply(B,D),E)) # answer(prove_quotient_condition4).  [para(4(a,1),51(a,1,1))].
% 2.34/2.68  275 multiply(multiply(A,a),multiply(d,c0)) = multiply(multiply(A,b),c_0).  [para(179(a,1),4(a,1)),flip(a)].
% 2.34/2.68  4177 multiply(multiply(multiply(A,a),multiply(b,B)),multiply(multiply(c,c0),multiply(a0,C))) = multiply(multiply(multiply(A,b),c_0),multiply(multiply(a,a0),multiply(B,C))).  [para(275(a,1),44(a,2,1)),rewrite([137(11)])].
% 2.34/2.68  4178 $F # answer(prove_quotient_condition4).  [resolve(4177,a,245,a)].
% 2.34/2.68  
% 2.34/2.68  % SZS output end Refutation
% 2.34/2.68  ============================== end of proof ==========================
% 2.34/2.68  
% 2.34/2.68  ============================== STATISTICS ============================
% 2.34/2.68  
% 2.34/2.68  Given=108. Generated=20726. Kept=4177. proofs=1.
% 2.34/2.68  Usable=97. Sos=3005. Demods=80. Limbo=420, Disabled=661. Hints=0.
% 2.34/2.68  Megabytes=5.11.
% 2.34/2.68  User_CPU=1.71, System_CPU=0.01, Wall_clock=2.
% 2.34/2.68  
% 2.34/2.68  ============================== end of statistics =====================
% 2.34/2.68  
% 2.34/2.68  ============================== end of search =========================
% 2.34/2.68  
% 2.34/2.68  THEOREM PROVED
% 2.34/2.68  % SZS status Unsatisfiable
% 2.34/2.68  
% 2.34/2.68  Exiting with 1 proof.
% 2.34/2.68  
% 2.34/2.68  Process 4397 exit (max_proofs) Wed Jun  8 19:57:19 2022
% 2.34/2.68  Prover9 interrupted
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