TSTP Solution File: ALG070+1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : ALG070+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n017.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 17:53:44 EDT 2022

% Result   : Theorem 0.74s 1.01s
% Output   : Refutation 0.74s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : ALG070+1 : TPTP v8.1.0. Released v2.7.0.
% 0.12/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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 : Tue Jun  7 21:23:02 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.74/1.01  ============================== Prover9 ===============================
% 0.74/1.01  Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.01  Process 3626 was started by sandbox2 on n017.cluster.edu,
% 0.74/1.01  Tue Jun  7 21:23:03 2022
% 0.74/1.01  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3473_n017.cluster.edu".
% 0.74/1.01  ============================== end of head ===========================
% 0.74/1.01  
% 0.74/1.01  ============================== INPUT =================================
% 0.74/1.01  
% 0.74/1.01  % Reading from file /tmp/Prover9_3473_n017.cluster.edu
% 0.74/1.01  
% 0.74/1.01  set(prolog_style_variables).
% 0.74/1.01  set(auto2).
% 0.74/1.01      % set(auto2) -> set(auto).
% 0.74/1.01      % set(auto) -> set(auto_inference).
% 0.74/1.01      % set(auto) -> set(auto_setup).
% 0.74/1.01      % set(auto_setup) -> set(predicate_elim).
% 0.74/1.01      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.01      % set(auto) -> set(auto_limits).
% 0.74/1.01      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.01      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.01      % set(auto) -> set(auto_denials).
% 0.74/1.01      % set(auto) -> set(auto_process).
% 0.74/1.01      % set(auto2) -> assign(new_constants, 1).
% 0.74/1.01      % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.01      % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.01      % set(auto2) -> assign(max_hours, 1).
% 0.74/1.01      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.01      % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.01      % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.01      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.01      % set(auto2) -> set(sort_initial_sos).
% 0.74/1.01      % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.01      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.01      % set(auto2) -> assign(max_megs, 400).
% 0.74/1.01      % set(auto2) -> assign(stats, some).
% 0.74/1.01      % set(auto2) -> clear(echo_input).
% 0.74/1.01      % set(auto2) -> set(quiet).
% 0.74/1.01      % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.01      % set(auto2) -> clear(print_given).
% 0.74/1.01  assign(lrs_ticks,-1).
% 0.74/1.01  assign(sos_limit,10000).
% 0.74/1.01  assign(order,kbo).
% 0.74/1.01  set(lex_order_vars).
% 0.74/1.01  clear(print_given).
% 0.74/1.01  
% 0.74/1.01  % formulas(sos).  % not echoed (5 formulas)
% 0.74/1.01  
% 0.74/1.01  ============================== end of input ==========================
% 0.74/1.01  
% 0.74/1.01  % From the command line: assign(max_seconds, 300).
% 0.74/1.01  
% 0.74/1.01  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.01  
% 0.74/1.01  % Formulas that are not ordinary clauses:
% 0.74/1.01  1 (all U (sorti1(U) -> (all V (sorti1(V) -> sorti1(op1(U,V)))))) # label(ax1) # label(axiom) # label(non_clause).  [assumption].
% 0.74/1.01  2 (all U (sorti2(U) -> (all V (sorti2(V) -> sorti2(op2(U,V)))))) # label(ax2) # label(axiom) # label(non_clause).  [assumption].
% 0.74/1.01  3 (all U (sorti1(U) -> (all V (sorti1(V) -> op1(U,U) != V | op1(U,V) = U)))) # label(ax3) # label(axiom) # label(non_clause).  [assumption].
% 0.74/1.01  4 -(all U (sorti2(U) -> (all V (sorti2(V) -> op2(U,U) != V | op2(U,V) = U)))) # label(ax4) # label(axiom) # label(non_clause).  [assumption].
% 0.74/1.01  5 -((all U (sorti1(U) -> sorti2(h(U)))) & (all V (sorti2(V) -> sorti1(j(V)))) -> -((all W (sorti1(W) -> (all X (sorti1(X) -> h(op1(W,X)) = op2(h(W),h(X)))))) & (all Y (sorti2(Y) -> (all Z (sorti2(Z) -> j(op2(Y,Z)) = op1(j(Y),j(Z)))))) & (all X1 (sorti2(X1) -> h(j(X1)) = X1)) & (all X2 (sorti1(X2) -> j(h(X2)) = X2)))) # label(co1) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.74/1.01  
% 0.74/1.01  ============================== end of process non-clausal formulas ===
% 0.74/1.01  
% 0.74/1.01  ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.01  
% 0.74/1.01  ============================== PREDICATE ELIMINATION =================
% 0.74/1.01  
% 0.74/1.01  ============================== end predicate elimination =============
% 0.74/1.01  
% 0.74/1.01  Auto_denials:
% 0.74/1.01    % copying label ax4 to answer in negative clause
% 0.74/1.01  
% 0.74/1.01  Term ordering decisions:
% 0.74/1.01  Function symbol KB weights:  c1=1. c2=1. op1=1. op2=1. h=1. j=1.
% 0.74/1.01  
% 0.74/1.01  ============================== end of process initial clauses ========
% 0.74/1.01  
% 0.74/1.01  ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.01  
% 0.74/1.01  ============================== end of clauses for search =============
% 0.74/1.01  
% 0.74/1.01  ============================== SEARCH ================================
% 0.74/1.01  
% 0.74/1.01  % Starting search at 0.01 seconds.
% 0.74/1.01  
% 0.74/1.01  ============================== PROOF =================================
% 0.74/1.01  % SZS status Theorem
% 0.74/1.01  % SZS output start Refutation
% 0.74/1.01  
% 0.74/1.01  % Proof 1 at 0.01 (+ 0.00) seconds: ax4.
% 0.74/1.01  % Length of proof is 27.
% 0.74/1.01  % Level of proof is 7.
% 0.74/1.01  % Maximum clause weight is 14.000.
% 0.74/1.01  % Given clauses 19.
% 0.74/1.01  
% 0.74/1.01  3 (all U (sorti1(U) -> (all V (sorti1(V) -> op1(U,U) != V | op1(U,V) = U)))) # label(ax3) # label(axiom) # label(non_clause).  [assumption].
% 0.74/1.01  4 -(all U (sorti2(U) -> (all V (sorti2(V) -> op2(U,U) != V | op2(U,V) = U)))) # label(ax4) # label(axiom) # label(non_clause).  [assumption].
% 0.74/1.01  5 -((all U (sorti1(U) -> sorti2(h(U)))) & (all V (sorti2(V) -> sorti1(j(V)))) -> -((all W (sorti1(W) -> (all X (sorti1(X) -> h(op1(W,X)) = op2(h(W),h(X)))))) & (all Y (sorti2(Y) -> (all Z (sorti2(Z) -> j(op2(Y,Z)) = op1(j(Y),j(Z)))))) & (all X1 (sorti2(X1) -> h(j(X1)) = X1)) & (all X2 (sorti1(X2) -> j(h(X2)) = X2)))) # label(co1) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.74/1.01  6 sorti2(c1) # label(ax4) # label(axiom).  [clausify(4)].
% 0.74/1.01  7 sorti2(c2) # label(ax4) # label(axiom).  [clausify(4)].
% 0.74/1.01  8 op2(c1,c1) = c2 # label(ax4) # label(axiom).  [clausify(4)].
% 0.74/1.01  9 c2 = op2(c1,c1).  [copy(8),flip(a)].
% 0.74/1.01  10 op2(c1,c2) != c1 # label(ax4) # label(axiom) # answer(ax4).  [clausify(4)].
% 0.74/1.01  11 op2(c1,op2(c1,c1)) != c1 # answer(ax4).  [copy(10),rewrite([9(2)])].
% 0.74/1.01  13 -sorti2(A) | sorti1(j(A)) # label(co1) # label(negated_conjecture).  [clausify(5)].
% 0.74/1.01  14 -sorti2(A) | h(j(A)) = A # label(co1) # label(negated_conjecture).  [clausify(5)].
% 0.74/1.01  18 -sorti1(A) | -sorti1(B) | op1(A,A) != B | op1(A,B) = A # label(ax3) # label(axiom).  [clausify(3)].
% 0.74/1.01  19 -sorti1(A) | -sorti1(B) | h(op1(A,B)) = op2(h(A),h(B)) # label(co1) # label(negated_conjecture).  [clausify(5)].
% 0.74/1.01  20 -sorti1(A) | -sorti1(B) | op2(h(A),h(B)) = h(op1(A,B)).  [copy(19),flip(c)].
% 0.74/1.01  21 -sorti2(A) | -sorti2(B) | j(op2(A,B)) = op1(j(A),j(B)) # label(co1) # label(negated_conjecture).  [clausify(5)].
% 0.74/1.01  22 -sorti2(A) | -sorti2(B) | op1(j(A),j(B)) = j(op2(A,B)).  [copy(21),flip(c)].
% 0.74/1.01  23 sorti2(op2(c1,c1)).  [back_rewrite(7),rewrite([9(1)])].
% 0.74/1.01  24 sorti1(j(c1)).  [hyper(13,a,6,a)].
% 0.74/1.01  25 h(j(c1)) = c1.  [hyper(14,a,6,a)].
% 0.74/1.01  26 op1(j(c1),j(c1)) = j(op2(c1,c1)).  [hyper(22,a,6,a,b,6,a)].
% 0.74/1.01  28 op1(j(c1),j(op2(c1,c1))) = j(op2(c1,op2(c1,c1))).  [hyper(22,a,6,a,b,23,a)].
% 0.74/1.01  33 h(j(op2(c1,c1))) = op2(c1,c1).  [hyper(14,a,23,a)].
% 0.74/1.01  34 sorti1(j(op2(c1,c1))).  [hyper(13,a,23,a)].
% 0.74/1.01  36 h(j(op2(c1,op2(c1,c1)))) = op2(c1,op2(c1,c1)).  [hyper(20,a,24,a,b,34,a),rewrite([25(3),33(6),28(12)]),flip(a)].
% 0.74/1.01  65 j(op2(c1,op2(c1,c1))) = j(c1).  [hyper(18,a,24,a,b,34,a,c,26,a),rewrite([28(7)])].
% 0.74/1.01  73 op2(c1,op2(c1,c1)) = c1.  [back_rewrite(36),rewrite([65(6),25(3)]),flip(a)].
% 0.74/1.01  74 $F # answer(ax4).  [resolve(73,a,11,a)].
% 0.74/1.01  
% 0.74/1.01  % SZS output end Refutation
% 0.74/1.01  ============================== end of proof ==========================
% 0.74/1.01  
% 0.74/1.01  ============================== STATISTICS ============================
% 0.74/1.01  
% 0.74/1.01  Given=19. Generated=89. Kept=64. proofs=1.
% 0.74/1.01  Usable=19. Sos=26. Demods=22. Limbo=8, Disabled=23. Hints=0.
% 0.74/1.01  Megabytes=0.11.
% 0.74/1.01  User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.74/1.01  
% 0.74/1.01  ============================== end of statistics =====================
% 0.74/1.01  
% 0.74/1.01  ============================== end of search =========================
% 0.74/1.01  
% 0.74/1.01  THEOREM PROVED
% 0.74/1.01  % SZS status Theorem
% 0.74/1.01  
% 0.74/1.01  Exiting with 1 proof.
% 0.74/1.01  
% 0.74/1.01  Process 3626 exit (max_proofs) Tue Jun  7 21:23:03 2022
% 0.74/1.01  Prover9 interrupted
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