TSTP Solution File: NUM374+2 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : NUM374+2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n004.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 13:27:00 EDT 2022

% Result   : Timeout 300.06s 300.31s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : NUM374+2 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14  % Command  : tptp2X_and_run_prover9 %d %s
% 0.14/0.36  % Computer : n004.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Wed Jul  6 02:20:22 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.48/1.04  ============================== Prover9 ===============================
% 0.48/1.04  Prover9 (32) version 2009-11A, November 2009.
% 0.48/1.04  Process 18983 was started by sandbox2 on n004.cluster.edu,
% 0.48/1.04  Wed Jul  6 02:20:23 2022
% 0.48/1.04  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_18828_n004.cluster.edu".
% 0.48/1.04  ============================== end of head ===========================
% 0.48/1.04  
% 0.48/1.04  ============================== INPUT =================================
% 0.48/1.04  
% 0.48/1.04  % Reading from file /tmp/Prover9_18828_n004.cluster.edu
% 0.48/1.04  
% 0.48/1.04  set(prolog_style_variables).
% 0.48/1.04  set(auto2).
% 0.48/1.04      % set(auto2) -> set(auto).
% 0.48/1.04      % set(auto) -> set(auto_inference).
% 0.48/1.04      % set(auto) -> set(auto_setup).
% 0.48/1.04      % set(auto_setup) -> set(predicate_elim).
% 0.48/1.04      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.48/1.04      % set(auto) -> set(auto_limits).
% 0.48/1.04      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.48/1.04      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.48/1.04      % set(auto) -> set(auto_denials).
% 0.48/1.04      % set(auto) -> set(auto_process).
% 0.48/1.04      % set(auto2) -> assign(new_constants, 1).
% 0.48/1.05      % set(auto2) -> assign(fold_denial_max, 3).
% 0.48/1.05      % set(auto2) -> assign(max_weight, "200.000").
% 0.48/1.05      % set(auto2) -> assign(max_hours, 1).
% 0.48/1.05      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.48/1.05      % set(auto2) -> assign(max_seconds, 0).
% 0.48/1.05      % set(auto2) -> assign(max_minutes, 5).
% 0.48/1.05      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.48/1.05      % set(auto2) -> set(sort_initial_sos).
% 0.48/1.05      % set(auto2) -> assign(sos_limit, -1).
% 0.48/1.05      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.48/1.05      % set(auto2) -> assign(max_megs, 400).
% 0.48/1.05      % set(auto2) -> assign(stats, some).
% 0.48/1.05      % set(auto2) -> clear(echo_input).
% 0.48/1.05      % set(auto2) -> set(quiet).
% 0.48/1.05      % set(auto2) -> clear(print_initial_clauses).
% 0.48/1.05      % set(auto2) -> clear(print_given).
% 0.48/1.05  assign(lrs_ticks,-1).
% 0.48/1.05  assign(sos_limit,10000).
% 0.48/1.05  assign(order,kbo).
% 0.48/1.05  set(lex_order_vars).
% 0.48/1.05  clear(print_given).
% 0.48/1.05  
% 0.48/1.05  % formulas(sos).  % not echoed (16 formulas)
% 0.48/1.05  
% 0.48/1.05  ============================== end of input ==========================
% 0.48/1.05  
% 0.48/1.05  % From the command line: assign(max_seconds, 300).
% 0.48/1.05  
% 0.48/1.05  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.48/1.05  
% 0.48/1.05  % Formulas that are not ordinary clauses:
% 0.48/1.05  1 (all X all Y sum(X,Y) = sum(Y,X)) # label(sum_symmetry) # label(axiom) # label(non_clause).  [assumption].
% 0.48/1.05  2 (all X all Y all Z sum(X,sum(Y,Z)) = sum(sum(X,Y),Z)) # label(sum_associativity) # label(axiom) # label(non_clause).  [assumption].
% 0.48/1.05  3 (all X product(X,n1) = X) # label(product_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.48/1.05  4 (all X all Y product(X,Y) = product(Y,X)) # label(product_symmetry) # label(axiom) # label(non_clause).  [assumption].
% 0.48/1.05  5 (all X all Y all Z product(X,product(Y,Z)) = product(product(X,Y),Z)) # label(product_associativity) # label(axiom) # label(non_clause).  [assumption].
% 0.48/1.05  6 (all X all Y all Z product(X,sum(Y,Z)) = sum(product(X,Y),product(X,Z))) # label(sum_product_distribution) # label(axiom) # label(non_clause).  [assumption].
% 0.48/1.05  7 (all X exponent(n1,X) = n1) # label(exponent_n1) # label(axiom) # label(non_clause).  [assumption].
% 0.48/1.05  8 (all X exponent(X,n1) = X) # label(exponent_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.79/1.05  9 (all X all Y all Z exponent(X,sum(Y,Z)) = product(exponent(X,Y),exponent(X,Z))) # label(exponent_sum_product) # label(axiom) # label(non_clause).  [assumption].
% 0.79/1.05  10 (all X all Y all Z exponent(product(X,Y),Z) = product(exponent(X,Z),exponent(Y,Z))) # label(exponent_product_distribution) # label(axiom) # label(non_clause).  [assumption].
% 0.79/1.05  11 (all X all Y all Z exponent(exponent(X,Y),Z) = exponent(X,product(Y,Z))) # label(exponent_exponent) # label(axiom) # label(non_clause).  [assumption].
% 0.79/1.05  12 (all C all P all Q all R all S all B (lemmas(C,P,Q,R,S,B) <-> n2 = sum(n1,n1) & B != n0 & B != n1 & B != n2 & (all X B != product(n0,X)) & (all X P != product(Q,X)) & (all X Q != product(P,X)) & (all X R != product(S,X)) & (all X S != product(R,X)) & sum(n1,n0) != n1 & sum(n2,n0) != n1 & sum(n0,n0) != n1 & C != n1 & sum(n1,C) != n1 & product(C,n0) != n1 & sum(n1,n0) != n0 & sum(n2,n0) != n0 & sum(n0,n0) != n0 & C != n0 & sum(n1,C) != n0 & sum(n2,n0) != sum(n1,n0) & C != sum(n1,n0) & product(C,n0) != sum(n1,n0) & C != sum(n2,n0) & C != sum(n0,n0) & sum(n1,C) != C)) # label(lemmas) # label(axiom) # label(non_clause).  [assumption].
% 0.79/1.05  13 -(all C all P all Q all R all S all A all B (C = product(A,A) & P = sum(n1,A) & Q = sum(P,C) & R = sum(n1,product(A,C)) & S = sum(sum(n1,C),product(C,C)) & lemmas(C,P,Q,R,S,B) -> product(exponent(sum(exponent(P,A),exponent(Q,A)),B),exponent(sum(exponent(R,B),exponent(S,B)),A)) = product(exponent(sum(exponent(P,B),exponent(Q,B)),A),exponent(sum(exponent(R,A),exponent(S,A)),B)))) # label(wilkie) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.79/1.05  
% 0.79/1.05  ============================== end of process non-clausal formulas ===
% 0.79/1.05  
% 0.79/1.05  ============================== PROCESS INITIAL CLAUSES ===============
% 0.79/1.05  
% 0.79/1.05  ============================== PREDICATE ELIMINATION =================
% 0.79/1.05  14 -lemmas(A,B,C,D,E,F) | n0 != F # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  15 lemmas(c1,c2,c3,c4,c5,c7) # label(wilkie) # label(negated_conjecture).  [clausify(13)].
% 0.79/1.05  Derived: n0 != c7.  [resolve(14,a,15,a)].
% 0.79/1.05  16 -lemmas(A,B,C,D,E,F) | F != n1 # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: c7 != n1.  [resolve(16,a,15,a)].
% 0.79/1.05  17 -lemmas(A,B,C,D,E,F) | n2 != F # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: n2 != c7.  [resolve(17,a,15,a)].
% 0.79/1.05  18 -lemmas(A,B,C,D,E,F) | A != n1 # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: c1 != n1.  [resolve(18,a,15,a)].
% 0.79/1.05  19 -lemmas(A,B,C,D,E,F) | n0 != A # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: n0 != c1.  [resolve(19,a,15,a)].
% 0.79/1.05  20 -lemmas(A,B,C,D,E,F) | product(n0,V6) != F # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: product(n0,A) != c7.  [resolve(20,a,15,a)].
% 0.79/1.05  21 -lemmas(A,B,C,D,E,F) | product(C,V6) != B # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: product(c3,A) != c2.  [resolve(21,a,15,a)].
% 0.79/1.05  22 -lemmas(A,B,C,D,E,F) | product(B,V6) != C # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: product(c2,A) != c3.  [resolve(22,a,15,a)].
% 0.79/1.05  23 -lemmas(A,B,C,D,E,F) | product(E,V6) != D # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: product(c5,A) != c4.  [resolve(23,a,15,a)].
% 0.79/1.05  24 -lemmas(A,B,C,D,E,F) | product(D,V6) != E # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: product(c4,A) != c5.  [resolve(24,a,15,a)].
% 0.79/1.05  25 -lemmas(A,B,C,D,E,F) | sum(n1,n0) != n1 # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: sum(n1,n0) != n1.  [resolve(25,a,15,a)].
% 0.79/1.05  26 -lemmas(A,B,C,D,E,F) | sum(n2,n0) != n1 # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: sum(n2,n0) != n1.  [resolve(26,a,15,a)].
% 0.79/1.05  27 -lemmas(A,B,C,D,E,F) | sum(n0,n0) != n1 # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: sum(n0,n0) != n1.  [resolve(27,a,15,a)].
% 0.79/1.05  28 -lemmas(A,B,C,D,E,F) | sum(n1,A) != n1 # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: sum(n1,c1) != n1.  [resolve(28,a,15,a)].
% 0.79/1.05  29 -lemmas(A,B,C,D,E,F) | product(A,n0) != n1 # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: product(c1,n0) != n1.  [resolve(29,a,15,a)].
% 0.79/1.05  30 -lemmas(A,B,C,D,E,F) | sum(n1,n0) != n0 # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: sum(n1,n0) != n0.  [resolve(30,a,15,a)].
% 0.79/1.05  31 -lemmas(A,B,C,D,E,F) | sum(n2,n0) != n0 # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: sum(n2,n0) != n0.  [resolve(31,a,15,a)].
% 0.79/1.05  32 -lemmas(A,B,C,D,E,F) | sum(n0,n0) != n0 # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: sum(n0,n0) != n0.  [resolve(32,a,15,a)].
% 0.79/1.05  33 -lemmas(A,B,C,D,E,F) | sum(n1,A) != n0 # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: sum(n1,c1) != n0.  [resolve(33,a,15,a)].
% 0.79/1.05  34 -lemmas(A,B,C,D,E,F) | sum(n1,n0) != A # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: sum(n1,n0) != c1.  [resolve(34,a,15,a)].
% 0.79/1.05  35 -lemmas(A,B,C,D,E,F) | sum(n2,n0) != A # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: sum(n2,n0) != c1.  [resolve(35,a,15,a)].
% 0.79/1.05  36 -lemmas(A,B,C,D,E,F) | sum(n0,n0) != A # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: sum(n0,n0) != c1.  [resolve(36,a,15,a)].
% 0.79/1.05  37 -lemmas(A,B,C,D,E,F) | sum(n1,A) != A # label(lemmas) # label(axiom).  [clausify(12)].
% 0.79/1.05  Derived: sum(n1,c1) != c1.  [resolve(37,a,15,a)].
% 0.82/1.07  38 -lemmas(A,B,C,D,E,F) | sum(n2,n0) != sum(n1,n0) # label(lemmas) # label(axiom).  [clausify(12)].
% 0.82/1.07  Derived: sum(n2,n0) != sum(n1,n0).  [resolve(38,a,15,a)].
% 0.82/1.07  39 -lemmas(A,B,C,D,E,F) | product(A,n0) != sum(n1,n0) # label(lemmas) # label(axiom).  [clausify(12)].
% 0.82/1.07  Derived: product(c1,n0) != sum(n1,n0).  [resolve(39,a,15,a)].
% 0.82/1.07  40 -lemmas(A,B,C,D,E,F) | sum(n1,n1) = n2 # label(lemmas) # label(axiom).  [clausify(12)].
% 0.82/1.07  Derived: sum(n1,n1) = n2.  [resolve(40,a,15,a)].
% 0.82/1.07  41 lemmas(A,B,C,D,E,F) | sum(n1,n1) != n2 | n0 = F | F = n1 | n2 = F | product(n0,f1(A,B,C,D,E,F)) = F | product(C,f2(A,B,C,D,E,F)) = B | product(B,f3(A,B,C,D,E,F)) = C | product(E,f4(A,B,C,D,E,F)) = D | product(D,f5(A,B,C,D,E,F)) = E | sum(n1,n0) = n1 | sum(n2,n0) = n1 | sum(n0,n0) = n1 | A = n1 | sum(n1,A) = n1 | product(A,n0) = n1 | sum(n1,n0) = n0 | sum(n2,n0) = n0 | sum(n0,n0) = n0 | n0 = A | sum(n1,A) = n0 | sum(n2,n0) = sum(n1,n0) | sum(n1,n0) = A | product(A,n0) = sum(n1,n0) | sum(n2,n0) = A | sum(n0,n0) = A | sum(n1,A) = A # label(lemmas) # label(axiom).  [clausify(12)].
% 0.82/1.07  Derived: sum(n1,n1) != n2 | n0 = A | A = n1 | n2 = A | product(n0,f1(B,C,D,E,F,A)) = A | product(D,f2(B,C,D,E,F,A)) = C | product(C,f3(B,C,D,E,F,A)) = D | product(F,f4(B,C,D,E,F,A)) = E | product(E,f5(B,C,D,E,F,A)) = F | sum(n1,n0) = n1 | sum(n2,n0) = n1 | sum(n0,n0) = n1 | B = n1 | sum(n1,B) = n1 | product(B,n0) = n1 | sum(n1,n0) = n0 | sum(n2,n0) = n0 | sum(n0,n0) = n0 | n0 = B | sum(n1,B) = n0 | sum(n2,n0) = sum(n1,n0) | sum(n1,n0) = B | product(B,n0) = sum(n1,n0) | sum(n2,n0) = B | sum(n0,n0) = B | sum(n1,B) = B | product(n0,V6) != A.  [resolve(41,a,20,a)].
% 0.82/1.07  Derived: sum(n1,n1) != n2 | n0 = A | A = n1 | n2 = A | product(n0,f1(B,C,D,E,F,A)) = A | product(D,f2(B,C,D,E,F,A)) = C | product(C,f3(B,C,D,E,F,A)) = D | product(F,f4(B,C,D,E,F,A)) = E | product(E,f5(B,C,D,E,F,A)) = F | sum(n1,n0) = n1 | sum(n2,n0) = n1 | sum(n0,n0) = n1 | B = n1 | sum(n1,B) = n1 | product(B,n0) = n1 | sum(n1,n0) = n0 | sum(n2,n0) = n0 | sum(n0,n0) = n0 | n0 = B | sum(n1,B) = n0 | sum(n2,n0) = sum(n1,n0) | sum(n1,n0) = B | product(B,n0) = sum(n1,n0) | sum(n2,n0) = B | sum(n0,n0) = B | sum(n1,B) = B | product(D,V6) != C.  [resolve(41,a,21,a)].
% 0.82/1.07  Derived: sum(n1,n1) != n2 | n0 = A | A = n1 | n2 = A | product(n0,f1(B,C,D,E,F,A)) = A | product(D,f2(B,C,D,E,F,A)) = C | product(C,f3(B,C,D,E,F,A)) = D | product(F,f4(B,C,D,E,F,A)) = E | product(E,f5(B,C,D,E,F,A)) = F | sum(n1,n0) = n1 | sum(n2,n0) = n1 | sum(n0,n0) = n1 | B = n1 | sum(n1,B) = n1 | product(B,n0) = n1 | sum(n1,n0) = n0 | sum(n2,n0) = n0 | sum(n0,n0) = n0 | n0 = B | sum(n1,B) = n0 | sum(n2,n0) = sum(n1,n0) | sum(n1,n0) = B | product(B,n0) = sum(n1,n0) | sum(n2,n0) = B | sum(n0,n0) = B | sum(n1,B) = B | product(C,V6) != D.  [resolve(41,a,22,a)].
% 0.82/1.07  Derived: sum(n1,n1) != n2 | n0 = A | A = n1 | n2 = A | product(n0,f1(B,C,D,E,F,A)) = A | product(D,f2(B,C,D,E,F,A)) = C | product(C,f3(B,C,D,E,F,A)) = D | product(F,f4(B,C,D,E,F,A)) = E | product(E,f5(B,C,D,E,F,A)) = F | sum(n1,n0) = n1 | sum(n2,n0) = n1 | sum(n0,n0) = n1 | B = n1 | sum(n1,B) = n1 | product(B,n0) = n1 | sum(n1,n0) = n0 | sum(n2,n0) = n0 | sum(n0,n0) = n0 | n0 = B | sum(n1,B) = n0 | sum(n2,n0) = sum(n1,n0) | sum(n1,n0) = B | product(B,n0) = sum(n1,n0) | sum(n2,n0) = B | sum(n0,n0) = B | sum(n1,B) = B | product(F,V6) != E.  [resolve(41,a,23,a)].
% 0.82/1.07  Derived: sum(n1,n1) != n2 | n0 = A | A = n1 | n2 = A | product(n0,f1(B,C,D,E,F,A)) = A | product(D,f2(B,C,D,E,F,A)) = C | product(C,f3(B,C,D,E,F,A)) = D | product(F,f4(B,C,D,E,F,A)) = E | product(E,f5(B,C,D,E,F,A)) = F | sum(n1,n0) = n1 | sum(n2,n0) = n1 | sum(n0,n0) = n1 | B = n1 | sum(n1,B) = n1 | product(B,n0) = n1 | sum(n1,n0) = n0 | sum(n2,n0) = n0 | sum(n0,n0) = n0 | n0 = B | sum(n1,B) = n0 | sum(n2,n0) = sum(n1,n0) | sum(n1,n0) = B | product(B,n0) = sum(n1,n0) | sum(n2,n0) = B | sum(n0,n0) = B | sum(n1,B) = B | product(E,V6) != F.  [resolve(41,a,24,a)].
% 0.82/1.07  
% 0.82/1.07  ============================== end predicate elimination =============
% 0.82/1.07  
% 0.82/1.07  Auto_denials:  (non-Horn, no changes).
% 0.82/1.07  
% 0.82/1.07  Term ordering decisions:
% 0.82/1.07  Function symbol KB weigCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------