TSTP Solution File: KLE089+1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : KLE089+1 : TPTP v6.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire_rel --proof tptp --output_axiom_names on --mode casc -t %d %s

% Computer : n142.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.11.2.el6.x86_64
% CPULimit : 300s
% DateTime : Mon Jun  9 23:49:12 EDT 2014

% Result   : Theorem 1.54s
% Output   : Refutation 1.54s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : KLE089+1 : TPTP v6.0.0. Released v4.0.0.
% % Command  : vampire_rel --proof tptp --output_axiom_names on --mode casc -t %d %s
% % Computer : n142.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.11.2.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jun  5 18:23:03 CDT 2014
% % CPUTime  : 1.54 
% ============================== Prover9 ===============================
% Prover9 (32) version 2009-11A, November 2009.
% Process 20720 was started by sandbox on n142.star.cs.uiowa.edu,
% Thu Jun  5 18:23:03 2014
% The command was "./prover9 -t 300 -f /tmp/Prover9_20688_n142.star.cs.uiowa.edu".
% ============================== end of head ===========================
% 
% ============================== INPUT =================================
% 
% % Reading from file /tmp/Prover9_20688_n142.star.cs.uiowa.edu
% 
% set(prolog_style_variables).
% set(auto2).
% % set(auto2) -> set(auto).
% % set(auto) -> set(auto_inference).
% % set(auto) -> set(auto_setup).
% % set(auto_setup) -> set(predicate_elim).
% % set(auto_setup) -> assign(eq_defs, unfold).
% % set(auto) -> set(auto_limits).
% % set(auto_limits) -> assign(max_weight, "100.000").
% % set(auto_limits) -> assign(sos_limit, 20000).
% % set(auto) -> set(auto_denials).
% % set(auto) -> set(auto_process).
% % set(auto2) -> assign(new_constants, 1).
% % set(auto2) -> assign(fold_denial_max, 3).
% % set(auto2) -> assign(max_weight, "200.000").
% % set(auto2) -> assign(max_hours, 1).
% % assign(max_hours, 1) -> assign(max_seconds, 3600).
% % set(auto2) -> assign(max_seconds, 0).
% % set(auto2) -> assign(max_minutes, 5).
% % assign(max_minutes, 5) -> assign(max_seconds, 300).
% % set(auto2) -> set(sort_initial_sos).
% % set(auto2) -> assign(sos_limit, -1).
% % set(auto2) -> assign(lrs_ticks, 3000).
% % set(auto2) -> assign(max_megs, 400).
% % set(auto2) -> assign(stats, some).
% % set(auto2) -> clear(echo_input).
% % set(auto2) -> set(quiet).
% % set(auto2) -> clear(print_initial_clauses).
% % set(auto2) -> clear(print_given).
% assign(lrs_ticks,-1).
% assign(sos_limit,10000).
% assign(order,kbo).
% set(lex_order_vars).
% clear(print_given).
% 
% % formulas(sos).  % not echoed (21 formulas)
% 
% ============================== end of input ==========================
% 
% % From the command line: assign(max_seconds, 300).
% 
% ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 
% % Formulas that are not ordinary clauses:
% 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause).  [assumption].
% 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
% 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
% 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause).  [assumption].
% 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
% 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
% 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause).  [assumption].
% 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause).  [assumption].
% 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause).  [assumption].
% 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause).  [assumption].
% 14 (all X0 all X1 addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1))))) # label(domain2) # label(axiom) # label(non_clause).  [assumption].
% 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause).  [assumption].
% 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause).  [assumption].
% 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause).  [assumption].
% 18 (all X0 all X1 addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) # label(codomain2) # label(axiom) # label(non_clause).  [assumption].
% 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause).  [assumption].
% 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause).  [assumption].
% 21 -(all X0 all X1 (addition(domain(X0),antidomain(X1)) = antidomain(X1) -> multiplication(domain(X0),X1) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 
% ============================== end of process non-clausal formulas ===
% 
% ============================== PROCESS INITIAL CLAUSES ===============
% 
% ============================== PREDICATE ELIMINATION =================
% 22 leq(A,B) | addition(A,B) != B # label(order) # label(axiom).  [clausify(12)].
% 23 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom).  [clausify(12)].
% 
% ============================== end predicate elimination =============
% 
% Auto_denials:
% % copying label goals to answer in negative clause
% 
% Term ordering decisions:
% Function symbol KB weights:  zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. antidomain=1. coantidomain=1. domain=1. codomain=1.
% 
% ============================== end of process initial clauses ========
% 
% ============================== CLAUSES FOR SEARCH ====================
% 
% ============================== end of clauses for search =============
% 
% ============================== SEARCH ================================
% 
% % Starting search at 0.01 seconds.
% 
% Low Water (keep): wt=43.000, iters=3336
% 
% Low Water (keep): wt=41.000, iters=3466
% 
% Low Water (keep): wt=36.000, iters=3406
% 
% Low Water (keep): wt=35.000, iters=3373
% 
% Low Water (keep): wt=33.000, iters=3346
% 
% Low Water (keep): wt=31.000, iters=3355
% 
% Low Water (keep): wt=30.000, iters=3360
% 
% ============================== PROOF =================================
% % SZS status Theorem
% % SZS output start Refutation
% 
% % Proof 1 at 1.37 (+ 0.02) seconds: goals.
% % Length of proof is 67.
% % Level of proof is 13.
% % Maximum clause weight is 18.000.
% % Given clauses 423.
% 
% 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause).  [assumption].
% 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
% 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
% 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause).  [assumption].
% 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
% 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
% 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause).  [assumption].
% 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause).  [assumption].
% 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause).  [assumption].
% 14 (all X0 all X1 addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1))))) # label(domain2) # label(axiom) # label(non_clause).  [assumption].
% 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause).  [assumption].
% 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause).  [assumption].
% 21 -(all X0 all X1 (addition(domain(X0),antidomain(X1)) = antidomain(X1) -> multiplication(domain(X0),X1) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 24 addition(A,zero) = A # label(additive_identity) # label(axiom).  [clausify(3)].
% 25 addition(A,A) = A # label(additive_idempotence) # label(axiom).  [clausify(4)].
% 26 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [clausify(6)].
% 27 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [clausify(7)].
% 28 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom).  [clausify(10)].
% 29 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom).  [clausify(11)].
% 30 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom).  [clausify(13)].
% 31 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom).  [clausify(16)].
% 34 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(1)].
% 35 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom).  [clausify(15)].
% 36 addition(antidomain(A),antidomain(antidomain(A))) = one.  [copy(35),rewrite([34(4)])].
% 39 antidomain(c2) = addition(domain(c1),antidomain(c2)) # label(goals) # label(negated_conjecture).  [clausify(21)].
% 40 addition(antidomain(c2),antidomain(antidomain(c1))) = antidomain(c2).  [copy(39),rewrite([31(4),34(8)]),flip(a)].
% 41 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom).  [clausify(2)].
% 42 addition(A,addition(B,C)) = addition(C,addition(A,B)).  [copy(41),rewrite([34(2)]),flip(a)].
% 43 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom).  [clausify(5)].
% 44 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom).  [clausify(8)].
% 45 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)).  [copy(44),flip(a)].
% 46 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom).  [clausify(9)].
% 47 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B).  [copy(46),flip(a)].
% 48 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom).  [clausify(14)].
% 49 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))).  [copy(48),flip(a)].
% 52 multiplication(domain(c1),c2) != zero # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(21)].
% 53 multiplication(antidomain(antidomain(c1)),c2) != zero # answer(goals).  [copy(52),rewrite([31(2)])].
% 54 antidomain(one) = zero.  [para(30(a,1),26(a,1)),flip(a)].
% 56 addition(A,addition(A,B)) = addition(A,B).  [para(42(a,1),25(a,1)),rewrite([34(1),34(2),42(2,R),25(1),34(3)])].
% 57 multiplication(antidomain(A),multiplication(A,B)) = zero.  [para(30(a,1),43(a,1,1)),rewrite([29(2)]),flip(a)].
% 60 addition(zero,multiplication(A,B)) = multiplication(A,B).  [para(24(a,1),45(a,2,2)),rewrite([28(3),34(3)])].
% 61 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)).  [para(26(a,1),45(a,1,1)),rewrite([34(4)]),flip(a)].
% 62 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B).  [para(30(a,1),45(a,1,1)),rewrite([60(4)]),flip(a)].
% 65 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B).  [para(30(a,1),47(a,1,1)),rewrite([60(3),34(3)]),flip(a)].
% 72 addition(antidomain(zero),antidomain(multiplication(antidomain(A),antidomain(antidomain(A))))) = antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))).  [para(30(a,1),49(a,1,1,1))].
% 83 addition(zero,antidomain(zero)) = one.  [para(54(a,1),36(a,1,1)),rewrite([54(3)])].
% 87 multiplication(A,antidomain(zero)) = A.  [para(83(a,1),45(a,2,2)),rewrite([28(2),60(5),26(5)])].
% 93 addition(one,antidomain(A)) = one.  [para(36(a,1),56(a,1,2)),rewrite([34(3),36(7)])].
% 95 antidomain(zero) = one.  [para(87(a,1),27(a,1)),flip(a)].
% 97 antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))) = one.  [back_rewrite(72),rewrite([95(2),93(7)]),flip(a)].
% 107 addition(A,multiplication(antidomain(B),A)) = A.  [para(93(a,1),47(a,2,1)),rewrite([27(2),27(5)])].
% 151 multiplication(antidomain(A),antidomain(antidomain(A))) = zero.  [para(97(a,1),30(a,1,1)),rewrite([27(6)])].
% 155 multiplication(antidomain(antidomain(c2)),antidomain(antidomain(c1))) = zero.  [para(40(a,1),62(a,1,2)),rewrite([30(6)]),flip(a)].
% 162 addition(addition(A,B),multiplication(antidomain(A),B)) = addition(A,B).  [para(62(a,1),107(a,1,2))].
% 166 multiplication(antidomain(A),addition(B,antidomain(antidomain(A)))) = multiplication(antidomain(A),B).  [para(151(a,1),45(a,1,1)),rewrite([60(4),34(6)]),flip(a)].
% 198 multiplication(addition(A,antidomain(antidomain(c2))),antidomain(antidomain(c1))) = multiplication(A,antidomain(antidomain(c1))).  [para(155(a,1),47(a,1,1)),rewrite([60(6),34(8)]),flip(a)].
% 253 multiplication(addition(A,antidomain(B)),addition(B,one)) = addition(A,addition(antidomain(B),multiplication(A,B))).  [para(65(a,1),61(a,2,2)),rewrite([34(9),42(9),34(8),42(9,R),34(8)])].
% 5274 multiplication(antidomain(c2),antidomain(antidomain(c1))) = antidomain(antidomain(c1)).  [para(36(a,1),198(a,1,1)),rewrite([27(5)]),flip(a)].
% 8190 addition(antidomain(c2),antidomain(antidomain(antidomain(c1)))) = one.  [para(5274(a,1),253(a,2,2,2)),rewrite([34(12),93(12),26(9),34(17),36(17),34(11),93(11)])].
% 8228 multiplication(antidomain(antidomain(c1)),antidomain(c2)) = antidomain(antidomain(c1)).  [para(8190(a,1),166(a,1,2)),rewrite([26(5)]),flip(a)].
% 8250 addition(antidomain(c1),antidomain(c2)) = one.  [para(8228(a,1),162(a,1,2)),rewrite([34(9),42(9),34(8),36(8),34(4),93(4)]),flip(a)].
% 8256 multiplication(antidomain(c1),c2) = c2.  [para(8250(a,1),65(a,1,1)),rewrite([27(3)]),flip(a)].
% 8290 multiplication(antidomain(antidomain(c1)),c2) = zero.  [para(8256(a,1),57(a,1,2))].
% 8291 $F # answer(goals).  [resolve(8290,a,53,a)].
% 
% % SZS output end Refutation
% ============================== end of proof ==========================
% 
% ============================== STATISTICS ============================
% 
% Given=423. Generated=63194. Kept=8258. proofs=1.
% Usable=338. Sos=6059. Demods=5885. Limbo=1, Disabled=1882. Hints=0.
% Megabytes=9.74.
% User_CPU=1.37, System_CPU=0.02, Wall_clock=2.
% 
% ============================== end of statistics =====================
% 
% ============================== end of search =========================
% 
% THEOREM PROVED
% % SZS status Theorem
% 
% Exiting with 1 proof.
% 
% Process 20720 exit (max_proofs) Thu Jun  5 18:23:05 2014
% Prover9 interrupted
% 
% EOF
%------------------------------------------------------------------------------