TSTP Solution File: KLE062+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE062+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 : Sun Jul 17 02:22:03 EDT 2022
% Result : Theorem 1.28s 1.58s
% Output : Refutation 1.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE062+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n008.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 13:29:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/1.01 ============================== Prover9 ===============================
% 0.75/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.01 Process 2511 was started by sandbox2 on n008.cluster.edu,
% 0.75/1.01 Thu Jun 16 13:29:53 2022
% 0.75/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2358_n008.cluster.edu".
% 0.75/1.01 ============================== end of head ===========================
% 0.75/1.01
% 0.75/1.01 ============================== INPUT =================================
% 0.75/1.01
% 0.75/1.01 % Reading from file /tmp/Prover9_2358_n008.cluster.edu
% 0.75/1.01
% 0.75/1.01 set(prolog_style_variables).
% 0.75/1.01 set(auto2).
% 0.75/1.01 % set(auto2) -> set(auto).
% 0.75/1.01 % set(auto) -> set(auto_inference).
% 0.75/1.01 % set(auto) -> set(auto_setup).
% 0.75/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.01 % set(auto) -> set(auto_limits).
% 0.75/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.01 % set(auto) -> set(auto_denials).
% 0.75/1.01 % set(auto) -> set(auto_process).
% 0.75/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.01 % set(auto2) -> assign(stats, some).
% 0.75/1.01 % set(auto2) -> clear(echo_input).
% 0.75/1.01 % set(auto2) -> set(quiet).
% 0.75/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.01 % set(auto2) -> clear(print_given).
% 0.75/1.01 assign(lrs_ticks,-1).
% 0.75/1.01 assign(sos_limit,10000).
% 0.75/1.01 assign(order,kbo).
% 0.75/1.01 set(lex_order_vars).
% 0.75/1.01 clear(print_given).
% 0.75/1.01
% 0.75/1.01 % formulas(sos). % not echoed (18 formulas)
% 0.75/1.01
% 0.75/1.01 ============================== end of input ==========================
% 0.75/1.01
% 0.75/1.01 % From the command line: assign(max_seconds, 300).
% 0.75/1.01
% 0.75/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.01
% 0.75/1.01 % Formulas that are not ordinary clauses:
% 0.75/1.01 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 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].
% 0.75/1.01 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 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].
% 0.75/1.01 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 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].
% 0.75/1.01 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].
% 0.75/1.01 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 13 (all X0 addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 14 (all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 15 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 16 (all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(domain5) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 17 -(all X0 all X1 multiplication(domain(X0),domain(X1)) = multiplication(domain(X1),domain(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.28/1.58
% 1.28/1.58 ============================== end of process non-clausal formulas ===
% 1.28/1.58
% 1.28/1.58 ============================== PROCESS INITIAL CLAUSES ===============
% 1.28/1.58
% 1.28/1.58 ============================== PREDICATE ELIMINATION =================
% 1.28/1.58 18 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 1.28/1.58 19 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 1.28/1.58
% 1.28/1.58 ============================== end predicate elimination =============
% 1.28/1.58
% 1.28/1.58 Auto_denials:
% 1.28/1.58 % copying label goals to answer in negative clause
% 1.28/1.58
% 1.28/1.58 Term ordering decisions:
% 1.28/1.58
% 1.28/1.58 % Assigning unary symbol domain kb_weight 0 and highest precedence (8).
% 1.28/1.58 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. domain=0.
% 1.28/1.58
% 1.28/1.58 ============================== end of process initial clauses ========
% 1.28/1.58
% 1.28/1.58 ============================== CLAUSES FOR SEARCH ====================
% 1.28/1.58
% 1.28/1.58 ============================== end of clauses for search =============
% 1.28/1.58
% 1.28/1.58 ============================== SEARCH ================================
% 1.28/1.58
% 1.28/1.58 % Starting search at 0.01 seconds.
% 1.28/1.58
% 1.28/1.58 ============================== PROOF =================================
% 1.28/1.58 % SZS status Theorem
% 1.28/1.58 % SZS output start Refutation
% 1.28/1.58
% 1.28/1.58 % Proof 1 at 0.55 (+ 0.02) seconds: goals.
% 1.28/1.58 % Length of proof is 54.
% 1.28/1.58 % Level of proof is 12.
% 1.28/1.58 % Maximum clause weight is 24.000.
% 1.28/1.58 % Given clauses 143.
% 1.28/1.58
% 1.28/1.58 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 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].
% 1.28/1.58 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 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].
% 1.28/1.58 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].
% 1.28/1.58 13 (all X0 addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 14 (all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 15 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 16 (all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(domain5) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.58 17 -(all X0 all X1 multiplication(domain(X0),domain(X1)) = multiplication(domain(X1),domain(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.28/1.58 23 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 1.28/1.58 24 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 1.28/1.58 27 addition(domain(A),one) = one # label(domain3) # label(axiom). [clausify(15)].
% 1.28/1.58 28 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 1.28/1.58 29 domain(multiplication(A,domain(B))) = domain(multiplication(A,B)) # label(domain2) # label(axiom). [clausify(14)].
% 1.28/1.58 30 domain(addition(A,B)) = addition(domain(A),domain(B)) # label(domain5) # label(axiom). [clausify(16)].
% 1.28/1.58 33 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 1.28/1.58 34 multiplication(domain(A),A) = addition(A,multiplication(domain(A),A)) # label(domain1) # label(axiom). [clausify(13)].
% 1.28/1.58 35 addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A). [copy(34),flip(a)].
% 1.28/1.58 36 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 1.28/1.58 37 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(36),flip(a)].
% 1.28/1.58 38 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 1.28/1.58 39 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(38),flip(a)].
% 1.28/1.58 40 multiplication(domain(c2),domain(c1)) != multiplication(domain(c1),domain(c2)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 1.28/1.58 43 domain(domain(A)) = domain(A). [para(24(a,1),29(a,1,1)),rewrite([24(4)])].
% 1.28/1.58 52 addition(multiplication(A,domain(B)),multiplication(domain(multiplication(A,B)),multiplication(A,domain(B)))) = multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))). [para(29(a,1),35(a,1,2,1)),rewrite([29(11)])].
% 1.28/1.58 57 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(23(a,1),37(a,1,1)),rewrite([28(4)]),flip(a)].
% 1.28/1.58 58 addition(A,multiplication(A,domain(B))) = A. [para(27(a,1),37(a,2,2)),rewrite([23(4),28(3),23(5)])].
% 1.28/1.58 61 addition(A,multiplication(domain(B),A)) = A. [para(27(a,1),39(a,2,1)),rewrite([24(4),28(3),24(5)])].
% 1.28/1.58 62 addition(domain(multiplication(A,B)),domain(multiplication(C,B))) = domain(multiplication(addition(A,C),B)). [para(39(a,1),30(a,1,1)),flip(a)].
% 1.28/1.58 65 multiplication(domain(A),multiplication(A,B)) = multiplication(A,B). [para(35(a,1),39(a,2,1)),rewrite([33(4),61(5),33(4)]),flip(a)].
% 1.28/1.58 67 multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))) = multiplication(A,domain(B)). [back_rewrite(52),rewrite([61(8)]),flip(a)].
% 1.28/1.58 68 multiplication(domain(A),A) = A. [back_rewrite(35),rewrite([61(3)]),flip(a)].
% 1.28/1.58 70 addition(A,multiplication(B,A)) = multiplication(addition(B,domain(A)),A). [para(68(a,1),39(a,1,1)),rewrite([28(4)])].
% 1.28/1.58 71 multiplication(domain(A),domain(A)) = domain(A). [para(43(a,1),68(a,1,1))].
% 1.28/1.58 72 multiplication(addition(domain(A),domain(B)),A) = A. [back_rewrite(61),rewrite([70(3),28(3)])].
% 1.28/1.58 79 addition(domain(A),domain(multiplication(A,B))) = domain(A). [para(58(a,1),30(a,1,1)),rewrite([29(5)]),flip(a)].
% 1.28/1.58 84 addition(domain(A),multiplication(domain(A),B)) = multiplication(domain(A),addition(B,domain(A))). [para(71(a,1),37(a,1,1)),rewrite([28(7)])].
% 1.28/1.58 96 multiplication(addition(domain(A),domain(B)),B) = B. [para(28(a,1),72(a,1,1))].
% 1.28/1.58 115 multiplication(domain(multiplication(A,B)),multiplication(A,multiplication(domain(B),C))) = multiplication(A,multiplication(domain(B),C)). [para(29(a,1),65(a,1,1)),rewrite([33(5),33(9)])].
% 1.28/1.58 125 addition(domain(A),domain(multiplication(domain(A),B))) = domain(A). [para(43(a,1),79(a,1,1)),rewrite([43(7)])].
% 1.28/1.58 174 addition(domain(A),domain(multiplication(domain(B),A))) = domain(A). [para(27(a,1),62(a,2,1,1)),rewrite([24(5),28(5),24(7)])].
% 1.28/1.58 207 multiplication(domain(A),multiplication(domain(B),A)) = multiplication(domain(B),A). [para(174(a,1),96(a,1,1))].
% 1.28/1.58 1107 multiplication(domain(multiplication(A,B)),domain(A)) = domain(multiplication(A,B)). [para(79(a,1),84(a,2,2)),rewrite([57(7,R),27(5),23(4)]),flip(a)].
% 1.28/1.58 1110 multiplication(domain(multiplication(domain(A),B)),domain(A)) = domain(multiplication(domain(A),B)). [para(125(a,1),84(a,2,2)),rewrite([57(9,R),27(6),23(5)]),flip(a)].
% 1.28/1.58 1111 multiplication(domain(multiplication(domain(A),B)),domain(B)) = domain(multiplication(domain(A),B)). [para(174(a,1),84(a,2,2)),rewrite([57(9,R),27(6),23(5)]),flip(a)].
% 1.28/1.58 1216 domain(multiplication(domain(multiplication(A,B)),A)) = domain(multiplication(A,B)). [para(1107(a,1),29(a,1,1)),rewrite([43(3)]),flip(a)].
% 1.28/1.58 1256 domain(multiplication(domain(multiplication(domain(A),B)),A)) = domain(multiplication(domain(A),B)). [para(1216(a,1),29(a,1)),flip(a)].
% 1.28/1.58 2750 multiplication(domain(multiplication(domain(A),B)),multiplication(domain(B),C)) = multiplication(domain(multiplication(domain(A),B)),C). [para(1111(a,1),33(a,1,1)),flip(a)].
% 1.28/1.58 2828 multiplication(domain(multiplication(domain(A),B)),A) = multiplication(domain(B),A). [para(207(a,1),115(a,1,2)),rewrite([2750(6),207(8)])].
% 1.28/1.58 2831 domain(multiplication(domain(A),B)) = multiplication(domain(B),domain(A)). [para(67(a,1),115(a,1,2)),rewrite([2828(4),2750(7),1110(5),67(10)])].
% 1.28/1.58 2874 multiplication(domain(A),domain(B)) = multiplication(domain(B),domain(A)). [back_rewrite(1256),rewrite([2831(3),33(4),68(3),2831(3),2831(6)])].
% 1.28/1.58 2875 $F # answer(goals). [resolve(2874,a,40,a)].
% 1.28/1.58
% 1.28/1.58 % SZS output end Refutation
% 1.28/1.58 ============================== end of proof ==========================
% 1.28/1.58
% 1.28/1.58 ============================== STATISTICS ============================
% 1.28/1.58
% 1.28/1.58 Given=143. Generated=22532. Kept=2851. proofs=1.
% 1.28/1.58 Usable=132. Sos=2289. Demods=2333. Limbo=46, Disabled=402. Hints=0.
% 1.28/1.58 Megabytes=3.78.
% 1.28/1.58 User_CPU=0.55, System_CPU=0.02, Wall_clock=0.
% 1.28/1.58
% 1.28/1.58 ============================== end of statistics =====================
% 1.28/1.58
% 1.28/1.58 ============================== end of search =========================
% 1.28/1.58
% 1.28/1.58 THEOREM PROVED
% 1.28/1.58 % SZS status Theorem
% 1.28/1.58
% 1.28/1.58 Exiting with 1 proof.
% 1.28/1.58
% 1.28/1.58 Process 2511 exit (max_proofs) Thu Jun 16 13:29:53 2022
% 1.28/1.58 Prover9 interrupted
%------------------------------------------------------------------------------