TSTP Solution File: KLE081+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE081+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 02:22:08 EDT 2022
% Result : Theorem 1.09s 1.43s
% Output : Refutation 1.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : KLE081+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.30 % Computer : n010.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Thu Jun 16 16:16:23 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.64/0.94 ============================== Prover9 ===============================
% 0.64/0.94 Prover9 (32) version 2009-11A, November 2009.
% 0.64/0.94 Process 8531 was started by sandbox on n010.cluster.edu,
% 0.64/0.94 Thu Jun 16 16:16:24 2022
% 0.64/0.94 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_8378_n010.cluster.edu".
% 0.64/0.94 ============================== end of head ===========================
% 0.64/0.94
% 0.64/0.94 ============================== INPUT =================================
% 0.64/0.94
% 0.64/0.94 % Reading from file /tmp/Prover9_8378_n010.cluster.edu
% 0.64/0.94
% 0.64/0.94 set(prolog_style_variables).
% 0.64/0.94 set(auto2).
% 0.64/0.94 % set(auto2) -> set(auto).
% 0.64/0.94 % set(auto) -> set(auto_inference).
% 0.64/0.94 % set(auto) -> set(auto_setup).
% 0.64/0.94 % set(auto_setup) -> set(predicate_elim).
% 0.64/0.94 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.64/0.94 % set(auto) -> set(auto_limits).
% 0.64/0.94 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.64/0.94 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.64/0.94 % set(auto) -> set(auto_denials).
% 0.64/0.94 % set(auto) -> set(auto_process).
% 0.64/0.94 % set(auto2) -> assign(new_constants, 1).
% 0.64/0.94 % set(auto2) -> assign(fold_denial_max, 3).
% 0.64/0.94 % set(auto2) -> assign(max_weight, "200.000").
% 0.64/0.94 % set(auto2) -> assign(max_hours, 1).
% 0.64/0.94 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.64/0.94 % set(auto2) -> assign(max_seconds, 0).
% 0.64/0.94 % set(auto2) -> assign(max_minutes, 5).
% 0.64/0.94 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.64/0.94 % set(auto2) -> set(sort_initial_sos).
% 0.64/0.94 % set(auto2) -> assign(sos_limit, -1).
% 0.64/0.94 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.64/0.94 % set(auto2) -> assign(max_megs, 400).
% 0.64/0.94 % set(auto2) -> assign(stats, some).
% 0.64/0.94 % set(auto2) -> clear(echo_input).
% 0.64/0.94 % set(auto2) -> set(quiet).
% 0.64/0.94 % set(auto2) -> clear(print_initial_clauses).
% 0.64/0.94 % set(auto2) -> clear(print_given).
% 0.64/0.94 assign(lrs_ticks,-1).
% 0.64/0.94 assign(sos_limit,10000).
% 0.64/0.94 assign(order,kbo).
% 0.64/0.94 set(lex_order_vars).
% 0.64/0.94 clear(print_given).
% 0.64/0.94
% 0.64/0.94 % formulas(sos). % not echoed (18 formulas)
% 0.64/0.94
% 0.64/0.94 ============================== end of input ==========================
% 0.64/0.94
% 0.64/0.94 % From the command line: assign(max_seconds, 300).
% 0.64/0.94
% 0.64/0.94 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.64/0.94
% 0.64/0.94 % Formulas that are not ordinary clauses:
% 0.64/0.94 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.94 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].
% 0.64/0.94 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.94 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.94 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].
% 0.64/0.94 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.94 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.94 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].
% 0.64/0.94 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].
% 0.64/0.94 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.94 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.94 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.94 13 (all X0 addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.94 14 (all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 15 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 16 (all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(domain5) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 17 -(all X0 ((all X1 (addition(domain(X1),antidomain(X1)) = one & multiplication(domain(X1),antidomain(X1)) = zero)) -> multiplication(antidomain(X0),X0) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.09/1.43
% 1.09/1.43 ============================== end of process non-clausal formulas ===
% 1.09/1.43
% 1.09/1.43 ============================== PROCESS INITIAL CLAUSES ===============
% 1.09/1.43
% 1.09/1.43 ============================== PREDICATE ELIMINATION =================
% 1.09/1.43 18 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 1.09/1.43 19 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 1.09/1.43
% 1.09/1.43 ============================== end predicate elimination =============
% 1.09/1.43
% 1.09/1.43 Auto_denials:
% 1.09/1.43 % copying label goals to answer in negative clause
% 1.09/1.43
% 1.09/1.43 Term ordering decisions:
% 1.09/1.43 Function symbol KB weights: zero=1. one=1. c1=1. multiplication=1. addition=1. domain=1. antidomain=1.
% 1.09/1.43
% 1.09/1.43 ============================== end of process initial clauses ========
% 1.09/1.43
% 1.09/1.43 ============================== CLAUSES FOR SEARCH ====================
% 1.09/1.43
% 1.09/1.43 ============================== end of clauses for search =============
% 1.09/1.43
% 1.09/1.43 ============================== SEARCH ================================
% 1.09/1.43
% 1.09/1.43 % Starting search at 0.01 seconds.
% 1.09/1.43
% 1.09/1.43 ============================== PROOF =================================
% 1.09/1.43 % SZS status Theorem
% 1.09/1.43 % SZS output start Refutation
% 1.09/1.43
% 1.09/1.43 % Proof 1 at 0.47 (+ 0.02) seconds: goals.
% 1.09/1.43 % Length of proof is 49.
% 1.09/1.43 % Level of proof is 12.
% 1.09/1.43 % Maximum clause weight is 24.000.
% 1.09/1.43 % Given clauses 213.
% 1.09/1.43
% 1.09/1.43 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 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].
% 1.09/1.43 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 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].
% 1.09/1.43 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].
% 1.09/1.43 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 13 (all X0 addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 14 (all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 15 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 16 (all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(domain5) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 17 -(all X0 ((all X1 (addition(domain(X1),antidomain(X1)) = one & multiplication(domain(X1),antidomain(X1)) = zero)) -> multiplication(antidomain(X0),X0) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.09/1.43 20 domain(zero) = zero # label(domain4) # label(axiom). [assumption].
% 1.09/1.43 23 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 1.09/1.43 24 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 1.09/1.43 26 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 1.09/1.43 27 addition(domain(A),one) = one # label(domain3) # label(axiom). [clausify(15)].
% 1.09/1.43 28 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 1.09/1.43 29 addition(domain(A),antidomain(A)) = one # label(goals) # label(negated_conjecture). [clausify(17)].
% 1.09/1.43 30 multiplication(domain(A),antidomain(A)) = zero # label(goals) # label(negated_conjecture). [clausify(17)].
% 1.09/1.43 31 domain(multiplication(A,domain(B))) = domain(multiplication(A,B)) # label(domain2) # label(axiom). [clausify(14)].
% 1.09/1.43 32 domain(addition(A,B)) = addition(domain(A),domain(B)) # label(domain5) # label(axiom). [clausify(16)].
% 1.09/1.43 33 addition(domain(A),domain(B)) = domain(addition(A,B)). [copy(32),flip(a)].
% 1.09/1.43 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 1.09/1.43 37 multiplication(domain(A),A) = addition(A,multiplication(domain(A),A)) # label(domain1) # label(axiom). [clausify(13)].
% 1.09/1.43 38 addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A). [copy(37),flip(a)].
% 1.09/1.43 39 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 1.09/1.43 40 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(39),flip(a)].
% 1.09/1.43 41 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 1.09/1.43 42 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(41),flip(a)].
% 1.09/1.43 43 multiplication(antidomain(c1),c1) != zero # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 1.09/1.43 44 addition(one,domain(A)) = one. [back_rewrite(27),rewrite([28(3)])].
% 1.09/1.43 56 addition(multiplication(A,domain(B)),multiplication(domain(multiplication(A,B)),multiplication(A,domain(B)))) = multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))). [para(31(a,1),38(a,1,2,1)),rewrite([31(11)])].
% 1.09/1.43 62 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(24(a,1),42(a,1,1)),rewrite([28(4)]),flip(a)].
% 1.09/1.43 67 multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))) = multiplication(A,domain(B)). [back_rewrite(56),rewrite([62(8,R),28(4),44(4),24(4)]),flip(a)].
% 1.09/1.43 70 addition(A,multiplication(domain(B),A)) = A. [para(44(a,1),42(a,2,1)),rewrite([24(2),24(5)])].
% 1.09/1.43 71 multiplication(domain(A),A) = A. [back_rewrite(38),rewrite([70(3)]),flip(a)].
% 1.09/1.43 84 addition(A,multiplication(domain(A),B)) = multiplication(domain(A),addition(A,B)). [para(71(a,1),40(a,1,1))].
% 1.09/1.43 85 multiplication(addition(A,domain(B)),B) = addition(B,multiplication(A,B)). [para(71(a,1),42(a,1,1)),rewrite([28(4)]),flip(a)].
% 1.09/1.43 108 addition(zero,antidomain(A)) = antidomain(A). [para(30(a,1),70(a,1,2)),rewrite([28(3)])].
% 1.09/1.43 507 multiplication(domain(A),domain(antidomain(A))) = zero. [para(30(a,1),67(a,1,1,1)),rewrite([20(2),26(6)]),flip(a)].
% 1.09/1.43 523 multiplication(domain(A),multiplication(domain(antidomain(A)),B)) = zero. [para(507(a,1),36(a,1,1)),rewrite([26(2)]),flip(a)].
% 1.09/1.43 645 multiplication(domain(addition(A,B)),B) = B. [para(33(a,1),85(a,1,1)),rewrite([70(6)])].
% 1.09/1.43 674 multiplication(domain(A),multiplication(domain(B),A)) = multiplication(domain(B),A). [para(70(a,1),645(a,1,1,1))].
% 1.09/1.43 2755 multiplication(domain(antidomain(A)),A) = zero. [para(674(a,1),523(a,1))].
% 1.09/1.43 2797 multiplication(domain(antidomain(A)),domain(A)) = zero. [para(2755(a,1),67(a,1,1,1)),rewrite([20(2),26(6)]),flip(a)].
% 1.09/1.43 2847 domain(antidomain(A)) = antidomain(A). [para(2797(a,1),84(a,1,2)),rewrite([28(3),108(3),28(6),29(6),23(5)]),flip(a)].
% 1.09/1.43 2926 multiplication(antidomain(A),A) = zero. [back_rewrite(2755),rewrite([2847(2)])].
% 1.09/1.43 2927 $F # answer(goals). [resolve(2926,a,43,a)].
% 1.09/1.43
% 1.09/1.43 % SZS output end Refutation
% 1.09/1.43 ============================== end of proof ==========================
% 1.09/1.43
% 1.09/1.43 ============================== STATISTICS ============================
% 1.09/1.43
% 1.09/1.43 Given=213. Generated=23311. Kept=2902. proofs=1.
% 1.09/1.43 Usable=201. Sos=2258. Demods=2503. Limbo=79, Disabled=384. Hints=0.
% 1.09/1.43 Megabytes=3.67.
% 1.09/1.43 User_CPU=0.48, System_CPU=0.02, Wall_clock=0.
% 1.09/1.43
% 1.09/1.43 ============================== end of statistics =====================
% 1.09/1.43
% 1.09/1.43 ============================== end of search =========================
% 1.09/1.43
% 1.09/1.43 THEOREM PROVED
% 1.09/1.43 % SZS status Theorem
% 1.09/1.43
% 1.09/1.43 Exiting with 1 proof.
% 1.09/1.43
% 1.09/1.43 Process 8531 exit (max_proofs) Thu Jun 16 16:16:24 2022
% 1.09/1.43 Prover9 interrupted
%------------------------------------------------------------------------------