TSTP Solution File: KLE088+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE088+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 02:22:10 EDT 2022
% Result : Theorem 2.42s 2.73s
% Output : Refutation 2.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : KLE088+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.09 % Command : tptp2X_and_run_prover9 %d %s
% 0.08/0.28 % Computer : n028.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Thu Jun 16 08:37:26 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.64/0.94 ============================== Prover9 ===============================
% 0.64/0.94 Prover9 (32) version 2009-11A, November 2009.
% 0.64/0.94 Process 18615 was started by sandbox on n028.cluster.edu,
% 0.64/0.94 Thu Jun 16 08:37:27 2022
% 0.64/0.94 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18462_n028.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_18462_n028.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 (21 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 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.94 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].
% 2.42/2.73 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 2.42/2.73 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 2.42/2.73 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 2.42/2.73 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].
% 2.42/2.73 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 2.42/2.73 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 2.42/2.73 21 -(all X0 all X1 (multiplication(domain(X0),X1) = zero -> addition(domain(X0),antidomain(X1)) = antidomain(X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.42/2.73
% 2.42/2.73 ============================== end of process non-clausal formulas ===
% 2.42/2.73
% 2.42/2.73 ============================== PROCESS INITIAL CLAUSES ===============
% 2.42/2.73
% 2.42/2.73 ============================== PREDICATE ELIMINATION =================
% 2.42/2.73 22 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.42/2.73 23 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.42/2.73
% 2.42/2.73 ============================== end predicate elimination =============
% 2.42/2.73
% 2.42/2.73 Auto_denials:
% 2.42/2.73 % copying label goals to answer in negative clause
% 2.42/2.73
% 2.42/2.73 Term ordering decisions:
% 2.42/2.73 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. antidomain=1. coantidomain=1. domain=1. codomain=1.
% 2.42/2.73
% 2.42/2.73 ============================== end of process initial clauses ========
% 2.42/2.73
% 2.42/2.73 ============================== CLAUSES FOR SEARCH ====================
% 2.42/2.73
% 2.42/2.73 ============================== end of clauses for search =============
% 2.42/2.73
% 2.42/2.73 ============================== SEARCH ================================
% 2.42/2.73
% 2.42/2.73 % Starting search at 0.01 seconds.
% 2.42/2.73
% 2.42/2.73 Low Water (keep): wt=38.000, iters=3334
% 2.42/2.73
% 2.42/2.73 Low Water (keep): wt=35.000, iters=3429
% 2.42/2.73
% 2.42/2.73 Low Water (keep): wt=32.000, iters=3335
% 2.42/2.73
% 2.42/2.73 ============================== PROOF =================================
% 2.42/2.73 % SZS status Theorem
% 2.42/2.73 % SZS output start Refutation
% 2.42/2.73
% 2.42/2.73 % Proof 1 at 1.73 (+ 0.07) seconds: goals.
% 2.42/2.73 % Length of proof is 51.
% 2.42/2.73 % Level of proof is 11.
% 2.42/2.73 % Maximum clause weight is 20.000.
% 2.42/2.73 % Given clauses 428.
% 2.42/2.73
% 2.42/2.73 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.42/2.73 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].
% 2.42/2.73 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 2.42/2.73 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 2.42/2.73 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 2.42/2.73 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 2.42/2.73 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].
% 2.42/2.73 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].
% 2.42/2.73 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.42/2.73 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 2.42/2.73 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].
% 2.42/2.73 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 2.42/2.73 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 2.42/2.73 21 -(all X0 all X1 (multiplication(domain(X0),X1) = zero -> addition(domain(X0),antidomain(X1)) = antidomain(X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.42/2.73 24 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 2.42/2.73 25 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 2.42/2.73 26 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 2.42/2.73 27 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 2.42/2.73 28 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 2.42/2.73 30 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 2.42/2.73 31 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 2.42/2.73 34 multiplication(domain(c1),c2) = zero # label(goals) # label(negated_conjecture). [clausify(21)].
% 2.42/2.73 35 multiplication(antidomain(antidomain(c1)),c2) = zero. [copy(34),rewrite([31(2)])].
% 2.42/2.73 36 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 2.42/2.73 37 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 2.42/2.73 38 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(37),rewrite([36(4)])].
% 2.42/2.73 41 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 2.42/2.73 42 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(41),rewrite([36(2)]),flip(a)].
% 2.42/2.73 44 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 2.42/2.73 45 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(44),flip(a)].
% 2.42/2.73 46 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 2.42/2.73 47 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(46),flip(a)].
% 2.42/2.73 48 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 2.42/2.73 49 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(48),flip(a)].
% 2.42/2.73 52 antidomain(c2) != addition(domain(c1),antidomain(c2)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(21)].
% 2.42/2.73 53 addition(antidomain(c2),antidomain(antidomain(c1))) != antidomain(c2) # answer(goals). [copy(52),rewrite([31(4),36(8)]),flip(a)].
% 2.42/2.73 54 antidomain(one) = zero. [para(30(a,1),26(a,1)),flip(a)].
% 2.42/2.73 56 addition(A,addition(A,B)) = addition(A,B). [para(42(a,1),25(a,1)),rewrite([36(1),36(2),42(2,R),25(1),36(3)])].
% 2.42/2.73 61 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(24(a,1),45(a,2,2)),rewrite([28(3),36(3)])].
% 2.42/2.73 78 addition(antidomain(zero),antidomain(multiplication(antidomain(antidomain(c1)),antidomain(antidomain(c2))))) = antidomain(multiplication(antidomain(antidomain(c1)),antidomain(antidomain(c2)))). [para(35(a,1),49(a,1,1,1))].
% 2.42/2.73 88 addition(zero,antidomain(zero)) = one. [para(54(a,1),38(a,1,1)),rewrite([54(3)])].
% 2.42/2.73 92 multiplication(A,antidomain(zero)) = A. [para(88(a,1),45(a,2,2)),rewrite([28(2),61(5),26(5)])].
% 2.42/2.73 98 addition(one,antidomain(A)) = one. [para(38(a,1),56(a,1,2)),rewrite([36(3),38(7)])].
% 2.42/2.73 100 antidomain(zero) = one. [para(92(a,1),27(a,1)),flip(a)].
% 2.42/2.73 101 antidomain(multiplication(antidomain(antidomain(c1)),antidomain(antidomain(c2)))) = one. [back_rewrite(78),rewrite([100(2),98(10)]),flip(a)].
% 2.42/2.73 114 addition(A,multiplication(antidomain(B),A)) = A. [para(98(a,1),47(a,2,1)),rewrite([27(2),27(5)])].
% 2.42/2.73 244 multiplication(antidomain(antidomain(c1)),antidomain(antidomain(c2))) = zero. [para(101(a,1),30(a,1,1)),rewrite([27(9)])].
% 2.42/2.73 247 multiplication(antidomain(antidomain(c1)),addition(A,antidomain(antidomain(c2)))) = multiplication(antidomain(antidomain(c1)),A). [para(244(a,1),45(a,1,1)),rewrite([61(6),36(11)]),flip(a)].
% 2.42/2.73 8245 multiplication(antidomain(antidomain(c1)),antidomain(c2)) = antidomain(antidomain(c1)). [para(38(a,1),247(a,1,2)),rewrite([26(5)]),flip(a)].
% 2.42/2.73 8280 addition(antidomain(c2),antidomain(antidomain(c1))) = antidomain(c2). [para(8245(a,1),114(a,1,2))].
% 2.42/2.73 8281 $F # answer(goals). [resolve(8280,a,53,a)].
% 2.42/2.73
% 2.42/2.73 % SZS output end Refutation
% 2.42/2.73 ============================== end of proof ==========================
% 2.42/2.73
% 2.42/2.73 ============================== STATISTICS ============================
% 2.42/2.73
% 2.42/2.73 Given=428. Generated=61304. Kept=8248. proofs=1.
% 2.42/2.73 Usable=328. Sos=5819. Demods=5807. Limbo=4, Disabled=2119. Hints=0.
% 2.42/2.73 Megabytes=9.73.
% 2.42/2.73 User_CPU=1.73, System_CPU=0.07, Wall_clock=1.
% 2.42/2.73
% 2.42/2.73 ============================== end of statistics =====================
% 2.42/2.73
% 2.42/2.73 ============================== end of search =========================
% 2.42/2.73
% 2.42/2.73 THEOREM PROVED
% 2.42/2.73 % SZS status Theorem
% 2.42/2.73
% 2.42/2.73 Exiting with 1 proof.
% 2.42/2.73
% 2.42/2.73 Process 18615 exit (max_proofs) Thu Jun 16 08:37:28 2022
% 2.42/2.73 Prover9 interrupted
%------------------------------------------------------------------------------