TSTP Solution File: KLE010+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE010+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 02:21:41 EDT 2022
% Result : Theorem 0.50s 1.09s
% Output : Refutation 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE010+2 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n022.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 : Thu Jun 16 15:12:47 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.50/1.06 ============================== Prover9 ===============================
% 0.50/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.50/1.06 Process 8501 was started by sandbox2 on n022.cluster.edu,
% 0.50/1.06 Thu Jun 16 15:12:48 2022
% 0.50/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_8348_n022.cluster.edu".
% 0.50/1.06 ============================== end of head ===========================
% 0.50/1.06
% 0.50/1.06 ============================== INPUT =================================
% 0.50/1.06
% 0.50/1.06 % Reading from file /tmp/Prover9_8348_n022.cluster.edu
% 0.50/1.06
% 0.50/1.06 set(prolog_style_variables).
% 0.50/1.06 set(auto2).
% 0.50/1.06 % set(auto2) -> set(auto).
% 0.50/1.06 % set(auto) -> set(auto_inference).
% 0.50/1.06 % set(auto) -> set(auto_setup).
% 0.50/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.50/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.50/1.06 % set(auto) -> set(auto_limits).
% 0.50/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.50/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.50/1.06 % set(auto) -> set(auto_denials).
% 0.50/1.06 % set(auto) -> set(auto_process).
% 0.50/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.50/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.50/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.50/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.50/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.50/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.50/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.50/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.50/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.50/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.50/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.50/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.50/1.06 % set(auto2) -> assign(stats, some).
% 0.50/1.06 % set(auto2) -> clear(echo_input).
% 0.50/1.06 % set(auto2) -> set(quiet).
% 0.50/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.50/1.06 % set(auto2) -> clear(print_given).
% 0.50/1.06 assign(lrs_ticks,-1).
% 0.50/1.06 assign(sos_limit,10000).
% 0.50/1.06 assign(order,kbo).
% 0.50/1.06 set(lex_order_vars).
% 0.50/1.06 clear(print_given).
% 0.50/1.06
% 0.50/1.06 % formulas(sos). % not echoed (17 formulas)
% 0.50/1.06
% 0.50/1.06 ============================== end of input ==========================
% 0.50/1.06
% 0.50/1.06 % From the command line: assign(max_seconds, 300).
% 0.50/1.06
% 0.50/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.50/1.06
% 0.50/1.06 % Formulas that are not ordinary clauses:
% 0.50/1.06 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.06 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].
% 0.50/1.06 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.06 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.06 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].
% 0.50/1.06 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.06 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.06 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].
% 0.50/1.06 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].
% 0.50/1.06 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.06 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.06 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.06 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.06 14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.09 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.09 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.09 17 -(all X0 all X1 (test(X1) & test(X0) -> leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.50/1.09
% 0.50/1.09 ============================== end of process non-clausal formulas ===
% 0.50/1.09
% 0.50/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.50/1.09
% 0.50/1.09 ============================== PREDICATE ELIMINATION =================
% 0.50/1.09 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.50/1.09 19 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.50/1.09 20 test(c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.50/1.09 21 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 0.50/1.09 22 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.50/1.09 Derived: complement(f1(c2),c2). [resolve(18,a,19,a)].
% 0.50/1.09 Derived: complement(f1(c1),c1). [resolve(18,a,20,a)].
% 0.50/1.09 Derived: complement(f1(A),A) | c(A) = zero. [resolve(18,a,21,a)].
% 0.50/1.09 Derived: complement(f1(A),A) | -complement(B,A). [resolve(18,a,22,a)].
% 0.50/1.09 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.50/1.09 Derived: c(c2) != A | complement(c2,A). [resolve(23,a,19,a)].
% 0.50/1.09 Derived: c(c1) != A | complement(c1,A). [resolve(23,a,20,a)].
% 0.50/1.09 Derived: c(A) != B | complement(A,B) | c(A) = zero. [resolve(23,a,21,a)].
% 0.50/1.09 Derived: c(A) != B | complement(A,B) | -complement(C,A). [resolve(23,a,22,a)].
% 0.50/1.09 24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.50/1.09 Derived: c(c2) = A | -complement(c2,A). [resolve(24,a,19,a)].
% 0.50/1.09 Derived: c(c1) = A | -complement(c1,A). [resolve(24,a,20,a)].
% 0.50/1.09 Derived: c(A) = B | -complement(A,B) | c(A) = zero. [resolve(24,a,21,a)].
% 0.50/1.09 Derived: c(A) = B | -complement(A,B) | -complement(C,A). [resolve(24,a,22,a)].
% 0.50/1.09
% 0.50/1.09 ============================== end predicate elimination =============
% 0.50/1.09
% 0.50/1.09 Auto_denials: (non-Horn, no changes).
% 0.50/1.09
% 0.50/1.09 Term ordering decisions:
% 0.50/1.09 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
% 0.50/1.09
% 0.50/1.09 ============================== end of process initial clauses ========
% 0.50/1.09
% 0.50/1.09 ============================== CLAUSES FOR SEARCH ====================
% 0.50/1.09
% 0.50/1.09 ============================== end of clauses for search =============
% 0.50/1.09
% 0.50/1.09 ============================== SEARCH ================================
% 0.50/1.09
% 0.50/1.09 % Starting search at 0.01 seconds.
% 0.50/1.09
% 0.50/1.09 ============================== PROOF =================================
% 0.50/1.09 % SZS status Theorem
% 0.50/1.09 % SZS output start Refutation
% 0.50/1.09
% 0.50/1.09 % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.50/1.09 % Length of proof is 47.
% 0.50/1.09 % Level of proof is 7.
% 0.50/1.09 % Maximum clause weight is 46.000.
% 0.50/1.09 % Given clauses 68.
% 0.50/1.09
% 0.50/1.09 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.09 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].
% 0.50/1.09 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.09 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.09 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.09 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].
% 0.50/1.09 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].
% 0.50/1.09 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.09 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.09 14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.09 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.09 17 -(all X0 all X1 (test(X1) & test(X0) -> leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.50/1.09 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.50/1.09 19 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.50/1.09 20 test(c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.50/1.09 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.50/1.09 26 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.50/1.09 27 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.50/1.09 28 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.50/1.09 31 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.50/1.09 32 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 0.50/1.09 33 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(32),rewrite([31(2)]),flip(a)].
% 0.50/1.09 35 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.50/1.09 36 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(35),flip(a)].
% 0.50/1.09 37 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 0.50/1.09 38 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(37),flip(a)].
% 0.50/1.09 39 -leq(one,addition(addition(addition(addition(multiplication(c2,c1),multiplication(c(c2),c1)),multiplication(c1,c2)),multiplication(c(c1),c2)),multiplication(c(c1),c(c2)))) | -leq(addition(addition(addition(addition(multiplication(c2,c1),multiplication(c(c2),c1)),multiplication(c1,c2)),multiplication(c(c1),c2)),multiplication(c(c1),c(c2))),one) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.50/1.09 40 -leq(one,addition(multiplication(c1,c2),addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(addition(c2,c(c2)),c1))))) | -leq(addition(multiplication(c1,c2),addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(addition(c2,c(c2)),c1)))),one). [copy(39),rewrite([38(9),31(11),31(16),33(16,R),31(15),31(22),33(22,R),31(21),33(21,R),31(20),38(31),31(33),31(38),33(38,R),31(37),31(44),33(44,R),31(43),33(43,R),31(42)])].
% 0.50/1.09 42 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.50/1.09 45 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.50/1.09 46 -complement(A,B) | addition(A,B) = one. [copy(45),rewrite([31(2)])].
% 0.50/1.09 49 complement(f1(c2),c2). [resolve(18,a,19,a)].
% 0.50/1.09 53 c(c2) != A | complement(c2,A). [resolve(23,a,19,a)].
% 0.50/1.09 54 c(c1) != A | complement(c1,A). [resolve(23,a,20,a)].
% 0.50/1.09 64 addition(A,addition(A,B)) = addition(A,B). [para(33(a,1),26(a,1)),rewrite([31(1),31(2),33(2,R),26(1),31(3)])].
% 0.50/1.09 66 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(27(a,1),36(a,1,1)),rewrite([31(4)]),flip(a)].
% 0.50/1.09 70 -leq(one,addition(multiplication(c1,c2),addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(addition(c2,c(c2)),c1))))) | -leq(addition(multiplication(c1,c2),addition(multiplication(addition(c2,c(c2)),c1),multiplication(c(c1),addition(c2,c(c2))))),one). [para(33(a,1),40(b,1,2)),rewrite([36(42)])].
% 0.50/1.09 72 leq(A,A). [resolve(42,b,26,a)].
% 0.50/1.09 82 addition(c2,f1(c2)) = one. [resolve(49,a,46,a),rewrite([31(4)])].
% 0.50/1.09 91 complement(c2,c(c2)). [resolve(53,a,28,a(flip)),rewrite([28(5)])].
% 0.50/1.09 93 complement(c1,c(c1)). [resolve(54,a,28,a(flip)),rewrite([28(5)])].
% 0.50/1.09 106 -leq(one,addition(multiplication(c1,c2),addition(multiplication(addition(c2,c(c2)),c1),multiplication(c(c1),addition(c2,c(c2)))))) | -leq(addition(multiplication(c1,c2),addition(multiplication(addition(c2,c(c2)),c1),multiplication(c(c1),addition(c2,c(c2))))),one). [para(33(a,1),70(a,2,2)),rewrite([36(20)])].
% 0.50/1.09 118 addition(c2,c(c2)) = one. [resolve(91,a,46,a)].
% 0.50/1.09 124 -leq(one,addition(c(c1),multiplication(c1,addition(one,c2)))) | -leq(addition(c(c1),multiplication(c1,addition(one,c2))),one). [back_rewrite(106),rewrite([118(8),28(7),118(11),27(9),33(9),31(8),66(8,R),31(7),118(17),28(16),118(20),27(18),33(18),31(17),66(17,R),31(16)])].
% 0.50/1.09 128 addition(c1,c(c1)) = one. [resolve(93,a,46,a)].
% 0.50/1.09 202 addition(one,c2) = one. [para(82(a,1),64(a,1,2)),rewrite([31(3),82(7)])].
% 0.50/1.09 208 $F. [back_rewrite(124),rewrite([202(7),27(6),31(5),128(5),202(9),27(8),31(7),128(7)]),merge(b),unit_del(a,72)].
% 0.50/1.09
% 0.50/1.09 % SZS output end Refutation
% 0.50/1.09 ============================== end of proof ==========================
% 0.50/1.09
% 0.50/1.09 ============================== STATISTICS ============================
% 0.50/1.09
% 0.50/1.09 Given=68. Generated=604. Kept=177. proofs=1.
% 0.50/1.09 Usable=55. Sos=94. Demods=50. Limbo=6, Disabled=59. Hints=0.
% 0.50/1.09 Megabytes=0.24.
% 0.50/1.09 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.50/1.09
% 0.50/1.09 ============================== end of statistics =====================
% 0.50/1.09
% 0.50/1.09 ============================== end of search =========================
% 0.50/1.09
% 0.50/1.09 THEOREM PROVED
% 0.50/1.09 % SZS status Theorem
% 0.50/1.09
% 0.50/1.09 Exiting with 1 proof.
% 0.50/1.09
% 0.50/1.09 Process 8501 exit (max_proofs) Thu Jun 16 15:12:48 2022
% 0.50/1.09 Prover9 interrupted
%------------------------------------------------------------------------------