TSTP Solution File: KLE093+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE093+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 02:22:12 EDT 2022
% Result : Theorem 0.67s 0.97s
% Output : Refutation 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE093+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Thu Jun 16 12:57:49 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.67/0.94 ============================== Prover9 ===============================
% 0.67/0.94 Prover9 (32) version 2009-11A, November 2009.
% 0.67/0.94 Process 5576 was started by sandbox on n020.cluster.edu,
% 0.67/0.94 Thu Jun 16 12:57:50 2022
% 0.67/0.94 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5423_n020.cluster.edu".
% 0.67/0.94 ============================== end of head ===========================
% 0.67/0.94
% 0.67/0.94 ============================== INPUT =================================
% 0.67/0.94
% 0.67/0.94 % Reading from file /tmp/Prover9_5423_n020.cluster.edu
% 0.67/0.94
% 0.67/0.94 set(prolog_style_variables).
% 0.67/0.94 set(auto2).
% 0.67/0.94 % set(auto2) -> set(auto).
% 0.67/0.94 % set(auto) -> set(auto_inference).
% 0.67/0.94 % set(auto) -> set(auto_setup).
% 0.67/0.94 % set(auto_setup) -> set(predicate_elim).
% 0.67/0.94 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.67/0.94 % set(auto) -> set(auto_limits).
% 0.67/0.94 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.67/0.94 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.67/0.94 % set(auto) -> set(auto_denials).
% 0.67/0.94 % set(auto) -> set(auto_process).
% 0.67/0.94 % set(auto2) -> assign(new_constants, 1).
% 0.67/0.94 % set(auto2) -> assign(fold_denial_max, 3).
% 0.67/0.94 % set(auto2) -> assign(max_weight, "200.000").
% 0.67/0.94 % set(auto2) -> assign(max_hours, 1).
% 0.67/0.94 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.67/0.94 % set(auto2) -> assign(max_seconds, 0).
% 0.67/0.94 % set(auto2) -> assign(max_minutes, 5).
% 0.67/0.94 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.67/0.94 % set(auto2) -> set(sort_initial_sos).
% 0.67/0.94 % set(auto2) -> assign(sos_limit, -1).
% 0.67/0.94 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.67/0.94 % set(auto2) -> assign(max_megs, 400).
% 0.67/0.94 % set(auto2) -> assign(stats, some).
% 0.67/0.94 % set(auto2) -> clear(echo_input).
% 0.67/0.94 % set(auto2) -> set(quiet).
% 0.67/0.94 % set(auto2) -> clear(print_initial_clauses).
% 0.67/0.94 % set(auto2) -> clear(print_given).
% 0.67/0.94 assign(lrs_ticks,-1).
% 0.67/0.94 assign(sos_limit,10000).
% 0.67/0.94 assign(order,kbo).
% 0.67/0.94 set(lex_order_vars).
% 0.67/0.94 clear(print_given).
% 0.67/0.94
% 0.67/0.94 % formulas(sos). % not echoed (22 formulas)
% 0.67/0.94
% 0.67/0.94 ============================== end of input ==========================
% 0.67/0.94
% 0.67/0.94 % From the command line: assign(max_seconds, 300).
% 0.67/0.94
% 0.67/0.94 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.67/0.94
% 0.67/0.94 % Formulas that are not ordinary clauses:
% 0.67/0.94 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.94 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].
% 0.67/0.94 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.94 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.94 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].
% 0.67/0.94 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.94 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.94 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].
% 0.67/0.94 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].
% 0.67/0.94 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.94 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.94 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.94 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.94 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.94 15 (all A all B all C (leq(addition(multiplication(A,B),C),B) -> leq(multiplication(star(A),C),B))) # label(star_induction_left) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 16 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 17 (all X0 addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 18 (all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 19 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 20 (all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(domain5) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 21 -(all X0 domain(star(X0)) = one) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.67/0.97
% 0.67/0.97 ============================== end of process non-clausal formulas ===
% 0.67/0.97
% 0.67/0.97 ============================== PROCESS INITIAL CLAUSES ===============
% 0.67/0.97
% 0.67/0.97 ============================== PREDICATE ELIMINATION =================
% 0.67/0.97
% 0.67/0.97 ============================== end predicate elimination =============
% 0.67/0.97
% 0.67/0.97 Auto_denials:
% 0.67/0.97 % copying label goals to answer in negative clause
% 0.67/0.97
% 0.67/0.97 Term ordering decisions:
% 0.67/0.97 Function symbol KB weights: zero=1. one=1. c1=1. multiplication=1. addition=1. domain=1. star=1.
% 0.67/0.97
% 0.67/0.97 ============================== end of process initial clauses ========
% 0.67/0.97
% 0.67/0.97 ============================== CLAUSES FOR SEARCH ====================
% 0.67/0.97
% 0.67/0.97 ============================== end of clauses for search =============
% 0.67/0.97
% 0.67/0.97 ============================== SEARCH ================================
% 0.67/0.97
% 0.67/0.97 % Starting search at 0.01 seconds.
% 0.67/0.97
% 0.67/0.97 ============================== PROOF =================================
% 0.67/0.97 % SZS status Theorem
% 0.67/0.97 % SZS output start Refutation
% 0.67/0.97
% 0.67/0.97 % Proof 1 at 0.04 (+ 0.00) seconds: goals.
% 0.67/0.97 % Length of proof is 34.
% 0.67/0.97 % Level of proof is 7.
% 0.67/0.97 % Maximum clause weight is 13.000.
% 0.67/0.97 % Given clauses 89.
% 0.67/0.97
% 0.67/0.97 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 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].
% 0.67/0.97 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 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].
% 0.67/0.97 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 17 (all X0 addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 18 (all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 19 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 20 (all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(domain5) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 21 -(all X0 domain(star(X0)) = one) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.67/0.97 25 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.67/0.97 29 addition(domain(A),one) = one # label(domain3) # label(axiom). [clausify(19)].
% 0.67/0.97 30 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.67/0.97 32 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(14)].
% 0.67/0.97 33 domain(multiplication(A,domain(B))) = domain(multiplication(A,B)) # label(domain2) # label(axiom). [clausify(18)].
% 0.67/0.97 34 domain(addition(A,B)) = addition(domain(A),domain(B)) # label(domain5) # label(axiom). [clausify(20)].
% 0.67/0.97 35 addition(domain(A),domain(B)) = domain(addition(A,B)). [copy(34),flip(a)].
% 0.67/0.97 36 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 0.67/0.97 37 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(36),rewrite([30(2)]),flip(a)].
% 0.67/0.97 39 multiplication(domain(A),A) = addition(A,multiplication(domain(A),A)) # label(domain1) # label(axiom). [clausify(17)].
% 0.67/0.97 40 addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A). [copy(39),flip(a)].
% 0.67/0.97 41 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.67/0.97 42 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(41),flip(a)].
% 0.67/0.97 45 domain(star(c1)) != one # label(goals) # label(negated_conjecture) # answer(goals). [clausify(21)].
% 0.67/0.97 46 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 0.67/0.97 52 addition(one,domain(A)) = one. [back_rewrite(29),rewrite([30(3)])].
% 0.67/0.97 61 domain(one) = one. [para(25(a,1),40(a,1,2)),rewrite([52(4),25(5)]),flip(a)].
% 0.67/0.97 65 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(25(a,1),42(a,1,1)),rewrite([30(4)]),flip(a)].
% 0.67/0.97 71 addition(one,multiplication(star(A),addition(A,one))) = star(A). [hyper(46,a,32,a),rewrite([30(6),37(6,R),30(5),65(5,R)])].
% 0.67/0.97 106 domain(addition(A,one)) = one. [para(61(a,1),35(a,1,1)),rewrite([52(3),30(3)]),flip(a)].
% 0.67/0.97 115 domain(multiplication(A,addition(B,one))) = domain(A). [para(106(a,1),33(a,1,1,2)),rewrite([25(2)]),flip(a)].
% 0.67/0.97 370 domain(star(A)) = one. [para(71(a,1),35(a,2,1)),rewrite([61(2),115(6),52(4)]),flip(a)].
% 0.67/0.97 371 $F # answer(goals). [resolve(370,a,45,a)].
% 0.67/0.97
% 0.67/0.97 % SZS output end Refutation
% 0.67/0.97 ============================== end of proof ==========================
% 0.67/0.97
% 0.67/0.97 ============================== STATISTICS ============================
% 0.67/0.97
% 0.67/0.97 Given=89. Generated=1788. Kept=342. proofs=1.
% 0.67/0.97 Usable=76. Sos=212. Demods=144. Limbo=0, Disabled=76. Hints=0.
% 0.67/0.97 Megabytes=0.39.
% 0.67/0.97 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.67/0.97
% 0.67/0.97 ============================== end of statistics =====================
% 0.67/0.97
% 0.67/0.97 ============================== end of search =========================
% 0.67/0.97
% 0.67/0.97 THEOREM PROVED
% 0.67/0.97 % SZS status Theorem
% 0.67/0.97
% 0.67/0.97 Exiting with 1 proof.
% 0.67/0.97
% 0.67/0.97 Process 5576 exit (max_proofs) Thu Jun 16 12:57:50 2022
% 0.67/0.97 Prover9 interrupted
%------------------------------------------------------------------------------