TSTP Solution File: KLE065+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE065+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 02:22:03 EDT 2022
% Result : Theorem 0.81s 1.10s
% Output : Refutation 0.81s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE065+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n010.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 07:32:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/1.00 ============================== Prover9 ===============================
% 0.46/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.00 Process 3964 was started by sandbox on n010.cluster.edu,
% 0.46/1.00 Thu Jun 16 07:32:24 2022
% 0.46/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3810_n010.cluster.edu".
% 0.46/1.00 ============================== end of head ===========================
% 0.46/1.00
% 0.46/1.00 ============================== INPUT =================================
% 0.46/1.00
% 0.46/1.00 % Reading from file /tmp/Prover9_3810_n010.cluster.edu
% 0.46/1.00
% 0.46/1.00 set(prolog_style_variables).
% 0.46/1.00 set(auto2).
% 0.46/1.00 % set(auto2) -> set(auto).
% 0.46/1.00 % set(auto) -> set(auto_inference).
% 0.46/1.00 % set(auto) -> set(auto_setup).
% 0.46/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.00 % set(auto) -> set(auto_limits).
% 0.46/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.00 % set(auto) -> set(auto_denials).
% 0.46/1.00 % set(auto) -> set(auto_process).
% 0.46/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.00 % set(auto2) -> assign(stats, some).
% 0.46/1.00 % set(auto2) -> clear(echo_input).
% 0.46/1.00 % set(auto2) -> set(quiet).
% 0.46/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.00 % set(auto2) -> clear(print_given).
% 0.46/1.00 assign(lrs_ticks,-1).
% 0.46/1.00 assign(sos_limit,10000).
% 0.46/1.00 assign(order,kbo).
% 0.46/1.00 set(lex_order_vars).
% 0.46/1.00 clear(print_given).
% 0.46/1.00
% 0.46/1.00 % formulas(sos). % not echoed (18 formulas)
% 0.46/1.00
% 0.46/1.00 ============================== end of input ==========================
% 0.46/1.00
% 0.46/1.00 % From the command line: assign(max_seconds, 300).
% 0.46/1.00
% 0.46/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.00
% 0.46/1.00 % Formulas that are not ordinary clauses:
% 0.46/1.00 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 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].
% 0.46/1.00 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 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].
% 0.46/1.00 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 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].
% 0.46/1.00 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].
% 0.46/1.00 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 13 (all X0 addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 14 (all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.10 15 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.10 16 (all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(domain5) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.10 17 -(all X0 all X1 (multiplication(X0,X1) = zero -> multiplication(X0,domain(X1)) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.10
% 0.81/1.10 ============================== end of process non-clausal formulas ===
% 0.81/1.10
% 0.81/1.10 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.10
% 0.81/1.10 ============================== PREDICATE ELIMINATION =================
% 0.81/1.10 18 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.81/1.10 19 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 0.81/1.10
% 0.81/1.10 ============================== end predicate elimination =============
% 0.81/1.10
% 0.81/1.10 Auto_denials:
% 0.81/1.10 % copying label goals to answer in negative clause
% 0.81/1.10
% 0.81/1.10 Term ordering decisions:
% 0.81/1.10
% 0.81/1.10 % Assigning unary symbol domain kb_weight 0 and highest precedence (8).
% 0.81/1.10 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. domain=0.
% 0.81/1.10
% 0.81/1.10 ============================== end of process initial clauses ========
% 0.81/1.10
% 0.81/1.10 ============================== CLAUSES FOR SEARCH ====================
% 0.81/1.10
% 0.81/1.10 ============================== end of clauses for search =============
% 0.81/1.10
% 0.81/1.10 ============================== SEARCH ================================
% 0.81/1.10
% 0.81/1.10 % Starting search at 0.01 seconds.
% 0.81/1.10
% 0.81/1.10 ============================== PROOF =================================
% 0.81/1.10 % SZS status Theorem
% 0.81/1.10 % SZS output start Refutation
% 0.81/1.10
% 0.81/1.10 % Proof 1 at 0.11 (+ 0.01) seconds: goals.
% 0.81/1.10 % Length of proof is 31.
% 0.81/1.10 % Level of proof is 6.
% 0.81/1.10 % Maximum clause weight is 24.000.
% 0.81/1.10 % Given clauses 69.
% 0.81/1.10
% 0.81/1.10 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.10 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].
% 0.81/1.10 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.10 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].
% 0.81/1.10 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.10 13 (all X0 addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.10 14 (all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.10 15 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.10 17 -(all X0 all X1 (multiplication(X0,X1) = zero -> multiplication(X0,domain(X1)) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.10 20 domain(zero) = zero # label(domain4) # label(axiom). [assumption].
% 0.81/1.10 24 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.81/1.10 26 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 0.81/1.10 27 multiplication(c1,c2) = zero # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.81/1.10 28 zero = multiplication(c1,c2). [copy(27),flip(a)].
% 0.81/1.10 29 addition(domain(A),one) = one # label(domain3) # label(axiom). [clausify(15)].
% 0.81/1.10 30 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.81/1.10 31 domain(multiplication(A,domain(B))) = domain(multiplication(A,B)) # label(domain2) # label(axiom). [clausify(14)].
% 0.81/1.10 35 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 0.81/1.10 36 multiplication(domain(A),A) = addition(A,multiplication(domain(A),A)) # label(domain1) # label(axiom). [clausify(13)].
% 0.81/1.10 37 addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A). [copy(36),flip(a)].
% 0.81/1.10 40 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 0.81/1.10 41 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(40),flip(a)].
% 0.81/1.10 42 multiplication(c1,domain(c2)) != zero # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 0.81/1.10 43 multiplication(c1,domain(c2)) != multiplication(c1,c2) # answer(goals). [copy(42),rewrite([28(5)])].
% 0.81/1.10 44 multiplication(c1,multiplication(c2,A)) = multiplication(c1,c2). [back_rewrite(26),rewrite([28(1),35(4),28(5)])].
% 0.81/1.10 47 domain(multiplication(c1,c2)) = multiplication(c1,c2). [back_rewrite(20),rewrite([28(1),28(5)])].
% 0.81/1.10 57 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),37(a,1,2,1)),rewrite([31(11)])].
% 0.81/1.10 65 addition(A,multiplication(domain(B),A)) = A. [para(29(a,1),41(a,2,1)),rewrite([24(4),30(3),24(5)])].
% 0.81/1.10 71 multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))) = multiplication(A,domain(B)). [back_rewrite(57),rewrite([65(8)]),flip(a)].
% 0.81/1.10 487 multiplication(c1,domain(c2)) = multiplication(c1,c2). [para(47(a,1),71(a,1,1)),rewrite([35(8),44(8)]),flip(a)].
% 0.81/1.10 488 $F # answer(goals). [resolve(487,a,43,a)].
% 0.81/1.10
% 0.81/1.10 % SZS output end Refutation
% 0.81/1.10 ============================== end of proof ==========================
% 0.81/1.10
% 0.81/1.10 ============================== STATISTICS ============================
% 0.81/1.10
% 0.81/1.10 Given=69. Generated=3027. Kept=462. proofs=1.
% 0.81/1.10 Usable=66. Sos=354. Demods=377. Limbo=2, Disabled=59. Hints=0.
% 0.81/1.10 Megabytes=0.57.
% 0.81/1.10 User_CPU=0.11, System_CPU=0.01, Wall_clock=0.
% 0.81/1.10
% 0.81/1.10 ============================== end of statistics =====================
% 0.81/1.10
% 0.81/1.10 ============================== end of search =========================
% 0.81/1.10
% 0.81/1.10 THEOREM PROVED
% 0.81/1.10 % SZS status Theorem
% 0.81/1.10
% 0.81/1.10 Exiting with 1 proof.
% 0.81/1.10
% 0.81/1.10 Process 3964 exit (max_proofs) Thu Jun 16 07:32:24 2022
% 0.81/1.10 Prover9 interrupted
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