TSTP Solution File: KLE054+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE054+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 02:22:01 EDT 2022
% Result : Theorem 0.44s 1.07s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE054+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 11:47:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.06 ============================== Prover9 ===============================
% 0.44/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.06 Process 19797 was started by sandbox2 on n025.cluster.edu,
% 0.44/1.06 Thu Jun 16 11:47:12 2022
% 0.44/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19600_n025.cluster.edu".
% 0.44/1.06 ============================== end of head ===========================
% 0.44/1.06
% 0.44/1.06 ============================== INPUT =================================
% 0.44/1.06
% 0.44/1.06 % Reading from file /tmp/Prover9_19600_n025.cluster.edu
% 0.44/1.06
% 0.44/1.06 set(prolog_style_variables).
% 0.44/1.06 set(auto2).
% 0.44/1.06 % set(auto2) -> set(auto).
% 0.44/1.06 % set(auto) -> set(auto_inference).
% 0.44/1.06 % set(auto) -> set(auto_setup).
% 0.44/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.06 % set(auto) -> set(auto_limits).
% 0.44/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.06 % set(auto) -> set(auto_denials).
% 0.44/1.06 % set(auto) -> set(auto_process).
% 0.44/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.06 % set(auto2) -> assign(stats, some).
% 0.44/1.06 % set(auto2) -> clear(echo_input).
% 0.44/1.06 % set(auto2) -> set(quiet).
% 0.44/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.06 % set(auto2) -> clear(print_given).
% 0.44/1.06 assign(lrs_ticks,-1).
% 0.44/1.06 assign(sos_limit,10000).
% 0.44/1.06 assign(order,kbo).
% 0.44/1.06 set(lex_order_vars).
% 0.44/1.06 clear(print_given).
% 0.44/1.06
% 0.44/1.06 % formulas(sos). % not echoed (18 formulas)
% 0.44/1.06
% 0.44/1.06 ============================== end of input ==========================
% 0.44/1.06
% 0.44/1.06 % From the command line: assign(max_seconds, 300).
% 0.44/1.06
% 0.44/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.06
% 0.44/1.06 % Formulas that are not ordinary clauses:
% 0.44/1.06 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 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].
% 0.44/1.06 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 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].
% 0.44/1.06 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 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].
% 0.44/1.06 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].
% 0.44/1.06 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 13 (all X0 addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 14 (all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 15 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 16 (all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(domain5) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 17 -(all X0 all X1 addition(domain(multiplication(X0,X1)),domain(X0)) = domain(X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.07
% 0.44/1.07 ============================== end of process non-clausal formulas ===
% 0.44/1.07
% 0.44/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.07
% 0.44/1.07 ============================== PREDICATE ELIMINATION =================
% 0.44/1.07 18 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.44/1.07 19 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 0.44/1.07
% 0.44/1.07 ============================== end predicate elimination =============
% 0.44/1.07
% 0.44/1.07 Auto_denials:
% 0.44/1.07 % copying label goals to answer in negative clause
% 0.44/1.07
% 0.44/1.07 Term ordering decisions:
% 0.44/1.07
% 0.44/1.07 % Assigning unary symbol domain kb_weight 0 and highest precedence (8).
% 0.44/1.07 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. domain=0.
% 0.44/1.07
% 0.44/1.07 ============================== end of process initial clauses ========
% 0.44/1.07
% 0.44/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.44/1.07
% 0.44/1.07 ============================== end of clauses for search =============
% 0.44/1.07
% 0.44/1.07 ============================== SEARCH ================================
% 0.44/1.07
% 0.44/1.07 % Starting search at 0.01 seconds.
% 0.44/1.07
% 0.44/1.07 ============================== PROOF =================================
% 0.44/1.07 % SZS status Theorem
% 0.44/1.07 % SZS output start Refutation
% 0.44/1.07
% 0.44/1.07 % Proof 1 at 0.02 (+ 0.00) seconds: goals.
% 0.44/1.07 % Length of proof is 19.
% 0.44/1.07 % Level of proof is 5.
% 0.44/1.07 % Maximum clause weight is 13.000.
% 0.44/1.07 % Given clauses 25.
% 0.44/1.07
% 0.44/1.07 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 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].
% 0.44/1.07 14 (all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 15 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 16 (all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(domain5) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 17 -(all X0 all X1 addition(domain(multiplication(X0,X1)),domain(X0)) = domain(X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.07 23 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.44/1.07 27 addition(domain(A),one) = one # label(domain3) # label(axiom). [clausify(15)].
% 0.44/1.07 28 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.44/1.07 29 domain(multiplication(A,domain(B))) = domain(multiplication(A,B)) # label(domain2) # label(axiom). [clausify(14)].
% 0.44/1.07 30 domain(addition(A,B)) = addition(domain(A),domain(B)) # label(domain5) # label(axiom). [clausify(16)].
% 0.44/1.07 36 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.44/1.07 37 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(36),flip(a)].
% 0.44/1.07 40 domain(c1) != addition(domain(multiplication(c1,c2)),domain(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 0.44/1.07 41 addition(domain(c1),domain(multiplication(c1,c2))) != domain(c1) # answer(goals). [copy(40),rewrite([28(9)]),flip(a)].
% 0.44/1.07 59 addition(A,multiplication(A,domain(B))) = A. [para(27(a,1),37(a,2,2)),rewrite([23(4),28(3),23(5)])].
% 0.44/1.07 80 addition(domain(A),domain(multiplication(A,B))) = domain(A). [para(59(a,1),30(a,1,1)),rewrite([29(5)]),flip(a)].
% 0.44/1.07 81 $F # answer(goals). [resolve(80,a,41,a)].
% 0.44/1.07
% 0.44/1.07 % SZS output end Refutation
% 0.44/1.07 ============================== end of proof ==========================
% 0.44/1.07
% 0.44/1.07 ============================== STATISTICS ============================
% 0.44/1.07
% 0.44/1.07 Given=25. Generated=329. Kept=56. proofs=1.
% 0.44/1.07 Usable=24. Sos=23. Demods=45. Limbo=0, Disabled=27. Hints=0.
% 0.44/1.07 Megabytes=0.09.
% 0.44/1.07 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.44/1.07
% 0.44/1.07 ============================== end of statistics =====================
% 0.44/1.07
% 0.44/1.07 ============================== end of search =========================
% 0.44/1.07
% 0.44/1.07 THEOREM PROVED
% 0.44/1.07 % SZS status Theorem
% 0.44/1.07
% 0.44/1.07 Exiting with 1 proof.
% 0.44/1.07
% 0.44/1.07 Process 19797 exit (max_proofs) Thu Jun 16 11:47:12 2022
% 0.44/1.07 Prover9 interrupted
%------------------------------------------------------------------------------