TSTP Solution File: BOO004-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO004-4 : TPTP v8.1.0. Released v1.1.0.
% 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 : Thu Jul 14 23:47:57 EDT 2022
% Result : Unsatisfiable 0.42s 0.97s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : BOO004-4 : TPTP v8.1.0. Released v1.1.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 1 17:01:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/0.97 ============================== Prover9 ===============================
% 0.42/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.97 Process 4176 was started by sandbox2 on n028.cluster.edu,
% 0.42/0.97 Wed Jun 1 17:01:23 2022
% 0.42/0.97 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4023_n028.cluster.edu".
% 0.42/0.97 ============================== end of head ===========================
% 0.42/0.97
% 0.42/0.97 ============================== INPUT =================================
% 0.42/0.97
% 0.42/0.97 % Reading from file /tmp/Prover9_4023_n028.cluster.edu
% 0.42/0.97
% 0.42/0.97 set(prolog_style_variables).
% 0.42/0.97 set(auto2).
% 0.42/0.97 % set(auto2) -> set(auto).
% 0.42/0.97 % set(auto) -> set(auto_inference).
% 0.42/0.97 % set(auto) -> set(auto_setup).
% 0.42/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.97 % set(auto) -> set(auto_limits).
% 0.42/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.97 % set(auto) -> set(auto_denials).
% 0.42/0.97 % set(auto) -> set(auto_process).
% 0.42/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.97 % set(auto2) -> assign(stats, some).
% 0.42/0.97 % set(auto2) -> clear(echo_input).
% 0.42/0.97 % set(auto2) -> set(quiet).
% 0.42/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.97 % set(auto2) -> clear(print_given).
% 0.42/0.97 assign(lrs_ticks,-1).
% 0.42/0.97 assign(sos_limit,10000).
% 0.42/0.97 assign(order,kbo).
% 0.42/0.97 set(lex_order_vars).
% 0.42/0.97 clear(print_given).
% 0.42/0.97
% 0.42/0.97 % formulas(sos). % not echoed (9 formulas)
% 0.42/0.97
% 0.42/0.97 ============================== end of input ==========================
% 0.42/0.97
% 0.42/0.97 % From the command line: assign(max_seconds, 300).
% 0.42/0.97
% 0.42/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.97
% 0.42/0.97 % Formulas that are not ordinary clauses:
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% 0.42/0.97 ============================== end of process non-clausal formulas ===
% 0.42/0.97
% 0.42/0.97 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.42/0.97 ============================== PREDICATE ELIMINATION =================
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% 0.42/0.97 ============================== end predicate elimination =============
% 0.42/0.97
% 0.42/0.97 Auto_denials:
% 0.42/0.97 % copying label prove_a_plus_a_is_a to answer in negative clause
% 0.42/0.97
% 0.42/0.97 Term ordering decisions:
% 0.42/0.97
% 0.42/0.97 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.42/0.97 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. a=1. add=1. multiply=1. inverse=0.
% 0.42/0.97
% 0.42/0.97 ============================== end of process initial clauses ========
% 0.42/0.97
% 0.42/0.97 ============================== CLAUSES FOR SEARCH ====================
% 0.42/0.97
% 0.42/0.97 ============================== end of clauses for search =============
% 0.42/0.97
% 0.42/0.97 ============================== SEARCH ================================
% 0.42/0.97
% 0.42/0.97 % Starting search at 0.01 seconds.
% 0.42/0.97
% 0.42/0.97 ============================== PROOF =================================
% 0.42/0.97 % SZS status Unsatisfiable
% 0.42/0.97 % SZS output start Refutation
% 0.42/0.97
% 0.42/0.97 % Proof 1 at 0.02 (+ 0.00) seconds: prove_a_plus_a_is_a.
% 0.42/0.97 % Length of proof is 18.
% 0.42/0.97 % Level of proof is 6.
% 0.42/0.97 % Maximum clause weight is 13.000.
% 0.42/0.97 % Given clauses 15.
% 0.42/0.97
% 0.42/0.97 1 add(A,additive_identity) = A # label(additive_id1) # label(axiom). [assumption].
% 0.42/0.97 2 multiply(A,multiplicative_identity) = A # label(multiplicative_id1) # label(axiom). [assumption].
% 0.42/0.97 3 add(A,inverse(A)) = multiplicative_identity # label(additive_inverse1) # label(axiom). [assumption].
% 0.42/0.97 4 multiply(A,inverse(A)) = additive_identity # label(multiplicative_inverse1) # label(axiom). [assumption].
% 0.42/0.97 5 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 0.42/0.97 6 multiply(A,B) = multiply(B,A) # label(commutativity_of_multiply) # label(axiom). [assumption].
% 0.42/0.97 7 add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)) # label(distributivity1) # label(axiom). [assumption].
% 0.42/0.97 8 multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)). [copy(7),flip(a)].
% 0.42/0.97 9 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distributivity2) # label(axiom). [assumption].
% 0.42/0.97 10 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(9),flip(a)].
% 0.42/0.97 11 add(a,a) != a # label(prove_a_plus_a_is_a) # label(negated_conjecture) # answer(prove_a_plus_a_is_a). [assumption].
% 0.42/0.97 13 multiply(multiplicative_identity,add(A,B)) = add(A,multiply(B,inverse(A))). [para(3(a,1),8(a,1,1)),rewrite([6(5)])].
% 0.42/0.97 53 multiply(multiplicative_identity,add(A,A)) = A. [para(4(a,1),13(a,2,2)),rewrite([1(5)])].
% 0.42/0.97 54 multiply(multiplicative_identity,add(A,B)) = add(B,multiply(A,inverse(B))). [para(13(a,2),5(a,2)),rewrite([5(3),5(5)]),flip(a)].
% 0.42/0.97 59 add(A,multiply(B,inverse(A))) = add(A,B). [para(13(a,1),10(a,2)),rewrite([6(2),2(2),6(2),2(2)]),flip(a)].
% 0.42/0.97 70 multiply(multiplicative_identity,add(A,B)) = add(A,B). [back_rewrite(54),rewrite([59(6),5(4)])].
% 0.42/0.97 74 add(A,A) = A. [back_rewrite(53),rewrite([70(3)])].
% 0.42/0.97 75 $F # answer(prove_a_plus_a_is_a). [resolve(74,a,11,a)].
% 0.42/0.97
% 0.42/0.97 % SZS output end Refutation
% 0.42/0.97 ============================== end of proof ==========================
% 0.42/0.97
% 0.42/0.97 ============================== STATISTICS ============================
% 0.42/0.97
% 0.42/0.97 Given=15. Generated=189. Kept=72. proofs=1.
% 0.42/0.97 Usable=12. Sos=39. Demods=41. Limbo=4, Disabled=25. Hints=0.
% 0.42/0.97 Megabytes=0.09.
% 0.42/0.97 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.42/0.97
% 0.42/0.97 ============================== end of statistics =====================
% 0.42/0.97
% 0.42/0.97 ============================== end of search =========================
% 0.42/0.97
% 0.42/0.97 THEOREM PROVED
% 0.42/0.97 % SZS status Unsatisfiable
% 0.42/0.97
% 0.42/0.97 Exiting with 1 proof.
% 0.42/0.97
% 0.42/0.97 Process 4176 exit (max_proofs) Wed Jun 1 17:01:23 2022
% 0.42/0.97 Prover9 interrupted
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