TSTP Solution File: BOO010-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO010-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 23:47:59 EDT 2022
% Result : Unsatisfiable 0.72s 1.01s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : BOO010-2 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n027.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 : Wed Jun 1 18:30:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.72/1.01 ============================== Prover9 ===============================
% 0.72/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.01 Process 10924 was started by sandbox2 on n027.cluster.edu,
% 0.72/1.01 Wed Jun 1 18:30:19 2022
% 0.72/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_10770_n027.cluster.edu".
% 0.72/1.01 ============================== end of head ===========================
% 0.72/1.01
% 0.72/1.01 ============================== INPUT =================================
% 0.72/1.01
% 0.72/1.01 % Reading from file /tmp/Prover9_10770_n027.cluster.edu
% 0.72/1.01
% 0.72/1.01 set(prolog_style_variables).
% 0.72/1.01 set(auto2).
% 0.72/1.01 % set(auto2) -> set(auto).
% 0.72/1.01 % set(auto) -> set(auto_inference).
% 0.72/1.01 % set(auto) -> set(auto_setup).
% 0.72/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.72/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.01 % set(auto) -> set(auto_limits).
% 0.72/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.01 % set(auto) -> set(auto_denials).
% 0.72/1.01 % set(auto) -> set(auto_process).
% 0.72/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.72/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.72/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.72/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.72/1.01 % set(auto2) -> assign(stats, some).
% 0.72/1.01 % set(auto2) -> clear(echo_input).
% 0.72/1.01 % set(auto2) -> set(quiet).
% 0.72/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.01 % set(auto2) -> clear(print_given).
% 0.72/1.01 assign(lrs_ticks,-1).
% 0.72/1.01 assign(sos_limit,10000).
% 0.72/1.01 assign(order,kbo).
% 0.72/1.01 set(lex_order_vars).
% 0.72/1.01 clear(print_given).
% 0.72/1.01
% 0.72/1.01 % formulas(sos). % not echoed (15 formulas)
% 0.72/1.01
% 0.72/1.01 ============================== end of input ==========================
% 0.72/1.01
% 0.72/1.01 % From the command line: assign(max_seconds, 300).
% 0.72/1.01
% 0.72/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/1.01
% 0.72/1.01 % Formulas that are not ordinary clauses:
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% 0.72/1.01 ============================== end of process non-clausal formulas ===
% 0.72/1.01
% 0.72/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/1.01
% 0.72/1.01 ============================== PREDICATE ELIMINATION =================
% 0.72/1.01
% 0.72/1.01 ============================== end predicate elimination =============
% 0.72/1.01
% 0.72/1.01 Auto_denials:
% 0.72/1.01 % copying label prove_a_plus_ab_is_a to answer in negative clause
% 0.72/1.01
% 0.72/1.01 Term ordering decisions:
% 0.72/1.01
% 0.72/1.01 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.72/1.01 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. a=1. b=1. add=1. multiply=1. inverse=0.
% 0.72/1.01
% 0.72/1.01 ============================== end of process initial clauses ========
% 0.72/1.01
% 0.72/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.72/1.01
% 0.72/1.01 ============================== end of clauses for search =============
% 0.72/1.01
% 0.72/1.01 ============================== SEARCH ================================
% 0.72/1.01
% 0.72/1.01 % Starting search at 0.01 seconds.
% 0.72/1.01
% 0.72/1.01 ============================== PROOF =================================
% 0.72/1.01 % SZS status Unsatisfiable
% 0.72/1.01 % SZS output start Refutation
% 0.72/1.01
% 0.72/1.01 % Proof 1 at 0.03 (+ 0.00) seconds: prove_a_plus_ab_is_a.
% 0.72/1.01 % Length of proof is 29.
% 0.72/1.01 % Level of proof is 11.
% 0.72/1.01 % Maximum clause weight is 13.000.
% 0.72/1.01 % Given clauses 32.
% 0.72/1.01
% 0.72/1.01 1 multiply(A,multiplicative_identity) = A # label(multiplicative_id1) # label(axiom). [assumption].
% 0.72/1.01 3 add(A,additive_identity) = A # label(additive_id1) # label(axiom). [assumption].
% 0.72/1.01 5 add(A,inverse(A)) = multiplicative_identity # label(additive_inverse1) # label(axiom). [assumption].
% 0.72/1.01 7 multiply(A,inverse(A)) = additive_identity # label(multiplicative_inverse1) # label(axiom). [assumption].
% 0.72/1.01 9 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 0.72/1.01 10 multiply(A,B) = multiply(B,A) # label(commutativity_of_multiply) # label(axiom). [assumption].
% 0.72/1.01 11 add(multiply(A,B),C) = multiply(add(A,C),add(B,C)) # label(distributivity1) # label(axiom). [assumption].
% 0.72/1.01 12 multiply(add(A,B),add(B,C)) = add(B,multiply(A,C)). [copy(11),rewrite([9(2)]),flip(a),rewrite([9(2)])].
% 0.72/1.01 15 multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)) # label(distributivity3) # label(axiom). [assumption].
% 0.72/1.01 16 add(multiply(A,B),multiply(B,C)) = multiply(B,add(A,C)). [copy(15),rewrite([10(2)]),flip(a),rewrite([10(2)])].
% 0.72/1.01 19 add(a,multiply(a,b)) != a # label(prove_a_plus_ab_is_a) # label(negated_conjecture) # answer(prove_a_plus_ab_is_a). [assumption].
% 0.72/1.01 20 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(3(a,1),12(a,1,1)),rewrite([9(2),3(2)]),flip(a)].
% 0.72/1.01 26 multiply(multiplicative_identity,add(A,B)) = add(A,B). [para(1(a,1),16(a,1,1)),rewrite([10(2),1(2)]),flip(a)].
% 0.72/1.01 27 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(B,A)). [para(1(a,1),16(a,1,2)),rewrite([9(2)]),flip(a)].
% 0.72/1.01 28 multiply(inverse(A),add(A,B)) = multiply(B,inverse(A)). [para(7(a,1),16(a,1,1)),rewrite([10(3),20(4)]),flip(a)].
% 0.72/1.01 29 multiply(A,add(B,inverse(A))) = multiply(B,A). [para(7(a,1),16(a,1,2)),rewrite([9(3),20(3)]),flip(a)].
% 0.72/1.01 47 add(additive_identity,add(A,B)) = add(A,B). [para(26(a,1),20(a,1,2)),rewrite([26(6)])].
% 0.72/1.01 49 add(additive_identity,multiplicative_identity) = multiplicative_identity. [para(5(a,1),47(a,1,2)),rewrite([5(5)])].
% 0.72/1.01 50 add(A,multiply(A,additive_identity)) = A. [para(49(a,1),16(a,2,2)),rewrite([10(2),1(4),9(3),1(5)])].
% 0.72/1.01 52 add(A,multiply(B,multiply(A,additive_identity))) = multiply(A,add(B,A)). [para(50(a,1),12(a,1,2)),rewrite([10(2)]),flip(a)].
% 0.72/1.01 54 multiply(additive_identity,additive_identity) = additive_identity. [para(50(a,1),20(a,1)),flip(a)].
% 0.72/1.01 73 multiply(A,A) = A. [para(54(a,1),12(a,2,2)),rewrite([9(2),3(2),3(2),3(3)])].
% 0.72/1.01 74 multiply(A,add(A,B)) = add(A,multiply(A,B)). [para(73(a,1),16(a,1,1)),flip(a)].
% 0.72/1.01 86 add(A,multiply(B,multiply(A,additive_identity))) = add(A,multiply(A,B)). [back_rewrite(52),rewrite([9(5),74(6)])].
% 0.72/1.01 87 multiply(multiplicative_identity,inverse(A)) = inverse(A). [para(7(a,1),27(a,2,2)),rewrite([28(4),3(6)])].
% 0.72/1.01 105 add(additive_identity,inverse(A)) = inverse(A). [para(87(a,1),20(a,1,2)),rewrite([87(6)])].
% 0.72/1.01 132 multiply(A,additive_identity) = additive_identity. [para(105(a,1),29(a,1,2)),rewrite([7(2),10(3)]),flip(a)].
% 0.72/1.01 135 add(A,multiply(A,B)) = A. [back_rewrite(86),rewrite([132(2),132(2),3(2)]),flip(a)].
% 0.72/1.01 136 $F # answer(prove_a_plus_ab_is_a). [resolve(135,a,19,a)].
% 0.72/1.01
% 0.72/1.01 % SZS output end Refutation
% 0.72/1.01 ============================== end of proof ==========================
% 0.72/1.01
% 0.72/1.01 ============================== STATISTICS ============================
% 0.72/1.01
% 0.72/1.01 Given=32. Generated=635. Kept=131. proofs=1.
% 0.72/1.01 Usable=28. Sos=64. Demods=81. Limbo=3, Disabled=50. Hints=0.
% 0.72/1.01 Megabytes=0.13.
% 0.72/1.01 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.72/1.01
% 0.72/1.01 ============================== end of statistics =====================
% 0.72/1.01
% 0.72/1.01 ============================== end of search =========================
% 0.72/1.01
% 0.72/1.01 THEOREM PROVED
% 0.72/1.01 % SZS status Unsatisfiable
% 0.72/1.01
% 0.72/1.01 Exiting with 1 proof.
% 0.72/1.01
% 0.72/1.01 Process 10924 exit (max_proofs) Wed Jun 1 18:30:19 2022
% 0.72/1.01 Prover9 interrupted
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