TSTP Solution File: BOO013-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO013-4 : TPTP v8.1.0. Released v1.1.0.
% 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 : Thu Jul 14 23:48:00 EDT 2022
% Result : Unsatisfiable 0.93s 1.22s
% Output : Refutation 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : BOO013-4 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n025.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
% 0.13/0.35 % DateTime : Wed Jun 1 16:07:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.93/1.22 ============================== Prover9 ===============================
% 0.93/1.22 Prover9 (32) version 2009-11A, November 2009.
% 0.93/1.22 Process 14901 was started by sandbox2 on n025.cluster.edu,
% 0.93/1.22 Wed Jun 1 16:07:59 2022
% 0.93/1.22 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_14748_n025.cluster.edu".
% 0.93/1.22 ============================== end of head ===========================
% 0.93/1.22
% 0.93/1.22 ============================== INPUT =================================
% 0.93/1.22
% 0.93/1.22 % Reading from file /tmp/Prover9_14748_n025.cluster.edu
% 0.93/1.22
% 0.93/1.22 set(prolog_style_variables).
% 0.93/1.22 set(auto2).
% 0.93/1.22 % set(auto2) -> set(auto).
% 0.93/1.22 % set(auto) -> set(auto_inference).
% 0.93/1.22 % set(auto) -> set(auto_setup).
% 0.93/1.22 % set(auto_setup) -> set(predicate_elim).
% 0.93/1.22 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.93/1.22 % set(auto) -> set(auto_limits).
% 0.93/1.22 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.93/1.22 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.93/1.22 % set(auto) -> set(auto_denials).
% 0.93/1.22 % set(auto) -> set(auto_process).
% 0.93/1.22 % set(auto2) -> assign(new_constants, 1).
% 0.93/1.22 % set(auto2) -> assign(fold_denial_max, 3).
% 0.93/1.22 % set(auto2) -> assign(max_weight, "200.000").
% 0.93/1.22 % set(auto2) -> assign(max_hours, 1).
% 0.93/1.22 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.93/1.22 % set(auto2) -> assign(max_seconds, 0).
% 0.93/1.22 % set(auto2) -> assign(max_minutes, 5).
% 0.93/1.22 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.93/1.22 % set(auto2) -> set(sort_initial_sos).
% 0.93/1.22 % set(auto2) -> assign(sos_limit, -1).
% 0.93/1.22 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.93/1.22 % set(auto2) -> assign(max_megs, 400).
% 0.93/1.22 % set(auto2) -> assign(stats, some).
% 0.93/1.22 % set(auto2) -> clear(echo_input).
% 0.93/1.22 % set(auto2) -> set(quiet).
% 0.93/1.22 % set(auto2) -> clear(print_initial_clauses).
% 0.93/1.22 % set(auto2) -> clear(print_given).
% 0.93/1.22 assign(lrs_ticks,-1).
% 0.93/1.22 assign(sos_limit,10000).
% 0.93/1.22 assign(order,kbo).
% 0.93/1.22 set(lex_order_vars).
% 0.93/1.22 clear(print_given).
% 0.93/1.22
% 0.93/1.22 % formulas(sos). % not echoed (11 formulas)
% 0.93/1.22
% 0.93/1.22 ============================== end of input ==========================
% 0.93/1.22
% 0.93/1.22 % From the command line: assign(max_seconds, 300).
% 0.93/1.22
% 0.93/1.22 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.93/1.22
% 0.93/1.22 % Formulas that are not ordinary clauses:
% 0.93/1.22
% 0.93/1.22 ============================== end of process non-clausal formulas ===
% 0.93/1.22
% 0.93/1.22 ============================== PROCESS INITIAL CLAUSES ===============
% 0.93/1.22
% 0.93/1.22 ============================== PREDICATE ELIMINATION =================
% 0.93/1.22
% 0.93/1.22 ============================== end predicate elimination =============
% 0.93/1.22
% 0.93/1.22 Auto_denials:
% 0.93/1.22 % copying label prove_a_inverse_is_b to answer in negative clause
% 0.93/1.22
% 0.93/1.22 Term ordering decisions:
% 0.93/1.22
% 0.93/1.22 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.93/1.22 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. a=1. b=1. add=1. multiply=1. inverse=0.
% 0.93/1.22
% 0.93/1.22 ============================== end of process initial clauses ========
% 0.93/1.22
% 0.93/1.22 ============================== CLAUSES FOR SEARCH ====================
% 0.93/1.22
% 0.93/1.22 ============================== end of clauses for search =============
% 0.93/1.22
% 0.93/1.22 ============================== SEARCH ================================
% 0.93/1.22
% 0.93/1.22 % Starting search at 0.01 seconds.
% 0.93/1.22
% 0.93/1.22 ============================== PROOF =================================
% 0.93/1.22 % SZS status Unsatisfiable
% 0.93/1.22 % SZS output start Refutation
% 0.93/1.22
% 0.93/1.22 % Proof 1 at 0.20 (+ 0.01) seconds: prove_a_inverse_is_b.
% 0.93/1.22 % Length of proof is 91.
% 0.93/1.22 % Level of proof is 23.
% 0.93/1.22 % Maximum clause weight is 20.000.
% 0.93/1.22 % Given clauses 117.
% 0.93/1.22
% 0.93/1.22 1 add(A,additive_identity) = A # label(additive_id1) # label(axiom). [assumption].
% 0.93/1.22 2 multiply(A,multiplicative_identity) = A # label(multiplicative_id1) # label(axiom). [assumption].
% 0.93/1.22 3 add(a,b) = multiplicative_identity # label(b_a_multiplicative_identity) # label(hypothesis). [assumption].
% 0.93/1.22 4 multiply(a,b) = additive_identity # label(b_an_additive_identity) # label(hypothesis). [assumption].
% 0.93/1.22 5 add(A,inverse(A)) = multiplicative_identity # label(additive_inverse1) # label(axiom). [assumption].
% 0.93/1.22 6 multiply(A,inverse(A)) = additive_identity # label(multiplicative_inverse1) # label(axiom). [assumption].
% 0.93/1.22 7 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 0.93/1.22 8 multiply(A,B) = multiply(B,A) # label(commutativity_of_multiply) # label(axiom). [assumption].
% 0.93/1.22 9 add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)) # label(distributivity1) # label(axiom). [assumption].
% 0.93/1.22 10 multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)). [copy(9),flip(a)].
% 0.93/1.22 11 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distributivity2) # label(axiom). [assumption].
% 0.93/1.22 12 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(11),flip(a)].
% 0.93/1.22 13 b != inverse(a) # label(prove_a_inverse_is_b) # label(negated_conjecture) # answer(prove_a_inverse_is_b). [assumption].
% 0.93/1.22 14 inverse(a) != b # answer(prove_a_inverse_is_b). [copy(13),flip(a)].
% 0.93/1.22 15 multiply(A,add(A,B)) = add(A,multiply(B,additive_identity)). [para(1(a,1),10(a,1,1)),rewrite([8(4)])].
% 0.93/1.22 16 multiply(multiplicative_identity,add(A,a)) = add(a,multiply(A,b)). [para(3(a,1),10(a,1,1)),rewrite([7(3),8(7)])].
% 0.93/1.22 17 multiply(multiplicative_identity,add(A,B)) = add(A,multiply(B,inverse(A))). [para(5(a,1),10(a,1,1)),rewrite([8(5)])].
% 0.93/1.22 18 multiply(add(A,B),add(B,C)) = add(B,multiply(A,C)). [para(7(a,1),10(a,1,1))].
% 0.93/1.22 19 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(A,B)). [para(2(a,1),12(a,1,1)),rewrite([7(4)]),flip(a)].
% 0.93/1.22 20 multiply(a,add(A,b)) = add(additive_identity,multiply(A,a)). [para(4(a,1),12(a,1,1)),rewrite([8(3),7(7)]),flip(a)].
% 0.93/1.22 21 multiply(A,add(B,inverse(A))) = add(additive_identity,multiply(A,B)). [para(6(a,1),12(a,1,1)),rewrite([7(5)]),flip(a)].
% 0.93/1.22 22 add(multiply(A,B),multiply(B,C)) = multiply(B,add(A,C)). [para(8(a,1),12(a,1,1))].
% 0.93/1.22 29 multiply(A,A) = add(A,multiply(additive_identity,additive_identity)). [para(1(a,1),15(a,1,2))].
% 0.93/1.22 30 add(a,multiply(additive_identity,b)) = multiply(multiplicative_identity,a). [para(3(a,1),15(a,1,2)),rewrite([8(3),8(7)]),flip(a)].
% 0.93/1.22 31 add(A,multiply(inverse(A),additive_identity)) = A. [para(5(a,1),15(a,1,2)),rewrite([2(2)]),flip(a)].
% 0.93/1.22 36 add(add(A,multiply(B,additive_identity)),multiply(A,C)) = multiply(A,add(C,add(A,B))). [para(15(a,1),12(a,1,1)),rewrite([7(7)])].
% 0.93/1.22 39 multiply(multiply(A,B),multiply(A,add(B,C))) = add(multiply(A,B),multiply(additive_identity,multiply(A,C))). [para(12(a,1),15(a,1,2)),rewrite([8(8)])].
% 0.93/1.22 42 add(A,multiply(B,multiply(inverse(A),additive_identity))) = multiply(A,add(A,B)). [para(31(a,1),10(a,1,1)),rewrite([8(6)]),flip(a)].
% 0.93/1.22 45 add(multiplicative_identity,multiply(additive_identity,additive_identity)) = multiplicative_identity. [para(29(a,1),2(a,1))].
% 0.93/1.22 46 add(add(A,B),multiply(additive_identity,additive_identity)) = add(A,multiply(B,B)). [para(29(a,1),10(a,1))].
% 0.93/1.22 52 multiply(A,A) = add(A,add(additive_identity,multiply(additive_identity,additive_identity))). [para(29(a,1),15(a,2,2)),rewrite([1(2)])].
% 0.93/1.22 55 add(additive_identity,multiplicative_identity) = multiplicative_identity. [para(45(a,1),10(a,2)),rewrite([7(3),7(6),10(7),2(4)])].
% 0.93/1.22 59 add(a,multiply(A,b)) = add(A,multiply(multiplicative_identity,a)). [para(16(a,1),12(a,2)),rewrite([8(2),2(2)]),flip(a)].
% 0.93/1.22 60 add(multiplicative_identity,multiply(multiplicative_identity,a)) = add(multiplicative_identity,multiply(additive_identity,a)). [para(16(a,1),15(a,1)),rewrite([59(5),8(9)])].
% 0.93/1.22 63 add(additive_identity,multiply(multiplicative_identity,a)) = multiply(multiplicative_identity,a). [back_rewrite(30),rewrite([59(5)])].
% 0.93/1.22 64 multiply(multiplicative_identity,add(A,a)) = add(A,multiply(multiplicative_identity,a)). [back_rewrite(16),rewrite([59(8)])].
% 0.93/1.22 65 add(A,multiply(A,additive_identity)) = A. [para(55(a,1),12(a,2,2)),rewrite([2(4),7(3),2(5)])].
% 0.93/1.22 66 multiply(A,A) = A. [back_rewrite(52),rewrite([65(6),1(3)])].
% 0.93/1.22 68 add(additive_identity,add(A,B)) = add(A,B). [back_rewrite(46),rewrite([66(4),7(3),66(4)])].
% 0.93/1.22 69 multiply(A,add(A,B)) = add(A,multiply(A,B)). [para(66(a,1),12(a,1,1)),flip(a)].
% 0.93/1.22 72 add(A,multiply(B,multiply(inverse(A),additive_identity))) = add(A,multiply(A,B)). [back_rewrite(42),rewrite([69(7)])].
% 0.93/1.22 78 add(A,multiply(B,additive_identity)) = add(A,multiply(A,B)). [back_rewrite(15),rewrite([69(2)]),flip(a)].
% 0.93/1.22 80 add(A,A) = A. [para(65(a,1),10(a,2)),rewrite([1(3),8(2),69(2),66(1)])].
% 0.93/1.22 82 multiply(multiplicative_identity,add(A,B)) = add(B,multiply(A,inverse(B))). [para(17(a,2),7(a,2)),rewrite([7(3),7(5)]),flip(a)].
% 0.93/1.22 87 add(A,multiply(B,inverse(A))) = add(A,B). [para(17(a,1),12(a,2)),rewrite([8(2),2(2),8(2),2(2)]),flip(a)].
% 0.93/1.22 94 multiply(multiplicative_identity,add(A,B)) = add(A,B). [back_rewrite(82),rewrite([87(6),7(4)])].
% 0.93/1.22 98 add(A,multiply(multiplicative_identity,a)) = add(A,a). [back_rewrite(64),rewrite([94(4)]),flip(a)].
% 0.93/1.22 99 multiply(multiplicative_identity,a) = add(additive_identity,a). [back_rewrite(63),rewrite([98(5)]),flip(a)].
% 0.93/1.22 100 add(multiplicative_identity,multiply(additive_identity,a)) = add(multiplicative_identity,add(additive_identity,a)). [back_rewrite(60),rewrite([99(4)]),flip(a)].
% 0.93/1.22 101 add(a,multiply(A,b)) = add(A,add(additive_identity,a)). [back_rewrite(59),rewrite([99(7)])].
% 0.93/1.22 102 add(A,add(additive_identity,a)) = add(A,a). [back_rewrite(98),rewrite([99(3)])].
% 0.93/1.22 103 add(a,multiply(A,b)) = add(A,a). [back_rewrite(101),rewrite([102(8)])].
% 0.93/1.22 104 add(multiplicative_identity,multiply(additive_identity,a)) = add(multiplicative_identity,a). [back_rewrite(100),rewrite([102(10)])].
% 0.93/1.22 107 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(1(a,1),18(a,1,1)),rewrite([7(2),1(2)]),flip(a)].
% 0.93/1.22 108 add(b,multiply(A,a)) = add(A,b). [para(3(a,1),18(a,1,1)),rewrite([7(3),94(4),8(5)]),flip(a)].
% 0.93/1.22 109 add(inverse(A),multiply(A,B)) = add(B,inverse(A)). [para(5(a,1),18(a,1,1)),rewrite([7(3),94(4)]),flip(a)].
% 0.93/1.22 114 multiply(A,add(B,A)) = add(A,multiply(B,A)). [para(31(a,1),18(a,1,2)),rewrite([8(2),72(7),8(3)])].
% 0.93/1.22 117 multiply(A,add(B,inverse(A))) = multiply(A,B). [back_rewrite(21),rewrite([107(6)])].
% 0.93/1.22 118 multiply(a,add(A,b)) = multiply(A,a). [back_rewrite(20),rewrite([107(8)])].
% 0.93/1.22 142 multiply(add(multiplicative_identity,a),add(A,multiplicative_identity)) = add(multiplicative_identity,multiply(A,multiply(additive_identity,a))). [para(104(a,1),10(a,1,1)),rewrite([7(5),8(11)])].
% 0.93/1.22 143 add(multiplicative_identity,multiply(A,multiply(additive_identity,a))) = add(multiplicative_identity,multiply(A,a)). [para(104(a,1),10(a,1,2)),rewrite([7(2),18(6)]),flip(a)].
% 0.93/1.22 146 multiply(add(multiplicative_identity,a),add(A,multiplicative_identity)) = add(multiplicative_identity,multiply(A,a)). [back_rewrite(142),rewrite([143(12)])].
% 0.93/1.22 154 multiply(b,add(multiplicative_identity,a)) = b. [para(108(a,1),19(a,2)),rewrite([7(4),80(8)])].
% 0.93/1.22 155 multiply(b,add(A,a)) = multiply(A,b). [para(4(a,1),22(a,1,1)),rewrite([8(3),107(4),7(5)]),flip(a)].
% 0.93/1.22 156 multiply(inverse(A),add(A,B)) = multiply(B,inverse(A)). [para(6(a,1),22(a,1,1)),rewrite([8(3),107(4)]),flip(a)].
% 0.93/1.22 164 multiply(multiplicative_identity,b) = b. [back_rewrite(154),rewrite([155(5)])].
% 0.93/1.22 168 add(multiplicative_identity,a) = multiplicative_identity. [para(164(a,1),103(a,1,2)),rewrite([3(3)]),flip(a)].
% 0.93/1.22 169 add(multiplicative_identity,multiply(A,a)) = add(A,multiplicative_identity). [back_rewrite(146),rewrite([168(3),114(4),2(3),7(2)]),flip(a)].
% 0.93/1.22 171 add(multiplicative_identity,multiply(A,multiply(additive_identity,a))) = add(A,multiplicative_identity). [back_rewrite(143),rewrite([169(10)])].
% 0.93/1.22 172 add(A,multiply(A,a)) = A. [para(168(a,1),12(a,2,2)),rewrite([2(2),2(5)])].
% 0.93/1.22 219 multiply(additive_identity,a) = additive_identity. [para(172(a,1),107(a,1)),flip(a)].
% 0.93/1.22 223 add(multiplicative_identity,multiply(A,additive_identity)) = add(A,multiplicative_identity). [back_rewrite(171),rewrite([219(4)])].
% 0.93/1.22 317 add(A,multiply(A,multiply(B,a))) = multiply(A,add(B,multiplicative_identity)). [para(169(a,1),12(a,2,2)),rewrite([2(2)])].
% 0.93/1.22 332 add(A,multiply(A,multiply(B,additive_identity))) = multiply(A,add(B,multiplicative_identity)). [para(223(a,1),12(a,2,2)),rewrite([2(2)])].
% 0.93/1.22 507 multiply(additive_identity,multiply(A,a)) = multiply(A,additive_identity). [para(4(a,1),39(a,1,1)),rewrite([7(4),118(5),4(7),8(8),317(10),19(8),8(7),107(8)])].
% 0.93/1.22 592 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(B,additive_identity)). [para(507(a,1),10(a,2,2)),rewrite([1(2),69(4),317(4)])].
% 0.93/1.22 608 add(A,multiply(A,multiply(B,additive_identity))) = add(A,multiply(B,additive_identity)). [back_rewrite(332),rewrite([592(7)])].
% 0.93/1.22 701 add(multiplicative_identity,inverse(A)) = multiplicative_identity. [para(2(a,1),109(a,1,2)),rewrite([7(2),5(2)]),flip(a)].
% 0.93/1.22 702 add(b,inverse(a)) = add(additive_identity,inverse(a)). [para(4(a,1),109(a,1,2)),rewrite([7(4)]),flip(a)].
% 0.93/1.22 732 add(additive_identity,inverse(A)) = inverse(A). [para(109(a,1),78(a,1)),rewrite([8(6),6(6),1(6)])].
% 0.93/1.22 734 add(b,inverse(a)) = inverse(a). [back_rewrite(702),rewrite([732(8)])].
% 0.93/1.22 737 add(A,multiply(A,inverse(B))) = A. [para(701(a,1),12(a,2,2)),rewrite([2(2),2(5)])].
% 0.93/1.22 748 multiply(A,add(add(A,B),multiply(additive_identity,inverse(add(A,multiply(B,additive_identity)))))) = add(A,multiply(B,additive_identity)). [para(72(a,1),36(a,1)),rewrite([8(7),69(7),608(7),80(7),8(9),7(11)]),flip(a)].
% 0.93/1.22 752 multiply(multiplicative_identity,inverse(A)) = inverse(A). [para(732(a,1),94(a,1,2)),rewrite([732(6)])].
% 0.93/1.22 755 multiply(A,additive_identity) = additive_identity. [para(732(a,1),117(a,1,2)),rewrite([6(2)]),flip(a)].
% 0.93/1.22 757 multiply(additive_identity,inverse(A)) = additive_identity. [para(732(a,1),69(a,1,2)),rewrite([737(8)])].
% 0.93/1.22 758 add(A,multiply(A,B)) = A. [back_rewrite(748),rewrite([755(4),1(4),757(4),7(3),68(3),69(2),755(4),1(4)])].
% 0.93/1.22 804 multiply(A,add(A,B)) = A. [back_rewrite(69),rewrite([758(4)])].
% 0.93/1.22 931 multiply(b,inverse(a)) = b. [para(734(a,1),804(a,1,2))].
% 0.93/1.22 1084 inverse(a) = b. [para(3(a,1),156(a,1,2)),rewrite([8(4),752(4),931(6)])].
% 0.93/1.22 1085 $F # answer(prove_a_inverse_is_b). [resolve(1084,a,14,a)].
% 0.93/1.22
% 0.93/1.22 % SZS output end Refutation
% 0.93/1.22 ============================== end of proof ==========================
% 0.93/1.22
% 0.93/1.22 ============================== STATISTICS ============================
% 0.93/1.22
% 0.93/1.22 Given=117. Generated=5756. Kept=1081. proofs=1.
% 0.93/1.22 Usable=75. Sos=337. Demods=397. Limbo=0, Disabled=679. Hints=0.
% 0.93/1.22 Megabytes=0.94.
% 0.93/1.22 User_CPU=0.20, System_CPU=0.01, Wall_clock=1.
% 0.93/1.22
% 0.93/1.22 ============================== end of statistics =====================
% 0.93/1.22
% 0.93/1.22 ============================== end of search =========================
% 0.93/1.22
% 0.93/1.22 THEOREM PROVED
% 0.93/1.22 % SZS status Unsatisfiable
% 0.93/1.22
% 0.93/1.22 Exiting with 1 proof.
% 0.93/1.22
% 0.93/1.22 Process 14901 exit (max_proofs) Wed Jun 1 16:08:00 2022
% 0.93/1.22 Prover9 interrupted
%------------------------------------------------------------------------------