TSTP Solution File: BOO012-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO012-4 : TPTP v8.1.0. Released v1.1.0.
% 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 23:48:00 EDT 2022
% Result : Unsatisfiable 0.81s 1.13s
% Output : Refutation 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : BOO012-4 : TPTP v8.1.0. Released v1.1.0.
% 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n027.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 : Wed Jun 1 17:43:48 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.81/1.13 ============================== Prover9 ===============================
% 0.81/1.13 Prover9 (32) version 2009-11A, November 2009.
% 0.81/1.13 Process 7498 was started by sandbox on n027.cluster.edu,
% 0.81/1.13 Wed Jun 1 17:43:49 2022
% 0.81/1.13 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_7345_n027.cluster.edu".
% 0.81/1.13 ============================== end of head ===========================
% 0.81/1.13
% 0.81/1.13 ============================== INPUT =================================
% 0.81/1.13
% 0.81/1.13 % Reading from file /tmp/Prover9_7345_n027.cluster.edu
% 0.81/1.13
% 0.81/1.13 set(prolog_style_variables).
% 0.81/1.13 set(auto2).
% 0.81/1.13 % set(auto2) -> set(auto).
% 0.81/1.13 % set(auto) -> set(auto_inference).
% 0.81/1.13 % set(auto) -> set(auto_setup).
% 0.81/1.13 % set(auto_setup) -> set(predicate_elim).
% 0.81/1.13 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.81/1.13 % set(auto) -> set(auto_limits).
% 0.81/1.13 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.81/1.13 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.81/1.13 % set(auto) -> set(auto_denials).
% 0.81/1.13 % set(auto) -> set(auto_process).
% 0.81/1.13 % set(auto2) -> assign(new_constants, 1).
% 0.81/1.13 % set(auto2) -> assign(fold_denial_max, 3).
% 0.81/1.13 % set(auto2) -> assign(max_weight, "200.000").
% 0.81/1.13 % set(auto2) -> assign(max_hours, 1).
% 0.81/1.13 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.81/1.13 % set(auto2) -> assign(max_seconds, 0).
% 0.81/1.13 % set(auto2) -> assign(max_minutes, 5).
% 0.81/1.13 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.81/1.13 % set(auto2) -> set(sort_initial_sos).
% 0.81/1.13 % set(auto2) -> assign(sos_limit, -1).
% 0.81/1.13 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.81/1.13 % set(auto2) -> assign(max_megs, 400).
% 0.81/1.13 % set(auto2) -> assign(stats, some).
% 0.81/1.13 % set(auto2) -> clear(echo_input).
% 0.81/1.13 % set(auto2) -> set(quiet).
% 0.81/1.13 % set(auto2) -> clear(print_initial_clauses).
% 0.81/1.13 % set(auto2) -> clear(print_given).
% 0.81/1.13 assign(lrs_ticks,-1).
% 0.81/1.13 assign(sos_limit,10000).
% 0.81/1.13 assign(order,kbo).
% 0.81/1.13 set(lex_order_vars).
% 0.81/1.13 clear(print_given).
% 0.81/1.13
% 0.81/1.13 % formulas(sos). % not echoed (9 formulas)
% 0.81/1.13
% 0.81/1.13 ============================== end of input ==========================
% 0.81/1.13
% 0.81/1.13 % From the command line: assign(max_seconds, 300).
% 0.81/1.13
% 0.81/1.13 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.81/1.13
% 0.81/1.13 % Formulas that are not ordinary clauses:
% 0.81/1.13
% 0.81/1.13 ============================== end of process non-clausal formulas ===
% 0.81/1.13
% 0.81/1.13 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.13
% 0.81/1.13 ============================== PREDICATE ELIMINATION =================
% 0.81/1.13
% 0.81/1.13 ============================== end predicate elimination =============
% 0.81/1.13
% 0.81/1.13 Auto_denials:
% 0.81/1.13 % copying label prove_inverse_is_an_involution to answer in negative clause
% 0.81/1.13
% 0.81/1.13 Term ordering decisions:
% 0.81/1.13
% 0.81/1.13 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.81/1.13 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. x=1. add=1. multiply=1. inverse=0.
% 0.81/1.13
% 0.81/1.13 ============================== end of process initial clauses ========
% 0.81/1.13
% 0.81/1.13 ============================== CLAUSES FOR SEARCH ====================
% 0.81/1.13
% 0.81/1.13 ============================== end of clauses for search =============
% 0.81/1.13
% 0.81/1.13 ============================== SEARCH ================================
% 0.81/1.13
% 0.81/1.13 % Starting search at 0.01 seconds.
% 0.81/1.13
% 0.81/1.13 ============================== PROOF =================================
% 0.81/1.13 % SZS status Unsatisfiable
% 0.81/1.13 % SZS output start Refutation
% 0.81/1.13
% 0.81/1.13 % Proof 1 at 0.18 (+ 0.00) seconds: prove_inverse_is_an_involution.
% 0.81/1.13 % Length of proof is 75.
% 0.81/1.13 % Level of proof is 21.
% 0.81/1.13 % Maximum clause weight is 27.000.
% 0.81/1.13 % Given clauses 86.
% 0.81/1.13
% 0.81/1.13 1 add(A,additive_identity) = A # label(additive_id1) # label(axiom). [assumption].
% 0.81/1.13 2 multiply(A,multiplicative_identity) = A # label(multiplicative_id1) # label(axiom). [assumption].
% 0.81/1.13 3 add(A,inverse(A)) = multiplicative_identity # label(additive_inverse1) # label(axiom). [assumption].
% 0.81/1.13 4 multiply(A,inverse(A)) = additive_identity # label(multiplicative_inverse1) # label(axiom). [assumption].
% 0.81/1.13 5 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 0.81/1.13 6 multiply(A,B) = multiply(B,A) # label(commutativity_of_multiply) # label(axiom). [assumption].
% 0.81/1.13 7 add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)) # label(distributivity1) # label(axiom). [assumption].
% 0.81/1.13 8 multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)). [copy(7),flip(a)].
% 0.81/1.13 9 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distributivity2) # label(axiom). [assumption].
% 0.81/1.13 10 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(9),flip(a)].
% 0.81/1.13 11 inverse(inverse(x)) != x # label(prove_inverse_is_an_involution) # label(negated_conjecture) # answer(prove_inverse_is_an_involution). [assumption].
% 0.81/1.13 12 multiply(A,add(A,B)) = add(A,multiply(B,additive_identity)). [para(1(a,1),8(a,1,1)),rewrite([6(4)])].
% 0.81/1.13 13 multiply(multiplicative_identity,add(A,B)) = add(A,multiply(B,inverse(A))). [para(3(a,1),8(a,1,1)),rewrite([6(5)])].
% 0.81/1.13 14 multiply(add(A,B),add(B,C)) = add(B,multiply(A,C)). [para(5(a,1),8(a,1,1))].
% 0.81/1.13 15 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(A,B)). [para(2(a,1),10(a,1,1)),rewrite([5(4)]),flip(a)].
% 0.81/1.13 16 multiply(A,add(B,inverse(A))) = add(additive_identity,multiply(A,B)). [para(4(a,1),10(a,1,1)),rewrite([5(5)]),flip(a)].
% 0.81/1.13 17 add(multiply(A,B),multiply(B,C)) = multiply(B,add(A,C)). [para(6(a,1),10(a,1,1))].
% 0.81/1.13 18 multiply(multiply(A,add(B,C)),add(D,multiply(A,B))) = add(multiply(A,B),multiply(D,multiply(A,C))). [para(10(a,1),8(a,1,1)),rewrite([5(4),6(8)])].
% 0.81/1.13 21 add(add(A,multiply(B,C)),multiply(D,add(A,B))) = multiply(add(A,B),add(D,add(A,C))). [para(8(a,1),10(a,1,1)),rewrite([6(4),5(8)])].
% 0.81/1.13 22 add(multiply(A,add(B,C)),add(B,multiply(C,D))) = multiply(add(B,C),add(A,add(B,D))). [para(8(a,1),10(a,1,2)),rewrite([6(2)])].
% 0.81/1.13 24 multiply(A,A) = add(A,multiply(additive_identity,additive_identity)). [para(1(a,1),12(a,1,2))].
% 0.81/1.13 25 add(A,multiply(inverse(A),additive_identity)) = A. [para(3(a,1),12(a,1,2)),rewrite([2(2)]),flip(a)].
% 0.81/1.13 36 add(A,multiply(B,multiply(inverse(A),additive_identity))) = multiply(A,add(A,B)). [para(25(a,1),8(a,1,1)),rewrite([6(6)]),flip(a)].
% 0.81/1.13 39 add(multiplicative_identity,multiply(additive_identity,additive_identity)) = multiplicative_identity. [para(24(a,1),2(a,1))].
% 0.81/1.13 40 add(add(A,B),multiply(additive_identity,additive_identity)) = add(A,multiply(B,B)). [para(24(a,1),8(a,1))].
% 0.81/1.13 46 multiply(A,A) = add(A,add(additive_identity,multiply(additive_identity,additive_identity))). [para(24(a,1),12(a,2,2)),rewrite([1(2)])].
% 0.81/1.13 49 add(additive_identity,multiplicative_identity) = multiplicative_identity. [para(39(a,1),8(a,2)),rewrite([5(3),5(6),8(7),2(4)])].
% 0.81/1.13 53 multiply(multiplicative_identity,add(A,A)) = A. [para(4(a,1),13(a,2,2)),rewrite([1(5)])].
% 0.81/1.13 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)].
% 0.81/1.13 57 multiply(add(A,B),multiply(multiplicative_identity,add(A,C))) = add(A,multiply(B,multiply(C,inverse(A)))). [para(13(a,2),8(a,1,2))].
% 0.81/1.13 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)].
% 0.81/1.13 63 add(multiplicative_identity,multiply(A,additive_identity)) = add(A,multiplicative_identity). [para(13(a,1),12(a,1)),rewrite([59(5),5(2)]),flip(a)].
% 0.81/1.13 70 multiply(multiplicative_identity,add(A,B)) = add(A,B). [back_rewrite(54),rewrite([59(6),5(4)])].
% 0.81/1.13 71 add(A,multiply(B,multiply(C,inverse(A)))) = add(A,multiply(B,C)). [back_rewrite(57),rewrite([70(4),8(3)]),flip(a)].
% 0.81/1.13 74 add(A,A) = A. [back_rewrite(53),rewrite([70(3)])].
% 0.81/1.13 75 add(A,multiply(A,additive_identity)) = A. [para(49(a,1),10(a,2,2)),rewrite([2(4),5(3),2(5)])].
% 0.81/1.13 76 multiply(A,A) = A. [back_rewrite(46),rewrite([75(6),1(3)])].
% 0.81/1.13 77 add(additive_identity,add(A,B)) = add(A,B). [back_rewrite(40),rewrite([76(4),5(3),76(4)])].
% 0.81/1.13 78 multiply(A,add(A,B)) = add(A,multiply(A,B)). [para(74(a,1),8(a,1,1))].
% 0.81/1.13 80 add(A,multiply(B,multiply(inverse(A),additive_identity))) = add(A,multiply(A,B)). [back_rewrite(36),rewrite([78(7)])].
% 0.81/1.13 86 add(A,multiply(B,additive_identity)) = add(A,multiply(A,B)). [back_rewrite(12),rewrite([78(2)]),flip(a)].
% 0.81/1.13 88 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(1(a,1),14(a,1,1)),rewrite([5(2),1(2)]),flip(a)].
% 0.81/1.13 89 add(inverse(A),multiply(A,B)) = add(B,inverse(A)). [para(3(a,1),14(a,1,1)),rewrite([5(3),70(4)]),flip(a)].
% 0.81/1.13 94 multiply(A,add(B,A)) = add(A,multiply(B,A)). [para(25(a,1),14(a,1,2)),rewrite([6(2),80(7),6(3)])].
% 0.81/1.13 96 multiply(A,add(B,inverse(A))) = multiply(A,B). [back_rewrite(16),rewrite([88(6)])].
% 0.81/1.13 97 multiply(add(A,multiplicative_identity),add(B,multiplicative_identity)) = add(multiplicative_identity,multiply(B,multiply(A,additive_identity))). [para(63(a,1),8(a,1,1)),rewrite([5(4),6(9)])].
% 0.81/1.13 101 add(add(A,B),multiply(C,add(A,B))) = add(add(A,B),multiply(C,additive_identity)). [para(77(a,1),14(a,1,1)),rewrite([5(3),94(4),6(7)])].
% 0.81/1.13 103 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(B,A)). [para(15(a,1),6(a,2)),rewrite([6(3),6(4)])].
% 0.81/1.13 110 add(multiply(A,B),add(A,multiply(A,C))) = multiply(A,add(B,add(C,multiplicative_identity))). [para(15(a,1),10(a,1,2))].
% 0.81/1.13 117 multiply(add(A,B),add(C,multiplicative_identity)) = add(add(A,B),multiply(C,additive_identity)). [back_rewrite(101),rewrite([103(4,R)])].
% 0.81/1.13 118 add(add(A,multiplicative_identity),multiply(B,additive_identity)) = add(multiplicative_identity,multiply(B,multiply(A,additive_identity))). [back_rewrite(97),rewrite([117(5)])].
% 0.81/1.13 124 multiply(inverse(A),add(A,B)) = multiply(B,inverse(A)). [para(4(a,1),17(a,1,1)),rewrite([6(3),88(4)]),flip(a)].
% 0.81/1.13 127 add(add(A,multiply(B,C)),multiply(D,add(A,C))) = multiply(add(A,C),add(D,add(A,B))). [para(8(a,1),17(a,1,1)),rewrite([6(4),5(8)])].
% 0.81/1.13 167 multiply(multiply(A,add(B,add(C,multiplicative_identity))),add(D,add(A,multiply(A,C)))) = add(multiply(A,add(C,multiplicative_identity)),multiply(D,multiply(A,B))). [para(15(a,1),18(a,1,2,2)),rewrite([5(3)])].
% 0.81/1.13 287 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(B,additive_identity)). [para(86(a,2),15(a,2))].
% 0.81/1.13 299 multiply(add(A,multiply(B,additive_identity)),add(C,add(A,D))) = multiply(add(A,multiply(A,B)),add(C,add(A,D))). [para(86(a,1),21(a,2,1)),rewrite([6(3),127(9)])].
% 0.81/1.13 313 multiply(multiply(A,add(B,add(C,multiplicative_identity))),add(D,add(A,multiply(A,C)))) = add(add(A,multiply(C,additive_identity)),multiply(D,multiply(A,B))). [back_rewrite(167),rewrite([287(11)])].
% 0.81/1.13 328 add(multiplicative_identity,inverse(A)) = multiplicative_identity. [para(2(a,1),89(a,1,2)),rewrite([5(2),3(2)]),flip(a)].
% 0.81/1.13 346 add(additive_identity,inverse(A)) = inverse(A). [para(89(a,1),86(a,1)),rewrite([6(6),4(6),1(6)])].
% 0.81/1.13 348 add(multiplicative_identity,multiply(A,inverse(B))) = add(A,multiplicative_identity). [para(328(a,1),8(a,1,1)),rewrite([5(3),94(4),2(3),5(2),6(5)]),flip(a)].
% 0.81/1.13 351 add(add(A,multiplicative_identity),add(B,multiply(A,additive_identity))) = add(multiplicative_identity,multiply(B,multiply(A,additive_identity))). [para(328(a,1),21(a,2,2,2)),rewrite([348(4),5(4),287(5),5(8),287(11),118(11)])].
% 0.81/1.13 353 add(multiply(A,B),add(B,multiply(C,additive_identity))) = multiply(B,add(A,add(B,C))). [para(1(a,1),22(a,1,1,2)),rewrite([6(3),1(7)])].
% 0.81/1.13 376 add(multiply(A,add(B,multiply(C,additive_identity))),add(B,multiply(D,multiply(B,C)))) = multiply(add(B,multiply(B,C)),add(A,add(B,D))). [para(86(a,2),22(a,1,1,2)),rewrite([6(6)])].
% 0.81/1.13 385 multiply(A,additive_identity) = additive_identity. [para(346(a,1),96(a,1,2)),rewrite([4(2)]),flip(a)].
% 0.81/1.13 390 multiply(add(A,multiply(A,B)),add(C,add(A,D))) = add(multiply(C,A),add(A,multiply(D,multiply(A,B)))). [back_rewrite(376),rewrite([385(2),1(2)]),flip(a)].
% 0.81/1.13 394 multiply(A,add(B,add(A,C))) = add(A,multiply(B,A)). [back_rewrite(353),rewrite([385(3),1(3),5(2)]),flip(a)].
% 0.81/1.13 395 add(A,add(B,multiplicative_identity)) = multiplicative_identity. [back_rewrite(351),rewrite([385(4),1(4),5(3),385(6),385(6),5(6),49(6)])].
% 0.81/1.13 399 add(A,multiply(B,multiply(A,C))) = add(A,multiply(A,B)). [back_rewrite(313),rewrite([395(3),2(2),394(4),6(1),385(4),1(4)]),flip(a)].
% 0.81/1.13 407 add(A,multiply(A,B)) = A. [back_rewrite(299),rewrite([385(2),1(2),394(3),6(1),390(7),6(3),399(6),110(6),395(5),2(4)])].
% 0.81/1.13 543 multiply(inverse(A),multiply(A,B)) = additive_identity. [para(407(a,1),124(a,1,2)),rewrite([6(2),4(2),6(4)]),flip(a)].
% 0.81/1.13 556 multiply(inverse(inverse(A)),multiply(B,inverse(A))) = additive_identity. [para(124(a,1),543(a,1,2))].
% 0.81/1.13 756 add(A,multiply(B,inverse(inverse(A)))) = A. [para(556(a,1),71(a,1,2)),rewrite([1(2),6(3)]),flip(a)].
% 0.81/1.13 760 add(A,inverse(inverse(A))) = A. [para(76(a,1),756(a,1,2))].
% 0.81/1.13 800 inverse(inverse(A)) = A. [para(760(a,1),89(a,2)),rewrite([6(4),4(4),1(4)])].
% 0.81/1.13 801 $F # answer(prove_inverse_is_an_involution). [resolve(800,a,11,a)].
% 0.81/1.13
% 0.81/1.13 % SZS output end Refutation
% 0.81/1.13 ============================== end of proof ==========================
% 0.81/1.13
% 0.81/1.13 ============================== STATISTICS ============================
% 0.81/1.13
% 0.81/1.13 Given=86. Generated=4445. Kept=798. proofs=1.
% 0.81/1.13 Usable=59. Sos=348. Demods=394. Limbo=2, Disabled=397. Hints=0.
% 0.81/1.13 Megabytes=0.77.
% 0.81/1.13 User_CPU=0.18, System_CPU=0.00, Wall_clock=0.
% 0.81/1.13
% 0.81/1.13 ============================== end of statistics =====================
% 0.81/1.13
% 0.81/1.13 ============================== end of search =========================
% 0.81/1.13
% 0.81/1.13 THEOREM PROVED
% 0.81/1.13 % SZS status Unsatisfiable
% 0.81/1.13
% 0.81/1.13 Exiting with 1 proof.
% 0.81/1.13
% 0.81/1.13 Process 7498 exit (max_proofs) Wed Jun 1 17:43:49 2022
% 0.81/1.13 Prover9 interrupted
%------------------------------------------------------------------------------