TSTP Solution File: TOP049-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : TOP049-1 : TPTP v8.1.0. Released v8.1.0.
% 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 21 21:33:55 EDT 2022
% Result : Unsatisfiable 0.66s 0.97s
% Output : Refutation 0.66s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : TOP049-1 : TPTP v8.1.0. Released v8.1.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n027.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 : Sun May 29 08:07:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.66/0.97 ============================== Prover9 ===============================
% 0.66/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.66/0.97 Process 12584 was started by sandbox on n027.cluster.edu,
% 0.66/0.97 Sun May 29 08:07:15 2022
% 0.66/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12430_n027.cluster.edu".
% 0.66/0.97 ============================== end of head ===========================
% 0.66/0.97
% 0.66/0.97 ============================== INPUT =================================
% 0.66/0.97
% 0.66/0.97 % Reading from file /tmp/Prover9_12430_n027.cluster.edu
% 0.66/0.97
% 0.66/0.97 set(prolog_style_variables).
% 0.66/0.97 set(auto2).
% 0.66/0.97 % set(auto2) -> set(auto).
% 0.66/0.97 % set(auto) -> set(auto_inference).
% 0.66/0.97 % set(auto) -> set(auto_setup).
% 0.66/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.66/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.66/0.97 % set(auto) -> set(auto_limits).
% 0.66/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.66/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.66/0.97 % set(auto) -> set(auto_denials).
% 0.66/0.97 % set(auto) -> set(auto_process).
% 0.66/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.66/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.66/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.66/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.66/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.66/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.66/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.66/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.66/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.66/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.66/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.66/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.66/0.97 % set(auto2) -> assign(stats, some).
% 0.66/0.97 % set(auto2) -> clear(echo_input).
% 0.66/0.97 % set(auto2) -> set(quiet).
% 0.66/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.66/0.97 % set(auto2) -> clear(print_given).
% 0.66/0.97 assign(lrs_ticks,-1).
% 0.66/0.97 assign(sos_limit,10000).
% 0.66/0.97 assign(order,kbo).
% 0.66/0.97 set(lex_order_vars).
% 0.66/0.97 clear(print_given).
% 0.66/0.97
% 0.66/0.97 % formulas(sos). % not echoed (14 formulas)
% 0.66/0.97
% 0.66/0.97 ============================== end of input ==========================
% 0.66/0.97
% 0.66/0.97 % From the command line: assign(max_seconds, 300).
% 0.66/0.97
% 0.66/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.66/0.97
% 0.66/0.97 % Formulas that are not ordinary clauses:
% 0.66/0.97
% 0.66/0.97 ============================== end of process non-clausal formulas ===
% 0.66/0.97
% 0.66/0.97 ============================== PROCESS INITIAL CLAUSES ===============
% 0.66/0.97
% 0.66/0.97 ============================== PREDICATE ELIMINATION =================
% 0.66/0.97
% 0.66/0.97 ============================== end predicate elimination =============
% 0.66/0.97
% 0.66/0.97 Auto_denials:
% 0.66/0.97 % copying label goal to answer in negative clause
% 0.66/0.97
% 0.66/0.97 Term ordering decisions:
% 0.66/0.97 Function symbol KB weights: a4=1. a1=1. a10=1. a2=1. a3=1. a7=1. a8=1. a9=1. a5=1. a6=1. product=1. tuple=1.
% 0.66/0.97
% 0.66/0.97 ============================== end of process initial clauses ========
% 0.66/0.97
% 0.66/0.97 ============================== CLAUSES FOR SEARCH ====================
% 0.66/0.97
% 0.66/0.97 ============================== end of clauses for search =============
% 0.66/0.97
% 0.66/0.97 ============================== SEARCH ================================
% 0.66/0.97
% 0.66/0.97 % Starting search at 0.01 seconds.
% 0.66/0.97
% 0.66/0.97 ============================== PROOF =================================
% 0.66/0.97 % SZS status Unsatisfiable
% 0.66/0.97 % SZS output start Refutation
% 0.66/0.97
% 0.66/0.97 % Proof 1 at 0.03 (+ 0.00) seconds: goal.
% 0.66/0.97 % Length of proof is 68.
% 0.66/0.97 % Level of proof is 15.
% 0.66/0.97 % Maximum clause weight is 21.000.
% 0.66/0.97 % Given clauses 47.
% 0.66/0.97
% 0.66/0.97 1 product(A,A) = A # label(involutory_quandle) # label(axiom). [assumption].
% 0.66/0.97 2 a1 = product(a9,a7) # label(knot) # label(axiom). [assumption].
% 0.66/0.97 3 product(a9,a7) = a1. [copy(2),flip(a)].
% 0.66/0.97 4 a3 = product(a1,a2) # label(knot_03) # label(axiom). [assumption].
% 0.66/0.97 5 product(a1,a2) = a3. [copy(4),flip(a)].
% 0.66/0.97 6 a2 = product(a3,a4) # label(knot_04) # label(axiom). [assumption].
% 0.66/0.97 7 product(a3,a4) = a2. [copy(6),flip(a)].
% 0.66/0.97 8 a5 = product(a2,a10) # label(knot_05) # label(axiom). [assumption].
% 0.66/0.97 9 product(a2,a10) = a5. [copy(8),flip(a)].
% 0.66/0.97 10 a6 = product(a5,a4) # label(knot_06) # label(axiom). [assumption].
% 0.66/0.97 11 product(a5,a4) = a6. [copy(10),flip(a)].
% 0.66/0.97 14 a8 = product(a7,a4) # label(knot_08) # label(axiom). [assumption].
% 0.66/0.97 15 product(a7,a4) = a8. [copy(14),flip(a)].
% 0.66/0.97 16 a10 = product(a8,a9) # label(knot_09) # label(axiom). [assumption].
% 0.66/0.97 17 product(a8,a9) = a10. [copy(16),flip(a)].
% 0.66/0.97 18 a4 = product(a10,a3) # label(knot_10) # label(axiom). [assumption].
% 0.66/0.97 19 product(a10,a3) = a4. [copy(18),flip(a)].
% 0.66/0.97 20 a9 = product(a4,a8) # label(knot_11) # label(axiom). [assumption].
% 0.66/0.97 21 product(a4,a8) = a9. [copy(20),flip(a)].
% 0.66/0.97 22 product(product(A,B),B) = A # label(involutory_quandle_01) # label(axiom). [assumption].
% 0.66/0.97 23 product(product(A,B),C) = product(product(A,C),product(B,C)) # label(involutory_quandle_02) # label(axiom). [assumption].
% 0.66/0.97 24 product(product(A,B),product(C,B)) = product(product(A,C),B). [copy(23),flip(a)].
% 0.66/0.97 25 tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) # label(goal) # label(negated_conjecture) # answer(goal). [assumption].
% 0.66/0.97 26 tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) != tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) # answer(goal). [copy(25),flip(a)].
% 0.66/0.97 28 product(a3,a2) = a1. [para(5(a,1),22(a,1,1))].
% 0.66/0.97 29 product(a2,a4) = a3. [para(7(a,1),22(a,1,1))].
% 0.66/0.97 30 product(a5,a10) = a2. [para(9(a,1),22(a,1,1))].
% 0.66/0.97 33 product(a8,a4) = a7. [para(15(a,1),22(a,1,1))].
% 0.66/0.97 34 product(a10,a9) = a8. [para(17(a,1),22(a,1,1))].
% 0.66/0.97 35 product(a4,a3) = a10. [para(19(a,1),22(a,1,1))].
% 0.66/0.97 36 product(a9,a8) = a4. [para(21(a,1),22(a,1,1))].
% 0.66/0.97 37 product(product(A,B),A) = product(A,product(B,A)). [para(1(a,1),24(a,1,1)),flip(a)].
% 0.66/0.97 38 product(product(a9,A),a7) = product(a1,product(A,a7)). [para(3(a,1),24(a,1,1)),flip(a)].
% 0.66/0.97 42 product(product(a3,A),a4) = product(a2,product(A,a4)). [para(7(a,1),24(a,1,1)),flip(a)].
% 0.66/0.97 45 product(product(A,a2),a10) = product(product(A,a10),a5). [para(9(a,1),24(a,1,2)),flip(a)].
% 0.66/0.97 80 product(product(a4,A),a3) = product(a10,product(A,a3)). [para(35(a,1),24(a,1,1)),flip(a)].
% 0.66/0.97 87 product(a3,a10) = product(a2,a3). [para(7(a,1),37(a,1,1)),rewrite([35(7)]),flip(a)].
% 0.66/0.97 88 product(a10,a4) = product(a4,a2). [para(7(a,1),37(a,2,2)),rewrite([35(3)])].
% 0.66/0.97 93 product(a10,a8) = a7. [para(17(a,1),37(a,1,1)),rewrite([36(7),33(6)])].
% 0.66/0.97 94 product(a9,a10) = product(a4,a9). [para(17(a,1),37(a,2,2)),rewrite([36(3)]),flip(a)].
% 0.66/0.97 95 product(a10,product(a2,a3)) = product(a4,a10). [para(19(a,1),37(a,1,1)),rewrite([87(7)]),flip(a)].
% 0.66/0.97 96 product(a9,a4) = product(a4,a7). [para(21(a,1),37(a,1,1)),rewrite([33(7)])].
% 0.66/0.97 97 product(a7,a8) = a10. [para(21(a,1),37(a,2,2)),rewrite([33(3),17(6)])].
% 0.66/0.97 106 product(a5,product(a10,a5)) = product(a2,a5). [para(30(a,1),37(a,1,1)),flip(a)].
% 0.66/0.97 108 product(a10,product(a4,a9)) = product(a8,a10). [para(34(a,1),37(a,1,1)),rewrite([94(7)]),flip(a)].
% 0.66/0.97 112 product(a10,product(a8,a10)) = product(a7,a10). [para(93(a,1),37(a,1,1)),flip(a)].
% 0.66/0.97 120 product(product(a4,a10),a5) = product(a10,product(a4,a10)). [para(88(a,1),37(a,1,1)),rewrite([45(5)])].
% 0.66/0.97 131 product(a1,product(a4,a7)) = a4. [para(96(a,1),38(a,1,1)),rewrite([22(5)]),flip(a)].
% 0.66/0.97 146 product(a4,product(a4,a7)) = a1. [para(131(a,1),22(a,1,1))].
% 0.66/0.97 157 product(a1,a4) = product(a4,a9). [para(146(a,1),37(a,1,1)),rewrite([37(9),15(8),21(7)])].
% 0.66/0.97 177 product(a2,a3) = product(a4,a9). [para(28(a,1),42(a,1,1)),rewrite([157(3),29(7)]),flip(a)].
% 0.66/0.97 183 product(a8,a10) = product(a4,a10). [back_rewrite(95),rewrite([177(4),108(5)])].
% 0.66/0.97 190 product(a10,product(a4,a10)) = product(a7,a10). [back_rewrite(112),rewrite([183(4)])].
% 0.66/0.97 192 product(product(a4,a10),a5) = product(a7,a10). [back_rewrite(120),rewrite([190(10)])].
% 0.66/0.97 193 product(a10,product(a9,a3)) = a2. [para(177(a,1),22(a,1,1)),rewrite([80(5)])].
% 0.66/0.97 198 a8 = a4. [para(183(a,1),22(a,1,1)),rewrite([22(5)]),flip(a)].
% 0.66/0.97 207 a10 = a4. [back_rewrite(97),rewrite([198(2),15(3),198(1)]),flip(a)].
% 0.66/0.97 208 a7 = a4. [back_rewrite(93),rewrite([207(1),198(2),1(3)]),flip(a)].
% 0.66/0.97 214 tuple(a2,a4,a9,a4,a4,a3,a4,a5,a6) != tuple(a1,a9,a4,a6,a4,a2,a3,a4,a5) # answer(goal). [back_rewrite(26),rewrite([207(2),208(4),198(5),198(13),208(15)])].
% 0.66/0.97 215 a9 = a4. [back_rewrite(21),rewrite([198(2),1(3)]),flip(a)].
% 0.66/0.97 224 a1 = a4. [back_rewrite(146),rewrite([208(3),1(4),1(3)]),flip(a)].
% 0.66/0.97 228 a2 = a4. [back_rewrite(193),rewrite([207(1),215(2),35(4),207(2),1(3)]),flip(a)].
% 0.66/0.97 229 product(a4,a5) = a4. [back_rewrite(192),rewrite([207(2),1(3),208(4),207(5),1(6)])].
% 0.66/0.97 232 a6 = a4. [back_rewrite(106),rewrite([207(2),229(4),11(3),228(2),229(4)])].
% 0.66/0.97 237 a5 = a4. [back_rewrite(9),rewrite([228(1),207(2),1(3)]),flip(a)].
% 0.66/0.97 238 tuple(a4,a4,a4,a4,a4,a3,a4,a4,a4) != tuple(a4,a4,a4,a4,a4,a4,a3,a4,a4) # answer(goal). [back_rewrite(214),rewrite([228(1),215(3),237(8),232(9),224(11),215(12),232(14),228(16),237(19)])].
% 0.66/0.97 246 a3 = a4. [back_rewrite(5),rewrite([224(1),228(2),1(3)]),flip(a)].
% 0.66/0.97 247 $F # answer(goal). [back_rewrite(238),rewrite([246(6),246(17)]),xx(a)].
% 0.66/0.97
% 0.66/0.97 % SZS output end Refutation
% 0.66/0.97 ============================== end of proof ==========================
% 0.66/0.97
% 0.66/0.97 ============================== STATISTICS ============================
% 0.66/0.97
% 0.66/0.97 Given=47. Generated=634. Kept=234. proofs=1.
% 0.66/0.97 Usable=4. Sos=19. Demods=24. Limbo=1, Disabled=224. Hints=0.
% 0.66/0.97 Megabytes=0.18.
% 0.66/0.97 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.66/0.97
% 0.66/0.97 ============================== end of statistics =====================
% 0.66/0.97
% 0.66/0.97 ============================== end of search =========================
% 0.66/0.97
% 0.66/0.97 THEOREM PROVED
% 0.66/0.97 % SZS status Unsatisfiable
% 0.66/0.97
% 0.66/0.97 Exiting with 1 proof.
% 0.66/0.97
% 0.66/0.97 Process 12584 exit (max_proofs) Sun May 29 08:07:15 2022
% 0.66/0.97 Prover9 interrupted
%------------------------------------------------------------------------------