TSTP Solution File: REL012-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL012-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 : Mon Jul 18 19:53:37 EDT 2022
% Result : Unsatisfiable 2.74s 3.08s
% Output : Refutation 2.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL012-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n004.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 : Fri Jul 8 15:31:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.74/3.08 ============================== Prover9 ===============================
% 2.74/3.08 Prover9 (32) version 2009-11A, November 2009.
% 2.74/3.08 Process 3706 was started by sandbox2 on n004.cluster.edu,
% 2.74/3.08 Fri Jul 8 15:31:23 2022
% 2.74/3.08 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3552_n004.cluster.edu".
% 2.74/3.08 ============================== end of head ===========================
% 2.74/3.08
% 2.74/3.08 ============================== INPUT =================================
% 2.74/3.08
% 2.74/3.08 % Reading from file /tmp/Prover9_3552_n004.cluster.edu
% 2.74/3.08
% 2.74/3.08 set(prolog_style_variables).
% 2.74/3.08 set(auto2).
% 2.74/3.08 % set(auto2) -> set(auto).
% 2.74/3.08 % set(auto) -> set(auto_inference).
% 2.74/3.08 % set(auto) -> set(auto_setup).
% 2.74/3.08 % set(auto_setup) -> set(predicate_elim).
% 2.74/3.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.74/3.08 % set(auto) -> set(auto_limits).
% 2.74/3.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.74/3.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.74/3.08 % set(auto) -> set(auto_denials).
% 2.74/3.08 % set(auto) -> set(auto_process).
% 2.74/3.08 % set(auto2) -> assign(new_constants, 1).
% 2.74/3.08 % set(auto2) -> assign(fold_denial_max, 3).
% 2.74/3.08 % set(auto2) -> assign(max_weight, "200.000").
% 2.74/3.08 % set(auto2) -> assign(max_hours, 1).
% 2.74/3.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.74/3.08 % set(auto2) -> assign(max_seconds, 0).
% 2.74/3.08 % set(auto2) -> assign(max_minutes, 5).
% 2.74/3.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.74/3.08 % set(auto2) -> set(sort_initial_sos).
% 2.74/3.08 % set(auto2) -> assign(sos_limit, -1).
% 2.74/3.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.74/3.08 % set(auto2) -> assign(max_megs, 400).
% 2.74/3.08 % set(auto2) -> assign(stats, some).
% 2.74/3.08 % set(auto2) -> clear(echo_input).
% 2.74/3.08 % set(auto2) -> set(quiet).
% 2.74/3.08 % set(auto2) -> clear(print_initial_clauses).
% 2.74/3.08 % set(auto2) -> clear(print_given).
% 2.74/3.08 assign(lrs_ticks,-1).
% 2.74/3.08 assign(sos_limit,10000).
% 2.74/3.08 assign(order,kbo).
% 2.74/3.08 set(lex_order_vars).
% 2.74/3.08 clear(print_given).
% 2.74/3.08
% 2.74/3.08 % formulas(sos). % not echoed (14 formulas)
% 2.74/3.08
% 2.74/3.08 ============================== end of input ==========================
% 2.74/3.08
% 2.74/3.08 % From the command line: assign(max_seconds, 300).
% 2.74/3.08
% 2.74/3.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.74/3.08
% 2.74/3.08 % Formulas that are not ordinary clauses:
% 2.74/3.08
% 2.74/3.08 ============================== end of process non-clausal formulas ===
% 2.74/3.08
% 2.74/3.08 ============================== PROCESS INITIAL CLAUSES ===============
% 2.74/3.08
% 2.74/3.08 ============================== PREDICATE ELIMINATION =================
% 2.74/3.08
% 2.74/3.08 ============================== end predicate elimination =============
% 2.74/3.08
% 2.74/3.08 Auto_denials:
% 2.74/3.08 % copying label goals_14 to answer in negative clause
% 2.74/3.08
% 2.74/3.08 Term ordering decisions:
% 2.74/3.08 Function symbol KB weights: one=1. top=1. zero=1. sk1=1. sk2=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 2.74/3.08
% 2.74/3.08 ============================== end of process initial clauses ========
% 2.74/3.08
% 2.74/3.08 ============================== CLAUSES FOR SEARCH ====================
% 2.74/3.08
% 2.74/3.08 ============================== end of clauses for search =============
% 2.74/3.08
% 2.74/3.08 ============================== SEARCH ================================
% 2.74/3.08
% 2.74/3.08 % Starting search at 0.01 seconds.
% 2.74/3.08
% 2.74/3.08 Low Water (keep): wt=38.000, iters=3354
% 2.74/3.08
% 2.74/3.08 Low Water (keep): wt=35.000, iters=3378
% 2.74/3.08
% 2.74/3.08 Low Water (keep): wt=32.000, iters=3358
% 2.74/3.08
% 2.74/3.08 Low Water (keep): wt=31.000, iters=3407
% 2.74/3.08
% 2.74/3.08 Low Water (keep): wt=30.000, iters=3370
% 2.74/3.08
% 2.74/3.08 Low Water (keep): wt=29.000, iters=3336
% 2.74/3.08
% 2.74/3.08 Low Water (keep): wt=28.000, iters=3339
% 2.74/3.08
% 2.74/3.08 Low Water (keep): wt=27.000, iters=3406
% 2.74/3.08
% 2.74/3.08 Low Water (keep): wt=26.000, iters=3336
% 2.74/3.08
% 2.74/3.08 Low Water (keep): wt=25.000, iters=3366
% 2.74/3.08
% 2.74/3.08 Low Water (keep): wt=24.000, iters=3335
% 2.74/3.08
% 2.74/3.08 Low Water (keep): wt=23.000, iters=3343
% 2.74/3.08
% 2.74/3.08 Low Water (keep): wt=22.000, iters=3343
% 2.74/3.08
% 2.74/3.08 Low Water (keep): wt=21.000, iters=3347
% 2.74/3.08
% 2.74/3.08 ============================== PROOF =================================
% 2.74/3.08 % SZS status Unsatisfiable
% 2.74/3.08 % SZS output start Refutation
% 2.74/3.08
% 2.74/3.08 % Proof 1 at 2.06 (+ 0.06) seconds: goals_14.
% 2.74/3.08 % Length of proof is 76.
% 2.74/3.08 % Level of proof is 28.
% 2.74/3.08 % Maximum clause weight is 15.000.
% 2.74/3.08 % Given clauses 638.
% 2.74/3.08
% 2.74/3.08 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 2.74/3.08 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 2.74/3.08 3 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 2.74/3.08 4 join(A,complement(A)) = top. [copy(3),flip(a)].
% 2.74/3.08 5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 2.74/3.08 6 meet(A,complement(A)) = zero. [copy(5),flip(a)].
% 2.74/3.08 7 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 2.74/3.08 8 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 2.74/3.08 9 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 2.74/3.08 10 join(converse(A),converse(B)) = converse(join(A,B)). [copy(9),flip(a)].
% 2.74/3.08 11 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 2.74/3.08 12 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(11),flip(a)].
% 2.74/3.08 13 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 2.74/3.08 14 join(A,join(B,C)) = join(C,join(A,B)). [copy(13),rewrite([7(4)])].
% 2.74/3.08 15 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 2.74/3.08 16 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(15),flip(a)].
% 2.74/3.08 19 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 2.74/3.08 20 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(19),rewrite([7(6)])].
% 2.74/3.08 21 A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) # label(maddux3_a_kind_of_de_Morgan_3) # label(axiom). [assumption].
% 2.74/3.08 22 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(21),rewrite([7(6),7(8)]),flip(a),rewrite([7(6)])].
% 2.74/3.08 23 join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)) != complement(sk1) # label(goals_14) # label(negated_conjecture) # answer(goals_14). [assumption].
% 2.74/3.08 24 join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))) != complement(sk1) # answer(goals_14). [copy(23),rewrite([7(10)])].
% 2.74/3.08 25 complement(top) = zero. [back_rewrite(6),rewrite([8(2),4(4)])].
% 2.74/3.08 27 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),12(a,1,1)),flip(a)].
% 2.74/3.08 28 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),12(a,1,2)),flip(a)].
% 2.74/3.08 29 join(A,join(B,complement(A))) = join(B,top). [para(4(a,1),14(a,2,2)),rewrite([7(2)])].
% 2.74/3.08 30 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),16(a,1,1)),flip(a)].
% 2.74/3.08 36 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),20(a,1,2,2,1))].
% 2.74/3.08 38 join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)). [para(20(a,1),10(a,2,1)),rewrite([28(7)])].
% 2.74/3.08 41 join(zero,complement(join(complement(A),complement(A)))) = A. [para(4(a,1),22(a,1,1,1)),rewrite([25(2)])].
% 2.74/3.08 49 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(25(a,1),22(a,1,2,1,1))].
% 2.74/3.08 62 composition(converse(one),A) = A. [para(1(a,1),28(a,1,1)),rewrite([2(2)]),flip(a)].
% 2.74/3.08 68 converse(one) = one. [para(62(a,1),1(a,1)),flip(a)].
% 2.74/3.08 72 join(complement(A),complement(composition(one,A))) = complement(A). [para(62(a,1),20(a,1,2))].
% 2.74/3.08 73 composition(one,A) = A. [para(62(a,1),30(a,2)),rewrite([68(2),30(4)])].
% 2.74/3.08 74 join(complement(A),complement(A)) = complement(A). [back_rewrite(72),rewrite([73(3)])].
% 2.74/3.08 75 join(zero,complement(complement(A))) = A. [back_rewrite(41),rewrite([74(4)])].
% 2.74/3.08 76 converse(join(A,one)) = join(one,converse(A)). [para(68(a,1),10(a,1,1)),rewrite([7(5)]),flip(a)].
% 2.74/3.08 80 join(top,complement(A)) = top. [para(74(a,1),29(a,1,2)),rewrite([4(2),7(4)]),flip(a)].
% 2.74/3.08 81 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(49),rewrite([80(3),25(2)])].
% 2.74/3.08 82 join(top,top) = join(A,top). [para(80(a,1),29(a,1,2)),flip(a)].
% 2.74/3.08 87 join(A,top) = join(B,top). [para(82(a,1),29(a,2)),rewrite([80(3)])].
% 2.74/3.08 88 join(A,top) = c_0. [new_symbol(87)].
% 2.74/3.08 91 join(A,join(B,complement(A))) = c_0. [back_rewrite(29),rewrite([88(5)])].
% 2.74/3.08 102 c_0 = top. [para(75(a,1),91(a,1,2)),rewrite([7(2),4(2)]),flip(a)].
% 2.74/3.08 103 join(A,join(B,complement(A))) = top. [back_rewrite(91),rewrite([102(4)])].
% 2.74/3.08 130 join(zero,complement(A)) = complement(A). [para(75(a,1),81(a,1,2,1))].
% 2.74/3.08 131 complement(complement(A)) = A. [back_rewrite(81),rewrite([130(4),130(4)])].
% 2.74/3.08 132 join(A,zero) = A. [back_rewrite(75),rewrite([131(3),7(2)])].
% 2.74/3.08 137 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(131(a,1),22(a,1,1,1,2)),rewrite([131(5),7(4)])].
% 2.74/3.08 139 join(A,A) = A. [para(131(a,1),74(a,1,1)),rewrite([131(2),131(3)])].
% 2.74/3.08 143 join(A,join(A,B)) = join(A,B). [para(139(a,1),14(a,1)),rewrite([7(3),14(4,R),7(3),14(3,R),139(2)]),flip(a)].
% 2.74/3.08 144 join(A,complement(join(B,complement(A)))) = A. [para(22(a,1),143(a,1,2)),rewrite([7(4),22(12)])].
% 2.74/3.08 146 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(144(a,1),14(a,2,2)),rewrite([7(4),7(6)])].
% 2.74/3.08 149 join(complement(A),complement(join(A,B))) = complement(A). [para(131(a,1),144(a,1,2,1,2)),rewrite([7(2)])].
% 2.74/3.08 157 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(131(a,1),36(a,1,2,2))].
% 2.74/3.08 160 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(10(a,1),149(a,1,2,1))].
% 2.74/3.08 211 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),157(a,1,2))].
% 2.74/3.08 215 converse(complement(one)) = complement(one). [para(211(a,1),10(a,2,1)),rewrite([2(7),7(6),211(6)]),flip(a)].
% 2.74/3.08 220 converse(top) = top. [para(215(a,1),76(a,2,2)),rewrite([7(4),4(4),4(6)])].
% 2.74/3.08 2501 join(A,complement(join(A,B))) = join(A,complement(B)). [para(137(a,1),146(a,1,2)),flip(a)].
% 2.74/3.08 2929 join(complement(converse(A)),converse(join(A,B))) = top. [para(160(a,1),103(a,1,2)),rewrite([7(5)])].
% 2.74/3.08 2955 join(A,join(B,converse(complement(converse(A))))) = top. [para(2929(a,1),10(a,2,1)),rewrite([2(6),14(5),7(4),14(5,R),7(4),220(7)])].
% 2.74/3.08 2986 join(A,converse(complement(converse(A)))) = top. [para(139(a,1),2955(a,1,2))].
% 2.74/3.08 3023 join(A,complement(converse(complement(converse(A))))) = A. [para(2986(a,1),2501(a,1,2,1)),rewrite([25(2),132(2)]),flip(a)].
% 2.74/3.08 3024 join(converse(A),complement(converse(complement(A)))) = converse(A). [para(2(a,1),3023(a,1,2,1,1,1))].
% 2.74/3.08 3027 join(A,converse(complement(converse(complement(A))))) = converse(complement(converse(complement(A)))). [para(3023(a,1),22(a,1,2,1)),rewrite([131(9),7(8),2501(8),131(6)])].
% 2.74/3.08 3146 converse(complement(converse(complement(A)))) = A. [para(3024(a,1),10(a,2,1)),rewrite([2(2),3027(5),2(6)])].
% 2.74/3.08 3169 complement(converse(complement(A))) = converse(A). [para(3146(a,1),2(a,1,1)),flip(a)].
% 2.74/3.08 3238 converse(complement(A)) = complement(converse(A)). [para(3169(a,1),131(a,1,1)),flip(a)].
% 2.74/3.08 3240 join(A,composition(complement(converse(composition(B,complement(converse(A))))),B)) = A. [para(3169(a,1),38(a,1,1,1)),rewrite([2(2),3238(2),3238(5),3238(9),131(10),2(9)])].
% 2.74/3.08 3430 converse(composition(A,complement(converse(B)))) = composition(complement(B),converse(A)). [para(3238(a,1),27(a,1,1,2))].
% 2.74/3.08 3507 join(A,composition(complement(composition(complement(A),converse(B))),B)) = A. [back_rewrite(3240),rewrite([3430(4)])].
% 2.74/3.08 9995 join(A,composition(complement(composition(complement(A),B)),converse(B))) = A. [para(2(a,1),3507(a,1,2,1,1,2))].
% 2.74/3.08 11611 join(complement(A),composition(complement(composition(A,B)),converse(B))) = complement(A). [para(131(a,1),9995(a,1,2,1,1,1))].
% 2.74/3.08 11612 $F # answer(goals_14). [resolve(11611,a,24,a)].
% 2.74/3.08
% 2.74/3.08 % SZS output end Refutation
% 2.74/3.08 ============================== end of proof ==========================
% 2.74/3.08
% 2.74/3.08 ============================== STATISTICS ============================
% 2.74/3.08
% 2.74/3.08 Given=638. Generated=108176. Kept=11601. proofs=1.
% 2.74/3.08 Usable=524. Sos=8886. Demods=8942. Limbo=3, Disabled=2201. Hints=0.
% 2.74/3.08 Megabytes=13.82.
% 2.74/3.08 User_CPU=2.06, System_CPU=0.06, Wall_clock=2.
% 2.74/3.08
% 2.74/3.08 ============================== end of statistics =====================
% 2.74/3.08
% 2.74/3.08 ============================== end of search =========================
% 2.74/3.08
% 2.74/3.08 THEOREM PROVED
% 2.74/3.08 % SZS status Unsatisfiable
% 2.74/3.08
% 2.74/3.08 Exiting with 1 proof.
% 2.74/3.08
% 2.74/3.08 Process 3706 exit (max_proofs) Fri Jul 8 15:31:25 2022
% 2.74/3.08 Prover9 interrupted
%------------------------------------------------------------------------------