TSTP Solution File: REL027-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL027-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 19:54:00 EDT 2022
% Result : Unsatisfiable 1.39s 1.67s
% Output : Refutation 1.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL027-2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n011.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 : Fri Jul 8 07:36:09 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.39/1.67 ============================== Prover9 ===============================
% 1.39/1.67 Prover9 (32) version 2009-11A, November 2009.
% 1.39/1.67 Process 4415 was started by sandbox on n011.cluster.edu,
% 1.39/1.67 Fri Jul 8 07:36:10 2022
% 1.39/1.67 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4261_n011.cluster.edu".
% 1.39/1.67 ============================== end of head ===========================
% 1.39/1.67
% 1.39/1.67 ============================== INPUT =================================
% 1.39/1.67
% 1.39/1.67 % Reading from file /tmp/Prover9_4261_n011.cluster.edu
% 1.39/1.67
% 1.39/1.67 set(prolog_style_variables).
% 1.39/1.67 set(auto2).
% 1.39/1.67 % set(auto2) -> set(auto).
% 1.39/1.67 % set(auto) -> set(auto_inference).
% 1.39/1.67 % set(auto) -> set(auto_setup).
% 1.39/1.67 % set(auto_setup) -> set(predicate_elim).
% 1.39/1.67 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.39/1.67 % set(auto) -> set(auto_limits).
% 1.39/1.67 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.39/1.67 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.39/1.67 % set(auto) -> set(auto_denials).
% 1.39/1.67 % set(auto) -> set(auto_process).
% 1.39/1.67 % set(auto2) -> assign(new_constants, 1).
% 1.39/1.67 % set(auto2) -> assign(fold_denial_max, 3).
% 1.39/1.67 % set(auto2) -> assign(max_weight, "200.000").
% 1.39/1.67 % set(auto2) -> assign(max_hours, 1).
% 1.39/1.67 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.39/1.67 % set(auto2) -> assign(max_seconds, 0).
% 1.39/1.67 % set(auto2) -> assign(max_minutes, 5).
% 1.39/1.67 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.39/1.67 % set(auto2) -> set(sort_initial_sos).
% 1.39/1.67 % set(auto2) -> assign(sos_limit, -1).
% 1.39/1.67 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.39/1.67 % set(auto2) -> assign(max_megs, 400).
% 1.39/1.67 % set(auto2) -> assign(stats, some).
% 1.39/1.67 % set(auto2) -> clear(echo_input).
% 1.39/1.67 % set(auto2) -> set(quiet).
% 1.39/1.67 % set(auto2) -> clear(print_initial_clauses).
% 1.39/1.67 % set(auto2) -> clear(print_given).
% 1.39/1.67 assign(lrs_ticks,-1).
% 1.39/1.67 assign(sos_limit,10000).
% 1.39/1.67 assign(order,kbo).
% 1.39/1.67 set(lex_order_vars).
% 1.39/1.67 clear(print_given).
% 1.39/1.67
% 1.39/1.67 % formulas(sos). % not echoed (15 formulas)
% 1.39/1.67
% 1.39/1.67 ============================== end of input ==========================
% 1.39/1.67
% 1.39/1.67 % From the command line: assign(max_seconds, 300).
% 1.39/1.67
% 1.39/1.67 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.39/1.67
% 1.39/1.67 % Formulas that are not ordinary clauses:
% 1.39/1.67
% 1.39/1.67 ============================== end of process non-clausal formulas ===
% 1.39/1.67
% 1.39/1.67 ============================== PROCESS INITIAL CLAUSES ===============
% 1.39/1.67
% 1.39/1.67 ============================== PREDICATE ELIMINATION =================
% 1.39/1.67
% 1.39/1.67 ============================== end predicate elimination =============
% 1.39/1.67
% 1.39/1.67 Auto_denials:
% 1.39/1.67 % copying label goals_15 to answer in negative clause
% 1.39/1.67
% 1.39/1.67 Term ordering decisions:
% 1.39/1.67 Function symbol KB weights: one=1. sk1=1. top=1. zero=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 1.39/1.67
% 1.39/1.67 ============================== end of process initial clauses ========
% 1.39/1.67
% 1.39/1.67 ============================== CLAUSES FOR SEARCH ====================
% 1.39/1.67
% 1.39/1.67 ============================== end of clauses for search =============
% 1.39/1.67
% 1.39/1.67 ============================== SEARCH ================================
% 1.39/1.67
% 1.39/1.67 % Starting search at 0.01 seconds.
% 1.39/1.67
% 1.39/1.67 ============================== PROOF =================================
% 1.39/1.67 % SZS status Unsatisfiable
% 1.39/1.67 % SZS output start Refutation
% 1.39/1.67
% 1.39/1.67 % Proof 1 at 0.66 (+ 0.03) seconds: goals_15.
% 1.39/1.67 % Length of proof is 72.
% 1.39/1.67 % Level of proof is 19.
% 1.39/1.67 % Maximum clause weight is 52.000.
% 1.39/1.67 % Given clauses 365.
% 1.39/1.67
% 1.39/1.67 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 1.39/1.67 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 1.39/1.67 3 join(sk1,one) = one # label(goals_14) # label(negated_conjecture). [assumption].
% 1.39/1.67 4 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 1.39/1.67 5 join(A,complement(A)) = top. [copy(4),flip(a)].
% 1.39/1.67 6 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 1.39/1.67 7 meet(A,complement(A)) = zero. [copy(6),flip(a)].
% 1.39/1.67 8 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 1.39/1.67 9 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 1.39/1.67 10 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 1.39/1.67 11 join(converse(A),converse(B)) = converse(join(A,B)). [copy(10),flip(a)].
% 1.39/1.67 12 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 1.39/1.67 13 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(12),flip(a)].
% 1.39/1.67 14 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 1.39/1.67 15 join(A,join(B,C)) = join(C,join(A,B)). [copy(14),rewrite([8(4)])].
% 1.39/1.67 16 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 1.39/1.67 17 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(16),flip(a)].
% 1.39/1.67 18 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 1.39/1.67 19 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(18),flip(a)].
% 1.39/1.67 20 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 1.39/1.67 21 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(20),rewrite([8(6)])].
% 1.39/1.67 22 A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) # label(maddux3_a_kind_of_de_Morgan_3) # label(axiom). [assumption].
% 1.39/1.67 23 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(22),rewrite([8(6),8(8)]),flip(a),rewrite([8(6)])].
% 1.39/1.67 24 join(meet(complement(sk1),one),meet(complement(composition(sk1,top)),one)) != meet(complement(composition(sk1,top)),one) | join(meet(complement(composition(sk1,top)),one),meet(complement(sk1),one)) != meet(complement(sk1),one) # label(goals_15) # label(negated_conjecture) # answer(goals_15). [assumption].
% 1.39/1.67 25 join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(composition(sk1,top))))) | join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(sk1)))) # answer(goals_15). [copy(24),rewrite([9(4),8(6),9(13),8(15),9(23),8(25),9(33),8(35),9(40),8(42),8(44),9(48),8(50)])].
% 1.39/1.67 26 join(one,sk1) = one. [back_rewrite(3),rewrite([8(3)])].
% 1.39/1.67 27 complement(top) = zero. [back_rewrite(7),rewrite([9(2),5(4)])].
% 1.39/1.67 28 converse(join(A,converse(B))) = join(B,converse(A)). [para(2(a,1),11(a,1,1)),rewrite([8(4)]),flip(a)].
% 1.39/1.67 29 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),13(a,1,1)),flip(a)].
% 1.39/1.67 30 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),13(a,1,2)),flip(a)].
% 1.39/1.67 31 join(A,join(B,complement(A))) = join(B,top). [para(5(a,1),15(a,2,2)),rewrite([8(2)])].
% 1.39/1.67 32 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),17(a,1,1)),flip(a)].
% 1.39/1.67 36 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(17(a,1),19(a,1,1)),rewrite([8(6)])].
% 1.39/1.67 38 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),21(a,1,2,2,1))].
% 1.39/1.67 43 join(zero,complement(join(complement(A),complement(A)))) = A. [para(5(a,1),23(a,1,1,1)),rewrite([27(2)])].
% 1.39/1.67 51 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(27(a,1),23(a,1,2,1,1))].
% 1.39/1.67 52 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(28(a,1),11(a,1,1)),rewrite([8(7),15(7,R),8(6)]),flip(a)].
% 1.39/1.67 53 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(28(a,1),11(a,1,2)),rewrite([15(4,R),8(3),11(3),52(7)]),flip(a)].
% 1.39/1.67 57 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(28(a,1),28(a,2,2)),rewrite([53(4),28(4),15(6,R),8(5)])].
% 1.39/1.67 60 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(29(a,1),11(a,1,1)),rewrite([8(7)]),flip(a)].
% 1.39/1.67 64 composition(converse(one),A) = A. [para(1(a,1),30(a,1,1)),rewrite([2(2)]),flip(a)].
% 1.39/1.67 70 converse(one) = one. [para(64(a,1),1(a,1)),flip(a)].
% 1.39/1.67 72 composition(join(A,one),B) = join(B,composition(A,B)). [para(64(a,1),19(a,1,1)),rewrite([70(4),8(4)]),flip(a)].
% 1.39/1.67 74 join(complement(A),complement(composition(one,A))) = complement(A). [para(64(a,1),21(a,1,2))].
% 1.39/1.67 75 composition(one,A) = A. [para(64(a,1),32(a,2)),rewrite([70(2),32(4)])].
% 1.39/1.67 76 join(complement(A),complement(A)) = complement(A). [back_rewrite(74),rewrite([75(3)])].
% 1.39/1.67 77 join(zero,complement(complement(A))) = A. [back_rewrite(43),rewrite([76(4)])].
% 1.39/1.67 78 converse(join(A,one)) = join(one,converse(A)). [para(70(a,1),11(a,1,1)),rewrite([8(5)]),flip(a)].
% 1.39/1.67 82 join(top,complement(A)) = top. [para(76(a,1),31(a,1,2)),rewrite([5(2),8(4)]),flip(a)].
% 1.39/1.67 83 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(51),rewrite([82(3),27(2)])].
% 1.39/1.67 128 composition(join(one,composition(A,B)),C) = join(C,composition(A,composition(B,C))). [para(75(a,1),36(a,1,2)),rewrite([8(3)]),flip(a)].
% 1.39/1.67 132 join(zero,complement(A)) = complement(A). [para(77(a,1),83(a,1,2,1))].
% 1.39/1.67 133 complement(complement(A)) = A. [back_rewrite(83),rewrite([132(4),132(4)])].
% 1.39/1.67 138 join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(complement(one),composition(sk1,top))) | join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(sk1,complement(one))) # answer(goals_15). [back_rewrite(25),rewrite([133(5),8(4),133(12),133(20),133(26),8(25),133(33),133(39),8(38)])].
% 1.39/1.67 142 join(A,A) = A. [para(133(a,1),76(a,1,1)),rewrite([133(2),133(3)])].
% 1.39/1.67 146 join(A,join(A,B)) = join(A,B). [para(142(a,1),15(a,1)),rewrite([8(3),15(4,R),8(3),15(3,R),142(2)]),flip(a)].
% 1.39/1.67 160 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(133(a,1),38(a,1,2,2))].
% 1.39/1.67 187 composition(join(A,join(B,one)),C) = join(C,composition(join(A,B),C)). [para(72(a,1),19(a,1,2)),rewrite([15(4,R),19(3),8(1)]),flip(a)].
% 1.39/1.67 214 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),160(a,1,2))].
% 1.39/1.67 218 converse(complement(one)) = complement(one). [para(214(a,1),11(a,2,1)),rewrite([2(7),8(6),214(6)]),flip(a)].
% 1.39/1.67 223 converse(top) = top. [para(218(a,1),78(a,2,2)),rewrite([8(4),5(4),5(6)])].
% 1.39/1.67 454 join(one,join(sk1,converse(A))) = join(one,converse(A)). [para(26(a,1),57(a,1,1)),flip(a)].
% 1.39/1.67 1349 join(A,join(one,converse(sk1))) = join(A,one). [para(454(a,1),11(a,2,1)),rewrite([70(2),28(5),15(5,R),8(4),28(9),70(7)])].
% 1.39/1.67 1377 join(one,converse(sk1)) = one. [para(142(a,1),1349(a,2)),rewrite([146(6)])].
% 1.39/1.67 1378 join(A,composition(converse(sk1),A)) = A. [para(1377(a,1),19(a,2,1)),rewrite([75(2),75(6)])].
% 1.39/1.67 1385 join(A,composition(A,sk1)) = A. [para(1378(a,1),60(a,1,1)),rewrite([2(2),2(3),2(4),8(3)]),flip(a)].
% 1.39/1.67 1767 join(A,composition(sk1,A)) = A. [para(1385(a,1),128(a,1,1)),rewrite([75(2),75(4)]),flip(a)].
% 1.39/1.67 1785 join(A,join(B,composition(sk1,A))) = join(A,B). [para(1767(a,1),15(a,2,2)),rewrite([8(3),8(5)])].
% 1.39/1.67 3832 join(A,composition(complement(one),A)) = composition(top,A). [para(38(a,1),187(a,2,2,1)),rewrite([8(7),15(8,R),8(7),38(7),5(4)]),flip(a)].
% 1.39/1.67 3976 join(A,composition(A,complement(one))) = composition(A,top). [para(3832(a,1),60(a,1,1)),rewrite([29(4),223(2),218(5),2(7),8(6)]),flip(a)].
% 1.39/1.67 4369 join(complement(one),composition(sk1,top)) = join(sk1,complement(one)). [para(3976(a,1),1785(a,1,2)),rewrite([8(10)])].
% 1.39/1.67 4371 $F # answer(goals_15). [back_rewrite(138),rewrite([4369(11),142(11),4369(11),4369(22),142(22)]),xx(a),xx(b)].
% 1.39/1.67
% 1.39/1.67 % SZS output end Refutation
% 1.39/1.67 ============================== end of proof ==========================
% 1.39/1.67
% 1.39/1.67 ============================== STATISTICS ============================
% 1.39/1.67
% 1.39/1.67 Given=365. Generated=28340. Kept=4360. proofs=1.
% 1.39/1.67 Usable=310. Sos=3554. Demods=3557. Limbo=2, Disabled=509. Hints=0.
% 1.39/1.67 Megabytes=5.62.
% 1.39/1.67 User_CPU=0.66, System_CPU=0.03, Wall_clock=1.
% 1.39/1.67
% 1.39/1.67 ============================== end of statistics =====================
% 1.39/1.67
% 1.39/1.67 ============================== end of search =========================
% 1.39/1.68
% 1.39/1.68 THEOREM PROVED
% 1.39/1.68 % SZS status Unsatisfiable
% 1.39/1.68
% 1.39/1.68 Exiting with 1 proof.
% 1.39/1.68
% 1.39/1.68 Process 4415 exit (max_proofs) Fri Jul 8 07:36:11 2022
% 1.39/1.68 Prover9 interrupted
%------------------------------------------------------------------------------