TSTP Solution File: REL042-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL042-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 19:54:24 EDT 2022
% Result : Unsatisfiable 38.32s 38.60s
% Output : Refutation 38.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : REL042-1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 8 10:09:21 EDT 2022
% 0.14/0.34 % CPUTime :
% 5.32/5.66 ============================== Prover9 ===============================
% 5.32/5.66 Prover9 (32) version 2009-11A, November 2009.
% 5.32/5.66 Process 26191 was started by sandbox2 on n014.cluster.edu,
% 5.32/5.66 Fri Jul 8 10:09:22 2022
% 5.32/5.66 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_26038_n014.cluster.edu".
% 5.32/5.66 ============================== end of head ===========================
% 5.32/5.66
% 5.32/5.66 ============================== INPUT =================================
% 5.32/5.66
% 5.32/5.66 % Reading from file /tmp/Prover9_26038_n014.cluster.edu
% 5.32/5.66
% 5.32/5.66 set(prolog_style_variables).
% 5.32/5.66 set(auto2).
% 5.32/5.66 % set(auto2) -> set(auto).
% 5.32/5.66 % set(auto) -> set(auto_inference).
% 5.32/5.66 % set(auto) -> set(auto_setup).
% 5.32/5.66 % set(auto_setup) -> set(predicate_elim).
% 5.32/5.66 % set(auto_setup) -> assign(eq_defs, unfold).
% 5.32/5.66 % set(auto) -> set(auto_limits).
% 5.32/5.66 % set(auto_limits) -> assign(max_weight, "100.000").
% 5.32/5.66 % set(auto_limits) -> assign(sos_limit, 20000).
% 5.32/5.66 % set(auto) -> set(auto_denials).
% 5.32/5.66 % set(auto) -> set(auto_process).
% 5.32/5.66 % set(auto2) -> assign(new_constants, 1).
% 5.32/5.66 % set(auto2) -> assign(fold_denial_max, 3).
% 5.32/5.66 % set(auto2) -> assign(max_weight, "200.000").
% 5.32/5.66 % set(auto2) -> assign(max_hours, 1).
% 5.32/5.66 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 5.32/5.66 % set(auto2) -> assign(max_seconds, 0).
% 5.32/5.66 % set(auto2) -> assign(max_minutes, 5).
% 5.32/5.66 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 5.32/5.66 % set(auto2) -> set(sort_initial_sos).
% 5.32/5.66 % set(auto2) -> assign(sos_limit, -1).
% 5.32/5.66 % set(auto2) -> assign(lrs_ticks, 3000).
% 5.32/5.66 % set(auto2) -> assign(max_megs, 400).
% 5.32/5.66 % set(auto2) -> assign(stats, some).
% 5.32/5.66 % set(auto2) -> clear(echo_input).
% 5.32/5.66 % set(auto2) -> set(quiet).
% 5.32/5.66 % set(auto2) -> clear(print_initial_clauses).
% 5.32/5.66 % set(auto2) -> clear(print_given).
% 5.32/5.66 assign(lrs_ticks,-1).
% 5.32/5.66 assign(sos_limit,10000).
% 5.32/5.66 assign(order,kbo).
% 5.32/5.66 set(lex_order_vars).
% 5.32/5.66 clear(print_given).
% 5.32/5.66
% 5.32/5.66 % formulas(sos). % not echoed (15 formulas)
% 5.32/5.66
% 5.32/5.66 ============================== end of input ==========================
% 5.32/5.66
% 5.32/5.66 % From the command line: assign(max_seconds, 300).
% 5.32/5.66
% 5.32/5.66 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 5.32/5.66
% 5.32/5.66 % Formulas that are not ordinary clauses:
% 5.32/5.66
% 5.32/5.66 ============================== end of process non-clausal formulas ===
% 5.32/5.66
% 5.32/5.66 ============================== PROCESS INITIAL CLAUSES ===============
% 5.32/5.66
% 5.32/5.66 ============================== PREDICATE ELIMINATION =================
% 5.32/5.66
% 5.32/5.66 ============================== end predicate elimination =============
% 5.32/5.66
% 5.32/5.66 Auto_denials:
% 5.32/5.66 % copying label goals_15 to answer in negative clause
% 5.32/5.66
% 5.32/5.66 Term ordering decisions:
% 5.32/5.66 Function symbol KB weights: sk1=1. zero=1. one=1. top=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 5.32/5.66
% 5.32/5.66 ============================== end of process initial clauses ========
% 5.32/5.66
% 5.32/5.66 ============================== CLAUSES FOR SEARCH ====================
% 5.32/5.66
% 5.32/5.66 ============================== end of clauses for search =============
% 5.32/5.66
% 5.32/5.66 ============================== SEARCH ================================
% 5.32/5.66
% 5.32/5.66 % Starting search at 0.01 seconds.
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=40.000, iters=3352
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=39.000, iters=3370
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=33.000, iters=3451
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=32.000, iters=3386
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=31.000, iters=3353
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=29.000, iters=3337
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=27.000, iters=3347
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=26.000, iters=3348
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=25.000, iters=3368
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=24.000, iters=3334
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=23.000, iters=3365
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=22.000, iters=3333
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=21.000, iters=3380
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=20.000, iters=3333
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=19.000, iters=3352
% 5.32/5.66
% 5.32/5.66 Low Water (displace): id=3276, wt=46.000
% 5.32/5.66
% 5.32/5.66 Low Water (displace): id=5828, wt=41.000
% 5.32/5.66
% 5.32/5.66 Low Water (displace): id=5804, wt=40.000
% 5.32/5.66
% 5.32/5.66 Low Water (displace): id=6576, wt=39.000
% 5.32/5.66
% 5.32/5.66 Low Water (displace): id=5797, wt=38.000
% 5.32/5.66
% 5.32/5.66 Low Water (displace): id=13111, wt=17.000
% 5.32/5.66
% 5.32/5.66 Low Water (displace): id=13127, wt=16.000
% 5.32/5.66
% 5.32/5.66 Low Water (displace): id=13264, wt=15.000
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=18.000, iters=3335
% 5.32/5.66
% 5.32/5.66 Low Water (displace): id=13934, wt=14.000
% 5.32/5.66
% 5.32/5.66 Low Water (displace): id=14011, wt=13.000
% 5.32/5.66
% 5.32/5.66 Low Water (displace): id=15851, wt=11.000
% 5.32/5.66
% 5.32/5.66 Low Water (keep): wt=17.000, iters=3343
% 38.32/38.60
% 38.32/38.60 Low Water (keep): wt=16.000, iters=3338
% 38.32/38.60
% 38.32/38.60 ============================== PROOF =================================
% 38.32/38.60 % SZS status Unsatisfiable
% 38.32/38.60 % SZS output start Refutation
% 38.32/38.60
% 38.32/38.60 % Proof 1 at 36.42 (+ 1.20) seconds: goals_15.
% 38.32/38.60 % Length of proof is 134.
% 38.32/38.60 % Level of proof is 28.
% 38.32/38.60 % Maximum clause weight is 21.000.
% 38.32/38.60 % Given clauses 2775.
% 38.32/38.60
% 38.32/38.60 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 38.32/38.60 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 38.32/38.60 3 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 38.32/38.60 4 join(A,complement(A)) = top. [copy(3),flip(a)].
% 38.32/38.60 5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 38.32/38.60 6 meet(A,complement(A)) = zero. [copy(5),flip(a)].
% 38.32/38.60 7 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 38.32/38.60 8 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 38.32/38.60 9 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 38.32/38.60 10 join(converse(A),converse(B)) = converse(join(A,B)). [copy(9),flip(a)].
% 38.32/38.60 11 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 38.32/38.60 12 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(11),flip(a)].
% 38.32/38.60 13 meet(composition(sk1,A),composition(sk1,complement(A))) = zero # label(goals_14) # label(negated_conjecture). [assumption].
% 38.32/38.60 14 complement(join(complement(composition(sk1,A)),complement(composition(sk1,complement(A))))) = zero. [copy(13),rewrite([8(6)])].
% 38.32/38.60 15 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 38.32/38.60 16 join(A,join(B,C)) = join(C,join(A,B)). [copy(15),rewrite([7(4)])].
% 38.32/38.60 17 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 38.32/38.60 18 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(17),flip(a)].
% 38.32/38.60 19 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 38.32/38.60 20 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(19),flip(a)].
% 38.32/38.60 21 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 38.32/38.60 22 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(21),rewrite([7(6)])].
% 38.32/38.60 23 A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) # label(maddux3_a_kind_of_de_Morgan_3) # label(axiom). [assumption].
% 38.32/38.60 24 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(23),rewrite([7(6),7(8)]),flip(a),rewrite([7(6)])].
% 38.32/38.60 25 join(composition(converse(sk1),sk1),one) != one # label(goals_15) # label(negated_conjecture) # answer(goals_15). [assumption].
% 38.32/38.60 26 join(one,composition(converse(sk1),sk1)) != one # answer(goals_15). [copy(25),rewrite([7(6)])].
% 38.32/38.60 27 complement(top) = zero. [back_rewrite(6),rewrite([8(2),4(4)])].
% 38.32/38.60 28 converse(join(A,converse(B))) = join(B,converse(A)). [para(2(a,1),10(a,1,1)),rewrite([7(4)]),flip(a)].
% 38.32/38.60 29 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),12(a,1,1)),flip(a)].
% 38.32/38.60 30 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),12(a,1,2)),flip(a)].
% 38.32/38.60 31 complement(join(complement(sk1),complement(composition(sk1,complement(one))))) = zero. [para(1(a,1),14(a,1,1,1,1))].
% 38.32/38.60 34 join(A,join(B,complement(A))) = join(B,top). [para(4(a,1),16(a,2,2)),rewrite([7(2)])].
% 38.32/38.60 35 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),18(a,1,1)),flip(a)].
% 38.32/38.60 37 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(12(a,1),20(a,1,1)),rewrite([7(7)])].
% 38.32/38.60 39 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(18(a,1),20(a,1,1)),rewrite([7(6)])].
% 38.32/38.60 41 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),22(a,1,2,2,1))].
% 38.32/38.60 43 join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)). [para(22(a,1),10(a,2,1)),rewrite([30(7)])].
% 38.32/38.60 47 join(zero,complement(join(complement(A),complement(A)))) = A. [para(4(a,1),24(a,1,1,1)),rewrite([27(2)])].
% 38.32/38.60 50 join(complement(composition(sk1,A)),complement(composition(sk1,complement(A)))) = join(complement(join(B,zero)),complement(join(zero,complement(B)))). [para(14(a,1),24(a,1,1,1,2)),rewrite([14(13),7(6)]),flip(a)].
% 38.32/38.60 53 join(zero,complement(join(composition(sk1,A),complement(composition(sk1,complement(A)))))) = composition(sk1,complement(A)). [para(14(a,1),24(a,1,2)),rewrite([7(10)])].
% 38.32/38.60 55 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(24(a,1),24(a,1,2,1)),rewrite([7(10)])].
% 38.32/38.60 56 join(complement(composition(sk1,A)),complement(composition(sk1,complement(A)))) = c_0. [new_symbol(50)].
% 38.32/38.60 58 join(complement(join(A,zero)),complement(join(zero,complement(A)))) = c_0. [back_rewrite(50),rewrite([56(8)]),flip(a)].
% 38.32/38.60 63 join(zero,top) = top. [para(27(a,1),4(a,1,2)),rewrite([7(3)])].
% 38.32/38.60 65 c_0 = top. [para(27(a,1),24(a,1,1,1,2)),rewrite([27(6),7(6),58(8)])].
% 38.32/38.60 66 join(complement(join(zero,complement(A))),complement(join(top,complement(A)))) = A. [para(27(a,1),24(a,1,2,1,1)),rewrite([7(9)])].
% 38.32/38.60 68 join(complement(join(A,zero)),complement(join(zero,complement(A)))) = top. [back_rewrite(58),rewrite([65(9)])].
% 38.32/38.60 69 join(complement(composition(sk1,A)),complement(composition(sk1,complement(A)))) = top. [back_rewrite(56),rewrite([65(9)])].
% 38.32/38.60 70 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(28(a,1),10(a,1,1)),rewrite([7(7),16(7,R),7(6)]),flip(a)].
% 38.32/38.60 71 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(28(a,1),10(a,1,2)),rewrite([16(4,R),7(3),10(3),70(7)]),flip(a)].
% 38.32/38.60 75 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(28(a,1),28(a,2,2)),rewrite([71(4),28(4),16(6,R),7(5)])].
% 38.32/38.60 78 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(29(a,1),10(a,1,1)),rewrite([7(7)]),flip(a)].
% 38.32/38.60 82 composition(converse(one),A) = A. [para(1(a,1),30(a,1,1)),rewrite([2(2)]),flip(a)].
% 38.32/38.60 86 converse(one) = one. [para(82(a,1),1(a,1)),flip(a)].
% 38.32/38.60 88 composition(join(A,one),B) = join(B,composition(A,B)). [para(82(a,1),20(a,1,1)),rewrite([86(4),7(4)]),flip(a)].
% 38.32/38.60 90 join(complement(A),complement(composition(one,A))) = complement(A). [para(82(a,1),22(a,1,2))].
% 38.32/38.60 91 composition(one,A) = A. [para(82(a,1),35(a,2)),rewrite([86(2),35(4)])].
% 38.32/38.60 92 join(complement(A),complement(A)) = complement(A). [back_rewrite(90),rewrite([91(3)])].
% 38.32/38.60 93 join(zero,complement(complement(A))) = A. [back_rewrite(47),rewrite([92(4)])].
% 38.32/38.60 94 converse(join(A,one)) = join(one,converse(A)). [para(86(a,1),10(a,1,1)),rewrite([7(5)]),flip(a)].
% 38.32/38.60 98 join(complement(sk1),complement(composition(sk1,complement(one)))) = top. [para(31(a,1),24(a,1,1,1,2)),rewrite([31(13),7(6),68(8)]),flip(a)].
% 38.32/38.60 100 join(zero,complement(join(sk1,complement(composition(sk1,complement(one)))))) = composition(sk1,complement(one)). [para(31(a,1),24(a,1,2)),rewrite([7(10)])].
% 38.32/38.60 106 composition(join(one,converse(A)),converse(B)) = converse(composition(B,join(A,one))). [para(94(a,1),12(a,1,1))].
% 38.32/38.60 111 join(top,complement(A)) = top. [para(92(a,1),34(a,1,2)),rewrite([4(2),7(4)]),flip(a)].
% 38.32/38.60 112 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(66),rewrite([111(7),27(6),7(6)])].
% 38.32/38.60 113 join(top,top) = join(A,top). [para(111(a,1),34(a,1,2)),flip(a)].
% 38.32/38.60 118 join(top,top) = top. [para(113(a,2),63(a,1))].
% 38.32/38.60 120 join(A,top) = top. [para(113(a,2),34(a,2)),rewrite([34(3),118(5)])].
% 38.32/38.60 122 join(A,join(B,complement(A))) = top. [back_rewrite(34),rewrite([120(5)])].
% 38.32/38.60 128 join(zero,complement(A)) = complement(A). [para(93(a,1),112(a,1,2,1))].
% 38.32/38.60 129 complement(complement(A)) = A. [back_rewrite(112),rewrite([128(4),128(4)])].
% 38.32/38.60 130 complement(join(sk1,complement(composition(sk1,complement(one))))) = composition(sk1,complement(one)). [back_rewrite(100),rewrite([128(10)])].
% 38.32/38.60 132 join(A,zero) = A. [back_rewrite(93),rewrite([129(3),7(2)])].
% 38.32/38.60 133 complement(join(composition(sk1,A),complement(composition(sk1,complement(A))))) = composition(sk1,complement(A)). [back_rewrite(53),rewrite([128(10)])].
% 38.32/38.60 138 join(A,composition(converse(B),complement(composition(B,complement(A))))) = A. [para(129(a,1),22(a,1,1)),rewrite([129(8)])].
% 38.32/38.60 139 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(129(a,1),24(a,1,1,1,2)),rewrite([129(5),7(4)])].
% 38.32/38.60 141 join(A,A) = A. [para(129(a,1),92(a,1,1)),rewrite([129(2),129(3)])].
% 38.32/38.60 148 converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))). [para(91(a,1),37(a,1,2)),rewrite([7(4),10(4),106(8)]),flip(a)].
% 38.32/38.60 150 join(A,join(A,B)) = join(A,B). [para(141(a,1),16(a,1)),rewrite([7(3),16(4,R),7(3),16(3,R),141(2)]),flip(a)].
% 38.32/38.60 151 join(A,complement(join(B,complement(A)))) = A. [para(24(a,1),150(a,1,2)),rewrite([7(4),24(12)])].
% 38.32/38.60 153 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(151(a,1),16(a,2,2)),rewrite([7(4),7(6)])].
% 38.32/38.60 156 join(complement(A),complement(join(A,B))) = complement(A). [para(129(a,1),151(a,1,2,1,2)),rewrite([7(2)])].
% 38.32/38.60 164 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(10(a,1),156(a,1,2,1))].
% 38.32/38.60 169 composition(join(one,composition(A,B)),C) = join(C,composition(A,composition(B,C))). [para(91(a,1),39(a,1,2)),rewrite([7(3)]),flip(a)].
% 38.32/38.60 171 join(complement(one),composition(A,complement(converse(A)))) = complement(one). [para(2(a,1),41(a,1,2,1))].
% 38.32/38.60 178 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(129(a,1),41(a,1,2,2))].
% 38.32/38.60 197 composition(join(A,join(B,one)),C) = join(C,composition(join(A,B),C)). [para(88(a,1),20(a,1,2)),rewrite([16(4,R),20(3),7(1)]),flip(a)].
% 38.32/38.60 225 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),178(a,1,2))].
% 38.32/38.60 229 converse(complement(one)) = complement(one). [para(225(a,1),10(a,2,1)),rewrite([2(7),7(6),225(6)]),flip(a)].
% 38.32/38.60 231 converse(composition(A,complement(one))) = composition(complement(one),converse(A)). [para(229(a,1),12(a,1,1)),flip(a)].
% 38.32/38.60 234 converse(top) = top. [para(229(a,1),94(a,2,2)),rewrite([7(4),4(4),4(6)])].
% 38.32/38.60 243 join(top,converse(A)) = top. [para(234(a,1),10(a,1,1)),rewrite([7(5),120(5),234(5)])].
% 38.32/38.60 244 converse(composition(A,top)) = composition(top,converse(A)). [para(234(a,1),12(a,1,1)),flip(a)].
% 38.32/38.60 248 join(top,composition(A,converse(B))) = top. [para(29(a,1),243(a,1,2))].
% 38.32/38.60 250 join(top,composition(A,B)) = top. [para(2(a,1),248(a,1,2,2))].
% 38.32/38.60 257 join(converse(A),composition(top,converse(B))) = converse(join(A,composition(B,top))). [para(244(a,1),10(a,1,2))].
% 38.32/38.60 323 join(complement(A),complement(join(B,A))) = complement(A). [para(151(a,1),55(a,2)),rewrite([129(2),129(4),129(8),55(13)])].
% 38.32/38.60 324 join(sk1,complement(composition(sk1,complement(one)))) = complement(composition(sk1,complement(one))). [para(98(a,1),55(a,1,2,1,1)),rewrite([129(9),130(14),250(11),27(7),7(7),128(7),129(8)]),flip(a)].
% 38.32/38.60 363 join(composition(sk1,A),complement(composition(sk1,complement(A)))) = complement(composition(sk1,complement(A))). [para(69(a,1),55(a,1,2,1,1)),rewrite([129(9),133(13),250(9),27(6),7(6),128(6),129(8)]),flip(a)].
% 38.32/38.60 504 join(join(A,B),composition(C,converse(D))) = join(A,join(B,composition(C,converse(D)))). [para(29(a,1),75(a,1,2)),rewrite([29(7)])].
% 38.32/38.60 559 join(one,complement(composition(A,complement(converse(A))))) = complement(composition(A,complement(converse(A)))). [para(171(a,1),323(a,1,2,1)),rewrite([129(7),7(6)])].
% 38.32/38.60 1548 composition(A,join(B,one)) = join(A,composition(A,B)). [para(148(a,1),2(a,1,1)),rewrite([2(4)]),flip(a)].
% 38.32/38.60 1650 composition(converse(complement(composition(A,complement(converse(A))))),A) = A. [para(138(a,1),148(a,2,1)),rewrite([7(7),559(7),30(7),2(8)])].
% 38.32/38.60 1769 join(A,complement(join(A,B))) = join(A,complement(B)). [para(139(a,1),153(a,1,2)),flip(a)].
% 38.32/38.60 1923 join(A,composition(A,join(B,one))) = join(A,composition(A,B)). [para(1548(a,2),150(a,1,2))].
% 38.32/38.60 2011 composition(A,complement(composition(converse(A),complement(A)))) = A. [para(1650(a,1),29(a,1,1)),rewrite([2(2),2(3),2(6)]),flip(a)].
% 38.32/38.60 2202 join(complement(converse(A)),converse(join(A,B))) = top. [para(164(a,1),122(a,1,2)),rewrite([7(5)])].
% 38.32/38.60 2225 join(A,join(B,converse(complement(converse(A))))) = top. [para(2202(a,1),10(a,2,1)),rewrite([2(6),16(5),7(4),16(5,R),7(4),234(7)])].
% 38.32/38.60 2254 join(A,converse(complement(converse(A)))) = top. [para(141(a,1),2225(a,1,2))].
% 38.32/38.60 2291 join(A,complement(converse(complement(converse(A))))) = A. [para(2254(a,1),1769(a,1,2,1)),rewrite([27(2),132(2)]),flip(a)].
% 38.32/38.60 2292 join(converse(A),complement(converse(complement(A)))) = converse(A). [para(2(a,1),2291(a,1,2,1,1,1))].
% 38.32/38.60 2295 join(A,converse(complement(converse(complement(A))))) = converse(complement(converse(complement(A)))). [para(2291(a,1),24(a,1,2,1)),rewrite([129(9),7(8),1769(8),129(6)])].
% 38.32/38.60 2394 converse(complement(converse(complement(A)))) = A. [para(2292(a,1),10(a,2,1)),rewrite([2(2),2295(5),2(6)])].
% 38.32/38.60 2414 complement(converse(complement(A))) = converse(A). [para(2394(a,1),2(a,1,1)),flip(a)].
% 38.32/38.60 2475 converse(complement(A)) = complement(converse(A)). [para(2414(a,1),129(a,1,1)),flip(a)].
% 38.32/38.60 2477 join(A,composition(complement(converse(composition(B,complement(converse(A))))),B)) = A. [para(2414(a,1),43(a,1,1,1)),rewrite([2(2),2475(2),2475(5),2475(9),129(10),2(9)])].
% 38.32/38.60 2610 join(converse(A),complement(converse(B))) = converse(join(A,complement(B))). [para(2475(a,1),10(a,1,2))].
% 38.32/38.60 2615 converse(composition(A,complement(converse(B)))) = composition(complement(B),converse(A)). [para(2475(a,1),29(a,1,1,2))].
% 38.32/38.60 2682 join(A,composition(complement(composition(complement(A),converse(B))),B)) = A. [back_rewrite(2477),rewrite([2615(4)])].
% 38.32/38.60 3127 composition(join(one,composition(A,B)),A) = composition(A,join(one,composition(B,A))). [para(169(a,2),1548(a,2)),rewrite([7(3)]),flip(a)].
% 38.32/38.60 4583 join(A,composition(complement(one),A)) = composition(top,A). [para(41(a,1),197(a,2,2,1)),rewrite([7(7),16(8,R),7(7),41(7),4(4)]),flip(a)].
% 38.32/38.60 4638 join(A,composition(A,complement(one))) = composition(A,top). [para(4583(a,1),78(a,1,1)),rewrite([29(4),234(2),2475(5),86(4),2(7),7(6)]),flip(a)].
% 38.32/38.60 4642 join(A,complement(composition(complement(one),A))) = join(A,complement(composition(top,A))). [para(4583(a,1),1769(a,1,2,1)),flip(a)].
% 38.32/38.60 4652 join(A,complement(composition(A,complement(one)))) = join(A,complement(composition(A,top))). [para(4638(a,1),1769(a,1,2,1)),flip(a)].
% 38.32/38.60 4656 join(sk1,complement(composition(sk1,top))) = complement(composition(sk1,complement(one))). [back_rewrite(324),rewrite([4652(7)])].
% 38.32/38.60 7183 join(converse(A),complement(composition(top,converse(B)))) = converse(join(A,complement(composition(B,top)))). [para(257(a,1),1769(a,1,2,1)),rewrite([2610(7),1769(5)]),flip(a)].
% 38.32/38.60 9259 join(A,composition(complement(composition(complement(one),converse(B))),composition(B,A))) = A. [para(2682(a,1),169(a,1,1)),rewrite([91(2)]),flip(a)].
% 38.32/38.60 9952 join(complement(sk1),composition(sk1,composition(converse(sk1),complement(sk1)))) = complement(sk1). [para(2011(a,1),363(a,1,2,1)),rewrite([7(10),2011(18)])].
% 38.32/38.60 14933 join(A,composition(A,join(one,composition(B,A)))) = composition(A,join(one,composition(B,A))). [para(169(a,2),1923(a,2)),rewrite([7(3),3127(9)])].
% 38.32/38.60 16570 join(join(A,B),composition(C,D)) = join(A,join(B,composition(C,D))). [para(2(a,1),504(a,1,2,2)),rewrite([2(5)])].
% 38.32/38.60 20528 composition(join(one,composition(sk1,converse(sk1))),complement(sk1)) = complement(sk1). [para(9952(a,1),169(a,2))].
% 38.32/38.60 20545 composition(sk1,join(one,composition(converse(sk1),sk1))) = sk1. [para(20528(a,1),22(a,1,2,2,1)),rewrite([129(3),78(8),86(7),7(7),129(10),3127(9),14933(10),129(11)])].
% 38.32/38.60 31351 join(one,composition(converse(sk1),sk1)) = one. [para(20545(a,1),9259(a,1,2,2)),rewrite([16570(15),20(14),4642(10),7183(9),4656(7),2475(7),231(6),2682(10)]),flip(a)].
% 38.32/38.60 31352 $F # answer(goals_15). [resolve(31351,a,26,a)].
% 38.32/38.60
% 38.32/38.60 % SZS output end Refutation
% 38.32/38.60 ============================== end of proof ==========================
% 38.32/38.60
% 38.32/38.60 ============================== STATISTICS ============================
% 38.32/38.60
% 38.32/38.60 Given=2775. Generated=2161872. Kept=31340. proofs=1.
% 38.32/38.60 Usable=2429. Sos=9995. Demods=12270. Limbo=2, Disabled=18928. Hints=0.
% 38.32/38.60 Megabytes=24.45.
% 38.32/38.60 User_CPU=36.42, System_CPU=1.20, Wall_clock=37.
% 38.32/38.60
% 38.32/38.60 ============================== end of statistics =====================
% 38.32/38.60
% 38.32/38.60 ============================== end of search =========================
% 38.32/38.60
% 38.32/38.60 THEOREM PROVED
% 38.32/38.60 % SZS status Unsatisfiable
% 38.32/38.60
% 38.32/38.60 Exiting with 1 proof.
% 38.32/38.60
% 38.32/38.60 Process 26191 exit (max_proofs) Fri Jul 8 10:09:59 2022
% 38.32/38.60 Prover9 interrupted
%------------------------------------------------------------------------------