TSTP Solution File: REL028+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL028+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 19:54:02 EDT 2022
% Result : Theorem 56.66s 56.94s
% Output : Refutation 56.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : REL028+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Fri Jul 8 10:33:25 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.49/1.05 ============================== Prover9 ===============================
% 0.49/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.49/1.05 Process 20114 was started by sandbox on n018.cluster.edu,
% 0.49/1.05 Fri Jul 8 10:33:26 2022
% 0.49/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19961_n018.cluster.edu".
% 0.49/1.05 ============================== end of head ===========================
% 0.49/1.05
% 0.49/1.05 ============================== INPUT =================================
% 0.49/1.05
% 0.49/1.05 % Reading from file /tmp/Prover9_19961_n018.cluster.edu
% 0.49/1.05
% 0.49/1.05 set(prolog_style_variables).
% 0.49/1.05 set(auto2).
% 0.49/1.05 % set(auto2) -> set(auto).
% 0.49/1.05 % set(auto) -> set(auto_inference).
% 0.49/1.05 % set(auto) -> set(auto_setup).
% 0.49/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.49/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.49/1.05 % set(auto) -> set(auto_limits).
% 0.49/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.49/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.49/1.05 % set(auto) -> set(auto_denials).
% 0.49/1.05 % set(auto) -> set(auto_process).
% 0.49/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.49/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.49/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.49/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.49/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.49/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.49/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.49/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.49/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.49/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.49/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.49/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.49/1.06 % set(auto2) -> assign(stats, some).
% 0.49/1.06 % set(auto2) -> clear(echo_input).
% 0.49/1.06 % set(auto2) -> set(quiet).
% 0.49/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.49/1.06 % set(auto2) -> clear(print_given).
% 0.49/1.06 assign(lrs_ticks,-1).
% 0.49/1.06 assign(sos_limit,10000).
% 0.49/1.06 assign(order,kbo).
% 0.49/1.06 set(lex_order_vars).
% 0.49/1.06 clear(print_given).
% 0.49/1.06
% 0.49/1.06 % formulas(sos). % not echoed (14 formulas)
% 0.49/1.06
% 0.49/1.06 ============================== end of input ==========================
% 0.49/1.06
% 0.49/1.06 % From the command line: assign(max_seconds, 300).
% 0.49/1.06
% 0.49/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.49/1.06
% 0.49/1.06 % Formulas that are not ordinary clauses:
% 0.49/1.06 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 2 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 3 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 4 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 5 (all X0 all X1 all X2 composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 7 (all X0 all X1 all X2 composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))) # label(composition_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 11 (all X0 all X1 join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1)) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 56.66/56.94 14 -(all X0 all X1 (join(X0,one) = one & join(X1,one) = one -> composition(X0,X1) = meet(X0,X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 56.66/56.94
% 56.66/56.94 ============================== end of process non-clausal formulas ===
% 56.66/56.94
% 56.66/56.94 ============================== PROCESS INITIAL CLAUSES ===============
% 56.66/56.94
% 56.66/56.94 ============================== PREDICATE ELIMINATION =================
% 56.66/56.94
% 56.66/56.94 ============================== end predicate elimination =============
% 56.66/56.94
% 56.66/56.94 Auto_denials:
% 56.66/56.94 % copying label goals to answer in negative clause
% 56.66/56.94
% 56.66/56.94 Term ordering decisions:
% 56.66/56.94 Function symbol KB weights: one=1. top=1. zero=1. c1=1. c2=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 56.66/56.94
% 56.66/56.94 ============================== end of process initial clauses ========
% 56.66/56.94
% 56.66/56.94 ============================== CLAUSES FOR SEARCH ====================
% 56.66/56.94
% 56.66/56.94 ============================== end of clauses for search =============
% 56.66/56.94
% 56.66/56.94 ============================== SEARCH ================================
% 56.66/56.94
% 56.66/56.94 % Starting search at 0.01 seconds.
% 56.66/56.94
% 56.66/56.94 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 32 (0.00 of 0.92 sec).
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=38.000, iters=3361
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=35.000, iters=3378
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=33.000, iters=3343
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=32.000, iters=3345
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=31.000, iters=3355
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=30.000, iters=3400
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=29.000, iters=3374
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=28.000, iters=3350
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=27.000, iters=3445
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=26.000, iters=3400
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=25.000, iters=3335
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=24.000, iters=3351
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=23.000, iters=3354
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=22.000, iters=3358
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=21.000, iters=3346
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=20.000, iters=3350
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=19.000, iters=3440
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=18.000, iters=3368
% 56.66/56.94
% 56.66/56.94 Low Water (displace): id=5885, wt=45.000
% 56.66/56.94
% 56.66/56.94 Low Water (displace): id=6042, wt=44.000
% 56.66/56.94
% 56.66/56.94 Low Water (displace): id=6200, wt=43.000
% 56.66/56.94
% 56.66/56.94 Low Water (displace): id=6020, wt=41.000
% 56.66/56.94
% 56.66/56.94 Low Water (displace): id=4493, wt=40.000
% 56.66/56.94
% 56.66/56.94 Low Water (displace): id=5605, wt=39.000
% 56.66/56.94
% 56.66/56.94 Low Water (displace): id=6043, wt=38.000
% 56.66/56.94
% 56.66/56.94 Low Water (displace): id=14432, wt=14.000
% 56.66/56.94
% 56.66/56.94 Low Water (displace): id=14433, wt=13.000
% 56.66/56.94
% 56.66/56.94 Low Water (displace): id=14696, wt=12.000
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=17.000, iters=3335
% 56.66/56.94
% 56.66/56.94 Low Water (displace): id=16053, wt=11.000
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=16.000, iters=3335
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=15.000, iters=3333
% 56.66/56.94
% 56.66/56.94 Low Water (keep): wt=14.000, iters=3341
% 56.66/56.94
% 56.66/56.94 ============================== PROOF =================================
% 56.66/56.94 % SZS status Theorem
% 56.66/56.94 % SZS output start Refutation
% 56.66/56.94
% 56.66/56.94 % Proof 1 at 54.44 (+ 1.45) seconds: goals.
% 56.66/56.94 % Length of proof is 125.
% 56.66/56.94 % Level of proof is 32.
% 56.66/56.94 % Maximum clause weight is 24.000.
% 56.66/56.94 % Given clauses 4653.
% 56.66/56.94
% 56.66/56.94 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 56.66/56.94 2 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause). [assumption].
% 56.66/56.94 3 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption].
% 56.66/56.94 4 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption].
% 56.66/56.94 5 (all X0 all X1 all X2 composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption].
% 56.66/56.94 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 56.66/56.94 7 (all X0 all X1 all X2 composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))) # label(composition_distributivity) # label(axiom) # label(non_clause). [assumption].
% 56.66/56.94 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 56.66/56.94 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 56.66/56.94 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 56.66/56.94 11 (all X0 all X1 join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1)) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption].
% 56.66/56.94 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 56.66/56.94 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 56.66/56.94 14 -(all X0 all X1 (join(X0,one) = one & join(X1,one) = one -> composition(X0,X1) = meet(X0,X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 56.66/56.94 15 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 56.66/56.94 16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 56.66/56.94 17 join(c1,one) = one # label(goals) # label(negated_conjecture). [clausify(14)].
% 56.66/56.94 18 join(c2,one) = one # label(goals) # label(negated_conjecture). [clausify(14)].
% 56.66/56.94 19 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 56.66/56.94 20 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 56.66/56.94 21 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 56.66/56.94 22 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 56.66/56.94 23 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 56.66/56.94 24 join(converse(A),converse(B)) = converse(join(A,B)). [copy(23),flip(a)].
% 56.66/56.94 25 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 56.66/56.94 26 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(25),flip(a)].
% 56.66/56.94 27 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 56.66/56.94 28 join(A,join(B,C)) = join(C,join(A,B)). [copy(27),rewrite([21(2)]),flip(a)].
% 56.66/56.94 29 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 56.66/56.94 30 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 56.66/56.94 31 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(30),flip(a)].
% 56.66/56.94 32 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 56.66/56.94 33 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(32),rewrite([21(7)]),flip(a)].
% 56.66/56.94 34 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 56.66/56.94 35 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(34),rewrite([21(6),21(8)]),rewrite([21(6)])].
% 56.66/56.94 36 composition(c1,c2) != meet(c1,c2) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)].
% 56.66/56.94 37 complement(join(complement(c1),complement(c2))) != composition(c1,c2) # answer(goals). [copy(36),rewrite([22(6)]),flip(a)].
% 56.66/56.94 38 join(one,c2) = one. [back_rewrite(18),rewrite([21(3)])].
% 56.66/56.94 39 join(one,c1) = one. [back_rewrite(17),rewrite([21(3)])].
% 56.66/56.94 40 complement(top) = zero. [back_rewrite(20),rewrite([22(2),19(4)])].
% 56.66/56.94 41 converse(join(A,converse(B))) = join(B,converse(A)). [para(16(a,1),24(a,1,1)),rewrite([21(4)]),flip(a)].
% 56.66/56.94 42 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(16(a,1),26(a,1,1)),flip(a)].
% 56.66/56.94 43 converse(composition(converse(A),B)) = composition(converse(B),A). [para(16(a,1),26(a,1,2)),flip(a)].
% 56.66/56.94 44 join(A,join(B,complement(A))) = join(B,top). [para(19(a,1),28(a,2,2)),rewrite([21(2)])].
% 56.66/56.94 45 composition(A,composition(one,B)) = composition(A,B). [para(15(a,1),29(a,1,1)),flip(a)].
% 56.66/56.94 47 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(26(a,1),31(a,1,1)),rewrite([21(7)])].
% 56.66/56.94 51 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(15(a,1),33(a,1,2,2,1))].
% 56.66/56.94 56 join(zero,complement(join(complement(A),complement(A)))) = A. [para(19(a,1),35(a,1,1,1)),rewrite([40(2)])].
% 56.66/56.94 60 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(35(a,1),35(a,1,2,1)),rewrite([21(10)])].
% 56.66/56.94 64 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(40(a,1),35(a,1,2,1,1))].
% 56.66/56.94 65 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(41(a,1),24(a,1,1)),rewrite([21(7),28(7,R),21(6)]),flip(a)].
% 56.66/56.94 66 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(41(a,1),24(a,1,2)),rewrite([28(4,R),21(3),24(3),65(7)]),flip(a)].
% 56.66/56.94 70 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(41(a,1),41(a,2,2)),rewrite([66(4),41(4),28(6,R),21(5)])].
% 56.66/56.94 71 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(65),rewrite([70(8),24(7)])].
% 56.66/56.94 73 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(42(a,1),24(a,1,1)),rewrite([21(7)]),flip(a)].
% 56.66/56.94 77 composition(converse(one),A) = A. [para(15(a,1),43(a,1,1)),rewrite([16(2)]),flip(a)].
% 56.66/56.94 83 converse(one) = one. [para(77(a,1),15(a,1)),flip(a)].
% 56.66/56.94 85 composition(join(A,one),B) = join(B,composition(A,B)). [para(77(a,1),31(a,1,1)),rewrite([83(4),21(4)]),flip(a)].
% 56.66/56.94 87 join(complement(A),complement(composition(one,A))) = complement(A). [para(77(a,1),33(a,1,2))].
% 56.66/56.94 88 composition(one,A) = A. [para(77(a,1),45(a,2)),rewrite([83(2),45(4)])].
% 56.66/56.94 89 join(complement(A),complement(A)) = complement(A). [back_rewrite(87),rewrite([88(3)])].
% 56.66/56.94 90 join(zero,complement(complement(A))) = A. [back_rewrite(56),rewrite([89(4)])].
% 56.66/56.94 91 converse(join(A,one)) = join(one,converse(A)). [para(83(a,1),24(a,1,1)),rewrite([21(5)]),flip(a)].
% 56.66/56.94 95 join(top,complement(A)) = top. [para(89(a,1),44(a,1,2)),rewrite([19(2),21(4)]),flip(a)].
% 56.66/56.94 96 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(64),rewrite([95(3),40(2)])].
% 56.66/56.94 97 join(top,top) = join(A,top). [para(95(a,1),44(a,1,2)),flip(a)].
% 56.66/56.94 102 join(A,top) = join(B,top). [para(97(a,1),44(a,2)),rewrite([95(3)])].
% 56.66/56.94 103 join(A,top) = c_0. [new_symbol(102)].
% 56.66/56.94 106 join(A,join(B,complement(A))) = c_0. [back_rewrite(44),rewrite([103(5)])].
% 56.66/56.94 112 converse(join(A,composition(A,B))) = composition(join(one,converse(B)),converse(A)). [para(88(a,1),47(a,1,2)),rewrite([21(4),24(4)])].
% 56.66/56.94 117 c_0 = top. [para(90(a,1),106(a,1,2)),rewrite([21(2),19(2)]),flip(a)].
% 56.66/56.94 118 join(A,join(B,complement(A))) = top. [back_rewrite(106),rewrite([117(4)])].
% 56.66/56.94 120 join(A,top) = top. [back_rewrite(103),rewrite([117(3)])].
% 56.66/56.94 130 converse(join(A,join(B,one))) = join(one,converse(join(A,B))). [para(91(a,1),24(a,1,1)),rewrite([70(5),24(4),21(7),28(7,R),21(6)]),flip(a)].
% 56.66/56.94 131 composition(join(one,converse(A)),converse(B)) = converse(composition(B,join(A,one))). [para(91(a,1),26(a,1,1))].
% 56.66/56.94 138 converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))). [back_rewrite(112),rewrite([131(8)]),flip(a)].
% 56.66/56.94 145 join(zero,complement(A)) = complement(A). [para(90(a,1),96(a,1,2,1))].
% 56.66/56.94 146 complement(complement(A)) = A. [back_rewrite(96),rewrite([145(4),145(4)])].
% 56.66/56.94 147 join(A,zero) = A. [back_rewrite(90),rewrite([146(3),21(2)])].
% 56.66/56.94 152 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(146(a,1),35(a,1,1,1,2)),rewrite([146(5),21(4)])].
% 56.66/56.94 154 join(A,A) = A. [para(146(a,1),89(a,1,1)),rewrite([146(2),146(3)])].
% 56.66/56.94 158 join(A,join(A,B)) = join(A,B). [para(154(a,1),28(a,1)),rewrite([21(3),28(4,R),21(3),28(3,R),154(2)]),flip(a)].
% 56.66/56.94 159 join(A,complement(join(B,complement(A)))) = A. [para(35(a,1),158(a,1,2)),rewrite([21(4),35(12)])].
% 56.66/56.94 161 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(159(a,1),28(a,2,2)),rewrite([21(4),21(6)])].
% 56.66/56.94 164 join(complement(A),complement(join(A,B))) = complement(A). [para(146(a,1),159(a,1,2,1,2)),rewrite([21(2)])].
% 56.66/56.94 172 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(146(a,1),51(a,1,2,2))].
% 56.66/56.94 175 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(24(a,1),164(a,1,2,1))].
% 56.66/56.94 176 join(complement(composition(A,B)),complement(composition(join(A,C),B))) = complement(composition(A,B)). [para(31(a,1),164(a,1,2,1))].
% 56.66/56.94 195 join(A,composition(join(B,one),C)) = join(C,join(A,composition(B,C))). [para(85(a,2),28(a,2,2)),rewrite([21(2)]),flip(a)].
% 56.66/56.94 226 join(complement(one),converse(complement(one))) = complement(one). [para(15(a,1),172(a,1,2))].
% 56.66/56.94 230 converse(complement(one)) = complement(one). [para(226(a,1),24(a,2,1)),rewrite([16(7),21(6),226(6)]),flip(a)].
% 56.66/56.94 235 converse(top) = top. [para(230(a,1),91(a,2,2)),rewrite([21(4),19(4),19(6)])].
% 56.66/56.94 299 join(complement(join(complement(A),complement(B))),complement(join(complement(B),join(join(A,complement(B)),complement(join(complement(A),complement(B))))))) = B. [para(35(a,1),60(a,1,2,1,2,1)),rewrite([21(13),35(23)])].
% 56.66/56.94 304 join(complement(A),complement(join(B,A))) = complement(A). [para(159(a,1),60(a,2)),rewrite([146(2),146(4),146(8),60(13)])].
% 56.66/56.94 305 join(A,complement(join(complement(A),complement(B)))) = A. [para(60(a,1),164(a,1,2,1)),rewrite([146(2),21(3),146(7)])].
% 56.66/56.94 563 join(complement(one),complement(c2)) = complement(c2). [para(38(a,1),304(a,1,2,1)),rewrite([21(5)])].
% 56.66/56.94 564 join(complement(one),complement(c1)) = complement(c1). [para(39(a,1),304(a,1,2,1)),rewrite([21(5)])].
% 56.66/56.94 594 join(A,join(complement(A),complement(B))) = top. [para(305(a,1),118(a,1,2)),rewrite([21(4)])].
% 56.66/56.94 598 join(one,complement(c2)) = top. [para(563(a,1),594(a,1,2))].
% 56.66/56.94 602 join(zero,c2) = c2. [para(598(a,1),35(a,1,1,1)),rewrite([40(2),563(6),146(4)])].
% 56.66/56.94 954 join(one,converse(c2)) = one. [para(602(a,1),130(a,2,2,1)),rewrite([21(4),38(4),21(3),147(3),83(2)]),flip(a)].
% 56.66/56.94 968 join(A,composition(converse(c2),A)) = A. [para(954(a,1),31(a,2,1)),rewrite([88(2),88(6)])].
% 56.66/56.94 978 join(A,composition(A,c2)) = A. [para(968(a,1),73(a,1,1)),rewrite([16(2),16(3),16(4),21(3)]),flip(a)].
% 56.66/56.94 980 join(A,join(B,composition(A,c2))) = join(A,B). [para(978(a,1),28(a,2,2)),rewrite([21(3),21(5)])].
% 56.66/56.94 1209 composition(A,join(B,one)) = join(A,composition(A,B)). [para(138(a,1),16(a,1,1)),rewrite([16(4)]),flip(a)].
% 56.66/56.94 1950 join(A,complement(join(A,B))) = join(A,complement(B)). [para(152(a,1),161(a,1,2)),flip(a)].
% 56.66/56.94 2297 join(complement(converse(A)),converse(join(A,B))) = top. [para(175(a,1),118(a,1,2)),rewrite([21(5)])].
% 56.66/56.94 2331 join(A,join(B,converse(complement(converse(A))))) = top. [para(2297(a,1),24(a,2,1)),rewrite([16(6),28(5),21(4),28(5,R),21(4),235(7)])].
% 56.66/56.94 2484 join(A,converse(complement(converse(A)))) = top. [para(154(a,1),2331(a,1,2))].
% 56.66/56.94 2505 join(complement(converse(A)),converse(join(B,A))) = top. [para(2484(a,1),71(a,1,1,2)),rewrite([120(2),235(2)]),flip(a)].
% 56.66/56.94 2605 join(converse(A),complement(composition(converse(A),c2))) = top. [para(968(a,1),2505(a,1,2,1)),rewrite([43(4),21(6)])].
% 56.66/56.94 2654 join(A,complement(composition(A,c2))) = top. [para(16(a,1),2605(a,1,1)),rewrite([16(2)])].
% 56.66/56.94 2662 join(A,join(B,complement(composition(A,c2)))) = top. [para(2654(a,1),28(a,2,2)),rewrite([21(4),120(7)])].
% 56.66/56.94 2988 join(join(A,B),complement(composition(A,c2))) = top. [para(176(a,1),2662(a,1,2))].
% 56.66/56.94 3422 join(complement(c1),complement(composition(complement(one),c2))) = top. [para(564(a,1),2988(a,1,1))].
% 56.66/56.94 4528 complement(join(complement(c1),composition(complement(one),c2))) = c1. [para(3422(a,1),152(a,1,2,1)),rewrite([21(7),40(10),21(10),145(10),146(11)])].
% 56.66/56.94 5354 join(complement(c1),composition(complement(one),c2)) = complement(c1). [para(4528(a,1),35(a,1,1,1,2)),rewrite([4528(12),21(6),152(8)]),flip(a)].
% 56.66/56.94 6067 join(complement(c1),composition(top,c2)) = join(c2,complement(c1)). [para(5354(a,1),195(a,2,2)),rewrite([21(6),19(6)])].
% 56.66/56.94 6984 join(A,composition(join(A,B),c2)) = join(A,composition(B,c2)). [para(31(a,1),980(a,1,2)),rewrite([21(1)])].
% 56.66/56.94 7710 join(complement(A),complement(join(B,complement(A)))) = join(complement(A),complement(B)). [para(305(a,1),299(a,1,2,1,2,1)),rewrite([1950(6),146(3),21(2),1950(13),146(10),21(9),159(11),21(8),305(8),21(5)])].
% 56.66/56.94 12017 join(complement(c1),complement(composition(top,c2))) = join(complement(c1),complement(c2)). [para(6067(a,1),1950(a,1,2,1)),rewrite([7710(8)]),flip(a)].
% 56.66/56.94 38296 join(A,composition(complement(A),c2)) = join(A,composition(top,c2)). [para(19(a,1),6984(a,1,2,1)),flip(a)].
% 56.66/56.94 38373 join(A,complement(composition(top,c2))) = complement(composition(complement(A),c2)). [para(38296(a,1),152(a,1,1,1)),rewrite([21(10),1209(10,R),21(9),38(9),15(8),146(7),21(6),1950(6)])].
% 56.66/56.94 38379 join(complement(c1),complement(c2)) = complement(composition(c1,c2)). [back_rewrite(12017),rewrite([38373(7),146(3)]),flip(a)].
% 56.66/56.94 38383 $F # answer(goals). [back_rewrite(37),rewrite([38379(5),146(5)]),xx(a)].
% 56.66/56.94
% 56.66/56.94 % SZS output end Refutation
% 56.66/56.94 ============================== end of proof ==========================
% 56.66/56.94
% 56.66/56.94 ============================== STATISTICS ============================
% 56.66/56.94
% 56.66/56.94 Given=4653. Generated=2720061. Kept=38361. proofs=1.
% 56.66/56.94 Usable=2878. Sos=9774. Demods=12382. Limbo=4, Disabled=25721. Hints=0.
% 56.66/56.94 Megabytes=27.30.
% 56.66/56.94 User_CPU=54.44, System_CPU=1.45, Wall_clock=56.
% 56.66/56.94
% 56.66/56.94 ============================== end of statistics =====================
% 56.66/56.94
% 56.66/56.94 ============================== end of search =========================
% 56.66/56.94
% 56.66/56.94 THEOREM PROVED
% 56.66/56.94 % SZS status Theorem
% 56.66/56.94
% 56.66/56.94 Exiting with 1 proof.
% 56.66/56.94
% 56.66/56.94 Process 20114 exit (max_proofs) Fri Jul 8 10:34:22 2022
% 56.66/56.94 Prover9 interrupted
%------------------------------------------------------------------------------