TSTP Solution File: REL005+4 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL005+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 19:53:28 EDT 2022
% Result : Theorem 3.16s 3.44s
% Output : Refutation 3.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL005+4 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 14:29:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.01 ============================== Prover9 ===============================
% 0.43/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.01 Process 17090 was started by sandbox on n020.cluster.edu,
% 0.43/1.01 Fri Jul 8 14:29:14 2022
% 0.43/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16937_n020.cluster.edu".
% 0.43/1.01 ============================== end of head ===========================
% 0.43/1.01
% 0.43/1.01 ============================== INPUT =================================
% 0.43/1.01
% 0.43/1.01 % Reading from file /tmp/Prover9_16937_n020.cluster.edu
% 0.43/1.01
% 0.43/1.01 set(prolog_style_variables).
% 0.43/1.01 set(auto2).
% 0.43/1.01 % set(auto2) -> set(auto).
% 0.43/1.01 % set(auto) -> set(auto_inference).
% 0.43/1.01 % set(auto) -> set(auto_setup).
% 0.43/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.01 % set(auto) -> set(auto_limits).
% 0.43/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.01 % set(auto) -> set(auto_denials).
% 0.43/1.01 % set(auto) -> set(auto_process).
% 0.43/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.01 % set(auto2) -> assign(stats, some).
% 0.43/1.01 % set(auto2) -> clear(echo_input).
% 0.43/1.01 % set(auto2) -> set(quiet).
% 0.43/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.01 % set(auto2) -> clear(print_given).
% 0.43/1.01 assign(lrs_ticks,-1).
% 0.43/1.01 assign(sos_limit,10000).
% 0.43/1.01 assign(order,kbo).
% 0.43/1.01 set(lex_order_vars).
% 0.43/1.01 clear(print_given).
% 0.43/1.01
% 0.43/1.01 % formulas(sos). % not echoed (17 formulas)
% 0.43/1.01
% 0.43/1.01 ============================== end of input ==========================
% 0.43/1.01
% 0.43/1.01 % From the command line: assign(max_seconds, 300).
% 0.43/1.01
% 0.43/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.01
% 0.43/1.01 % Formulas that are not ordinary clauses:
% 0.43/1.01 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 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].
% 0.43/1.01 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].
% 0.43/1.01 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].
% 0.43/1.01 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 3.16/3.44 14 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) # label(dedekind_law) # label(axiom) # label(non_clause). [assumption].
% 3.16/3.44 15 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) # label(modular_law_1) # label(axiom) # label(non_clause). [assumption].
% 3.16/3.44 16 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) = meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) # label(modular_law_2) # label(axiom) # label(non_clause). [assumption].
% 3.16/3.44 17 -(all X0 all X1 (join(converse(meet(X0,X1)),meet(converse(X0),converse(X1))) = meet(converse(X0),converse(X1)) & join(meet(converse(X0),converse(X1)),converse(meet(X0,X1))) = converse(meet(X0,X1)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.16/3.44
% 3.16/3.44 ============================== end of process non-clausal formulas ===
% 3.16/3.44
% 3.16/3.44 ============================== PROCESS INITIAL CLAUSES ===============
% 3.16/3.44
% 3.16/3.44 ============================== PREDICATE ELIMINATION =================
% 3.16/3.44
% 3.16/3.44 ============================== end predicate elimination =============
% 3.16/3.44
% 3.16/3.44 Auto_denials:
% 3.16/3.44 % copying label goals to answer in negative clause
% 3.16/3.44
% 3.16/3.44 Term ordering decisions:
% 3.16/3.44 Function symbol KB weights: one=1. top=1. zero=1. c1=1. c2=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 3.16/3.44
% 3.16/3.44 ============================== end of process initial clauses ========
% 3.16/3.44
% 3.16/3.44 ============================== CLAUSES FOR SEARCH ====================
% 3.16/3.44
% 3.16/3.44 ============================== end of clauses for search =============
% 3.16/3.44
% 3.16/3.44 ============================== SEARCH ================================
% 3.16/3.44
% 3.16/3.44 % Starting search at 0.01 seconds.
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=86.000, iters=3414
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=84.000, iters=3355
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=76.000, iters=3491
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=70.000, iters=3384
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=69.000, iters=3385
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=68.000, iters=3407
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=67.000, iters=3383
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=66.000, iters=3339
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=65.000, iters=3396
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=61.000, iters=3390
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=60.000, iters=3336
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=58.000, iters=3372
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=57.000, iters=3340
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=56.000, iters=3334
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=55.000, iters=3356
% 3.16/3.44
% 3.16/3.44 Low Water (keep): wt=53.000, iters=3399
% 3.16/3.44
% 3.16/3.44 ============================== PROOF =================================
% 3.16/3.44 % SZS status Theorem
% 3.16/3.44 % SZS output start Refutation
% 3.16/3.44
% 3.16/3.44 % Proof 1 at 2.41 (+ 0.04) seconds: goals.
% 3.16/3.44 % Length of proof is 121.
% 3.16/3.44 % Level of proof is 32.
% 3.16/3.44 % Maximum clause weight is 49.000.
% 3.16/3.44 % Given clauses 470.
% 3.16/3.44
% 3.16/3.44 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 3.16/3.44 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].
% 3.16/3.44 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].
% 3.16/3.44 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].
% 3.16/3.44 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].
% 3.16/3.44 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 3.16/3.44 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].
% 3.16/3.44 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 3.16/3.44 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 3.16/3.44 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 3.16/3.44 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].
% 3.16/3.44 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 3.16/3.44 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 3.16/3.44 14 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) # label(dedekind_law) # label(axiom) # label(non_clause). [assumption].
% 3.16/3.44 15 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) # label(modular_law_1) # label(axiom) # label(non_clause). [assumption].
% 3.16/3.44 16 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) = meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) # label(modular_law_2) # label(axiom) # label(non_clause). [assumption].
% 3.16/3.44 17 -(all X0 all X1 (join(converse(meet(X0,X1)),meet(converse(X0),converse(X1))) = meet(converse(X0),converse(X1)) & join(meet(converse(X0),converse(X1)),converse(meet(X0,X1))) = converse(meet(X0,X1)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.16/3.44 18 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 3.16/3.44 19 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 3.16/3.44 20 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 3.16/3.44 21 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 3.16/3.44 22 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 3.16/3.44 23 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 3.16/3.44 24 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 3.16/3.44 25 join(converse(A),converse(B)) = converse(join(A,B)). [copy(24),flip(a)].
% 3.16/3.44 26 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 3.16/3.44 27 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(26),flip(a)].
% 3.16/3.44 28 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 3.16/3.44 29 join(A,join(B,C)) = join(C,join(A,B)). [copy(28),rewrite([22(2)]),flip(a)].
% 3.16/3.44 30 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 3.16/3.44 31 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 3.16/3.44 32 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(31),flip(a)].
% 3.16/3.44 33 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 3.16/3.44 34 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(33),rewrite([22(7)]),flip(a)].
% 3.16/3.44 35 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 3.16/3.44 36 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(35),rewrite([22(6),22(8)]),rewrite([22(6)])].
% 3.16/3.44 37 meet(composition(A,meet(B,composition(converse(A),C))),C) = join(meet(composition(A,B),C),meet(composition(A,meet(B,composition(converse(A),C))),C)) # label(modular_law_1) # label(axiom). [clausify(15)].
% 3.16/3.44 38 join(complement(join(complement(A),complement(composition(B,C)))),complement(join(complement(A),complement(composition(B,complement(join(complement(C),complement(composition(converse(B),A))))))))) = complement(join(complement(A),complement(composition(B,complement(join(complement(C),complement(composition(converse(B),A)))))))). [copy(37),rewrite([23(3),23(8),22(10),23(13),22(15),23(19),23(24),22(26)]),flip(a)].
% 3.16/3.44 39 meet(composition(meet(A,composition(B,converse(C))),C),B) = join(meet(composition(A,C),B),meet(composition(meet(A,composition(B,converse(C))),C),B)) # label(modular_law_2) # label(axiom). [clausify(16)].
% 3.16/3.44 40 join(complement(join(complement(A),complement(composition(B,C)))),complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,converse(C))))),C))))) = complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,converse(C))))),C)))). [copy(39),rewrite([23(3),23(8),22(10),23(13),22(15),23(19),23(24),22(26)]),flip(a)].
% 3.16/3.44 41 composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))) # label(dedekind_law) # label(axiom). [clausify(14)].
% 3.16/3.44 42 join(complement(join(complement(A),complement(composition(B,C)))),composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A))))). [copy(41),rewrite([23(3),23(9),23(15),22(17),23(21),23(27)]),flip(a)].
% 3.16/3.44 43 meet(converse(c1),converse(c2)) != join(converse(meet(c1,c2)),meet(converse(c1),converse(c2))) | converse(meet(c1,c2)) != join(meet(converse(c1),converse(c2)),converse(meet(c1,c2))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 3.16/3.44 44 join(converse(complement(join(complement(c1),complement(c2)))),complement(join(complement(converse(c1)),complement(converse(c2))))) != complement(join(complement(converse(c1)),complement(converse(c2)))) | join(converse(complement(join(complement(c1),complement(c2)))),complement(join(complement(converse(c1)),complement(converse(c2))))) != converse(complement(join(complement(c1),complement(c2)))) # answer(goals). [copy(43),rewrite([23(5),23(11),23(20),23(28),23(37),23(43),22(48)]),flip(a),flip(b)].
% 3.16/3.44 45 complement(top) = zero. [back_rewrite(21),rewrite([23(2),20(4)])].
% 3.16/3.44 46 converse(join(A,converse(B))) = join(B,converse(A)). [para(19(a,1),25(a,1,1)),rewrite([22(4)]),flip(a)].
% 3.16/3.44 47 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(19(a,1),27(a,1,1)),flip(a)].
% 3.16/3.44 48 converse(composition(converse(A),B)) = composition(converse(B),A). [para(19(a,1),27(a,1,2)),flip(a)].
% 3.16/3.44 49 join(A,join(B,complement(A))) = join(B,top). [para(20(a,1),29(a,2,2)),rewrite([22(2)])].
% 3.16/3.44 50 composition(A,composition(one,B)) = composition(A,B). [para(18(a,1),30(a,1,1)),flip(a)].
% 3.16/3.44 54 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(30(a,1),32(a,1,1)),rewrite([22(6)])].
% 3.16/3.44 56 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(18(a,1),34(a,1,2,2,1))].
% 3.16/3.44 57 join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A). [para(19(a,1),34(a,1,2,1))].
% 3.16/3.44 61 join(zero,complement(join(complement(A),complement(A)))) = A. [para(20(a,1),36(a,1,1,1)),rewrite([45(2)])].
% 3.16/3.44 62 join(zero,complement(join(A,complement(complement(A))))) = complement(A). [para(20(a,1),36(a,1,2,1)),rewrite([45(6),22(6)])].
% 3.16/3.44 91 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(45(a,1),34(a,1,1)),rewrite([45(9)])].
% 3.16/3.44 101 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(46(a,1),25(a,1,1)),rewrite([22(7),29(7,R),22(6)]),flip(a)].
% 3.16/3.44 102 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(46(a,1),25(a,1,2)),rewrite([29(4,R),22(3),25(3),101(7)]),flip(a)].
% 3.16/3.44 110 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(46(a,1),46(a,2,2)),rewrite([102(4),46(4),29(6,R),22(5)])].
% 3.16/3.44 111 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(101),rewrite([110(8),25(7)])].
% 3.16/3.44 118 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(47(a,1),25(a,1,1)),rewrite([22(7)]),flip(a)].
% 3.16/3.44 126 composition(converse(one),A) = A. [para(18(a,1),48(a,1,1)),rewrite([19(2)]),flip(a)].
% 3.16/3.44 135 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(36(a,1),49(a,1,2)),rewrite([22(4),49(4),22(3),22(8)]),flip(a)].
% 3.16/3.44 136 join(top,complement(complement(A))) = top. [para(38(a,1),49(a,1,2)),rewrite([20(22),22(8),135(8)]),flip(a)].
% 3.16/3.44 137 converse(one) = one. [para(126(a,1),18(a,1)),flip(a)].
% 3.16/3.44 139 composition(join(A,one),B) = join(B,composition(A,B)). [para(126(a,1),32(a,1,1)),rewrite([137(4),22(4)]),flip(a)].
% 3.16/3.44 141 join(complement(A),complement(composition(one,A))) = complement(A). [para(126(a,1),34(a,1,2))].
% 3.16/3.44 155 composition(one,A) = A. [para(126(a,1),50(a,2)),rewrite([137(2),50(4)])].
% 3.16/3.44 161 join(complement(A),complement(A)) = complement(A). [back_rewrite(141),rewrite([155(3)])].
% 3.16/3.44 162 join(zero,complement(complement(A))) = A. [back_rewrite(61),rewrite([161(4)])].
% 3.16/3.44 163 converse(join(A,one)) = join(one,converse(A)). [para(137(a,1),25(a,1,1)),rewrite([22(5)]),flip(a)].
% 3.16/3.44 164 join(zero,complement(A)) = complement(A). [para(136(a,1),36(a,1,1,1)),rewrite([45(2),45(3),162(5)])].
% 3.16/3.44 166 join(top,complement(A)) = join(top,top). [para(136(a,1),49(a,1,2)),rewrite([22(3)])].
% 3.16/3.44 167 complement(complement(A)) = A. [back_rewrite(162),rewrite([164(4)])].
% 3.16/3.44 177 complement(join(A,A)) = complement(A). [back_rewrite(62),rewrite([167(3),164(4)])].
% 3.16/3.44 179 join(A,top) = top. [back_rewrite(136),rewrite([167(3),22(2)])].
% 3.16/3.44 185 join(top,complement(A)) = top. [back_rewrite(166),rewrite([179(6)])].
% 3.16/3.44 195 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(167(a,1),36(a,1,1,1,2)),rewrite([167(5),22(4)])].
% 3.16/3.44 203 complement(zero) = top. [para(45(a,1),167(a,1,1))].
% 3.16/3.44 218 join(A,A) = A. [para(177(a,1),36(a,1,1,1,2)),rewrite([177(6),36(8)]),flip(a)].
% 3.16/3.44 225 join(A,join(A,B)) = join(A,B). [para(218(a,1),29(a,1)),rewrite([22(3),29(4,R),22(3),29(3,R),218(2)]),flip(a)].
% 3.16/3.44 260 join(complement(one),composition(A,complement(converse(A)))) = complement(one). [para(19(a,1),56(a,1,2,1))].
% 3.16/3.44 266 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(167(a,1),56(a,1,2,2))].
% 3.16/3.44 279 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero. [para(163(a,1),91(a,1,2,1))].
% 3.16/3.44 315 join(complement(one),converse(complement(one))) = complement(one). [para(18(a,1),266(a,1,2))].
% 3.16/3.44 319 converse(complement(one)) = complement(one). [para(315(a,1),25(a,2,1)),rewrite([19(7),22(6),315(6)]),flip(a)].
% 3.16/3.44 328 converse(top) = top. [para(319(a,1),163(a,2,2)),rewrite([22(4),20(4),20(6)])].
% 3.16/3.44 339 join(top,converse(A)) = top. [para(328(a,1),25(a,1,1)),rewrite([22(5),179(5),328(5)])].
% 3.16/3.44 346 join(top,composition(A,converse(B))) = top. [para(47(a,1),339(a,1,2))].
% 3.16/3.44 348 join(top,composition(A,B)) = top. [para(19(a,1),346(a,1,2,2))].
% 3.16/3.44 349 composition(join(A,one),top) = top. [para(328(a,1),346(a,1,2,2)),rewrite([139(4,R)])].
% 3.16/3.44 350 composition(join(one,converse(A)),zero) = zero. [back_rewrite(279),rewrite([349(8),45(6),139(7,R),22(5),225(5)])].
% 3.16/3.44 377 composition(top,zero) = zero. [para(319(a,1),350(a,1,1,2)),rewrite([20(4)])].
% 3.16/3.44 382 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)). [para(377(a,1),42(a,1,1,1,2,1)),rewrite([203(3),22(3),185(3),45(2),45(3),164(7),167(6),203(6),328(7),185(9),45(6),30(6),45(9),164(13),167(12),203(12),328(13),185(15),45(12),30(12)])].
% 3.16/3.44 386 join(zero,composition(A,composition(B,zero))) = zero. [para(377(a,1),54(a,1,2)),rewrite([22(5),348(8),377(8)])].
% 3.16/3.44 389 composition(A,composition(converse(zero),zero)) = zero. [back_rewrite(382),rewrite([386(7)]),flip(a)].
% 3.16/3.44 468 composition(A,composition(converse(zero),composition(zero,B))) = composition(zero,B). [para(389(a,1),30(a,1,1)),rewrite([30(7)]),flip(a)].
% 3.16/3.44 469 composition(A,zero) = zero. [para(389(a,1),30(a,1)),rewrite([389(6)]),flip(a)].
% 3.16/3.44 470 composition(converse(zero),A) = converse(zero). [para(389(a,1),48(a,1,1)),rewrite([469(6)]),flip(a)].
% 3.16/3.44 475 composition(zero,A) = composition(B,converse(zero)). [back_rewrite(468),rewrite([470(5)]),flip(a)].
% 3.16/3.44 477 composition(zero,A) = c_0. [new_symbol(475)].
% 3.16/3.44 493 c_0 = zero. [para(477(a,1),18(a,1))].
% 3.16/3.44 497 composition(zero,A) = zero. [back_rewrite(477),rewrite([493(3)])].
% 3.16/3.44 2487 join(A,join(complement(A),converse(B))) = top. [para(20(a,1),110(a,1,1)),rewrite([339(3)]),flip(a)].
% 3.16/3.44 2571 join(A,join(complement(A),composition(B,converse(C)))) = top. [para(47(a,1),2487(a,1,2,2))].
% 3.16/3.44 3167 join(A,join(complement(A),composition(B,C))) = top. [para(19(a,1),2571(a,1,2,2,2))].
% 3.16/3.44 3170 join(A,composition(join(B,one),complement(A))) = top. [para(139(a,2),3167(a,1,2))].
% 3.16/3.44 3224 join(A,join(B,composition(join(C,one),complement(A)))) = top. [para(3170(a,1),29(a,2,2)),rewrite([22(5),179(8)])].
% 3.16/3.44 7343 join(complement(A),composition(join(one,converse(B)),A)) = top. [para(57(a,1),3224(a,1,2)),rewrite([163(3),22(6)])].
% 3.16/3.44 7404 join(converse(complement(converse(A))),composition(A,join(B,one))) = top. [para(7343(a,1),118(a,1,1)),rewrite([328(2),46(5),137(3),22(8)]),flip(a)].
% 3.16/3.44 9349 join(A,converse(complement(converse(A)))) = top. [para(218(a,1),7404(a,1,2,2)),rewrite([18(5),22(4)])].
% 3.16/3.44 9388 join(complement(converse(A)),converse(join(B,A))) = top. [para(9349(a,1),111(a,1,1,2)),rewrite([179(2),328(2)]),flip(a)].
% 3.16/3.44 9394 complement(join(complement(A),converse(complement(converse(A))))) = complement(converse(complement(converse(A)))). [para(9349(a,1),195(a,1,1,1)),rewrite([45(2),22(6),164(8)])].
% 3.16/3.44 9429 join(complement(one),complement(composition(converse(complement(A)),A))) = top. [para(56(a,1),9388(a,1,2,1)),rewrite([48(4),319(7),22(7)])].
% 3.16/3.44 9432 join(complement(one),complement(converse(composition(A,complement(converse(A)))))) = top. [para(260(a,1),9388(a,1,2,1)),rewrite([319(8),22(8)])].
% 3.16/3.44 9540 complement(join(complement(A),complement(converse(complement(converse(A)))))) = zero. [para(9429(a,1),40(a,1,2,1,2,1,1,1)),rewrite([155(6),22(6),45(13),497(13),203(13),22(13),185(13),45(9),22(9),164(9),27(18),9432(19),45(13),497(13),203(13),22(13),185(13),45(9)])].
% 3.16/3.44 9615 complement(join(A,complement(converse(complement(converse(A)))))) = converse(complement(converse(A))). [para(9540(a,1),36(a,1,1)),rewrite([167(3),164(8)])].
% 3.16/3.44 9628 complement(converse(complement(converse(A)))) = A. [para(9540(a,1),195(a,1,2)),rewrite([22(5),9394(6),22(6),164(6),167(6)])].
% 3.16/3.44 9631 converse(complement(converse(A))) = complement(A). [back_rewrite(9615),rewrite([9628(4),218(1)]),flip(a)].
% 3.16/3.44 9661 complement(converse(A)) = converse(complement(A)). [para(9631(a,1),19(a,1,1)),flip(a)].
% 3.16/3.44 10605 $F # answer(goals). [back_rewrite(44),rewrite([9661(10),9661(13),25(14),9661(14),218(15),9661(10),9661(13),25(14),9661(14),9661(25),9661(28),25(29),9661(29),218(30)]),xx(a),xx(b)].
% 3.16/3.44
% 3.16/3.44 % SZS output end Refutation
% 3.16/3.44 ============================== end of proof ==========================
% 3.16/3.44
% 3.16/3.44 ============================== STATISTICS ============================
% 3.16/3.44
% 3.16/3.44 Given=470. Generated=65900. Kept=10577. proofs=1.
% 3.16/3.44 Usable=333. Sos=6110. Demods=7338. Limbo=944, Disabled=3207. Hints=0.
% 3.16/3.44 Megabytes=21.73.
% 3.16/3.44 User_CPU=2.41, System_CPU=0.04, Wall_clock=2.
% 3.16/3.44
% 3.16/3.44 ============================== end of statistics =====================
% 3.16/3.44
% 3.16/3.44 ============================== end of search =========================
% 3.16/3.44
% 3.16/3.44 THEOREM PROVED
% 3.16/3.44 % SZS status Theorem
% 3.16/3.44
% 3.16/3.44 Exiting with 1 proof.
% 3.16/3.44
% 3.16/3.44 Process 17090 exit (max_proofs) Fri Jul 8 14:29:16 2022
% 3.16/3.44 Prover9 interrupted
%------------------------------------------------------------------------------