TSTP Solution File: REL004+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL004+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 19:53:25 EDT 2022
% Result : Theorem 2.14s 2.42s
% Output : Refutation 2.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : REL004+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 13:43:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.70/0.98 ============================== Prover9 ===============================
% 0.70/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.70/0.98 Process 12732 was started by sandbox2 on n029.cluster.edu,
% 0.70/0.98 Fri Jul 8 13:43:15 2022
% 0.70/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12579_n029.cluster.edu".
% 0.70/0.98 ============================== end of head ===========================
% 0.70/0.98
% 0.70/0.98 ============================== INPUT =================================
% 0.70/0.98
% 0.70/0.98 % Reading from file /tmp/Prover9_12579_n029.cluster.edu
% 0.70/0.98
% 0.70/0.98 set(prolog_style_variables).
% 0.70/0.98 set(auto2).
% 0.70/0.98 % set(auto2) -> set(auto).
% 0.70/0.98 % set(auto) -> set(auto_inference).
% 0.70/0.98 % set(auto) -> set(auto_setup).
% 0.70/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.70/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/0.98 % set(auto) -> set(auto_limits).
% 0.70/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/0.98 % set(auto) -> set(auto_denials).
% 0.70/0.98 % set(auto) -> set(auto_process).
% 0.70/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.70/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.70/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.70/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.70/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.70/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.70/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.70/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.70/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.70/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.70/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.70/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.70/0.98 % set(auto2) -> assign(stats, some).
% 0.70/0.98 % set(auto2) -> clear(echo_input).
% 0.70/0.98 % set(auto2) -> set(quiet).
% 0.70/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.70/0.98 % set(auto2) -> clear(print_given).
% 0.70/0.98 assign(lrs_ticks,-1).
% 0.70/0.98 assign(sos_limit,10000).
% 0.70/0.98 assign(order,kbo).
% 0.70/0.98 set(lex_order_vars).
% 0.70/0.98 clear(print_given).
% 0.70/0.98
% 0.70/0.98 % formulas(sos). % not echoed (17 formulas)
% 0.70/0.98
% 0.70/0.98 ============================== end of input ==========================
% 0.70/0.98
% 0.70/0.98 % From the command line: assign(max_seconds, 300).
% 0.70/0.98
% 0.70/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.70/0.98
% 0.70/0.98 % Formulas that are not ordinary clauses:
% 0.70/0.98 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.98 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].
% 0.70/0.98 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].
% 0.70/0.98 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].
% 0.70/0.98 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].
% 0.70/0.98 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.98 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].
% 0.70/0.98 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.98 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.98 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.98 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].
% 0.70/0.98 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.98 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.42 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].
% 2.14/2.42 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].
% 2.14/2.42 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].
% 2.14/2.42 17 -(all X0 converse(complement(X0)) = complement(converse(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.14/2.42
% 2.14/2.42 ============================== end of process non-clausal formulas ===
% 2.14/2.42
% 2.14/2.42 ============================== PROCESS INITIAL CLAUSES ===============
% 2.14/2.42
% 2.14/2.42 ============================== PREDICATE ELIMINATION =================
% 2.14/2.42
% 2.14/2.42 ============================== end predicate elimination =============
% 2.14/2.42
% 2.14/2.42 Auto_denials:
% 2.14/2.42 % copying label goals to answer in negative clause
% 2.14/2.42
% 2.14/2.42 Term ordering decisions:
% 2.14/2.42 Function symbol KB weights: one=1. top=1. zero=1. c1=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 2.14/2.42
% 2.14/2.42 ============================== end of process initial clauses ========
% 2.14/2.42
% 2.14/2.42 ============================== CLAUSES FOR SEARCH ====================
% 2.14/2.42
% 2.14/2.42 ============================== end of clauses for search =============
% 2.14/2.42
% 2.14/2.42 ============================== SEARCH ================================
% 2.14/2.42
% 2.14/2.42 % Starting search at 0.01 seconds.
% 2.14/2.42
% 2.14/2.42 Low Water (keep): wt=125.000, iters=3594
% 2.14/2.42
% 2.14/2.42 Low Water (keep): wt=105.000, iters=3578
% 2.14/2.42
% 2.14/2.42 ============================== PROOF =================================
% 2.14/2.42 % SZS status Theorem
% 2.14/2.42 % SZS output start Refutation
% 2.14/2.42
% 2.14/2.42 % Proof 1 at 1.42 (+ 0.04) seconds: goals.
% 2.14/2.42 % Length of proof is 112.
% 2.14/2.42 % Level of proof is 36.
% 2.14/2.42 % Maximum clause weight is 48.000.
% 2.14/2.42 % Given clauses 430.
% 2.14/2.42
% 2.14/2.42 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.42 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].
% 2.14/2.42 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].
% 2.14/2.42 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].
% 2.14/2.42 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].
% 2.14/2.42 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.42 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].
% 2.14/2.42 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.42 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.42 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.42 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].
% 2.14/2.42 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.42 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.42 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].
% 2.14/2.42 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].
% 2.14/2.42 17 -(all X0 converse(complement(X0)) = complement(converse(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.14/2.42 18 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 2.14/2.42 19 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 2.14/2.42 20 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 2.14/2.42 21 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 2.14/2.42 22 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 2.14/2.42 23 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 2.14/2.42 24 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 2.14/2.42 25 join(converse(A),converse(B)) = converse(join(A,B)). [copy(24),flip(a)].
% 2.14/2.42 26 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 2.14/2.42 27 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(26),flip(a)].
% 2.14/2.42 28 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 2.14/2.42 29 join(A,join(B,C)) = join(C,join(A,B)). [copy(28),rewrite([22(2)]),flip(a)].
% 2.14/2.42 30 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 2.14/2.42 31 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 2.14/2.42 32 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(31),flip(a)].
% 2.14/2.42 33 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 2.14/2.42 34 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(33),rewrite([22(7)]),flip(a)].
% 2.14/2.42 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)].
% 2.14/2.42 36 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(35),rewrite([22(6),22(8)]),rewrite([22(6)])].
% 2.14/2.42 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)].
% 2.14/2.42 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)].
% 2.14/2.42 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)].
% 2.14/2.42 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)].
% 2.14/2.42 43 converse(complement(c1)) != complement(converse(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 2.14/2.42 44 complement(converse(c1)) != converse(complement(c1)) # answer(goals). [copy(43),flip(a)].
% 2.14/2.42 45 complement(top) = zero. [back_rewrite(21),rewrite([23(2),20(4)])].
% 2.14/2.42 46 complement(converse(c1)) = c_0. [new_symbol(44)].
% 2.14/2.42 47 converse(complement(c1)) != c_0 # answer(goals). [back_rewrite(44),rewrite([46(3)]),flip(a)].
% 2.14/2.42 49 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(19(a,1),27(a,1,1)),flip(a)].
% 2.14/2.42 50 converse(composition(converse(A),B)) = composition(converse(B),A). [para(19(a,1),27(a,1,2)),flip(a)].
% 2.14/2.42 51 join(A,join(B,complement(A))) = join(B,top). [para(20(a,1),29(a,2,2)),rewrite([22(2)])].
% 2.14/2.42 52 composition(A,composition(one,B)) = composition(A,B). [para(18(a,1),30(a,1,1)),flip(a)].
% 2.14/2.42 56 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)])].
% 2.14/2.42 63 join(zero,complement(join(complement(A),complement(A)))) = A. [para(20(a,1),36(a,1,1,1)),rewrite([45(2)])].
% 2.14/2.42 64 join(zero,complement(join(A,complement(complement(A))))) = complement(A). [para(20(a,1),36(a,1,2,1)),rewrite([45(6),22(6)])].
% 2.14/2.42 95 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(45(a,1),36(a,1,2,1,1))].
% 2.14/2.42 103 join(c_0,converse(c1)) = top. [para(46(a,1),20(a,1,2)),rewrite([22(4)])].
% 2.14/2.42 125 join(c1,converse(c_0)) = converse(top). [para(103(a,1),25(a,2,1)),rewrite([19(5),22(4)])].
% 2.14/2.42 140 composition(converse(one),A) = A. [para(18(a,1),50(a,1,1)),rewrite([19(2)]),flip(a)].
% 2.14/2.42 148 converse(one) = one. [para(140(a,1),18(a,1)),flip(a)].
% 2.14/2.42 150 composition(join(A,one),B) = join(B,composition(A,B)). [para(140(a,1),32(a,1,1)),rewrite([148(4),22(4)]),flip(a)].
% 2.14/2.42 152 join(complement(A),complement(composition(one,A))) = complement(A). [para(140(a,1),34(a,1,2))].
% 2.14/2.42 166 composition(one,A) = A. [para(140(a,1),52(a,2)),rewrite([148(2),52(4)])].
% 2.14/2.42 172 join(complement(A),complement(A)) = complement(A). [back_rewrite(152),rewrite([166(3)])].
% 2.14/2.42 173 join(zero,complement(complement(A))) = A. [back_rewrite(63),rewrite([172(4)])].
% 2.14/2.42 174 converse(join(A,one)) = join(one,converse(A)). [para(148(a,1),25(a,1,1)),rewrite([22(5)]),flip(a)].
% 2.14/2.42 176 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(36(a,1),51(a,1,2)),rewrite([22(4),51(4),22(3),22(8)]),flip(a)].
% 2.14/2.42 177 join(top,complement(complement(A))) = top. [para(38(a,1),51(a,1,2)),rewrite([20(22),22(8),176(8)]),flip(a)].
% 2.14/2.42 179 join(zero,complement(c_0)) = converse(c1). [para(46(a,1),173(a,1,2,1))].
% 2.14/2.42 180 join(zero,complement(A)) = complement(A). [para(177(a,1),36(a,1,1,1)),rewrite([45(2),45(3),173(5)])].
% 2.14/2.42 183 join(top,complement(A)) = join(top,top). [para(177(a,1),51(a,1,2)),rewrite([22(3)])].
% 2.14/2.42 184 complement(c_0) = converse(c1). [back_rewrite(179),rewrite([180(4)])].
% 2.14/2.42 185 complement(complement(A)) = A. [back_rewrite(173),rewrite([180(4)])].
% 2.14/2.42 193 join(A,complement(join(top,top))) = A. [back_rewrite(95),rewrite([183(3),180(7),185(6),22(5)])].
% 2.14/2.42 195 complement(join(A,A)) = complement(A). [back_rewrite(64),rewrite([185(3),180(4)])].
% 2.14/2.42 198 join(A,top) = top. [back_rewrite(177),rewrite([185(3),22(2)])].
% 2.14/2.42 204 join(A,zero) = A. [back_rewrite(193),rewrite([198(3),45(2)])].
% 2.14/2.42 205 join(top,complement(A)) = top. [back_rewrite(183),rewrite([198(6)])].
% 2.14/2.42 207 join(A,join(B,complement(A))) = top. [back_rewrite(51),rewrite([198(5)])].
% 2.14/2.42 209 join(complement(join(A,converse(c1))),complement(join(complement(A),converse(c1)))) = c_0. [para(184(a,1),36(a,1,1,1,2)),rewrite([184(7)])].
% 2.14/2.42 218 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(185(a,1),36(a,1,1,1,2)),rewrite([185(5),22(4)])].
% 2.14/2.42 226 complement(zero) = top. [para(45(a,1),185(a,1,1))].
% 2.14/2.42 255 join(A,A) = A. [para(195(a,1),36(a,1,1,1,2)),rewrite([195(6),36(8)]),flip(a)].
% 2.14/2.42 262 join(A,join(A,B)) = join(A,B). [para(255(a,1),29(a,1)),rewrite([22(3),29(4,R),22(3),29(3,R),255(2)]),flip(a)].
% 2.14/2.42 280 join(A,complement(join(B,complement(A)))) = A. [para(36(a,1),262(a,1,2)),rewrite([22(4),36(12)])].
% 2.14/2.42 287 join(c_0,complement(join(A,converse(c1)))) = c_0. [para(184(a,1),280(a,1,2,1,2))].
% 2.14/2.42 289 join(c_0,complement(converse(join(A,c1)))) = c_0. [para(25(a,1),287(a,1,2,1))].
% 2.14/2.42 292 join(c_0,converse(join(A,c1))) = top. [para(289(a,1),207(a,1,2)),rewrite([22(5)])].
% 2.14/2.42 293 join(A,converse(top)) = converse(top). [para(292(a,1),25(a,2,1)),rewrite([19(6),29(5),22(4),29(5,R),22(4),125(4)])].
% 2.14/2.42 305 join(top,converse(A)) = top. [para(293(a,1),25(a,2,1)),rewrite([19(4),22(3),19(6)])].
% 2.14/2.42 306 join(top,composition(A,converse(B))) = top. [para(49(a,1),305(a,1,2))].
% 2.14/2.42 308 converse(top) = top. [para(305(a,1),293(a,1)),flip(a)].
% 2.14/2.42 312 join(c1,converse(c_0)) = top. [back_rewrite(125),rewrite([308(6)])].
% 2.14/2.42 326 join(top,composition(A,B)) = top. [para(19(a,1),306(a,1,2,2))].
% 2.14/2.42 327 composition(join(A,one),top) = top. [para(308(a,1),306(a,1,2,2)),rewrite([150(4,R)])].
% 2.14/2.42 328 composition(top,join(one,converse(A))) = top. [para(327(a,1),27(a,2,1)),rewrite([308(2),174(4),308(7)])].
% 2.14/2.42 355 composition(top,top) = top. [para(308(a,1),328(a,1,2,2)),rewrite([198(4)])].
% 2.14/2.42 358 composition(top,zero) = zero. [para(355(a,1),34(a,1,2,2,1)),rewrite([45(2),308(3),45(4),150(5,R),22(3),198(3),45(5)])].
% 2.14/2.42 367 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)). [para(358(a,1),42(a,1,1,1,2,1)),rewrite([226(3),22(3),205(3),45(2),45(3),180(7),185(6),226(6),308(7),205(9),45(6),30(6),45(9),180(13),185(12),226(12),308(13),205(15),45(12),30(12)])].
% 2.14/2.42 371 join(zero,composition(A,composition(B,zero))) = zero. [para(358(a,1),56(a,1,2)),rewrite([22(5),326(8),358(8)])].
% 2.14/2.42 373 composition(A,composition(converse(zero),zero)) = zero. [back_rewrite(367),rewrite([371(7)]),flip(a)].
% 2.14/2.42 429 composition(A,composition(converse(zero),composition(zero,B))) = composition(zero,B). [para(373(a,1),30(a,1,1)),rewrite([30(7)]),flip(a)].
% 2.14/2.42 430 composition(A,zero) = zero. [para(373(a,1),30(a,1)),rewrite([373(6)]),flip(a)].
% 2.14/2.42 431 composition(converse(zero),A) = converse(zero). [para(373(a,1),50(a,1,1)),rewrite([430(6)]),flip(a)].
% 2.14/2.42 436 composition(zero,A) = composition(B,converse(zero)). [back_rewrite(429),rewrite([431(5)]),flip(a)].
% 2.14/2.42 438 composition(zero,A) = c_1. [new_symbol(436)].
% 2.14/2.42 439 composition(A,converse(zero)) = c_1. [back_rewrite(436),rewrite([438(2)]),flip(a)].
% 2.14/2.42 454 c_1 = zero. [para(438(a,1),18(a,1))].
% 2.14/2.42 455 converse(zero) = zero. [para(438(a,1),27(a,2,1)),rewrite([439(4),454(1),454(2)]),flip(a)].
% 2.14/2.42 483 join(zero,converse(A)) = converse(A). [para(455(a,1),25(a,1,1)),rewrite([22(5),204(5)])].
% 2.14/2.42 6595 complement(join(converse(c_0),complement(c1))) = complement(converse(c_0)). [para(312(a,1),218(a,1,1,1)),rewrite([45(2),180(8)])].
% 2.14/2.42 6742 join(converse(c_0),complement(c1)) = converse(c_0). [para(6595(a,1),36(a,1,1,1,2)),rewrite([6595(12),36(12)]),flip(a)].
% 2.14/2.42 6755 join(c_0,converse(complement(c1))) = c_0. [para(6742(a,1),25(a,2,1)),rewrite([19(3),19(8)])].
% 2.14/2.42 6760 complement(converse(complement(c1))) = converse(c1). [para(6755(a,1),218(a,1,1,1)),rewrite([184(2),184(7),22(8),25(8),20(6),308(4),45(4),22(4),483(4)]),flip(a)].
% 2.14/2.42 6877 converse(complement(c1)) = c_0. [para(6760(a,1),36(a,1,1,1,2)),rewrite([6760(9),209(10)]),flip(a)].
% 2.14/2.42 6878 $F # answer(goals). [resolve(6877,a,47,a)].
% 2.14/2.42
% 2.14/2.42 % SZS output end Refutation
% 2.14/2.42 ============================== end of proof ==========================
% 2.14/2.42
% 2.14/2.42 ============================== STATISTICS ============================
% 2.14/2.42
% 2.14/2.42 Given=430. Generated=39104. Kept=6850. proofs=1.
% 2.14/2.42 Usable=374. Sos=5905. Demods=6243. Limbo=1, Disabled=586. Hints=0.
% 2.14/2.42 Megabytes=16.46.
% 2.14/2.42 User_CPU=1.42, System_CPU=0.04, Wall_clock=2.
% 2.14/2.42
% 2.14/2.42 ============================== end of statistics =====================
% 2.14/2.42
% 2.14/2.42 ============================== end of search =========================
% 2.14/2.42
% 2.14/2.42 THEOREM PROVED
% 2.14/2.42 % SZS status Theorem
% 2.14/2.42
% 2.14/2.42 Exiting with 1 proof.
% 2.14/2.42
% 2.14/2.42 Process 12732 exit (max_proofs) Fri Jul 8 13:43:17 2022
% 2.14/2.42 Prover9 interrupted
%------------------------------------------------------------------------------