TSTP Solution File: REL012+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL012+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 19:53:38 EDT 2022
% Result : Theorem 6.27s 6.60s
% Output : Refutation 6.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : REL012+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 8 09:52:40 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.71/1.00 ============================== Prover9 ===============================
% 0.71/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.71/1.00 Process 12677 was started by sandbox on n026.cluster.edu,
% 0.71/1.00 Fri Jul 8 09:52:40 2022
% 0.71/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12506_n026.cluster.edu".
% 0.71/1.00 ============================== end of head ===========================
% 0.71/1.00
% 0.71/1.00 ============================== INPUT =================================
% 0.71/1.00
% 0.71/1.00 % Reading from file /tmp/Prover9_12506_n026.cluster.edu
% 0.71/1.00
% 0.71/1.00 set(prolog_style_variables).
% 0.71/1.00 set(auto2).
% 0.71/1.00 % set(auto2) -> set(auto).
% 0.71/1.00 % set(auto) -> set(auto_inference).
% 0.71/1.00 % set(auto) -> set(auto_setup).
% 0.71/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.71/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/1.00 % set(auto) -> set(auto_limits).
% 0.71/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/1.00 % set(auto) -> set(auto_denials).
% 0.71/1.00 % set(auto) -> set(auto_process).
% 0.71/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.71/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.71/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.71/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.71/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.71/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.71/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.71/1.00 % set(auto2) -> assign(stats, some).
% 0.71/1.00 % set(auto2) -> clear(echo_input).
% 0.71/1.00 % set(auto2) -> set(quiet).
% 0.71/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.71/1.00 % set(auto2) -> clear(print_given).
% 0.71/1.00 assign(lrs_ticks,-1).
% 0.71/1.00 assign(sos_limit,10000).
% 0.71/1.00 assign(order,kbo).
% 0.71/1.00 set(lex_order_vars).
% 0.71/1.00 clear(print_given).
% 0.71/1.00
% 0.71/1.00 % formulas(sos). % not echoed (17 formulas)
% 0.71/1.00
% 0.71/1.00 ============================== end of input ==========================
% 0.71/1.00
% 0.71/1.00 % From the command line: assign(max_seconds, 300).
% 0.71/1.00
% 0.71/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/1.00
% 0.71/1.00 % Formulas that are not ordinary clauses:
% 0.71/1.00 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 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].
% 0.71/1.00 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].
% 0.71/1.00 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].
% 0.71/1.00 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].
% 0.71/1.00 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 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].
% 0.71/1.00 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 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].
% 0.71/1.00 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 6.27/6.60 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].
% 6.27/6.60 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].
% 6.27/6.60 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].
% 6.27/6.60 17 -(all X0 all X1 join(composition(complement(composition(X0,X1)),converse(X1)),complement(X0)) = complement(X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 6.27/6.60
% 6.27/6.60 ============================== end of process non-clausal formulas ===
% 6.27/6.60
% 6.27/6.60 ============================== PROCESS INITIAL CLAUSES ===============
% 6.27/6.60
% 6.27/6.60 ============================== PREDICATE ELIMINATION =================
% 6.27/6.60
% 6.27/6.60 ============================== end predicate elimination =============
% 6.27/6.60
% 6.27/6.60 Auto_denials:
% 6.27/6.60 % copying label goals to answer in negative clause
% 6.27/6.60
% 6.27/6.60 Term ordering decisions:
% 6.27/6.60 Function symbol KB weights: one=1. top=1. zero=1. c1=1. c2=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 6.27/6.60
% 6.27/6.60 ============================== end of process initial clauses ========
% 6.27/6.60
% 6.27/6.60 ============================== CLAUSES FOR SEARCH ====================
% 6.27/6.60
% 6.27/6.60 ============================== end of clauses for search =============
% 6.27/6.60
% 6.27/6.60 ============================== SEARCH ================================
% 6.27/6.60
% 6.27/6.60 % Starting search at 0.01 seconds.
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=86.000, iters=3414
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=84.000, iters=3355
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=76.000, iters=3491
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=70.000, iters=3384
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=69.000, iters=3385
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=68.000, iters=3407
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=67.000, iters=3383
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=66.000, iters=3339
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=65.000, iters=3396
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=61.000, iters=3390
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% 6.27/6.60 Low Water (keep): wt=60.000, iters=3336
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=58.000, iters=3372
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% 6.27/6.60 Low Water (keep): wt=57.000, iters=3340
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% 6.27/6.60 Low Water (keep): wt=56.000, iters=3334
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% 6.27/6.60 Low Water (keep): wt=55.000, iters=3356
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% 6.27/6.60 Low Water (keep): wt=53.000, iters=3399
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% 6.27/6.60 Low Water (keep): wt=51.000, iters=3357
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% 6.27/6.60 Low Water (keep): wt=50.000, iters=3335
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% 6.27/6.60 Low Water (keep): wt=49.000, iters=3359
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% 6.27/6.60 Low Water (keep): wt=48.000, iters=3370
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% 6.27/6.60 Low Water (keep): wt=45.000, iters=3383
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% 6.27/6.60 Low Water (keep): wt=40.000, iters=3436
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=38.000, iters=3562
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=33.000, iters=3377
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=31.000, iters=3341
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=30.000, iters=3340
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=29.000, iters=3359
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=28.000, iters=3432
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=27.000, iters=3349
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=26.000, iters=3394
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=25.000, iters=3333
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=24.000, iters=3339
% 6.27/6.60
% 6.27/6.60 Low Water (displace): id=5811, wt=89.000
% 6.27/6.60
% 6.27/6.60 Low Water (displace): id=16569, wt=22.000
% 6.27/6.60
% 6.27/6.60 Low Water (displace): id=16570, wt=20.000
% 6.27/6.60
% 6.27/6.60 Low Water (displace): id=16716, wt=18.000
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=23.000, iters=3351
% 6.27/6.60
% 6.27/6.60 Low Water (displace): id=17037, wt=16.000
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=22.000, iters=3336
% 6.27/6.60
% 6.27/6.60 Low Water (displace): id=17858, wt=15.000
% 6.27/6.60
% 6.27/6.60 Low Water (displace): id=17861, wt=14.000
% 6.27/6.60
% 6.27/6.60 Low Water (displace): id=18104, wt=13.000
% 6.27/6.60
% 6.27/6.60 Low Water (keep): wt=21.000, iters=3333
% 6.27/6.60
% 6.27/6.60 ============================== PROOF =================================
% 6.27/6.60 % SZS status Theorem
% 6.27/6.60 % SZS output start Refutation
% 6.27/6.60
% 6.27/6.60 % Proof 1 at 5.49 (+ 0.11) seconds: goals.
% 6.27/6.60 % Length of proof is 127.
% 6.27/6.60 % Level of proof is 35.
% 6.27/6.60 % Maximum clause weight is 48.000.
% 6.27/6.60 % Given clauses 821.
% 6.27/6.60
% 6.27/6.60 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 6.27/6.60 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].
% 6.27/6.60 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].
% 6.27/6.60 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].
% 6.27/6.60 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].
% 6.27/6.60 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 6.27/6.60 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].
% 6.27/6.60 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 6.27/6.60 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 6.27/6.60 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 6.27/6.60 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].
% 6.27/6.60 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 6.27/6.60 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 6.27/6.60 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].
% 6.27/6.60 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].
% 6.27/6.60 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].
% 6.27/6.60 17 -(all X0 all X1 join(composition(complement(composition(X0,X1)),converse(X1)),complement(X0)) = complement(X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 6.27/6.60 18 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 6.27/6.60 19 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 6.27/6.60 20 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 6.27/6.60 21 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 6.27/6.60 22 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 6.27/6.60 23 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 6.27/6.60 24 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 6.27/6.60 25 join(converse(A),converse(B)) = converse(join(A,B)). [copy(24),flip(a)].
% 6.27/6.60 26 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 6.27/6.60 27 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(26),flip(a)].
% 6.27/6.60 28 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 6.27/6.60 29 join(A,join(B,C)) = join(C,join(A,B)). [copy(28),rewrite([22(2)]),flip(a)].
% 6.27/6.60 30 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 6.27/6.60 31 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 6.27/6.60 32 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(31),flip(a)].
% 6.27/6.60 33 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 6.27/6.60 34 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(33),rewrite([22(7)]),flip(a)].
% 6.27/6.60 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)].
% 6.27/6.60 36 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(35),rewrite([22(6),22(8)]),rewrite([22(6)])].
% 6.27/6.60 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)].
% 6.27/6.60 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)].
% 6.27/6.60 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)].
% 6.27/6.60 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)].
% 6.27/6.60 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)].
% 6.27/6.60 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)].
% 6.27/6.60 43 complement(c1) != join(composition(complement(composition(c1,c2)),converse(c2)),complement(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 6.27/6.60 44 join(complement(c1),composition(complement(composition(c1,c2)),converse(c2))) != complement(c1) # answer(goals). [copy(43),rewrite([22(12)]),flip(a)].
% 6.27/6.60 45 complement(top) = zero. [back_rewrite(21),rewrite([23(2),20(4)])].
% 6.27/6.60 46 converse(join(A,converse(B))) = join(B,converse(A)). [para(19(a,1),25(a,1,1)),rewrite([22(4)]),flip(a)].
% 6.27/6.60 47 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(19(a,1),27(a,1,1)),flip(a)].
% 6.27/6.60 48 converse(composition(converse(A),B)) = composition(converse(B),A). [para(19(a,1),27(a,1,2)),flip(a)].
% 6.27/6.60 49 join(A,join(B,complement(A))) = join(B,top). [para(20(a,1),29(a,2,2)),rewrite([22(2)])].
% 6.27/6.60 50 composition(A,composition(one,B)) = composition(A,B). [para(18(a,1),30(a,1,1)),flip(a)].
% 6.27/6.60 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)])].
% 6.27/6.60 56 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(18(a,1),34(a,1,2,2,1))].
% 6.27/6.60 57 join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A). [para(19(a,1),34(a,1,2,1))].
% 6.27/6.60 58 join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)). [para(34(a,1),25(a,2,1)),rewrite([48(7)])].
% 6.27/6.60 61 join(zero,complement(join(complement(A),complement(A)))) = A. [para(20(a,1),36(a,1,1,1)),rewrite([45(2)])].
% 6.27/6.60 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)])].
% 6.27/6.60 91 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(45(a,1),34(a,1,1)),rewrite([45(9)])].
% 6.27/6.60 101 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)].
% 6.27/6.60 102 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)].
% 6.27/6.60 110 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)])].
% 6.27/6.60 111 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(101),rewrite([110(8),25(7)])].
% 6.27/6.60 118 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)].
% 6.27/6.60 126 composition(converse(one),A) = A. [para(18(a,1),48(a,1,1)),rewrite([19(2)]),flip(a)].
% 6.27/6.60 135 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)].
% 6.27/6.60 136 join(top,complement(complement(A))) = top. [para(38(a,1),49(a,1,2)),rewrite([20(22),22(8),135(8)]),flip(a)].
% 6.27/6.60 137 converse(one) = one. [para(126(a,1),18(a,1)),flip(a)].
% 6.27/6.60 139 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)].
% 6.27/6.60 141 join(complement(A),complement(composition(one,A))) = complement(A). [para(126(a,1),34(a,1,2))].
% 6.27/6.60 155 composition(one,A) = A. [para(126(a,1),50(a,2)),rewrite([137(2),50(4)])].
% 6.27/6.60 161 join(complement(A),complement(A)) = complement(A). [back_rewrite(141),rewrite([155(3)])].
% 6.27/6.60 162 join(zero,complement(complement(A))) = A. [back_rewrite(61),rewrite([161(4)])].
% 6.27/6.60 163 converse(join(A,one)) = join(one,converse(A)). [para(137(a,1),25(a,1,1)),rewrite([22(5)]),flip(a)].
% 6.27/6.60 164 join(zero,complement(A)) = complement(A). [para(136(a,1),36(a,1,1,1)),rewrite([45(2),45(3),162(5)])].
% 6.27/6.60 166 join(top,complement(A)) = join(top,top). [para(136(a,1),49(a,1,2)),rewrite([22(3)])].
% 6.27/6.60 167 complement(complement(A)) = A. [back_rewrite(162),rewrite([164(4)])].
% 6.27/6.60 177 complement(join(A,A)) = complement(A). [back_rewrite(62),rewrite([167(3),164(4)])].
% 6.27/6.60 179 join(A,top) = top. [back_rewrite(136),rewrite([167(3),22(2)])].
% 6.27/6.60 185 join(top,complement(A)) = top. [back_rewrite(166),rewrite([179(6)])].
% 6.27/6.60 195 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)])].
% 6.27/6.60 203 complement(zero) = top. [para(45(a,1),167(a,1,1))].
% 6.27/6.60 218 join(A,A) = A. [para(177(a,1),36(a,1,1,1,2)),rewrite([177(6),36(8)]),flip(a)].
% 6.27/6.60 225 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)].
% 6.27/6.60 260 join(complement(one),composition(A,complement(converse(A)))) = complement(one). [para(19(a,1),56(a,1,2,1))].
% 6.27/6.60 266 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(167(a,1),56(a,1,2,2))].
% 6.27/6.60 279 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero. [para(163(a,1),91(a,1,2,1))].
% 6.27/6.60 315 join(complement(one),converse(complement(one))) = complement(one). [para(18(a,1),266(a,1,2))].
% 6.27/6.60 319 converse(complement(one)) = complement(one). [para(315(a,1),25(a,2,1)),rewrite([19(7),22(6),315(6)]),flip(a)].
% 6.27/6.60 328 converse(top) = top. [para(319(a,1),163(a,2,2)),rewrite([22(4),20(4),20(6)])].
% 6.27/6.60 336 join(converse(A),composition(converse(complement(composition(B,complement(A)))),B)) = converse(A). [para(167(a,1),58(a,1,1,1)),rewrite([167(9)])].
% 6.27/6.60 339 join(top,converse(A)) = top. [para(328(a,1),25(a,1,1)),rewrite([22(5),179(5),328(5)])].
% 6.27/6.60 346 join(top,composition(A,converse(B))) = top. [para(47(a,1),339(a,1,2))].
% 6.27/6.60 348 join(top,composition(A,B)) = top. [para(19(a,1),346(a,1,2,2))].
% 6.27/6.60 349 composition(join(A,one),top) = top. [para(328(a,1),346(a,1,2,2)),rewrite([139(4,R)])].
% 6.27/6.60 350 composition(join(one,converse(A)),zero) = zero. [back_rewrite(279),rewrite([349(8),45(6),139(7,R),22(5),225(5)])].
% 6.27/6.60 377 composition(top,zero) = zero. [para(319(a,1),350(a,1,1,2)),rewrite([20(4)])].
% 6.27/6.60 382 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)])].
% 6.27/6.60 386 join(zero,composition(A,composition(B,zero))) = zero. [para(377(a,1),54(a,1,2)),rewrite([22(5),348(8),377(8)])].
% 6.27/6.60 389 composition(A,composition(converse(zero),zero)) = zero. [back_rewrite(382),rewrite([386(7)]),flip(a)].
% 6.27/6.60 468 composition(A,composition(converse(zero),composition(zero,B))) = composition(zero,B). [para(389(a,1),30(a,1,1)),rewrite([30(7)]),flip(a)].
% 6.27/6.60 469 composition(A,zero) = zero. [para(389(a,1),30(a,1)),rewrite([389(6)]),flip(a)].
% 6.27/6.60 470 composition(converse(zero),A) = converse(zero). [para(389(a,1),48(a,1,1)),rewrite([469(6)]),flip(a)].
% 6.27/6.60 475 composition(zero,A) = composition(B,converse(zero)). [back_rewrite(468),rewrite([470(5)]),flip(a)].
% 6.27/6.60 477 composition(zero,A) = c_0. [new_symbol(475)].
% 6.27/6.60 493 c_0 = zero. [para(477(a,1),18(a,1))].
% 6.27/6.60 497 composition(zero,A) = zero. [back_rewrite(477),rewrite([493(3)])].
% 6.27/6.60 2487 join(A,join(complement(A),converse(B))) = top. [para(20(a,1),110(a,1,1)),rewrite([339(3)]),flip(a)].
% 6.27/6.60 2571 join(A,join(complement(A),composition(B,converse(C)))) = top. [para(47(a,1),2487(a,1,2,2))].
% 6.27/6.60 3167 join(A,join(complement(A),composition(B,C))) = top. [para(19(a,1),2571(a,1,2,2,2))].
% 6.27/6.60 3170 join(A,composition(join(B,one),complement(A))) = top. [para(139(a,2),3167(a,1,2))].
% 6.27/6.60 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)])].
% 6.27/6.60 7343 join(complement(A),composition(join(one,converse(B)),A)) = top. [para(57(a,1),3224(a,1,2)),rewrite([163(3),22(6)])].
% 6.27/6.60 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)].
% 6.27/6.60 9349 join(A,converse(complement(converse(A)))) = top. [para(218(a,1),7404(a,1,2,2)),rewrite([18(5),22(4)])].
% 6.27/6.60 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)].
% 6.27/6.60 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)])].
% 6.27/6.60 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)])].
% 6.27/6.60 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)])].
% 6.27/6.60 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)])].
% 6.27/6.60 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)])].
% 6.27/6.60 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)])].
% 6.27/6.60 9631 converse(complement(converse(A))) = complement(A). [back_rewrite(9615),rewrite([9628(4),218(1)]),flip(a)].
% 6.27/6.60 9661 complement(converse(A)) = converse(complement(A)). [para(9631(a,1),19(a,1,1)),flip(a)].
% 6.27/6.60 9665 converse(complement(composition(A,converse(B)))) = complement(composition(B,converse(A))). [para(47(a,1),9631(a,1,1,1))].
% 6.27/6.60 17710 join(A,composition(complement(composition(complement(A),converse(B))),B)) = A. [para(19(a,1),336(a,1,1)),rewrite([9661(2),9665(5),19(8)])].
% 6.27/6.60 19236 join(A,composition(complement(composition(complement(A),B)),converse(B))) = A. [para(19(a,1),17710(a,1,2,1,1,2))].
% 6.27/6.60 19860 join(complement(A),composition(complement(composition(A,B)),converse(B))) = complement(A). [para(167(a,1),19236(a,1,2,1,1,1))].
% 6.27/6.60 19861 $F # answer(goals). [resolve(19860,a,44,a)].
% 6.27/6.60
% 6.27/6.60 % SZS output end Refutation
% 6.27/6.60 ============================== end of proof ==========================
% 6.27/6.60
% 6.27/6.60 ============================== STATISTICS ============================
% 6.27/6.60
% 6.27/6.60 Given=821. Generated=182043. Kept=19833. proofs=1.
% 6.27/6.60 Usable=639. Sos=9999. Demods=10264. Limbo=5, Disabled=9206. Hints=0.
% 6.27/6.60 Megabytes=28.48.
% 6.27/6.60 User_CPU=5.49, System_CPU=0.11, Wall_clock=6.
% 6.27/6.60
% 6.27/6.60 ============================== end of statistics =====================
% 6.27/6.60
% 6.27/6.60 ============================== end of search =========================
% 6.27/6.60
% 6.27/6.60 THEOREM PROVED
% 6.27/6.60 % SZS status Theorem
% 6.27/6.60
% 6.27/6.60 Exiting with 1 proof.
% 6.27/6.60
% 6.27/6.60 Process 12677 exit (max_proofs) Fri Jul 8 09:52:46 2022
% 6.27/6.60 Prover9 interrupted
%------------------------------------------------------------------------------