TSTP Solution File: REL004+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL004+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 19:53:24 EDT 2022
% Result : Theorem 1.21s 1.50s
% Output : Refutation 1.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL004+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 12:08:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.45/1.02 ============================== Prover9 ===============================
% 0.45/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.02 Process 1695 was started by sandbox2 on n025.cluster.edu,
% 0.45/1.02 Fri Jul 8 12:09:00 2022
% 0.45/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_1535_n025.cluster.edu".
% 0.45/1.02 ============================== end of head ===========================
% 0.45/1.02
% 0.45/1.02 ============================== INPUT =================================
% 0.45/1.02
% 0.45/1.02 % Reading from file /tmp/Prover9_1535_n025.cluster.edu
% 0.45/1.02
% 0.45/1.02 set(prolog_style_variables).
% 0.45/1.02 set(auto2).
% 0.45/1.02 % set(auto2) -> set(auto).
% 0.45/1.02 % set(auto) -> set(auto_inference).
% 0.45/1.02 % set(auto) -> set(auto_setup).
% 0.45/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.02 % set(auto) -> set(auto_limits).
% 0.45/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.02 % set(auto) -> set(auto_denials).
% 0.45/1.02 % set(auto) -> set(auto_process).
% 0.45/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.02 % set(auto2) -> assign(stats, some).
% 0.45/1.02 % set(auto2) -> clear(echo_input).
% 0.45/1.02 % set(auto2) -> set(quiet).
% 0.45/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.02 % set(auto2) -> clear(print_given).
% 0.45/1.02 assign(lrs_ticks,-1).
% 0.45/1.02 assign(sos_limit,10000).
% 0.45/1.02 assign(order,kbo).
% 0.45/1.02 set(lex_order_vars).
% 0.45/1.02 clear(print_given).
% 0.45/1.02
% 0.45/1.02 % formulas(sos). % not echoed (14 formulas)
% 0.45/1.02
% 0.45/1.02 ============================== end of input ==========================
% 0.45/1.02
% 0.45/1.02 % From the command line: assign(max_seconds, 300).
% 0.45/1.02
% 0.45/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.02
% 0.45/1.02 % Formulas that are not ordinary clauses:
% 0.45/1.02 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 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].
% 0.45/1.02 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].
% 0.45/1.02 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].
% 0.45/1.02 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].
% 0.45/1.02 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 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].
% 0.45/1.02 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 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].
% 0.45/1.02 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.50 14 -(all X0 converse(complement(X0)) = complement(converse(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.21/1.50
% 1.21/1.50 ============================== end of process non-clausal formulas ===
% 1.21/1.50
% 1.21/1.50 ============================== PROCESS INITIAL CLAUSES ===============
% 1.21/1.50
% 1.21/1.50 ============================== PREDICATE ELIMINATION =================
% 1.21/1.50
% 1.21/1.50 ============================== end predicate elimination =============
% 1.21/1.50
% 1.21/1.50 Auto_denials:
% 1.21/1.50 % copying label goals to answer in negative clause
% 1.21/1.50
% 1.21/1.50 Term ordering decisions:
% 1.21/1.50 Function symbol KB weights: one=1. top=1. zero=1. c1=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 1.21/1.50
% 1.21/1.50 ============================== end of process initial clauses ========
% 1.21/1.50
% 1.21/1.50 ============================== CLAUSES FOR SEARCH ====================
% 1.21/1.50
% 1.21/1.50 ============================== end of clauses for search =============
% 1.21/1.50
% 1.21/1.50 ============================== SEARCH ================================
% 1.21/1.50
% 1.21/1.50 % Starting search at 0.01 seconds.
% 1.21/1.50
% 1.21/1.50 ============================== PROOF =================================
% 1.21/1.50 % SZS status Theorem
% 1.21/1.50 % SZS output start Refutation
% 1.21/1.50
% 1.21/1.50 % Proof 1 at 0.48 (+ 0.02) seconds: goals.
% 1.21/1.50 % Length of proof is 78.
% 1.21/1.50 % Level of proof is 25.
% 1.21/1.50 % Maximum clause weight is 14.000.
% 1.21/1.50 % Given clauses 286.
% 1.21/1.50
% 1.21/1.50 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.50 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].
% 1.21/1.50 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].
% 1.21/1.50 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].
% 1.21/1.50 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].
% 1.21/1.50 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.50 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.50 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.50 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.50 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].
% 1.21/1.50 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.50 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.50 14 -(all X0 converse(complement(X0)) = complement(converse(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.21/1.50 15 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 1.21/1.50 16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 1.21/1.50 17 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 1.21/1.50 18 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 1.21/1.50 19 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 1.21/1.50 20 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 1.21/1.50 21 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 1.21/1.50 22 join(converse(A),converse(B)) = converse(join(A,B)). [copy(21),flip(a)].
% 1.21/1.50 23 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 1.21/1.50 24 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(23),flip(a)].
% 1.21/1.50 25 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 1.21/1.50 26 join(A,join(B,C)) = join(C,join(A,B)). [copy(25),rewrite([19(2)]),flip(a)].
% 1.21/1.50 27 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 1.21/1.50 30 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 1.21/1.50 31 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(30),rewrite([19(7)]),flip(a)].
% 1.21/1.50 32 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 1.21/1.50 33 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(32),rewrite([19(6),19(8)]),rewrite([19(6)])].
% 1.21/1.50 34 converse(complement(c1)) != complement(converse(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)].
% 1.21/1.50 35 complement(top) = zero. [back_rewrite(18),rewrite([20(2),17(4)])].
% 1.21/1.50 38 converse(composition(converse(A),B)) = composition(converse(B),A). [para(16(a,1),24(a,1,2)),flip(a)].
% 1.21/1.50 39 join(A,join(B,complement(A))) = join(B,top). [para(17(a,1),26(a,2,2)),rewrite([19(2)])].
% 1.21/1.50 40 composition(A,composition(one,B)) = composition(A,B). [para(15(a,1),27(a,1,1)),flip(a)].
% 1.21/1.50 46 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(15(a,1),31(a,1,2,2,1))].
% 1.21/1.50 51 join(zero,complement(join(complement(A),complement(A)))) = A. [para(17(a,1),33(a,1,1,1)),rewrite([35(2)])].
% 1.21/1.50 59 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(35(a,1),33(a,1,2,1,1))].
% 1.21/1.50 72 composition(converse(one),A) = A. [para(15(a,1),38(a,1,1)),rewrite([16(2)]),flip(a)].
% 1.21/1.50 78 converse(one) = one. [para(72(a,1),15(a,1)),flip(a)].
% 1.21/1.50 82 join(complement(A),complement(composition(one,A))) = complement(A). [para(72(a,1),31(a,1,2))].
% 1.21/1.50 83 composition(one,A) = A. [para(72(a,1),40(a,2)),rewrite([78(2),40(4)])].
% 1.21/1.50 84 join(complement(A),complement(A)) = complement(A). [back_rewrite(82),rewrite([83(3)])].
% 1.21/1.50 85 join(zero,complement(complement(A))) = A. [back_rewrite(51),rewrite([84(4)])].
% 1.21/1.50 86 converse(join(A,one)) = join(one,converse(A)). [para(78(a,1),22(a,1,1)),rewrite([19(5)]),flip(a)].
% 1.21/1.50 90 join(top,complement(A)) = top. [para(84(a,1),39(a,1,2)),rewrite([17(2),19(4)]),flip(a)].
% 1.21/1.50 91 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(59),rewrite([90(3),35(2)])].
% 1.21/1.50 92 join(top,top) = join(A,top). [para(90(a,1),39(a,1,2)),flip(a)].
% 1.21/1.50 97 join(A,top) = join(B,top). [para(92(a,1),39(a,2)),rewrite([90(3)])].
% 1.21/1.50 98 join(A,top) = c_0. [new_symbol(97)].
% 1.21/1.50 101 join(A,join(B,complement(A))) = c_0. [back_rewrite(39),rewrite([98(5)])].
% 1.21/1.50 112 c_0 = top. [para(85(a,1),101(a,1,2)),rewrite([19(2),17(2)]),flip(a)].
% 1.21/1.50 113 join(A,join(B,complement(A))) = top. [back_rewrite(101),rewrite([112(4)])].
% 1.21/1.50 140 join(zero,complement(A)) = complement(A). [para(85(a,1),91(a,1,2,1))].
% 1.21/1.50 141 complement(complement(A)) = A. [back_rewrite(91),rewrite([140(4),140(4)])].
% 1.21/1.50 142 join(A,zero) = A. [back_rewrite(85),rewrite([141(3),19(2)])].
% 1.21/1.50 147 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(141(a,1),33(a,1,1,1,2)),rewrite([141(5),19(4)])].
% 1.21/1.50 149 join(A,A) = A. [para(141(a,1),84(a,1,1)),rewrite([141(2),141(3)])].
% 1.21/1.50 153 join(A,join(A,B)) = join(A,B). [para(149(a,1),26(a,1)),rewrite([19(3),26(4,R),19(3),26(3,R),149(2)]),flip(a)].
% 1.21/1.50 154 join(A,complement(join(B,complement(A)))) = A. [para(33(a,1),153(a,1,2)),rewrite([19(4),33(12)])].
% 1.21/1.50 156 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(154(a,1),26(a,2,2)),rewrite([19(4),19(6)])].
% 1.21/1.50 159 join(complement(A),complement(join(A,B))) = complement(A). [para(141(a,1),154(a,1,2,1,2)),rewrite([19(2)])].
% 1.21/1.50 167 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(141(a,1),46(a,1,2,2))].
% 1.21/1.50 170 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(22(a,1),159(a,1,2,1))].
% 1.21/1.50 221 join(complement(one),converse(complement(one))) = complement(one). [para(15(a,1),167(a,1,2))].
% 1.21/1.50 225 converse(complement(one)) = complement(one). [para(221(a,1),22(a,2,1)),rewrite([16(7),19(6),221(6)]),flip(a)].
% 1.21/1.50 230 converse(top) = top. [para(225(a,1),86(a,2,2)),rewrite([19(4),17(4),17(6)])].
% 1.21/1.50 2511 join(A,complement(join(A,B))) = join(A,complement(B)). [para(147(a,1),156(a,1,2)),flip(a)].
% 1.21/1.50 2939 join(complement(converse(A)),converse(join(A,B))) = top. [para(170(a,1),113(a,1,2)),rewrite([19(5)])].
% 1.21/1.50 2965 join(A,join(B,converse(complement(converse(A))))) = top. [para(2939(a,1),22(a,2,1)),rewrite([16(6),26(5),19(4),26(5,R),19(4),230(7)])].
% 1.21/1.50 2996 join(A,converse(complement(converse(A)))) = top. [para(149(a,1),2965(a,1,2))].
% 1.21/1.50 3033 join(A,complement(converse(complement(converse(A))))) = A. [para(2996(a,1),2511(a,1,2,1)),rewrite([35(2),142(2)]),flip(a)].
% 1.21/1.50 3034 join(converse(A),complement(converse(complement(A)))) = converse(A). [para(16(a,1),3033(a,1,2,1,1,1))].
% 1.21/1.50 3037 join(A,converse(complement(converse(complement(A))))) = converse(complement(converse(complement(A)))). [para(3033(a,1),33(a,1,2,1)),rewrite([141(9),19(8),2511(8),141(6)])].
% 1.21/1.50 3156 converse(complement(converse(complement(A)))) = A. [para(3034(a,1),22(a,2,1)),rewrite([16(2),3037(5),16(6)])].
% 1.21/1.50 3179 complement(converse(complement(A))) = converse(A). [para(3156(a,1),16(a,1,1)),flip(a)].
% 1.21/1.50 3248 converse(complement(A)) = complement(converse(A)). [para(3179(a,1),141(a,1,1)),flip(a)].
% 1.21/1.50 3249 $F # answer(goals). [resolve(3248,a,34,a)].
% 1.21/1.50
% 1.21/1.50 % SZS output end Refutation
% 1.21/1.50 ============================== end of proof ==========================
% 1.21/1.50
% 1.21/1.50 ============================== STATISTICS ============================
% 1.21/1.50
% 1.21/1.50 Given=286. Generated=20642. Kept=3228. proofs=1.
% 1.21/1.50 Usable=231. Sos=2428. Demods=2540. Limbo=3, Disabled=579. Hints=0.
% 1.21/1.50 Megabytes=4.07.
% 1.21/1.50 User_CPU=0.48, System_CPU=0.02, Wall_clock=1.
% 1.21/1.50
% 1.21/1.50 ============================== end of statistics =====================
% 1.21/1.50
% 1.21/1.50 ============================== end of search =========================
% 1.21/1.50
% 1.21/1.50 THEOREM PROVED
% 1.21/1.50 % SZS status Theorem
% 1.21/1.50
% 1.21/1.50 Exiting with 1 proof.
% 1.21/1.50
% 1.21/1.50 Process 1695 exit (max_proofs) Fri Jul 8 12:09:01 2022
% 1.21/1.50 Prover9 interrupted
%------------------------------------------------------------------------------