TSTP Solution File: REL023+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL023+1 : 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 19:53:53 EDT 2022
% Result : Theorem 0.73s 1.05s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL023+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 : n026.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 09:27:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.00 ============================== Prover9 ===============================
% 0.43/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.00 Process 20939 was started by sandbox on n026.cluster.edu,
% 0.43/1.00 Fri Jul 8 09:27:25 2022
% 0.43/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20786_n026.cluster.edu".
% 0.43/1.00 ============================== end of head ===========================
% 0.43/1.00
% 0.43/1.00 ============================== INPUT =================================
% 0.43/1.00
% 0.43/1.00 % Reading from file /tmp/Prover9_20786_n026.cluster.edu
% 0.43/1.00
% 0.43/1.00 set(prolog_style_variables).
% 0.43/1.00 set(auto2).
% 0.43/1.00 % set(auto2) -> set(auto).
% 0.43/1.00 % set(auto) -> set(auto_inference).
% 0.43/1.00 % set(auto) -> set(auto_setup).
% 0.43/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.00 % set(auto) -> set(auto_limits).
% 0.43/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.00 % set(auto) -> set(auto_denials).
% 0.43/1.00 % set(auto) -> set(auto_process).
% 0.43/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.00 % set(auto2) -> assign(stats, some).
% 0.43/1.00 % set(auto2) -> clear(echo_input).
% 0.43/1.00 % set(auto2) -> set(quiet).
% 0.43/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.00 % set(auto2) -> clear(print_given).
% 0.43/1.00 assign(lrs_ticks,-1).
% 0.43/1.00 assign(sos_limit,10000).
% 0.43/1.00 assign(order,kbo).
% 0.43/1.00 set(lex_order_vars).
% 0.43/1.00 clear(print_given).
% 0.43/1.00
% 0.43/1.00 % formulas(sos). % not echoed (14 formulas)
% 0.43/1.00
% 0.43/1.00 ============================== end of input ==========================
% 0.43/1.00
% 0.43/1.00 % From the command line: assign(max_seconds, 300).
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.00
% 0.43/1.00 % Formulas that are not ordinary clauses:
% 0.43/1.00 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 14 -(all X0 all X1 all X2 join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.05
% 0.73/1.05 ============================== end of process non-clausal formulas ===
% 0.73/1.05
% 0.73/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.05
% 0.73/1.05 ============================== PREDICATE ELIMINATION =================
% 0.73/1.05
% 0.73/1.05 ============================== end predicate elimination =============
% 0.73/1.05
% 0.73/1.05 Auto_denials:
% 0.73/1.05 % copying label goals to answer in negative clause
% 0.73/1.05
% 0.73/1.05 Term ordering decisions:
% 0.73/1.05 Function symbol KB weights: one=1. top=1. zero=1. c1=1. c2=1. c3=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 0.73/1.05
% 0.73/1.05 ============================== end of process initial clauses ========
% 0.73/1.05
% 0.73/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.05
% 0.73/1.05 ============================== end of clauses for search =============
% 0.73/1.05
% 0.73/1.05 ============================== SEARCH ================================
% 0.73/1.05
% 0.73/1.05 % Starting search at 0.01 seconds.
% 0.73/1.05
% 0.73/1.05 ============================== PROOF =================================
% 0.73/1.05 % SZS status Theorem
% 0.73/1.05 % SZS output start Refutation
% 0.73/1.05
% 0.73/1.05 % Proof 1 at 0.05 (+ 0.01) seconds: goals.
% 0.73/1.05 % Length of proof is 55.
% 0.73/1.05 % Level of proof is 17.
% 0.73/1.05 % Maximum clause weight is 25.000.
% 0.73/1.05 % Given clauses 75.
% 0.73/1.05
% 0.73/1.05 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 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].
% 0.73/1.05 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].
% 0.73/1.05 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].
% 0.73/1.05 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].
% 0.73/1.05 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 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].
% 0.73/1.05 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 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].
% 0.73/1.05 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 14 -(all X0 all X1 all X2 join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.05 15 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 0.73/1.05 16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 0.73/1.05 17 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 0.73/1.05 18 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 0.73/1.05 19 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 0.73/1.05 20 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 0.73/1.05 23 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 0.73/1.05 24 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(23),flip(a)].
% 0.73/1.05 25 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 0.73/1.05 26 join(A,join(B,C)) = join(C,join(A,B)). [copy(25),rewrite([19(2)]),flip(a)].
% 0.73/1.05 27 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 0.73/1.05 28 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 0.73/1.05 29 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(28),flip(a)].
% 0.73/1.05 30 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 0.73/1.05 31 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(30),rewrite([19(7)]),flip(a)].
% 0.73/1.05 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)].
% 0.73/1.05 33 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(32),rewrite([19(6),19(8)]),rewrite([19(6)])].
% 0.73/1.05 34 composition(c1,meet(c2,c3)) != join(composition(meet(c1,converse(c2)),meet(c2,c3)),composition(c1,meet(c2,c3))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)].
% 0.73/1.05 35 composition(join(c1,complement(join(complement(c1),complement(converse(c2))))),complement(join(complement(c2),complement(c3)))) != composition(c1,complement(join(complement(c2),complement(c3)))) # answer(goals). [copy(34),rewrite([20(4),20(12),20(18),20(26),19(31),29(31)]),flip(a)].
% 0.73/1.05 36 complement(top) = zero. [back_rewrite(18),rewrite([20(2),17(4)])].
% 0.73/1.05 39 converse(composition(converse(A),B)) = composition(converse(B),A). [para(16(a,1),24(a,1,2)),flip(a)].
% 0.73/1.05 40 join(A,join(B,complement(A))) = join(B,top). [para(17(a,1),26(a,2,2)),rewrite([19(2)])].
% 0.73/1.05 41 composition(A,composition(one,B)) = composition(A,B). [para(15(a,1),27(a,1,1)),flip(a)].
% 0.73/1.05 52 join(zero,complement(join(complement(A),complement(A)))) = A. [para(17(a,1),33(a,1,1,1)),rewrite([36(2)])].
% 0.73/1.05 56 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(33(a,1),33(a,1,2,1)),rewrite([19(10)])].
% 0.73/1.05 60 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(36(a,1),33(a,1,2,1,1))].
% 0.73/1.05 73 composition(converse(one),A) = A. [para(15(a,1),39(a,1,1)),rewrite([16(2)]),flip(a)].
% 0.73/1.05 79 converse(one) = one. [para(73(a,1),15(a,1)),flip(a)].
% 0.73/1.05 83 join(complement(A),complement(composition(one,A))) = complement(A). [para(73(a,1),31(a,1,2))].
% 0.73/1.05 84 composition(one,A) = A. [para(73(a,1),41(a,2)),rewrite([79(2),41(4)])].
% 0.73/1.05 85 join(complement(A),complement(A)) = complement(A). [back_rewrite(83),rewrite([84(3)])].
% 0.73/1.05 86 join(zero,complement(complement(A))) = A. [back_rewrite(52),rewrite([85(4)])].
% 0.73/1.05 91 join(top,complement(A)) = top. [para(85(a,1),40(a,1,2)),rewrite([17(2),19(4)]),flip(a)].
% 0.73/1.05 92 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(60),rewrite([91(3),36(2)])].
% 0.73/1.05 141 join(zero,complement(A)) = complement(A). [para(86(a,1),92(a,1,2,1))].
% 0.73/1.05 142 complement(complement(A)) = A. [back_rewrite(92),rewrite([141(4),141(4)])].
% 0.73/1.05 150 join(A,A) = A. [para(142(a,1),85(a,1,1)),rewrite([142(2),142(3)])].
% 0.73/1.05 154 join(A,join(A,B)) = join(A,B). [para(150(a,1),26(a,1)),rewrite([19(3),26(4,R),19(3),26(3,R),150(2)]),flip(a)].
% 0.73/1.05 155 join(A,complement(join(B,complement(A)))) = A. [para(33(a,1),154(a,1,2)),rewrite([19(4),33(12)])].
% 0.73/1.05 160 join(complement(A),complement(join(A,B))) = complement(A). [para(142(a,1),155(a,1,2,1,2)),rewrite([19(2)])].
% 0.73/1.05 301 join(A,complement(join(complement(A),complement(B)))) = A. [para(56(a,1),160(a,1,2,1)),rewrite([142(2),19(3),142(7)])].
% 0.73/1.05 306 $F # answer(goals). [back_rewrite(35),rewrite([301(9)]),xx(a)].
% 0.73/1.05
% 0.73/1.05 % SZS output end Refutation
% 0.73/1.05 ============================== end of proof ==========================
% 0.73/1.05
% 0.73/1.05 ============================== STATISTICS ============================
% 0.73/1.05
% 0.73/1.05 Given=75. Generated=1569. Kept=284. proofs=1.
% 0.73/1.05 Usable=56. Sos=146. Demods=194. Limbo=5, Disabled=91. Hints=0.
% 0.73/1.05 Megabytes=0.36.
% 0.73/1.05 User_CPU=0.06, System_CPU=0.01, Wall_clock=0.
% 0.73/1.05
% 0.73/1.05 ============================== end of statistics =====================
% 0.73/1.05
% 0.73/1.05 ============================== end of search =========================
% 0.73/1.05
% 0.73/1.05 THEOREM PROVED
% 0.73/1.05 % SZS status Theorem
% 0.73/1.05
% 0.73/1.05 Exiting with 1 proof.
% 0.73/1.05
% 0.73/1.05 Process 20939 exit (max_proofs) Fri Jul 8 09:27:25 2022
% 0.73/1.05 Prover9 interrupted
%------------------------------------------------------------------------------