TSTP Solution File: REL015+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL015+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 19:53:41 EDT 2022
% Result : Theorem 0.73s 1.04s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL015+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n014.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 08:48:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/0.99 ============================== Prover9 ===============================
% 0.43/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.99 Process 31890 was started by sandbox on n014.cluster.edu,
% 0.43/0.99 Fri Jul 8 08:48:52 2022
% 0.43/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31736_n014.cluster.edu".
% 0.43/0.99 ============================== end of head ===========================
% 0.43/0.99
% 0.43/0.99 ============================== INPUT =================================
% 0.43/0.99
% 0.43/0.99 % Reading from file /tmp/Prover9_31736_n014.cluster.edu
% 0.43/0.99
% 0.43/0.99 set(prolog_style_variables).
% 0.43/0.99 set(auto2).
% 0.43/0.99 % set(auto2) -> set(auto).
% 0.43/0.99 % set(auto) -> set(auto_inference).
% 0.43/0.99 % set(auto) -> set(auto_setup).
% 0.43/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.99 % set(auto) -> set(auto_limits).
% 0.43/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.99 % set(auto) -> set(auto_denials).
% 0.43/0.99 % set(auto) -> set(auto_process).
% 0.43/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.99 % set(auto2) -> assign(stats, some).
% 0.43/0.99 % set(auto2) -> clear(echo_input).
% 0.43/0.99 % set(auto2) -> set(quiet).
% 0.43/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.99 % set(auto2) -> clear(print_given).
% 0.43/0.99 assign(lrs_ticks,-1).
% 0.43/0.99 assign(sos_limit,10000).
% 0.43/0.99 assign(order,kbo).
% 0.43/0.99 set(lex_order_vars).
% 0.43/0.99 clear(print_given).
% 0.43/0.99
% 0.43/0.99 % formulas(sos). % not echoed (14 formulas)
% 0.43/0.99
% 0.43/0.99 ============================== end of input ==========================
% 0.43/0.99
% 0.43/0.99 % From the command line: assign(max_seconds, 300).
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.99
% 0.43/0.99 % Formulas that are not ordinary clauses:
% 0.43/0.99 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 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].
% 0.43/0.99 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].
% 0.43/0.99 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].
% 0.43/0.99 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04
% 0.73/1.04 ============================== end of process non-clausal formulas ===
% 0.73/1.04
% 0.73/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.04
% 0.73/1.04 ============================== PREDICATE ELIMINATION =================
% 0.73/1.04
% 0.73/1.04 ============================== end predicate elimination =============
% 0.73/1.04
% 0.73/1.04 Auto_denials:
% 0.73/1.04 % copying label goals to answer in negative clause
% 0.73/1.04
% 0.73/1.04 Term ordering decisions:
% 0.73/1.04 Function symbol KB weights: one=1. top=1. zero=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 0.73/1.04
% 0.73/1.04 ============================== end of process initial clauses ========
% 0.73/1.04
% 0.73/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.04
% 0.73/1.04 ============================== end of clauses for search =============
% 0.73/1.04
% 0.73/1.04 ============================== SEARCH ================================
% 0.73/1.04
% 0.73/1.04 % Starting search at 0.01 seconds.
% 0.73/1.04
% 0.73/1.04 ============================== PROOF =================================
% 0.73/1.04 % SZS status Theorem
% 0.73/1.04 % SZS output start Refutation
% 0.73/1.04
% 0.73/1.04 % Proof 1 at 0.05 (+ 0.00) seconds: goals.
% 0.73/1.04 % Length of proof is 70.
% 0.73/1.04 % Level of proof is 21.
% 0.73/1.04 % Maximum clause weight is 14.000.
% 0.73/1.04 % Given clauses 72.
% 0.73/1.04
% 0.73/1.04 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 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].
% 0.73/1.04 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].
% 0.73/1.04 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].
% 0.73/1.04 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].
% 0.73/1.04 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 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].
% 0.73/1.04 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 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].
% 0.73/1.04 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 14 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 0.73/1.04 15 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 0.73/1.04 16 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 0.73/1.04 17 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 0.73/1.04 18 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 0.73/1.04 19 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 0.73/1.04 20 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 0.73/1.04 21 join(converse(A),converse(B)) = converse(join(A,B)). [copy(20),flip(a)].
% 0.73/1.04 22 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 0.73/1.04 23 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(22),flip(a)].
% 0.73/1.04 24 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 0.73/1.04 25 join(A,join(B,C)) = join(C,join(A,B)). [copy(24),rewrite([18(2)]),flip(a)].
% 0.73/1.04 26 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 0.73/1.04 27 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 0.73/1.04 28 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(27),flip(a)].
% 0.73/1.04 29 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 0.73/1.04 30 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(29),rewrite([18(7)]),flip(a)].
% 0.73/1.04 31 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 0.73/1.04 32 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(31),rewrite([18(6),18(8)]),rewrite([18(6)])].
% 0.73/1.04 33 composition(top,top) != top # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 0.73/1.04 34 complement(top) = zero. [back_rewrite(17),rewrite([19(2),16(4)])].
% 0.73/1.04 36 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(15(a,1),23(a,1,1)),flip(a)].
% 0.73/1.04 37 converse(composition(converse(A),B)) = composition(converse(B),A). [para(15(a,1),23(a,1,2)),flip(a)].
% 0.73/1.04 38 join(A,join(B,complement(A))) = join(B,top). [para(16(a,1),25(a,2,2)),rewrite([18(2)])].
% 0.73/1.04 39 composition(A,composition(one,B)) = composition(A,B). [para(14(a,1),26(a,1,1)),flip(a)].
% 0.73/1.04 45 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(14(a,1),30(a,1,2,2,1))].
% 0.73/1.04 50 join(zero,complement(join(complement(A),complement(A)))) = A. [para(16(a,1),32(a,1,1,1)),rewrite([34(2)])].
% 0.73/1.04 58 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(34(a,1),32(a,1,2,1,1))].
% 0.73/1.04 71 composition(converse(one),A) = A. [para(14(a,1),37(a,1,1)),rewrite([15(2)]),flip(a)].
% 0.73/1.04 77 converse(one) = one. [para(71(a,1),14(a,1)),flip(a)].
% 0.73/1.04 79 composition(join(A,one),B) = join(B,composition(A,B)). [para(71(a,1),28(a,1,1)),rewrite([77(4),18(4)]),flip(a)].
% 0.73/1.04 81 join(complement(A),complement(composition(one,A))) = complement(A). [para(71(a,1),30(a,1,2))].
% 0.73/1.04 82 composition(one,A) = A. [para(71(a,1),39(a,2)),rewrite([77(2),39(4)])].
% 0.73/1.04 83 join(complement(A),complement(A)) = complement(A). [back_rewrite(81),rewrite([82(3)])].
% 0.73/1.04 84 join(zero,complement(complement(A))) = A. [back_rewrite(50),rewrite([83(4)])].
% 0.73/1.04 85 converse(join(A,one)) = join(one,converse(A)). [para(77(a,1),21(a,1,1)),rewrite([18(5)]),flip(a)].
% 0.73/1.04 89 join(top,complement(A)) = top. [para(83(a,1),38(a,1,2)),rewrite([16(2),18(4)]),flip(a)].
% 0.73/1.04 90 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(58),rewrite([89(3),34(2)])].
% 0.73/1.04 91 join(top,top) = join(A,top). [para(89(a,1),38(a,1,2)),flip(a)].
% 0.73/1.04 96 join(A,top) = join(B,top). [para(91(a,1),38(a,2)),rewrite([89(3)])].
% 0.73/1.04 97 join(A,top) = c_0. [new_symbol(96)].
% 0.73/1.04 100 join(A,join(B,complement(A))) = c_0. [back_rewrite(38),rewrite([97(5)])].
% 0.73/1.04 111 c_0 = top. [para(84(a,1),100(a,1,2)),rewrite([18(2),16(2)]),flip(a)].
% 0.73/1.04 114 join(A,top) = top. [back_rewrite(97),rewrite([111(3)])].
% 0.73/1.04 139 join(zero,complement(A)) = complement(A). [para(84(a,1),90(a,1,2,1))].
% 0.73/1.04 140 complement(complement(A)) = A. [back_rewrite(90),rewrite([139(4),139(4)])].
% 0.73/1.04 166 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(140(a,1),45(a,1,2,2))].
% 0.73/1.04 220 join(complement(one),converse(complement(one))) = complement(one). [para(14(a,1),166(a,1,2))].
% 0.73/1.04 224 converse(complement(one)) = complement(one). [para(220(a,1),21(a,2,1)),rewrite([15(7),18(6),220(6)]),flip(a)].
% 0.73/1.04 229 converse(top) = top. [para(224(a,1),85(a,2,2)),rewrite([18(4),16(4),16(6)])].
% 0.73/1.04 233 join(top,converse(A)) = top. [para(229(a,1),21(a,1,1)),rewrite([18(5),114(5),229(5)])].
% 0.73/1.04 234 converse(composition(A,top)) = composition(top,converse(A)). [para(229(a,1),23(a,1,1)),flip(a)].
% 0.73/1.04 242 join(top,composition(A,converse(B))) = top. [para(36(a,1),233(a,1,2))].
% 0.73/1.04 244 join(top,composition(A,B)) = top. [para(15(a,1),242(a,1,2,2))].
% 0.73/1.04 260 composition(top,join(one,converse(A))) = top. [para(85(a,1),234(a,2,2)),rewrite([79(4),244(4),229(2)]),flip(a)].
% 0.73/1.04 275 composition(top,top) = top. [para(224(a,1),260(a,1,2,2)),rewrite([16(5)])].
% 0.73/1.04 276 $F # answer(goals). [resolve(275,a,33,a)].
% 0.73/1.04
% 0.73/1.04 % SZS output end Refutation
% 0.73/1.04 ============================== end of proof ==========================
% 0.73/1.04
% 0.73/1.04 ============================== STATISTICS ============================
% 0.73/1.04
% 0.73/1.04 Given=72. Generated=1447. Kept=256. proofs=1.
% 0.73/1.04 Usable=54. Sos=119. Demods=169. Limbo=10, Disabled=86. Hints=0.
% 0.73/1.04 Megabytes=0.31.
% 0.73/1.04 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.73/1.04
% 0.73/1.04 ============================== end of statistics =====================
% 0.73/1.04
% 0.73/1.04 ============================== end of search =========================
% 0.73/1.04
% 0.73/1.04 THEOREM PROVED
% 0.73/1.04 % SZS status Theorem
% 0.73/1.04
% 0.73/1.04 Exiting with 1 proof.
% 0.73/1.04
% 0.73/1.04 Process 31890 exit (max_proofs) Fri Jul 8 08:48:52 2022
% 0.73/1.04 Prover9 interrupted
%------------------------------------------------------------------------------