TSTP Solution File: REL013-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL013-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 19:53:39 EDT 2022
% Result : Unsatisfiable 0.71s 1.03s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL013-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n004.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 15:43:37 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.71/1.03 ============================== Prover9 ===============================
% 0.71/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.71/1.03 Process 18531 was started by sandbox2 on n004.cluster.edu,
% 0.71/1.03 Fri Jul 8 15:43:38 2022
% 0.71/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_18377_n004.cluster.edu".
% 0.71/1.03 ============================== end of head ===========================
% 0.71/1.03
% 0.71/1.03 ============================== INPUT =================================
% 0.71/1.03
% 0.71/1.03 % Reading from file /tmp/Prover9_18377_n004.cluster.edu
% 0.71/1.03
% 0.71/1.03 set(prolog_style_variables).
% 0.71/1.03 set(auto2).
% 0.71/1.03 % set(auto2) -> set(auto).
% 0.71/1.03 % set(auto) -> set(auto_inference).
% 0.71/1.03 % set(auto) -> set(auto_setup).
% 0.71/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.71/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/1.03 % set(auto) -> set(auto_limits).
% 0.71/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/1.03 % set(auto) -> set(auto_denials).
% 0.71/1.03 % set(auto) -> set(auto_process).
% 0.71/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.71/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.71/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.71/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.71/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.71/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.71/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.71/1.03 % set(auto2) -> assign(stats, some).
% 0.71/1.03 % set(auto2) -> clear(echo_input).
% 0.71/1.03 % set(auto2) -> set(quiet).
% 0.71/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.71/1.03 % set(auto2) -> clear(print_given).
% 0.71/1.03 assign(lrs_ticks,-1).
% 0.71/1.03 assign(sos_limit,10000).
% 0.71/1.03 assign(order,kbo).
% 0.71/1.03 set(lex_order_vars).
% 0.71/1.03 clear(print_given).
% 0.71/1.03
% 0.71/1.03 % formulas(sos). % not echoed (14 formulas)
% 0.71/1.03
% 0.71/1.03 ============================== end of input ==========================
% 0.71/1.03
% 0.71/1.03 % From the command line: assign(max_seconds, 300).
% 0.71/1.03
% 0.71/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/1.03
% 0.71/1.03 % Formulas that are not ordinary clauses:
% 0.71/1.03
% 0.71/1.03 ============================== end of process non-clausal formulas ===
% 0.71/1.03
% 0.71/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.71/1.03
% 0.71/1.03 ============================== PREDICATE ELIMINATION =================
% 0.71/1.03
% 0.71/1.03 ============================== end predicate elimination =============
% 0.71/1.03
% 0.71/1.03 Auto_denials:
% 0.71/1.03 % copying label goals_14 to answer in negative clause
% 0.71/1.03
% 0.71/1.03 Term ordering decisions:
% 0.71/1.03 Function symbol KB weights: one=1. top=1. zero=1. sk1=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 0.71/1.03
% 0.71/1.03 ============================== end of process initial clauses ========
% 0.71/1.03
% 0.71/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.71/1.03
% 0.71/1.03 ============================== end of clauses for search =============
% 0.71/1.03
% 0.71/1.03 ============================== SEARCH ================================
% 0.71/1.03
% 0.71/1.03 % Starting search at 0.01 seconds.
% 0.71/1.03
% 0.71/1.03 ============================== PROOF =================================
% 0.71/1.03 % SZS status Unsatisfiable
% 0.71/1.03 % SZS output start Refutation
% 0.71/1.03
% 0.71/1.03 % Proof 1 at 0.06 (+ 0.00) seconds: goals_14.
% 0.71/1.03 % Length of proof is 72.
% 0.71/1.03 % Level of proof is 27.
% 0.71/1.03 % Maximum clause weight is 15.000.
% 0.71/1.03 % Given clauses 79.
% 0.71/1.03
% 0.71/1.03 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 0.71/1.03 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 0.71/1.03 3 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 0.71/1.03 4 join(A,complement(A)) = top. [copy(3),flip(a)].
% 0.71/1.03 5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 0.71/1.03 6 meet(A,complement(A)) = zero. [copy(5),flip(a)].
% 0.71/1.03 7 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 0.71/1.03 8 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 0.71/1.03 9 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 0.71/1.03 10 join(converse(A),converse(B)) = converse(join(A,B)). [copy(9),flip(a)].
% 0.71/1.03 11 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 0.71/1.03 12 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(11),flip(a)].
% 0.71/1.03 13 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 0.71/1.03 14 join(A,join(B,C)) = join(C,join(A,B)). [copy(13),rewrite([7(4)])].
% 0.71/1.03 15 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 0.71/1.03 16 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(15),flip(a)].
% 0.71/1.03 17 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 0.71/1.03 18 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(17),flip(a)].
% 0.71/1.03 19 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 0.71/1.03 20 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(19),rewrite([7(6)])].
% 0.71/1.03 21 A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) # label(maddux3_a_kind_of_de_Morgan_3) # label(axiom). [assumption].
% 0.71/1.03 22 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(21),rewrite([7(6),7(8)]),flip(a),rewrite([7(6)])].
% 0.71/1.03 23 composition(sk1,zero) != zero | composition(zero,sk1) != zero # label(goals_14) # label(negated_conjecture) # answer(goals_14). [assumption].
% 0.71/1.03 24 complement(top) = zero. [back_rewrite(6),rewrite([8(2),4(4)])].
% 0.71/1.03 26 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),12(a,1,1)),flip(a)].
% 0.71/1.03 27 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),12(a,1,2)),flip(a)].
% 0.71/1.03 28 join(A,join(B,complement(A))) = join(B,top). [para(4(a,1),14(a,2,2)),rewrite([7(2)])].
% 0.71/1.03 29 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),16(a,1,1)),flip(a)].
% 0.71/1.03 35 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),20(a,1,2,2,1))].
% 0.71/1.03 38 join(complement(converse(A)),composition(B,complement(converse(composition(A,B))))) = complement(converse(A)). [para(12(a,1),20(a,1,2,2,1)),rewrite([2(4)])].
% 0.71/1.03 40 join(zero,complement(join(complement(A),complement(A)))) = A. [para(4(a,1),22(a,1,1,1)),rewrite([24(2)])].
% 0.71/1.03 48 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(24(a,1),22(a,1,2,1,1))].
% 0.71/1.03 61 composition(converse(one),A) = A. [para(1(a,1),27(a,1,1)),rewrite([2(2)]),flip(a)].
% 0.71/1.03 67 converse(one) = one. [para(61(a,1),1(a,1)),flip(a)].
% 0.71/1.03 69 composition(join(A,one),B) = join(B,composition(A,B)). [para(61(a,1),18(a,1,1)),rewrite([67(4),7(4)]),flip(a)].
% 0.71/1.03 71 join(complement(A),complement(composition(one,A))) = complement(A). [para(61(a,1),20(a,1,2))].
% 0.71/1.03 72 composition(one,A) = A. [para(61(a,1),29(a,2)),rewrite([67(2),29(4)])].
% 0.71/1.03 73 join(complement(A),complement(A)) = complement(A). [back_rewrite(71),rewrite([72(3)])].
% 0.71/1.03 74 join(zero,complement(complement(A))) = A. [back_rewrite(40),rewrite([73(4)])].
% 0.71/1.03 75 converse(join(A,one)) = join(one,converse(A)). [para(67(a,1),10(a,1,1)),rewrite([7(5)]),flip(a)].
% 0.71/1.03 79 join(top,complement(A)) = top. [para(73(a,1),28(a,1,2)),rewrite([4(2),7(4)]),flip(a)].
% 0.71/1.03 80 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(48),rewrite([79(3),24(2)])].
% 0.71/1.03 81 join(top,top) = join(A,top). [para(79(a,1),28(a,1,2)),flip(a)].
% 0.71/1.03 86 join(A,top) = join(B,top). [para(81(a,1),28(a,2)),rewrite([79(3)])].
% 0.71/1.03 87 join(A,top) = c_0. [new_symbol(86)].
% 0.71/1.03 90 join(A,join(B,complement(A))) = c_0. [back_rewrite(28),rewrite([87(5)])].
% 0.71/1.03 101 c_0 = top. [para(74(a,1),90(a,1,2)),rewrite([7(2),4(2)]),flip(a)].
% 0.71/1.03 104 join(A,top) = top. [back_rewrite(87),rewrite([101(3)])].
% 0.71/1.03 129 join(zero,complement(A)) = complement(A). [para(74(a,1),80(a,1,2,1))].
% 0.71/1.03 130 complement(complement(A)) = A. [back_rewrite(80),rewrite([129(4),129(4)])].
% 0.71/1.03 131 join(A,zero) = A. [back_rewrite(74),rewrite([130(3),7(2)])].
% 0.71/1.03 138 join(A,A) = A. [para(130(a,1),73(a,1,1)),rewrite([130(2),130(3)])].
% 0.71/1.03 142 join(A,join(A,B)) = join(A,B). [para(138(a,1),14(a,1)),rewrite([7(3),14(4,R),7(3),14(3,R),138(2)]),flip(a)].
% 0.71/1.03 156 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(130(a,1),35(a,1,2,2))].
% 0.71/1.03 210 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),156(a,1,2))].
% 0.71/1.03 214 converse(complement(one)) = complement(one). [para(210(a,1),10(a,2,1)),rewrite([2(7),7(6),210(6)]),flip(a)].
% 0.71/1.03 219 converse(top) = top. [para(214(a,1),75(a,2,2)),rewrite([7(4),4(4),4(6)])].
% 0.71/1.03 223 join(top,converse(A)) = top. [para(219(a,1),10(a,1,1)),rewrite([7(5),104(5),219(5)])].
% 0.71/1.03 224 converse(composition(A,top)) = composition(top,converse(A)). [para(219(a,1),12(a,1,1)),flip(a)].
% 0.71/1.03 232 join(top,composition(A,converse(B))) = top. [para(26(a,1),223(a,1,2))].
% 0.71/1.03 234 join(top,composition(A,B)) = top. [para(2(a,1),232(a,1,2,2))].
% 0.71/1.03 250 composition(top,join(one,converse(A))) = top. [para(75(a,1),224(a,2,2)),rewrite([69(4),234(4),219(2)]),flip(a)].
% 0.71/1.03 255 composition(top,join(A,one)) = top. [para(2(a,1),250(a,1,2,2)),rewrite([7(3)])].
% 0.71/1.03 279 join(zero,composition(A,zero)) = zero. [para(255(a,1),38(a,1,2,2,1,1)),rewrite([219(2),24(2),219(5),24(5),69(5),142(6),219(6),24(6)])].
% 0.71/1.03 294 join(A,composition(B,zero)) = A. [para(279(a,1),14(a,1,2)),rewrite([131(2),131(4),7(3)]),flip(a)].
% 0.71/1.03 298 composition(join(A,B),zero) = composition(A,zero). [para(294(a,1),18(a,1)),flip(a)].
% 0.71/1.03 300 composition(A,zero) = zero. [para(294(a,1),69(a,2)),rewrite([298(4)])].
% 0.71/1.03 301 composition(zero,sk1) != zero # answer(goals_14). [back_rewrite(23),rewrite([300(3)]),xx(a)].
% 0.71/1.03 303 composition(converse(zero),A) = converse(zero). [para(300(a,1),27(a,1,1)),flip(a)].
% 0.71/1.03 316 converse(zero) = zero. [para(303(a,1),300(a,1))].
% 0.71/1.03 321 composition(zero,A) = zero. [back_rewrite(303),rewrite([316(2),316(4)])].
% 0.71/1.03 322 $F # answer(goals_14). [resolve(321,a,301,a)].
% 0.71/1.03
% 0.71/1.03 % SZS output end Refutation
% 0.71/1.03 ============================== end of proof ==========================
% 0.71/1.03
% 0.71/1.03 ============================== STATISTICS ============================
% 0.71/1.03
% 0.71/1.03 Given=79. Generated=1700. Kept=312. proofs=1.
% 0.71/1.03 Usable=55. Sos=150. Demods=196. Limbo=5, Disabled=115. Hints=0.
% 0.71/1.03 Megabytes=0.37.
% 0.71/1.03 User_CPU=0.06, System_CPU=0.00, Wall_clock=0.
% 0.71/1.03
% 0.71/1.03 ============================== end of statistics =====================
% 0.71/1.03
% 0.71/1.03 ============================== end of search =========================
% 0.71/1.03
% 0.71/1.03 THEOREM PROVED
% 0.71/1.03 % SZS status Unsatisfiable
% 0.71/1.03
% 0.71/1.03 Exiting with 1 proof.
% 0.71/1.03
% 0.71/1.03 Process 18531 exit (max_proofs) Fri Jul 8 15:43:38 2022
% 0.71/1.03 Prover9 interrupted
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