TSTP Solution File: REL018-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL018-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 19:53:47 EDT 2022
% Result : Unsatisfiable 0.71s 1.07s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : REL018-1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n018.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 16:03:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.71/1.07 ============================== Prover9 ===============================
% 0.71/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.71/1.07 Process 30529 was started by sandbox2 on n018.cluster.edu,
% 0.71/1.07 Fri Jul 8 16:03:26 2022
% 0.71/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30375_n018.cluster.edu".
% 0.71/1.07 ============================== end of head ===========================
% 0.71/1.07
% 0.71/1.07 ============================== INPUT =================================
% 0.71/1.07
% 0.71/1.07 % Reading from file /tmp/Prover9_30375_n018.cluster.edu
% 0.71/1.07
% 0.71/1.07 set(prolog_style_variables).
% 0.71/1.07 set(auto2).
% 0.71/1.07 % set(auto2) -> set(auto).
% 0.71/1.07 % set(auto) -> set(auto_inference).
% 0.71/1.07 % set(auto) -> set(auto_setup).
% 0.71/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.71/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/1.07 % set(auto) -> set(auto_limits).
% 0.71/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/1.07 % set(auto) -> set(auto_denials).
% 0.71/1.07 % set(auto) -> set(auto_process).
% 0.71/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.71/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.71/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.71/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.71/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.71/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.71/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.71/1.07 % set(auto2) -> assign(stats, some).
% 0.71/1.07 % set(auto2) -> clear(echo_input).
% 0.71/1.07 % set(auto2) -> set(quiet).
% 0.71/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.71/1.07 % set(auto2) -> clear(print_given).
% 0.71/1.07 assign(lrs_ticks,-1).
% 0.71/1.07 assign(sos_limit,10000).
% 0.71/1.07 assign(order,kbo).
% 0.71/1.07 set(lex_order_vars).
% 0.71/1.07 clear(print_given).
% 0.71/1.07
% 0.71/1.07 % formulas(sos). % not echoed (15 formulas)
% 0.71/1.07
% 0.71/1.07 ============================== end of input ==========================
% 0.71/1.07
% 0.71/1.07 % From the command line: assign(max_seconds, 300).
% 0.71/1.07
% 0.71/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/1.07
% 0.71/1.07 % Formulas that are not ordinary clauses:
% 0.71/1.07
% 0.71/1.07 ============================== end of process non-clausal formulas ===
% 0.71/1.07
% 0.71/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.71/1.07
% 0.71/1.07 ============================== PREDICATE ELIMINATION =================
% 0.71/1.07
% 0.71/1.07 ============================== end predicate elimination =============
% 0.71/1.07
% 0.71/1.07 Auto_denials:
% 0.71/1.07 % copying label goals_15 to answer in negative clause
% 0.71/1.07
% 0.71/1.07 Term ordering decisions:
% 0.71/1.07 Function symbol KB weights: sk1=1. top=1. one=1. zero=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 0.71/1.07
% 0.71/1.07 ============================== end of process initial clauses ========
% 0.71/1.07
% 0.71/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.71/1.07
% 0.71/1.07 ============================== end of clauses for search =============
% 0.71/1.07
% 0.71/1.07 ============================== SEARCH ================================
% 0.71/1.07
% 0.71/1.07 % Starting search at 0.01 seconds.
% 0.71/1.07
% 0.71/1.07 ============================== PROOF =================================
% 0.71/1.07 % SZS status Unsatisfiable
% 0.71/1.07 % SZS output start Refutation
% 0.71/1.07
% 0.71/1.07 % Proof 1 at 0.12 (+ 0.01) seconds: goals_15.
% 0.71/1.07 % Length of proof is 81.
% 0.71/1.07 % Level of proof is 31.
% 0.71/1.07 % Maximum clause weight is 17.000.
% 0.71/1.07 % Given clauses 119.
% 0.71/1.07
% 0.71/1.07 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 0.71/1.07 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 0.71/1.07 3 composition(sk1,top) = sk1 # label(goals_14) # label(negated_conjecture). [assumption].
% 0.71/1.07 4 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 0.71/1.07 5 join(A,complement(A)) = top. [copy(4),flip(a)].
% 0.71/1.07 6 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 0.71/1.07 7 meet(A,complement(A)) = zero. [copy(6),flip(a)].
% 0.71/1.07 8 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 0.71/1.07 9 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 0.71/1.07 10 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 0.71/1.07 11 join(converse(A),converse(B)) = converse(join(A,B)). [copy(10),flip(a)].
% 0.71/1.07 12 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 0.71/1.07 13 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(12),flip(a)].
% 0.71/1.07 14 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 0.71/1.07 15 join(A,join(B,C)) = join(C,join(A,B)). [copy(14),rewrite([8(4)])].
% 0.71/1.07 16 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 0.71/1.07 17 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(16),flip(a)].
% 0.71/1.07 18 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 0.71/1.07 19 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(18),flip(a)].
% 0.71/1.07 20 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 0.71/1.07 21 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(20),rewrite([8(6)])].
% 0.71/1.07 22 A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) # label(maddux3_a_kind_of_de_Morgan_3) # label(axiom). [assumption].
% 0.71/1.07 23 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(22),rewrite([8(6),8(8)]),flip(a),rewrite([8(6)])].
% 0.71/1.07 24 composition(complement(sk1),top) != complement(sk1) # label(goals_15) # label(negated_conjecture) # answer(goals_15). [assumption].
% 0.71/1.07 25 complement(top) = zero. [back_rewrite(7),rewrite([9(2),5(4)])].
% 0.71/1.07 27 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),13(a,1,1)),flip(a)].
% 0.71/1.07 28 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),13(a,1,2)),flip(a)].
% 0.71/1.07 29 join(A,join(B,complement(A))) = join(B,top). [para(5(a,1),15(a,2,2)),rewrite([8(2)])].
% 0.71/1.07 30 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),17(a,1,1)),flip(a)].
% 0.71/1.07 36 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(17(a,1),19(a,1,1)),rewrite([8(6)])].
% 0.71/1.07 38 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),21(a,1,2,2,1))].
% 0.71/1.07 40 join(zero,composition(converse(sk1),complement(sk1))) = zero. [para(3(a,1),21(a,1,2,2,1)),rewrite([25(2),25(9)])].
% 0.71/1.07 41 join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)). [para(21(a,1),11(a,2,1)),rewrite([28(7)])].
% 0.71/1.07 44 join(zero,complement(join(complement(A),complement(A)))) = A. [para(5(a,1),23(a,1,1,1)),rewrite([25(2)])].
% 0.71/1.07 52 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(25(a,1),23(a,1,2,1,1))].
% 0.71/1.07 63 join(converse(zero),composition(converse(complement(sk1)),sk1)) = converse(zero). [para(40(a,1),11(a,2,1)),rewrite([28(8)])].
% 0.71/1.07 68 composition(converse(one),A) = A. [para(1(a,1),28(a,1,1)),rewrite([2(2)]),flip(a)].
% 0.71/1.07 72 converse(one) = one. [para(68(a,1),1(a,1)),flip(a)].
% 0.71/1.07 74 composition(join(A,one),B) = join(B,composition(A,B)). [para(68(a,1),19(a,1,1)),rewrite([72(4),8(4)]),flip(a)].
% 0.71/1.07 76 join(complement(A),complement(composition(one,A))) = complement(A). [para(68(a,1),21(a,1,2))].
% 0.71/1.07 77 composition(one,A) = A. [para(68(a,1),30(a,2)),rewrite([72(2),30(4)])].
% 0.71/1.07 78 join(complement(A),complement(A)) = complement(A). [back_rewrite(76),rewrite([77(3)])].
% 0.71/1.07 79 join(zero,complement(complement(A))) = A. [back_rewrite(44),rewrite([78(4)])].
% 0.71/1.07 80 converse(join(A,one)) = join(one,converse(A)). [para(72(a,1),11(a,1,1)),rewrite([8(5)]),flip(a)].
% 0.71/1.07 85 join(top,complement(A)) = top. [para(78(a,1),29(a,1,2)),rewrite([5(2),8(4)]),flip(a)].
% 0.71/1.07 86 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(52),rewrite([85(3),25(2)])].
% 0.71/1.07 87 join(top,top) = join(A,top). [para(85(a,1),29(a,1,2)),flip(a)].
% 0.71/1.07 93 join(A,top) = join(B,top). [para(87(a,1),29(a,2)),rewrite([85(3)])].
% 0.71/1.07 94 join(A,top) = c_0. [new_symbol(93)].
% 0.71/1.07 97 join(A,join(B,complement(A))) = c_0. [back_rewrite(29),rewrite([94(5)])].
% 0.71/1.07 102 c_0 = top. [para(79(a,1),97(a,1,2)),rewrite([8(2),5(2)]),flip(a)].
% 0.71/1.07 105 join(A,top) = top. [back_rewrite(94),rewrite([102(3)])].
% 0.71/1.07 134 join(zero,complement(A)) = complement(A). [para(79(a,1),86(a,1,2,1))].
% 0.71/1.07 135 complement(complement(A)) = A. [back_rewrite(86),rewrite([134(4),134(4)])].
% 0.71/1.07 136 join(A,zero) = A. [back_rewrite(79),rewrite([135(3),8(2)])].
% 0.71/1.07 142 complement(zero) = top. [para(25(a,1),135(a,1,1))].
% 0.71/1.07 178 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(135(a,1),38(a,1,2,2))].
% 0.71/1.07 229 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),178(a,1,2))].
% 0.71/1.07 240 converse(complement(one)) = complement(one). [para(229(a,1),11(a,2,1)),rewrite([2(7),8(6),229(6)]),flip(a)].
% 0.71/1.07 245 converse(top) = top. [para(240(a,1),80(a,2,2)),rewrite([8(4),5(4),5(6)])].
% 0.71/1.07 252 join(top,converse(A)) = top. [para(245(a,1),11(a,1,1)),rewrite([8(5),105(5),245(5)])].
% 0.71/1.07 253 converse(composition(A,top)) = composition(top,converse(A)). [para(245(a,1),13(a,1,1)),flip(a)].
% 0.71/1.07 258 join(top,composition(A,converse(B))) = top. [para(27(a,1),252(a,1,2))].
% 0.71/1.07 260 join(top,one) = top. [para(72(a,1),252(a,1,2))].
% 0.71/1.07 269 join(A,composition(top,A)) = composition(top,A). [para(260(a,1),19(a,2,1)),rewrite([77(4),8(3)])].
% 0.71/1.07 270 join(top,composition(A,B)) = top. [para(2(a,1),258(a,1,2,2))].
% 0.71/1.07 295 composition(top,join(one,converse(A))) = top. [para(80(a,1),253(a,2,2)),rewrite([74(4),270(4),245(2)]),flip(a)].
% 0.71/1.07 318 composition(top,top) = top. [para(240(a,1),295(a,1,2,2)),rewrite([5(5)])].
% 0.71/1.07 334 composition(top,zero) = zero. [para(318(a,1),21(a,1,2,2,1)),rewrite([25(2),245(3),25(4),269(5),25(5)])].
% 0.71/1.07 340 join(zero,composition(A,zero)) = zero. [para(334(a,1),19(a,1,1)),rewrite([8(6),105(6),334(7)])].
% 0.71/1.07 375 join(A,composition(B,zero)) = A. [para(340(a,1),15(a,1,2)),rewrite([136(2),136(4),8(3)]),flip(a)].
% 0.71/1.07 388 composition(join(A,B),zero) = composition(A,zero). [para(375(a,1),19(a,1)),flip(a)].
% 0.71/1.07 390 composition(A,zero) = zero. [para(375(a,1),74(a,2)),rewrite([388(4)])].
% 0.71/1.07 392 composition(converse(zero),A) = converse(zero). [para(390(a,1),28(a,1,1)),flip(a)].
% 0.71/1.07 416 composition(join(A,composition(B,converse(zero))),C) = join(composition(B,converse(zero)),composition(A,C)). [para(392(a,1),36(a,1,1,2)),flip(a)].
% 0.71/1.07 420 converse(zero) = zero. [para(392(a,1),390(a,1))].
% 0.71/1.07 423 join(zero,composition(A,B)) = composition(A,B). [back_rewrite(416),rewrite([420(2),390(2),136(2),420(3),390(3)]),flip(a)].
% 0.71/1.07 428 composition(converse(complement(sk1)),sk1) = zero. [back_rewrite(63),rewrite([420(2),423(7),420(7)])].
% 0.71/1.07 448 composition(top,converse(complement(sk1))) = converse(complement(sk1)). [para(428(a,1),41(a,1,2,1,1,1)),rewrite([142(5),245(5),269(9)])].
% 0.71/1.07 618 composition(complement(sk1),top) = complement(sk1). [para(448(a,1),13(a,2,1)),rewrite([2(4),245(4),2(8)])].
% 0.71/1.07 619 $F # answer(goals_15). [resolve(618,a,24,a)].
% 0.71/1.07
% 0.71/1.07 % SZS output end Refutation
% 0.71/1.07 ============================== end of proof ==========================
% 0.71/1.07
% 0.71/1.07 ============================== STATISTICS ============================
% 0.71/1.07
% 0.71/1.07 Given=119. Generated=3435. Kept=609. proofs=1.
% 0.71/1.07 Usable=91. Sos=356. Demods=430. Limbo=0, Disabled=176. Hints=0.
% 0.71/1.07 Megabytes=0.71.
% 0.71/1.07 User_CPU=0.12, System_CPU=0.01, Wall_clock=0.
% 0.71/1.07
% 0.71/1.07 ============================== end of statistics =====================
% 0.71/1.07
% 0.71/1.07 ============================== end of search =========================
% 0.71/1.07
% 0.71/1.07 THEOREM PROVED
% 0.71/1.07 % SZS status Unsatisfiable
% 0.71/1.07
% 0.71/1.07 Exiting with 1 proof.
% 0.71/1.07
% 0.71/1.07 Process 30529 exit (max_proofs) Fri Jul 8 16:03:26 2022
% 0.71/1.07 Prover9 interrupted
%------------------------------------------------------------------------------