TSTP Solution File: REL042-2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL042-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 19:54:25 EDT 2022
% Result : Unsatisfiable 2.48s 2.84s
% Output : Refutation 2.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL042-2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n028.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 13:59:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.48/2.84 ============================== Prover9 ===============================
% 2.48/2.84 Prover9 (32) version 2009-11A, November 2009.
% 2.48/2.84 Process 5525 was started by sandbox2 on n028.cluster.edu,
% 2.48/2.84 Fri Jul 8 13:59:40 2022
% 2.48/2.84 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5372_n028.cluster.edu".
% 2.48/2.84 ============================== end of head ===========================
% 2.48/2.84
% 2.48/2.84 ============================== INPUT =================================
% 2.48/2.84
% 2.48/2.84 % Reading from file /tmp/Prover9_5372_n028.cluster.edu
% 2.48/2.84
% 2.48/2.84 set(prolog_style_variables).
% 2.48/2.84 set(auto2).
% 2.48/2.84 % set(auto2) -> set(auto).
% 2.48/2.84 % set(auto) -> set(auto_inference).
% 2.48/2.84 % set(auto) -> set(auto_setup).
% 2.48/2.84 % set(auto_setup) -> set(predicate_elim).
% 2.48/2.84 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.48/2.84 % set(auto) -> set(auto_limits).
% 2.48/2.84 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.48/2.84 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.48/2.84 % set(auto) -> set(auto_denials).
% 2.48/2.84 % set(auto) -> set(auto_process).
% 2.48/2.84 % set(auto2) -> assign(new_constants, 1).
% 2.48/2.84 % set(auto2) -> assign(fold_denial_max, 3).
% 2.48/2.84 % set(auto2) -> assign(max_weight, "200.000").
% 2.48/2.84 % set(auto2) -> assign(max_hours, 1).
% 2.48/2.84 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.48/2.84 % set(auto2) -> assign(max_seconds, 0).
% 2.48/2.84 % set(auto2) -> assign(max_minutes, 5).
% 2.48/2.84 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.48/2.84 % set(auto2) -> set(sort_initial_sos).
% 2.48/2.84 % set(auto2) -> assign(sos_limit, -1).
% 2.48/2.84 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.48/2.84 % set(auto2) -> assign(max_megs, 400).
% 2.48/2.84 % set(auto2) -> assign(stats, some).
% 2.48/2.84 % set(auto2) -> clear(echo_input).
% 2.48/2.84 % set(auto2) -> set(quiet).
% 2.48/2.84 % set(auto2) -> clear(print_initial_clauses).
% 2.48/2.84 % set(auto2) -> clear(print_given).
% 2.48/2.84 assign(lrs_ticks,-1).
% 2.48/2.84 assign(sos_limit,10000).
% 2.48/2.84 assign(order,kbo).
% 2.48/2.84 set(lex_order_vars).
% 2.48/2.84 clear(print_given).
% 2.48/2.84
% 2.48/2.84 % formulas(sos). % not echoed (18 formulas)
% 2.48/2.84
% 2.48/2.84 ============================== end of input ==========================
% 2.48/2.84
% 2.48/2.84 % From the command line: assign(max_seconds, 300).
% 2.48/2.84
% 2.48/2.84 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.48/2.84
% 2.48/2.84 % Formulas that are not ordinary clauses:
% 2.48/2.84
% 2.48/2.84 ============================== end of process non-clausal formulas ===
% 2.48/2.84
% 2.48/2.84 ============================== PROCESS INITIAL CLAUSES ===============
% 2.48/2.84
% 2.48/2.84 ============================== PREDICATE ELIMINATION =================
% 2.48/2.84
% 2.48/2.84 ============================== end predicate elimination =============
% 2.48/2.84
% 2.48/2.84 Auto_denials:
% 2.48/2.84 % copying label goals_18 to answer in negative clause
% 2.48/2.84
% 2.48/2.84 Term ordering decisions:
% 2.48/2.84 Function symbol KB weights: sk1=1. zero=1. one=1. top=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 2.48/2.84
% 2.48/2.84 ============================== end of process initial clauses ========
% 2.48/2.84
% 2.48/2.84 ============================== CLAUSES FOR SEARCH ====================
% 2.48/2.84
% 2.48/2.84 ============================== end of clauses for search =============
% 2.48/2.84
% 2.48/2.84 ============================== SEARCH ================================
% 2.48/2.84
% 2.48/2.84 % Starting search at 0.01 seconds.
% 2.48/2.84
% 2.48/2.84 Low Water (keep): wt=80.000, iters=3357
% 2.48/2.84
% 2.48/2.84 Low Water (keep): wt=77.000, iters=3389
% 2.48/2.84
% 2.48/2.84 Low Water (keep): wt=73.000, iters=3341
% 2.48/2.84
% 2.48/2.84 Low Water (keep): wt=72.000, iters=3345
% 2.48/2.84
% 2.48/2.84 Low Water (keep): wt=70.000, iters=3349
% 2.48/2.84
% 2.48/2.84 Low Water (keep): wt=68.000, iters=3355
% 2.48/2.84
% 2.48/2.84 Low Water (keep): wt=67.000, iters=3379
% 2.48/2.84
% 2.48/2.84 Low Water (keep): wt=65.000, iters=3387
% 2.48/2.84
% 2.48/2.84 Low Water (keep): wt=64.000, iters=3346
% 2.48/2.84
% 2.48/2.84 ============================== PROOF =================================
% 2.48/2.84 % SZS status Unsatisfiable
% 2.48/2.84 % SZS output start Refutation
% 2.48/2.84
% 2.48/2.84 % Proof 1 at 1.84 (+ 0.03) seconds: goals_18.
% 2.48/2.84 % Length of proof is 89.
% 2.48/2.84 % Level of proof is 27.
% 2.48/2.84 % Maximum clause weight is 48.000.
% 2.48/2.84 % Given clauses 431.
% 2.48/2.84
% 2.48/2.84 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 2.48/2.84 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 2.48/2.84 3 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 2.48/2.84 4 join(A,complement(A)) = top. [copy(3),flip(a)].
% 2.48/2.84 5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 2.48/2.84 6 meet(A,complement(A)) = zero. [copy(5),flip(a)].
% 2.48/2.84 7 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 2.48/2.84 8 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 2.48/2.84 9 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 2.48/2.84 10 join(converse(A),converse(B)) = converse(join(A,B)). [copy(9),flip(a)].
% 2.48/2.84 11 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 2.48/2.84 12 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(11),flip(a)].
% 2.48/2.84 13 meet(composition(sk1,A),composition(sk1,complement(A))) = zero # label(goals_17) # label(negated_conjecture). [assumption].
% 2.48/2.84 14 complement(join(complement(composition(sk1,A)),complement(composition(sk1,complement(A))))) = zero. [copy(13),rewrite([8(6)])].
% 2.48/2.84 15 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 2.48/2.84 16 join(A,join(B,C)) = join(C,join(A,B)). [copy(15),rewrite([7(4)])].
% 2.48/2.84 17 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 2.48/2.84 18 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(17),flip(a)].
% 2.48/2.84 19 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 2.48/2.84 20 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(19),flip(a)].
% 2.48/2.84 21 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 2.48/2.84 22 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(21),rewrite([7(6)])].
% 2.48/2.84 23 A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) # label(maddux3_a_kind_of_de_Morgan_3) # label(axiom). [assumption].
% 2.48/2.84 24 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(23),rewrite([7(6),7(8)]),flip(a),rewrite([7(6)])].
% 2.48/2.84 25 join(meet(composition(A,B),C),meet(composition(A,meet(B,composition(converse(A),C))),C)) = meet(composition(A,meet(B,composition(converse(A),C))),C) # label(modular_law_1_15) # label(axiom). [assumption].
% 2.48/2.84 26 join(complement(join(complement(A),complement(composition(B,C)))),complement(join(complement(A),complement(composition(B,complement(join(complement(C),complement(composition(converse(B),A))))))))) = complement(join(complement(A),complement(composition(B,complement(join(complement(C),complement(composition(converse(B),A)))))))). [copy(25),rewrite([8(2),7(4),8(8),8(13),7(15),8(20),8(25),7(27)])].
% 2.48/2.84 29 join(meet(composition(A,B),C),composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C)))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))) # label(dedekind_law_14) # label(axiom). [assumption].
% 2.48/2.84 30 join(complement(join(complement(A),complement(composition(B,C)))),composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A))))). [copy(29),rewrite([8(2),7(4),8(8),8(14),8(22),8(28)])].
% 2.48/2.84 31 join(composition(converse(sk1),sk1),one) != one # label(goals_18) # label(negated_conjecture) # answer(goals_18). [assumption].
% 2.48/2.84 32 join(one,composition(converse(sk1),sk1)) != one # answer(goals_18). [copy(31),rewrite([7(6)])].
% 2.48/2.84 33 complement(top) = zero. [back_rewrite(6),rewrite([8(2),4(4)])].
% 2.48/2.84 35 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),12(a,1,1)),flip(a)].
% 2.48/2.84 36 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),12(a,1,2)),flip(a)].
% 2.48/2.84 37 complement(join(complement(sk1),complement(composition(sk1,complement(one))))) = zero. [para(1(a,1),14(a,1,1,1,1))].
% 2.48/2.84 40 join(A,join(B,complement(A))) = join(B,top). [para(4(a,1),16(a,2,2)),rewrite([7(2)])].
% 2.48/2.84 41 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),18(a,1,1)),flip(a)].
% 2.48/2.84 45 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(18(a,1),20(a,1,1)),rewrite([7(6)])].
% 2.48/2.84 47 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),22(a,1,2,2,1))].
% 2.48/2.84 53 join(zero,complement(join(complement(A),complement(A)))) = A. [para(4(a,1),24(a,1,1,1)),rewrite([33(2)])].
% 2.48/2.84 56 join(complement(composition(sk1,A)),complement(composition(sk1,complement(A)))) = join(complement(join(B,zero)),complement(join(zero,complement(B)))). [para(14(a,1),24(a,1,1,1,2)),rewrite([14(13),7(6)]),flip(a)].
% 2.48/2.84 62 join(complement(composition(sk1,A)),complement(composition(sk1,complement(A)))) = c_0. [new_symbol(56)].
% 2.48/2.84 64 join(complement(join(A,zero)),complement(join(zero,complement(A)))) = c_0. [back_rewrite(56),rewrite([62(8)]),flip(a)].
% 2.48/2.84 71 join(complement(join(complement(A),complement(composition(converse(B),C)))),complement(join(complement(A),complement(composition(converse(B),complement(join(complement(C),complement(composition(B,A))))))))) = complement(join(complement(A),complement(composition(converse(B),complement(join(complement(C),complement(composition(B,A)))))))). [para(2(a,1),26(a,1,2,1,2,1,2,1,2,1,1)),rewrite([2(23)])].
% 2.48/2.84 93 join(zero,top) = top. [para(33(a,1),4(a,1,2)),rewrite([7(3)])].
% 2.48/2.84 94 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(33(a,1),22(a,1,1)),rewrite([33(9)])].
% 2.48/2.84 95 c_0 = top. [para(33(a,1),24(a,1,1,1,2)),rewrite([33(6),7(6),64(8)])].
% 2.48/2.84 96 join(complement(join(zero,complement(A))),complement(join(top,complement(A)))) = A. [para(33(a,1),24(a,1,2,1,1)),rewrite([7(9)])].
% 2.48/2.84 105 join(complement(join(A,zero)),complement(join(zero,complement(A)))) = top. [back_rewrite(64),rewrite([95(9)])].
% 2.48/2.84 132 composition(converse(one),A) = A. [para(1(a,1),36(a,1,1)),rewrite([2(2)]),flip(a)].
% 2.48/2.84 140 converse(one) = one. [para(132(a,1),1(a,1)),flip(a)].
% 2.48/2.84 142 composition(join(A,one),B) = join(B,composition(A,B)). [para(132(a,1),20(a,1,1)),rewrite([140(4),7(4)]),flip(a)].
% 2.48/2.84 144 join(complement(A),complement(composition(one,A))) = complement(A). [para(132(a,1),22(a,1,2))].
% 2.48/2.84 158 composition(one,A) = A. [para(132(a,1),41(a,2)),rewrite([140(2),41(4)])].
% 2.48/2.84 164 join(complement(A),complement(A)) = complement(A). [back_rewrite(144),rewrite([158(3)])].
% 2.48/2.84 165 join(zero,complement(complement(A))) = A. [back_rewrite(53),rewrite([164(4)])].
% 2.48/2.84 166 converse(join(A,one)) = join(one,converse(A)). [para(140(a,1),10(a,1,1)),rewrite([7(5)]),flip(a)].
% 2.48/2.84 170 join(complement(sk1),complement(composition(sk1,complement(one)))) = top. [para(37(a,1),24(a,1,1,1,2)),rewrite([37(13),7(6),105(8)]),flip(a)].
% 2.48/2.84 201 join(top,complement(A)) = top. [para(164(a,1),40(a,1,2)),rewrite([4(2),7(4)]),flip(a)].
% 2.48/2.84 202 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(96),rewrite([201(7),33(6),7(6)])].
% 2.48/2.84 203 join(top,top) = join(A,top). [para(201(a,1),40(a,1,2)),flip(a)].
% 2.48/2.84 208 join(top,top) = top. [para(203(a,2),93(a,1))].
% 2.48/2.84 210 join(A,top) = top. [para(203(a,2),40(a,2)),rewrite([40(3),208(5)])].
% 2.48/2.84 240 join(zero,complement(A)) = complement(A). [para(165(a,1),202(a,1,2,1))].
% 2.48/2.84 241 complement(complement(A)) = A. [back_rewrite(202),rewrite([240(4),240(4)])].
% 2.48/2.84 244 join(A,zero) = A. [back_rewrite(165),rewrite([241(3),7(2)])].
% 2.48/2.84 277 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(241(a,1),24(a,1,1,1,2)),rewrite([241(5),7(4)])].
% 2.48/2.84 285 complement(zero) = top. [para(33(a,1),241(a,1,1))].
% 2.48/2.84 286 join(A,A) = A. [para(241(a,1),164(a,1,1)),rewrite([241(2),241(3)])].
% 2.48/2.84 302 join(A,join(A,B)) = join(A,B). [para(286(a,1),16(a,1)),rewrite([7(3),16(4,R),7(3),16(3,R),286(2)]),flip(a)].
% 2.48/2.84 333 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(241(a,1),47(a,1,2,2))].
% 2.48/2.84 345 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero. [para(166(a,1),94(a,1,2,1))].
% 2.48/2.84 397 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),333(a,1,2))].
% 2.48/2.84 401 converse(complement(one)) = complement(one). [para(397(a,1),10(a,2,1)),rewrite([2(7),7(6),397(6)]),flip(a)].
% 2.48/2.84 411 converse(top) = top. [para(401(a,1),166(a,2,2)),rewrite([7(4),4(4),4(6)])].
% 2.48/2.84 418 join(top,converse(A)) = top. [para(411(a,1),10(a,1,1)),rewrite([7(5),210(5),411(5)])].
% 2.48/2.84 430 join(top,composition(A,converse(B))) = top. [para(35(a,1),418(a,1,2))].
% 2.48/2.84 432 join(top,composition(A,B)) = top. [para(2(a,1),430(a,1,2,2))].
% 2.48/2.84 433 composition(join(A,one),top) = top. [para(411(a,1),430(a,1,2,2)),rewrite([142(4,R)])].
% 2.48/2.84 434 composition(join(one,converse(A)),zero) = zero. [back_rewrite(345),rewrite([433(8),33(6),142(7,R),7(5),302(5)])].
% 2.48/2.84 465 composition(top,zero) = zero. [para(401(a,1),434(a,1,1,2)),rewrite([4(4)])].
% 2.48/2.84 474 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)). [para(465(a,1),30(a,1,1,1,2,1)),rewrite([285(3),7(3),201(3),33(2),33(3),240(7),241(6),285(6),411(7),201(9),33(6),18(6),33(9),240(13),241(12),285(12),411(13),201(15),33(12),18(12)])].
% 2.48/2.84 478 join(zero,composition(A,composition(B,zero))) = zero. [para(465(a,1),45(a,1,2)),rewrite([7(5),432(8),465(8)])].
% 2.48/2.84 481 composition(A,composition(converse(zero),zero)) = zero. [back_rewrite(474),rewrite([478(7)]),flip(a)].
% 2.48/2.84 595 composition(A,zero) = zero. [para(481(a,1),18(a,1)),rewrite([481(6)]),flip(a)].
% 2.48/2.84 661 complement(join(one,complement(composition(converse(sk1),sk1)))) = zero. [para(170(a,1),71(a,1,2,1,2,1,2,1)),rewrite([241(3),241(11),33(13),595(13),285(11),210(11),33(10),7(10),240(10),241(11),170(19),33(13),595(13),285(11),210(11),33(10)])].
% 2.48/2.84 984 join(one,complement(composition(converse(sk1),sk1))) = top. [para(661(a,1),24(a,1,1,1,2)),rewrite([244(2),661(10),7(4),240(4),241(3),7(2),4(2)]),flip(a)].
% 2.48/2.84 8413 complement(join(one,composition(converse(sk1),sk1))) = complement(one). [para(984(a,1),277(a,1,2,1)),rewrite([7(6),33(9),7(9),240(9)])].
% 2.48/2.84 8522 join(one,composition(converse(sk1),sk1)) = one. [para(8413(a,1),24(a,1,1,1,2)),rewrite([8413(12),24(10)]),flip(a)].
% 2.48/2.84 8523 $F # answer(goals_18). [resolve(8522,a,32,a)].
% 2.48/2.84
% 2.48/2.84 % SZS output end Refutation
% 2.48/2.84 ============================== end of proof ==========================
% 2.48/2.84
% 2.48/2.84 ============================== STATISTICS ============================
% 2.48/2.84
% 2.48/2.84 Given=431. Generated=52188. Kept=8508. proofs=1.
% 2.48/2.84 Usable=353. Sos=6998. Demods=7305. Limbo=1, Disabled=1173. Hints=0.
% 2.48/2.84 Megabytes=19.89.
% 2.48/2.84 User_CPU=1.84, System_CPU=0.03, Wall_clock=2.
% 2.48/2.84
% 2.48/2.84 ============================== end of statistics =====================
% 2.48/2.84
% 2.48/2.84 ============================== end of search =========================
% 2.48/2.84
% 2.48/2.84 THEOREM PROVED
% 2.48/2.84 % SZS status Unsatisfiable
% 2.48/2.84
% 2.48/2.84 Exiting with 1 proof.
% 2.48/2.84
% 2.48/2.84 Process 5525 exit (max_proofs) Fri Jul 8 13:59:42 2022
% 2.48/2.84 Prover9 interrupted
%------------------------------------------------------------------------------