TSTP Solution File: REL004-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL004-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 19:53:23 EDT 2022
% Result : Unsatisfiable 0.94s 1.29s
% Output : Refutation 0.94s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : REL004-1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.08 % Command : tptp2X_and_run_prover9 %d %s
% 0.07/0.27 % Computer : n027.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 600
% 0.07/0.27 % DateTime : Fri Jul 8 12:04:45 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.94/1.29 ============================== Prover9 ===============================
% 0.94/1.29 Prover9 (32) version 2009-11A, November 2009.
% 0.94/1.29 Process 14616 was started by sandbox on n027.cluster.edu,
% 0.94/1.29 Fri Jul 8 12:04:46 2022
% 0.94/1.29 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_14463_n027.cluster.edu".
% 0.94/1.29 ============================== end of head ===========================
% 0.94/1.29
% 0.94/1.29 ============================== INPUT =================================
% 0.94/1.29
% 0.94/1.29 % Reading from file /tmp/Prover9_14463_n027.cluster.edu
% 0.94/1.29
% 0.94/1.29 set(prolog_style_variables).
% 0.94/1.29 set(auto2).
% 0.94/1.29 % set(auto2) -> set(auto).
% 0.94/1.29 % set(auto) -> set(auto_inference).
% 0.94/1.29 % set(auto) -> set(auto_setup).
% 0.94/1.29 % set(auto_setup) -> set(predicate_elim).
% 0.94/1.29 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.94/1.29 % set(auto) -> set(auto_limits).
% 0.94/1.29 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.94/1.29 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.94/1.29 % set(auto) -> set(auto_denials).
% 0.94/1.29 % set(auto) -> set(auto_process).
% 0.94/1.29 % set(auto2) -> assign(new_constants, 1).
% 0.94/1.29 % set(auto2) -> assign(fold_denial_max, 3).
% 0.94/1.29 % set(auto2) -> assign(max_weight, "200.000").
% 0.94/1.29 % set(auto2) -> assign(max_hours, 1).
% 0.94/1.29 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.94/1.29 % set(auto2) -> assign(max_seconds, 0).
% 0.94/1.29 % set(auto2) -> assign(max_minutes, 5).
% 0.94/1.29 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.94/1.29 % set(auto2) -> set(sort_initial_sos).
% 0.94/1.29 % set(auto2) -> assign(sos_limit, -1).
% 0.94/1.29 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.94/1.29 % set(auto2) -> assign(max_megs, 400).
% 0.94/1.29 % set(auto2) -> assign(stats, some).
% 0.94/1.29 % set(auto2) -> clear(echo_input).
% 0.94/1.29 % set(auto2) -> set(quiet).
% 0.94/1.29 % set(auto2) -> clear(print_initial_clauses).
% 0.94/1.29 % set(auto2) -> clear(print_given).
% 0.94/1.29 assign(lrs_ticks,-1).
% 0.94/1.29 assign(sos_limit,10000).
% 0.94/1.29 assign(order,kbo).
% 0.94/1.29 set(lex_order_vars).
% 0.94/1.29 clear(print_given).
% 0.94/1.29
% 0.94/1.29 % formulas(sos). % not echoed (14 formulas)
% 0.94/1.29
% 0.94/1.29 ============================== end of input ==========================
% 0.94/1.29
% 0.94/1.29 % From the command line: assign(max_seconds, 300).
% 0.94/1.29
% 0.94/1.29 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.94/1.29
% 0.94/1.29 % Formulas that are not ordinary clauses:
% 0.94/1.29
% 0.94/1.29 ============================== end of process non-clausal formulas ===
% 0.94/1.29
% 0.94/1.29 ============================== PROCESS INITIAL CLAUSES ===============
% 0.94/1.29
% 0.94/1.29 ============================== PREDICATE ELIMINATION =================
% 0.94/1.29
% 0.94/1.29 ============================== end predicate elimination =============
% 0.94/1.29
% 0.94/1.29 Auto_denials:
% 0.94/1.29 % copying label goals_14 to answer in negative clause
% 0.94/1.29
% 0.94/1.29 Term ordering decisions:
% 0.94/1.29 Function symbol KB weights: one=1. top=1. zero=1. sk1=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 0.94/1.29
% 0.94/1.29 ============================== end of process initial clauses ========
% 0.94/1.29
% 0.94/1.29 ============================== CLAUSES FOR SEARCH ====================
% 0.94/1.29
% 0.94/1.29 ============================== end of clauses for search =============
% 0.94/1.29
% 0.94/1.29 ============================== SEARCH ================================
% 0.94/1.29
% 0.94/1.29 % Starting search at 0.01 seconds.
% 0.94/1.29
% 0.94/1.29 ============================== PROOF =================================
% 0.94/1.29 % SZS status Unsatisfiable
% 0.94/1.29 % SZS output start Refutation
% 0.94/1.29
% 0.94/1.29 % Proof 1 at 0.40 (+ 0.02) seconds: goals_14.
% 0.94/1.29 % Length of proof is 64.
% 0.94/1.29 % Level of proof is 25.
% 0.94/1.29 % Maximum clause weight is 14.000.
% 0.94/1.29 % Given clauses 283.
% 0.94/1.29
% 0.94/1.29 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 0.94/1.29 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 0.94/1.29 3 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 0.94/1.29 4 join(A,complement(A)) = top. [copy(3),flip(a)].
% 0.94/1.29 5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 0.94/1.29 6 meet(A,complement(A)) = zero. [copy(5),flip(a)].
% 0.94/1.29 7 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 0.94/1.29 8 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 0.94/1.29 9 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 0.94/1.29 10 join(converse(A),converse(B)) = converse(join(A,B)). [copy(9),flip(a)].
% 0.94/1.29 11 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 0.94/1.29 12 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(11),flip(a)].
% 0.94/1.29 13 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 0.94/1.29 14 join(A,join(B,C)) = join(C,join(A,B)). [copy(13),rewrite([7(4)])].
% 0.94/1.29 15 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 0.94/1.29 16 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(15),flip(a)].
% 0.94/1.29 19 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 0.94/1.29 20 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(19),rewrite([7(6)])].
% 0.94/1.29 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].
% 0.94/1.29 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)])].
% 0.94/1.29 23 converse(complement(sk1)) != complement(converse(sk1)) # label(goals_14) # label(negated_conjecture) # answer(goals_14). [assumption].
% 0.94/1.29 24 complement(top) = zero. [back_rewrite(6),rewrite([8(2),4(4)])].
% 0.94/1.29 25 converse(complement(sk1)) = c_0. [new_symbol(23)].
% 0.94/1.29 26 complement(converse(sk1)) != c_0 # answer(goals_14). [back_rewrite(23),rewrite([25(3)]),flip(a)].
% 0.94/1.29 27 converse(join(A,converse(B))) = join(B,converse(A)). [para(2(a,1),10(a,1,1)),rewrite([7(4)]),flip(a)].
% 0.94/1.29 29 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),12(a,1,2)),flip(a)].
% 0.94/1.29 30 join(A,join(B,complement(A))) = join(B,top). [para(4(a,1),14(a,2,2)),rewrite([7(2)])].
% 0.94/1.29 31 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),16(a,1,1)),flip(a)].
% 0.94/1.29 42 join(zero,complement(join(complement(A),complement(A)))) = A. [para(4(a,1),22(a,1,1,1)),rewrite([24(2)])].
% 0.94/1.29 50 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(24(a,1),22(a,1,2,1,1))].
% 0.94/1.29 51 converse(c_0) = complement(sk1). [para(25(a,1),2(a,1,1))].
% 0.94/1.29 52 converse(join(A,complement(sk1))) = join(c_0,converse(A)). [para(25(a,1),10(a,1,1)),rewrite([7(6)]),flip(a)].
% 0.94/1.29 61 join(complement(sk1),converse(A)) = converse(join(A,c_0)). [para(25(a,1),27(a,1,1,2)),flip(a)].
% 0.94/1.29 64 join(converse(A),complement(sk1)) = converse(join(A,c_0)). [para(51(a,1),10(a,1,2))].
% 0.94/1.29 73 composition(converse(one),A) = A. [para(1(a,1),29(a,1,1)),rewrite([2(2)]),flip(a)].
% 0.94/1.29 77 converse(one) = one. [para(73(a,1),1(a,1)),flip(a)].
% 0.94/1.29 81 join(complement(A),complement(composition(one,A))) = complement(A). [para(73(a,1),20(a,1,2))].
% 0.94/1.29 82 composition(one,A) = A. [para(73(a,1),31(a,2)),rewrite([77(2),31(4)])].
% 0.94/1.29 83 join(complement(A),complement(A)) = complement(A). [back_rewrite(81),rewrite([82(3)])].
% 0.94/1.29 84 join(zero,complement(complement(A))) = A. [back_rewrite(42),rewrite([83(4)])].
% 0.94/1.29 90 join(top,complement(A)) = top. [para(83(a,1),30(a,1,2)),rewrite([4(2),7(4)]),flip(a)].
% 0.94/1.29 91 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(50),rewrite([90(3),24(2)])].
% 0.94/1.29 92 join(top,top) = join(A,top). [para(90(a,1),30(a,1,2)),flip(a)].
% 0.94/1.29 97 join(A,top) = join(B,top). [para(92(a,1),30(a,2)),rewrite([90(3)])].
% 0.94/1.29 98 join(A,top) = c_1. [new_symbol(97)].
% 0.94/1.29 101 join(A,join(B,complement(A))) = c_1. [back_rewrite(30),rewrite([98(5)])].
% 0.94/1.29 109 c_1 = top. [para(84(a,1),101(a,1,2)),rewrite([7(2),4(2)]),flip(a)].
% 0.94/1.29 110 join(A,join(B,complement(A))) = top. [back_rewrite(101),rewrite([109(4)])].
% 0.94/1.29 141 join(zero,complement(A)) = complement(A). [para(84(a,1),91(a,1,2,1))].
% 0.94/1.29 142 complement(complement(A)) = A. [back_rewrite(91),rewrite([141(4),141(4)])].
% 0.94/1.29 148 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(142(a,1),22(a,1,1,1,2)),rewrite([142(5),7(4)])].
% 0.94/1.29 174 join(c_0,converse(sk1)) = converse(top). [para(4(a,1),52(a,1,1)),flip(a)].
% 0.94/1.29 213 join(sk1,converse(join(A,c_0))) = top. [para(64(a,1),110(a,1,2))].
% 0.94/1.29 215 join(A,converse(top)) = converse(top). [para(213(a,1),10(a,2,1)),rewrite([2(6),14(5),7(4),14(5,R),7(4),174(4)])].
% 0.94/1.29 223 join(top,converse(A)) = top. [para(215(a,1),10(a,2,1)),rewrite([2(4),7(3),2(6)])].
% 0.94/1.29 229 converse(top) = top. [para(223(a,1),215(a,1)),flip(a)].
% 0.94/1.29 231 join(c_0,converse(sk1)) = top. [back_rewrite(174),rewrite([229(6)])].
% 0.94/1.29 1979 complement(join(complement(c_0),converse(sk1))) = complement(converse(sk1)). [para(231(a,1),148(a,1,1,1)),rewrite([24(2),7(6),141(8)])].
% 0.94/1.29 2048 join(complement(c_0),converse(sk1)) = converse(sk1). [para(1979(a,1),22(a,1,1,1,2)),rewrite([1979(12),22(12)]),flip(a)].
% 0.94/1.29 2056 join(sk1,converse(complement(c_0))) = sk1. [para(2048(a,1),10(a,2,1)),rewrite([2(6),7(5),2(8)])].
% 0.94/1.29 2061 complement(converse(complement(c_0))) = complement(sk1). [para(2056(a,1),148(a,1,1,1)),rewrite([7(8),61(8),7(6),4(6),229(4),24(4),7(4),141(4)]),flip(a)].
% 0.94/1.29 2149 converse(complement(c_0)) = sk1. [para(2061(a,1),22(a,1,1,1,2)),rewrite([2061(9),22(10)]),flip(a)].
% 0.94/1.29 2156 converse(sk1) = complement(c_0). [para(2149(a,1),2(a,1,1))].
% 0.94/1.29 2208 $F # answer(goals_14). [back_rewrite(26),rewrite([2156(2),142(3)]),xx(a)].
% 0.94/1.29
% 0.94/1.29 % SZS output end Refutation
% 0.94/1.29 ============================== end of proof ==========================
% 0.94/1.29
% 0.94/1.29 ============================== STATISTICS ============================
% 0.94/1.29
% 0.94/1.29 Given=283. Generated=15451. Kept=2198. proofs=1.
% 0.94/1.29 Usable=227. Sos=1584. Demods=1793. Limbo=52, Disabled=349. Hints=0.
% 0.94/1.29 Megabytes=2.79.
% 0.94/1.29 User_CPU=0.41, System_CPU=0.02, Wall_clock=0.
% 0.94/1.29
% 0.94/1.29 ============================== end of statistics =====================
% 0.94/1.29
% 0.94/1.29 ============================== end of search =========================
% 0.94/1.29
% 0.94/1.29 THEOREM PROVED
% 0.94/1.29 % SZS status Unsatisfiable
% 0.94/1.29
% 0.94/1.29 Exiting with 1 proof.
% 0.94/1.29
% 0.94/1.29 Process 14616 exit (max_proofs) Fri Jul 8 12:04:46 2022
% 0.94/1.29 Prover9 interrupted
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