TSTP Solution File: REL024-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL024-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 19:53:55 EDT 2022
% Result : Unsatisfiable 1.53s 1.81s
% Output : Refutation 1.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL024-2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 10:57:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.53/1.81 ============================== Prover9 ===============================
% 1.53/1.81 Prover9 (32) version 2009-11A, November 2009.
% 1.53/1.81 Process 13832 was started by sandbox on n025.cluster.edu,
% 1.53/1.81 Fri Jul 8 10:57:15 2022
% 1.53/1.81 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13677_n025.cluster.edu".
% 1.53/1.81 ============================== end of head ===========================
% 1.53/1.81
% 1.53/1.81 ============================== INPUT =================================
% 1.53/1.81
% 1.53/1.81 % Reading from file /tmp/Prover9_13677_n025.cluster.edu
% 1.53/1.81
% 1.53/1.81 set(prolog_style_variables).
% 1.53/1.81 set(auto2).
% 1.53/1.81 % set(auto2) -> set(auto).
% 1.53/1.81 % set(auto) -> set(auto_inference).
% 1.53/1.81 % set(auto) -> set(auto_setup).
% 1.53/1.81 % set(auto_setup) -> set(predicate_elim).
% 1.53/1.81 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.53/1.81 % set(auto) -> set(auto_limits).
% 1.53/1.81 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.53/1.81 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.53/1.81 % set(auto) -> set(auto_denials).
% 1.53/1.81 % set(auto) -> set(auto_process).
% 1.53/1.81 % set(auto2) -> assign(new_constants, 1).
% 1.53/1.81 % set(auto2) -> assign(fold_denial_max, 3).
% 1.53/1.81 % set(auto2) -> assign(max_weight, "200.000").
% 1.53/1.81 % set(auto2) -> assign(max_hours, 1).
% 1.53/1.81 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.53/1.81 % set(auto2) -> assign(max_seconds, 0).
% 1.53/1.81 % set(auto2) -> assign(max_minutes, 5).
% 1.53/1.81 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.53/1.81 % set(auto2) -> set(sort_initial_sos).
% 1.53/1.81 % set(auto2) -> assign(sos_limit, -1).
% 1.53/1.81 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.53/1.81 % set(auto2) -> assign(max_megs, 400).
% 1.53/1.81 % set(auto2) -> assign(stats, some).
% 1.53/1.81 % set(auto2) -> clear(echo_input).
% 1.53/1.81 % set(auto2) -> set(quiet).
% 1.53/1.81 % set(auto2) -> clear(print_initial_clauses).
% 1.53/1.81 % set(auto2) -> clear(print_given).
% 1.53/1.81 assign(lrs_ticks,-1).
% 1.53/1.81 assign(sos_limit,10000).
% 1.53/1.81 assign(order,kbo).
% 1.53/1.81 set(lex_order_vars).
% 1.53/1.81 clear(print_given).
% 1.53/1.81
% 1.53/1.81 % formulas(sos). % not echoed (17 formulas)
% 1.53/1.81
% 1.53/1.81 ============================== end of input ==========================
% 1.53/1.81
% 1.53/1.81 % From the command line: assign(max_seconds, 300).
% 1.53/1.81
% 1.53/1.81 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.53/1.81
% 1.53/1.81 % Formulas that are not ordinary clauses:
% 1.53/1.81
% 1.53/1.81 ============================== end of process non-clausal formulas ===
% 1.53/1.81
% 1.53/1.81 ============================== PROCESS INITIAL CLAUSES ===============
% 1.53/1.81
% 1.53/1.81 ============================== PREDICATE ELIMINATION =================
% 1.53/1.81
% 1.53/1.81 ============================== end predicate elimination =============
% 1.53/1.81
% 1.53/1.81 Auto_denials:
% 1.53/1.81 % copying label goals_17 to answer in negative clause
% 1.53/1.81
% 1.53/1.81 Term ordering decisions:
% 1.53/1.81 Function symbol KB weights: one=1. top=1. zero=1. sk1=1. sk2=1. sk3=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 1.53/1.81
% 1.53/1.81 ============================== end of process initial clauses ========
% 1.53/1.81
% 1.53/1.81 ============================== CLAUSES FOR SEARCH ====================
% 1.53/1.81
% 1.53/1.81 ============================== end of clauses for search =============
% 1.53/1.81
% 1.53/1.81 ============================== SEARCH ================================
% 1.53/1.81
% 1.53/1.81 % Starting search at 0.01 seconds.
% 1.53/1.81
% 1.53/1.81 ============================== PROOF =================================
% 1.53/1.81 % SZS status Unsatisfiable
% 1.53/1.81 % SZS output start Refutation
% 1.53/1.81
% 1.53/1.81 % Proof 1 at 0.80 (+ 0.02) seconds: goals_17.
% 1.53/1.81 % Length of proof is 50.
% 1.53/1.81 % Level of proof is 14.
% 1.53/1.81 % Maximum clause weight is 42.000.
% 1.53/1.81 % Given clauses 248.
% 1.53/1.81
% 1.53/1.81 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 1.53/1.81 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 1.53/1.81 3 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 1.53/1.81 4 join(A,complement(A)) = top. [copy(3),flip(a)].
% 1.53/1.81 5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 1.53/1.81 6 meet(A,complement(A)) = zero. [copy(5),flip(a)].
% 1.53/1.81 7 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 1.53/1.81 8 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 1.53/1.81 9 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 1.53/1.81 10 join(converse(A),converse(B)) = converse(join(A,B)). [copy(9),flip(a)].
% 1.53/1.81 11 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 1.53/1.81 12 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(11),flip(a)].
% 1.53/1.81 13 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 1.53/1.81 14 join(A,join(B,C)) = join(C,join(A,B)). [copy(13),rewrite([7(4)])].
% 1.53/1.81 15 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 1.53/1.81 16 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(15),flip(a)].
% 1.53/1.81 17 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 1.53/1.81 18 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(17),flip(a)].
% 1.53/1.81 19 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 1.53/1.81 20 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(19),rewrite([7(6)])].
% 1.53/1.81 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].
% 1.53/1.81 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)])].
% 1.53/1.81 23 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].
% 1.53/1.81 24 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(23),rewrite([8(2),7(4),8(8),8(13),7(15),8(20),8(25),7(27)])].
% 1.53/1.81 29 join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),sk3)) != composition(meet(sk1,converse(sk2)),sk3) # label(goals_17) # label(negated_conjecture) # answer(goals_17). [assumption].
% 1.53/1.81 30 join(composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3),composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3))))) != composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3) # answer(goals_17). [copy(29),rewrite([8(4),8(10),8(18),7(24),8(28)])].
% 1.53/1.81 31 complement(top) = zero. [back_rewrite(6),rewrite([8(2),4(4)])].
% 1.53/1.81 34 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),12(a,1,2)),flip(a)].
% 1.53/1.81 35 join(A,join(B,complement(A))) = join(B,top). [para(4(a,1),14(a,2,2)),rewrite([7(2)])].
% 1.53/1.81 36 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),16(a,1,1)),flip(a)].
% 1.53/1.81 38 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(12(a,1),18(a,1,1)),rewrite([7(7)])].
% 1.53/1.81 47 join(zero,complement(join(complement(A),complement(A)))) = A. [para(4(a,1),22(a,1,1,1)),rewrite([31(2)])].
% 1.53/1.81 48 join(zero,complement(join(A,complement(complement(A))))) = complement(A). [para(4(a,1),22(a,1,2,1)),rewrite([31(6),7(6)])].
% 1.53/1.81 112 composition(converse(one),A) = A. [para(1(a,1),34(a,1,1)),rewrite([2(2)]),flip(a)].
% 1.53/1.81 113 converse(join(A,composition(converse(B),C))) = join(composition(converse(C),B),converse(A)). [para(34(a,1),10(a,1,1)),rewrite([7(7)]),flip(a)].
% 1.53/1.81 121 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(22(a,1),35(a,1,2)),rewrite([7(4),35(4),7(3),7(8)]),flip(a)].
% 1.53/1.81 122 join(top,complement(complement(A))) = top. [para(24(a,1),35(a,1,2)),rewrite([4(22),7(8),121(8)]),flip(a)].
% 1.53/1.81 123 converse(one) = one. [para(112(a,1),1(a,1)),flip(a)].
% 1.53/1.81 127 join(complement(A),complement(composition(one,A))) = complement(A). [para(112(a,1),20(a,1,2))].
% 1.53/1.81 141 composition(one,A) = A. [para(112(a,1),36(a,2)),rewrite([123(2),36(4)])].
% 1.53/1.81 147 join(complement(A),complement(A)) = complement(A). [back_rewrite(127),rewrite([141(3)])].
% 1.53/1.81 148 join(zero,complement(complement(A))) = A. [back_rewrite(47),rewrite([147(4)])].
% 1.53/1.81 150 join(zero,complement(A)) = complement(A). [para(122(a,1),22(a,1,1,1)),rewrite([31(2),31(3),148(5)])].
% 1.53/1.81 153 complement(complement(A)) = A. [back_rewrite(148),rewrite([150(4)])].
% 1.53/1.81 163 complement(join(A,A)) = complement(A). [back_rewrite(48),rewrite([153(3),150(4)])].
% 1.53/1.81 204 join(A,A) = A. [para(163(a,1),22(a,1,1,1,2)),rewrite([163(6),22(8)]),flip(a)].
% 1.53/1.81 211 join(A,join(A,B)) = join(A,B). [para(204(a,1),14(a,1)),rewrite([7(3),14(4,R),7(3),14(3,R),204(2)]),flip(a)].
% 1.53/1.81 229 join(A,complement(join(B,complement(A)))) = A. [para(22(a,1),211(a,1,2)),rewrite([7(4),22(12)])].
% 1.53/1.81 3442 join(composition(A,B),composition(A,C)) = composition(A,join(B,C)). [para(38(a,1),113(a,1,1)),rewrite([10(3),12(4),2(4),2(4),2(6)]),flip(a)].
% 1.53/1.81 3560 $F # answer(goals_17). [back_rewrite(30),rewrite([3442(24),229(15)]),xx(a)].
% 1.53/1.81
% 1.53/1.81 % SZS output end Refutation
% 1.53/1.81 ============================== end of proof ==========================
% 1.53/1.81
% 1.53/1.81 ============================== STATISTICS ============================
% 1.53/1.81
% 1.53/1.81 Given=248. Generated=20946. Kept=3546. proofs=1.
% 1.53/1.81 Usable=207. Sos=2837. Demods=3129. Limbo=118, Disabled=401. Hints=0.
% 1.53/1.81 Megabytes=8.32.
% 1.53/1.81 User_CPU=0.80, System_CPU=0.02, Wall_clock=1.
% 1.53/1.81
% 1.53/1.81 ============================== end of statistics =====================
% 1.53/1.81
% 1.53/1.81 ============================== end of search =========================
% 1.53/1.81
% 1.53/1.81 THEOREM PROVED
% 1.53/1.81 % SZS status Unsatisfiable
% 1.53/1.81
% 1.53/1.81 Exiting with 1 proof.
% 1.53/1.81
% 1.53/1.81 Process 13832 exit (max_proofs) Fri Jul 8 10:57:16 2022
% 1.53/1.81 Prover9 interrupted
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