TSTP Solution File: REL048-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL048-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 19:54:31 EDT 2022
% Result : Unsatisfiable 1.86s 2.15s
% Output : Refutation 1.86s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL048-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n012.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 08:34:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.86/2.15 ============================== Prover9 ===============================
% 1.86/2.15 Prover9 (32) version 2009-11A, November 2009.
% 1.86/2.15 Process 8223 was started by sandbox2 on n012.cluster.edu,
% 1.86/2.15 Fri Jul 8 08:34:30 2022
% 1.86/2.15 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_8068_n012.cluster.edu".
% 1.86/2.15 ============================== end of head ===========================
% 1.86/2.15
% 1.86/2.15 ============================== INPUT =================================
% 1.86/2.15
% 1.86/2.15 % Reading from file /tmp/Prover9_8068_n012.cluster.edu
% 1.86/2.15
% 1.86/2.15 set(prolog_style_variables).
% 1.86/2.15 set(auto2).
% 1.86/2.15 % set(auto2) -> set(auto).
% 1.86/2.15 % set(auto) -> set(auto_inference).
% 1.86/2.15 % set(auto) -> set(auto_setup).
% 1.86/2.15 % set(auto_setup) -> set(predicate_elim).
% 1.86/2.15 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.86/2.15 % set(auto) -> set(auto_limits).
% 1.86/2.15 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.86/2.15 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.86/2.15 % set(auto) -> set(auto_denials).
% 1.86/2.15 % set(auto) -> set(auto_process).
% 1.86/2.15 % set(auto2) -> assign(new_constants, 1).
% 1.86/2.15 % set(auto2) -> assign(fold_denial_max, 3).
% 1.86/2.15 % set(auto2) -> assign(max_weight, "200.000").
% 1.86/2.15 % set(auto2) -> assign(max_hours, 1).
% 1.86/2.15 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.86/2.15 % set(auto2) -> assign(max_seconds, 0).
% 1.86/2.15 % set(auto2) -> assign(max_minutes, 5).
% 1.86/2.15 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.86/2.15 % set(auto2) -> set(sort_initial_sos).
% 1.86/2.15 % set(auto2) -> assign(sos_limit, -1).
% 1.86/2.15 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.86/2.15 % set(auto2) -> assign(max_megs, 400).
% 1.86/2.15 % set(auto2) -> assign(stats, some).
% 1.86/2.15 % set(auto2) -> clear(echo_input).
% 1.86/2.15 % set(auto2) -> set(quiet).
% 1.86/2.15 % set(auto2) -> clear(print_initial_clauses).
% 1.86/2.15 % set(auto2) -> clear(print_given).
% 1.86/2.15 assign(lrs_ticks,-1).
% 1.86/2.15 assign(sos_limit,10000).
% 1.86/2.15 assign(order,kbo).
% 1.86/2.15 set(lex_order_vars).
% 1.86/2.15 clear(print_given).
% 1.86/2.15
% 1.86/2.15 % formulas(sos). % not echoed (15 formulas)
% 1.86/2.15
% 1.86/2.15 ============================== end of input ==========================
% 1.86/2.15
% 1.86/2.15 % From the command line: assign(max_seconds, 300).
% 1.86/2.15
% 1.86/2.15 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.86/2.15
% 1.86/2.15 % Formulas that are not ordinary clauses:
% 1.86/2.15
% 1.86/2.15 ============================== end of process non-clausal formulas ===
% 1.86/2.15
% 1.86/2.15 ============================== PROCESS INITIAL CLAUSES ===============
% 1.86/2.15
% 1.86/2.15 ============================== PREDICATE ELIMINATION =================
% 1.86/2.15
% 1.86/2.15 ============================== end predicate elimination =============
% 1.86/2.15
% 1.86/2.15 Auto_denials:
% 1.86/2.15 % copying label goals_15 to answer in negative clause
% 1.86/2.15
% 1.86/2.15 Term ordering decisions:
% 1.86/2.15 Function symbol KB weights: sk3=1. one=1. sk1=1. sk2=1. top=1. zero=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 1.86/2.15
% 1.86/2.15 ============================== end of process initial clauses ========
% 1.86/2.15
% 1.86/2.15 ============================== CLAUSES FOR SEARCH ====================
% 1.86/2.15
% 1.86/2.15 ============================== end of clauses for search =============
% 1.86/2.15
% 1.86/2.15 ============================== SEARCH ================================
% 1.86/2.15
% 1.86/2.15 % Starting search at 0.01 seconds.
% 1.86/2.15
% 1.86/2.15 Low Water (keep): wt=37.000, iters=3348
% 1.86/2.15
% 1.86/2.15 Low Water (keep): wt=35.000, iters=3365
% 1.86/2.15
% 1.86/2.15 Low Water (keep): wt=32.000, iters=3353
% 1.86/2.15
% 1.86/2.15 ============================== PROOF =================================
% 1.86/2.15 % SZS status Unsatisfiable
% 1.86/2.15 % SZS output start Refutation
% 1.86/2.15
% 1.86/2.15 % Proof 1 at 1.15 (+ 0.03) seconds: goals_15.
% 1.86/2.15 % Length of proof is 64.
% 1.86/2.15 % Level of proof is 21.
% 1.86/2.15 % Maximum clause weight is 21.000.
% 1.86/2.15 % Given clauses 453.
% 1.86/2.15
% 1.86/2.15 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 1.86/2.15 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 1.86/2.15 3 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 1.86/2.15 4 join(A,complement(A)) = top. [copy(3),flip(a)].
% 1.86/2.15 5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 1.86/2.15 6 meet(A,complement(A)) = zero. [copy(5),flip(a)].
% 1.86/2.15 7 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 1.86/2.15 8 join(join(sk1,sk2),sk3) = sk3 # label(goals_14) # label(negated_conjecture). [assumption].
% 1.86/2.15 9 join(sk3,join(sk1,sk2)) = sk3. [copy(8),rewrite([7(5)])].
% 1.86/2.15 10 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 1.86/2.15 13 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 1.86/2.15 14 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(13),flip(a)].
% 1.86/2.15 15 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 1.86/2.15 16 join(A,join(B,C)) = join(C,join(A,B)). [copy(15),rewrite([7(4)])].
% 1.86/2.15 17 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 1.86/2.15 18 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(17),flip(a)].
% 1.86/2.15 21 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 1.86/2.15 22 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(21),rewrite([7(6)])].
% 1.86/2.15 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].
% 1.86/2.15 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)])].
% 1.86/2.15 25 join(sk1,sk3) != sk3 | join(sk2,sk3) != sk3 # label(goals_15) # label(negated_conjecture) # answer(goals_15). [assumption].
% 1.86/2.15 26 join(sk3,sk1) != sk3 | join(sk3,sk2) != sk3 # answer(goals_15). [copy(25),rewrite([7(3),7(8)])].
% 1.86/2.15 27 complement(top) = zero. [back_rewrite(6),rewrite([10(2),4(4)])].
% 1.86/2.15 30 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),14(a,1,2)),flip(a)].
% 1.86/2.15 31 join(A,join(B,complement(A))) = join(B,top). [para(4(a,1),16(a,2,2)),rewrite([7(2)])].
% 1.86/2.15 32 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),18(a,1,1)),flip(a)].
% 1.86/2.15 43 join(zero,complement(join(complement(A),complement(A)))) = A. [para(4(a,1),24(a,1,1,1)),rewrite([27(2)])].
% 1.86/2.15 47 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(24(a,1),24(a,1,2,1)),rewrite([7(10)])].
% 1.86/2.15 51 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(27(a,1),24(a,1,2,1,1))].
% 1.86/2.15 64 composition(converse(one),A) = A. [para(1(a,1),30(a,1,1)),rewrite([2(2)]),flip(a)].
% 1.86/2.15 70 converse(one) = one. [para(64(a,1),1(a,1)),flip(a)].
% 1.86/2.15 74 join(complement(A),complement(composition(one,A))) = complement(A). [para(64(a,1),22(a,1,2))].
% 1.86/2.15 75 composition(one,A) = A. [para(64(a,1),32(a,2)),rewrite([70(2),32(4)])].
% 1.86/2.15 76 join(complement(A),complement(A)) = complement(A). [back_rewrite(74),rewrite([75(3)])].
% 1.86/2.15 77 join(zero,complement(complement(A))) = A. [back_rewrite(43),rewrite([76(4)])].
% 1.86/2.15 82 join(top,complement(A)) = top. [para(76(a,1),31(a,1,2)),rewrite([4(2),7(4)]),flip(a)].
% 1.86/2.15 83 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(51),rewrite([82(3),27(2)])].
% 1.86/2.15 84 join(top,top) = join(A,top). [para(82(a,1),31(a,1,2)),flip(a)].
% 1.86/2.15 89 join(A,top) = join(B,top). [para(84(a,1),31(a,2)),rewrite([82(3)])].
% 1.86/2.15 90 join(A,top) = c_0. [new_symbol(89)].
% 1.86/2.15 93 join(A,join(B,complement(A))) = c_0. [back_rewrite(31),rewrite([90(5)])].
% 1.86/2.15 104 c_0 = top. [para(77(a,1),93(a,1,2)),rewrite([7(2),4(2)]),flip(a)].
% 1.86/2.15 105 join(A,join(B,complement(A))) = top. [back_rewrite(93),rewrite([104(4)])].
% 1.86/2.15 107 join(A,top) = top. [back_rewrite(90),rewrite([104(3)])].
% 1.86/2.15 132 join(zero,complement(A)) = complement(A). [para(77(a,1),83(a,1,2,1))].
% 1.86/2.15 133 complement(complement(A)) = A. [back_rewrite(83),rewrite([132(4),132(4)])].
% 1.86/2.15 134 join(A,zero) = A. [back_rewrite(77),rewrite([133(3),7(2)])].
% 1.86/2.15 139 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(133(a,1),24(a,1,1,1,2)),rewrite([133(5),7(4)])].
% 1.86/2.15 141 join(A,A) = A. [para(133(a,1),76(a,1,1)),rewrite([133(2),133(3)])].
% 1.86/2.15 145 join(A,join(A,B)) = join(A,B). [para(141(a,1),16(a,1)),rewrite([7(3),16(4,R),7(3),16(3,R),141(2)]),flip(a)].
% 1.86/2.15 146 join(A,complement(join(B,complement(A)))) = A. [para(24(a,1),145(a,1,2)),rewrite([7(4),24(12)])].
% 1.86/2.15 148 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(146(a,1),16(a,2,2)),rewrite([7(4),7(6)])].
% 1.86/2.15 151 join(complement(A),complement(join(A,B))) = complement(A). [para(133(a,1),146(a,1,2,1,2)),rewrite([7(2)])].
% 1.86/2.15 291 join(complement(A),complement(join(B,A))) = complement(A). [para(146(a,1),47(a,2)),rewrite([133(2),133(4),133(8),47(13)])].
% 1.86/2.15 292 join(A,complement(join(complement(A),complement(B)))) = A. [para(47(a,1),151(a,1,2,1)),rewrite([133(2),7(3),133(7)])].
% 1.86/2.15 547 join(complement(sk3),complement(join(sk1,sk2))) = complement(join(sk1,sk2)). [para(9(a,1),291(a,1,2,1)),rewrite([7(7)])].
% 1.86/2.15 561 join(A,join(complement(A),complement(B))) = top. [para(292(a,1),105(a,1,2)),rewrite([7(4)])].
% 1.86/2.15 563 join(A,join(B,join(complement(A),complement(C)))) = top. [para(561(a,1),16(a,2,2)),rewrite([7(4),107(7)])].
% 1.86/2.15 2502 join(A,complement(join(A,B))) = join(A,complement(B)). [para(139(a,1),148(a,1,2)),flip(a)].
% 1.86/2.15 2567 join(A,complement(join(B,join(complement(A),complement(C))))) = A. [para(563(a,1),2502(a,1,2,1)),rewrite([27(2),134(2)]),flip(a)].
% 1.86/2.15 7347 join(sk3,complement(join(A,complement(join(sk1,sk2))))) = sk3. [para(547(a,1),2567(a,1,2,1,2))].
% 1.86/2.15 7348 join(sk3,sk1) = sk3. [para(151(a,1),7347(a,1,2,1)),rewrite([133(4)])].
% 1.86/2.15 7350 join(sk3,sk2) = sk3. [para(291(a,1),7347(a,1,2,1)),rewrite([133(4)])].
% 1.86/2.15 7356 $F # answer(goals_15). [back_rewrite(26),rewrite([7348(3),7350(6)]),xx(a),xx(b)].
% 1.86/2.15
% 1.86/2.15 % SZS output end Refutation
% 1.86/2.15 ============================== end of proof ==========================
% 1.86/2.15
% 1.86/2.15 ============================== STATISTICS ============================
% 1.86/2.15
% 1.86/2.15 Given=453. Generated=50522. Kept=7344. proofs=1.
% 1.86/2.15 Usable=369. Sos=5788. Demods=5741. Limbo=8, Disabled=1194. Hints=0.
% 1.86/2.15 Megabytes=9.56.
% 1.86/2.15 User_CPU=1.15, System_CPU=0.03, Wall_clock=1.
% 1.86/2.15
% 1.86/2.15 ============================== end of statistics =====================
% 1.86/2.15
% 1.86/2.15 ============================== end of search =========================
% 1.86/2.15
% 1.86/2.15 THEOREM PROVED
% 1.86/2.15 % SZS status Unsatisfiable
% 1.86/2.15
% 1.86/2.15 Exiting with 1 proof.
% 1.86/2.15
% 1.86/2.15 Process 8223 exit (max_proofs) Fri Jul 8 08:34:31 2022
% 1.86/2.15 Prover9 interrupted
%------------------------------------------------------------------------------