TSTP Solution File: LAT006-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT006-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 : Sun Jul 17 06:25:04 EDT 2022
% Result : Unsatisfiable 1.49s 1.78s
% Output : Refutation 1.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT006-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n024.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 : Thu Jun 30 04:48:45 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.49/1.78 ============================== Prover9 ===============================
% 1.49/1.78 Prover9 (32) version 2009-11A, November 2009.
% 1.49/1.78 Process 19583 was started by sandbox on n024.cluster.edu,
% 1.49/1.78 Thu Jun 30 04:48:46 2022
% 1.49/1.78 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19430_n024.cluster.edu".
% 1.49/1.78 ============================== end of head ===========================
% 1.49/1.78
% 1.49/1.78 ============================== INPUT =================================
% 1.49/1.78
% 1.49/1.78 % Reading from file /tmp/Prover9_19430_n024.cluster.edu
% 1.49/1.78
% 1.49/1.78 set(prolog_style_variables).
% 1.49/1.78 set(auto2).
% 1.49/1.78 % set(auto2) -> set(auto).
% 1.49/1.78 % set(auto) -> set(auto_inference).
% 1.49/1.78 % set(auto) -> set(auto_setup).
% 1.49/1.78 % set(auto_setup) -> set(predicate_elim).
% 1.49/1.78 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.49/1.78 % set(auto) -> set(auto_limits).
% 1.49/1.78 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.49/1.78 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.49/1.78 % set(auto) -> set(auto_denials).
% 1.49/1.78 % set(auto) -> set(auto_process).
% 1.49/1.78 % set(auto2) -> assign(new_constants, 1).
% 1.49/1.78 % set(auto2) -> assign(fold_denial_max, 3).
% 1.49/1.78 % set(auto2) -> assign(max_weight, "200.000").
% 1.49/1.78 % set(auto2) -> assign(max_hours, 1).
% 1.49/1.78 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.49/1.78 % set(auto2) -> assign(max_seconds, 0).
% 1.49/1.78 % set(auto2) -> assign(max_minutes, 5).
% 1.49/1.78 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.49/1.78 % set(auto2) -> set(sort_initial_sos).
% 1.49/1.78 % set(auto2) -> assign(sos_limit, -1).
% 1.49/1.78 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.49/1.78 % set(auto2) -> assign(max_megs, 400).
% 1.49/1.78 % set(auto2) -> assign(stats, some).
% 1.49/1.78 % set(auto2) -> clear(echo_input).
% 1.49/1.78 % set(auto2) -> set(quiet).
% 1.49/1.78 % set(auto2) -> clear(print_initial_clauses).
% 1.49/1.78 % set(auto2) -> clear(print_given).
% 1.49/1.78 assign(lrs_ticks,-1).
% 1.49/1.78 assign(sos_limit,10000).
% 1.49/1.78 assign(order,kbo).
% 1.49/1.78 set(lex_order_vars).
% 1.49/1.78 clear(print_given).
% 1.49/1.78
% 1.49/1.78 % formulas(sos). % not echoed (3 formulas)
% 1.49/1.78
% 1.49/1.78 ============================== end of input ==========================
% 1.49/1.78
% 1.49/1.78 % From the command line: assign(max_seconds, 300).
% 1.49/1.78
% 1.49/1.78 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.49/1.78
% 1.49/1.78 % Formulas that are not ordinary clauses:
% 1.49/1.78
% 1.49/1.78 ============================== end of process non-clausal formulas ===
% 1.49/1.78
% 1.49/1.78 ============================== PROCESS INITIAL CLAUSES ===============
% 1.49/1.78
% 1.49/1.78 ============================== PREDICATE ELIMINATION =================
% 1.49/1.78
% 1.49/1.78 ============================== end predicate elimination =============
% 1.49/1.78
% 1.49/1.78 Auto_denials:
% 1.49/1.78 % copying label prove_associativity_of_meet to answer in negative clause
% 1.49/1.78
% 1.49/1.78 Term ordering decisions:
% 1.49/1.78 Function symbol KB weights: a=1. b=1. c=1. meet=1. join=1.
% 1.49/1.78
% 1.49/1.78 ============================== end of process initial clauses ========
% 1.49/1.78
% 1.49/1.78 ============================== CLAUSES FOR SEARCH ====================
% 1.49/1.78
% 1.49/1.78 ============================== end of clauses for search =============
% 1.49/1.78
% 1.49/1.78 ============================== SEARCH ================================
% 1.49/1.78
% 1.49/1.78 % Starting search at 0.01 seconds.
% 1.49/1.78
% 1.49/1.78 ============================== PROOF =================================
% 1.49/1.78 % SZS status Unsatisfiable
% 1.49/1.78 % SZS output start Refutation
% 1.49/1.78
% 1.49/1.78 % Proof 1 at 0.78 (+ 0.02) seconds: prove_associativity_of_meet.
% 1.49/1.78 % Length of proof is 62.
% 1.49/1.78 % Level of proof is 27.
% 1.49/1.78 % Maximum clause weight is 27.000.
% 1.49/1.78 % Given clauses 148.
% 1.49/1.78
% 1.49/1.78 1 meet(A,join(A,B)) = A # label(absorption) # label(axiom). [assumption].
% 1.49/1.78 2 meet(A,join(B,C)) = join(meet(C,A),meet(B,A)) # label(distribution) # label(axiom). [assumption].
% 1.49/1.78 3 join(meet(A,B),meet(C,B)) = meet(B,join(C,A)). [copy(2),flip(a)].
% 1.49/1.78 4 meet(meet(a,b),c) != meet(a,meet(b,c)) # label(prove_associativity_of_meet) # label(negated_conjecture) # answer(prove_associativity_of_meet). [assumption].
% 1.49/1.78 5 meet(meet(A,B),meet(B,join(C,A))) = meet(A,B). [para(3(a,1),1(a,1,2))].
% 1.49/1.78 6 join(A,meet(B,join(A,C))) = meet(join(A,C),join(B,A)). [para(1(a,1),3(a,1,1))].
% 1.49/1.78 7 join(meet(A,join(B,C)),B) = meet(join(B,C),join(B,A)). [para(1(a,1),3(a,1,2))].
% 1.49/1.78 8 meet(A,meet(join(A,B),join(C,A))) = A. [para(1(a,1),5(a,1,1)),rewrite([1(6)])].
% 1.49/1.78 9 meet(meet(A,B),B) = meet(A,B). [para(1(a,1),5(a,1,2))].
% 1.49/1.78 12 meet(meet(meet(A,B),C),meet(C,meet(B,join(A,D)))) = meet(meet(A,B),C). [para(3(a,1),5(a,1,2,2))].
% 1.49/1.78 14 meet(A,join(B,meet(C,A))) = meet(A,join(B,C)). [para(9(a,1),3(a,1,1)),rewrite([3(3)]),flip(a)].
% 1.49/1.78 15 meet(A,join(meet(B,A),C)) = meet(A,join(B,C)). [para(9(a,1),3(a,1,2)),rewrite([3(3)]),flip(a)].
% 1.49/1.78 18 meet(meet(A,B),meet(join(meet(A,B),C),meet(B,join(A,D)))) = meet(A,B). [para(3(a,1),8(a,1,2,2))].
% 1.49/1.78 22 meet(A,meet(A,join(B,C))) = meet(A,join(C,B)). [para(3(a,1),14(a,1,2)),rewrite([15(6)])].
% 1.49/1.78 33 meet(join(A,B),join(A,A)) = join(A,A). [para(1(a,1),6(a,1,2)),flip(a)].
% 1.49/1.78 39 meet(meet(A,join(B,C)),meet(A,join(C,C))) = meet(A,join(C,C)). [para(3(a,1),33(a,1,1)),rewrite([3(5),3(8)])].
% 1.49/1.78 50 meet(A,join(B,A)) = meet(A,A). [para(1(a,1),22(a,1,2)),flip(a)].
% 1.49/1.78 73 meet(A,A) = A. [para(50(a,1),1(a,1))].
% 1.49/1.78 76 join(A,meet(B,A)) = A. [para(50(a,1),3(a,2)),rewrite([73(1),73(3)])].
% 1.49/1.78 77 meet(meet(A,B),meet(B,join(A,C))) = meet(A,B). [para(3(a,1),50(a,1,2)),rewrite([73(7)])].
% 1.49/1.78 79 join(A,B) = join(B,A). [para(50(a,1),7(a,1,1)),rewrite([73(1),73(4)])].
% 1.49/1.78 100 meet(meet(A,B),meet(join(C,meet(A,B)),meet(B,join(A,D)))) = meet(A,B). [back_rewrite(18),rewrite([79(3)])].
% 1.49/1.78 105 join(meet(A,B),meet(C,B)) = meet(B,join(A,C)). [back_rewrite(3),rewrite([79(4)])].
% 1.49/1.78 109 join(A,A) = A. [para(76(a,1),33(a,1,1)),rewrite([1(2)]),flip(a)].
% 1.49/1.78 117 meet(meet(A,join(B,C)),meet(A,C)) = meet(A,C). [back_rewrite(39),rewrite([109(3),109(5)])].
% 1.49/1.78 118 meet(join(A,B),A) = A. [back_rewrite(33),rewrite([109(2),109(3)])].
% 1.49/1.78 119 meet(A,meet(B,A)) = meet(A,B). [para(109(a,1),14(a,1,2)),rewrite([79(4),14(5),109(3)])].
% 1.49/1.78 127 meet(meet(meet(A,B),C),meet(meet(C,meet(B,join(A,D))),meet(C,join(E,meet(A,B))))) = meet(meet(A,B),C). [para(12(a,1),12(a,1,1)),rewrite([79(7),12(16)])].
% 1.49/1.78 130 meet(join(A,B),B) = B. [para(79(a,1),118(a,1,1))].
% 1.49/1.78 131 meet(A,B) = meet(B,A). [para(76(a,1),130(a,1,1)),rewrite([119(2)])].
% 1.49/1.78 134 meet(A,join(B,A)) = A. [back_rewrite(130),rewrite([131(2)])].
% 1.49/1.78 135 meet(meet(A,meet(B,C)),meet(meet(A,meet(C,join(B,D))),meet(A,join(E,meet(B,C))))) = meet(A,meet(B,C)). [back_rewrite(127),rewrite([131(2),131(12)])].
% 1.49/1.78 140 meet(A,meet(A,B)) = meet(A,B). [back_rewrite(119),rewrite([131(1)])].
% 1.49/1.78 141 meet(meet(A,B),meet(A,join(C,B))) = meet(A,B). [back_rewrite(117),rewrite([131(4)])].
% 1.49/1.78 143 join(meet(A,B),meet(B,C)) = meet(B,join(A,C)). [back_rewrite(105),rewrite([131(2)])].
% 1.49/1.78 150 join(A,meet(A,B)) = A. [back_rewrite(76),rewrite([131(1)])].
% 1.49/1.78 156 meet(c,meet(a,b)) != meet(a,meet(b,c)) # answer(prove_associativity_of_meet). [back_rewrite(4),rewrite([131(5)])].
% 1.49/1.78 169 meet(meet(A,B),join(A,C)) = meet(A,B). [para(140(a,1),77(a,1,1)),rewrite([140(5),140(5)])].
% 1.49/1.78 176 meet(join(A,B),meet(A,C)) = meet(A,C). [para(169(a,1),131(a,1)),flip(a)].
% 1.49/1.78 191 meet(join(A,B),meet(B,C)) = meet(B,C). [para(79(a,1),176(a,1,1))].
% 1.49/1.78 193 join(join(A,B),meet(A,C)) = join(A,B). [para(176(a,1),150(a,1,2))].
% 1.49/1.78 220 join(join(A,B),meet(B,C)) = join(A,B). [para(191(a,1),150(a,1,2))].
% 1.49/1.78 221 meet(A,meet(B,meet(A,C))) = meet(B,meet(A,C)). [para(150(a,1),191(a,1,1)),rewrite([131(2),131(5)])].
% 1.49/1.78 224 join(meet(A,B),join(A,C)) = join(A,C). [para(193(a,1),79(a,1)),flip(a)].
% 1.49/1.78 243 join(meet(A,B),join(C,A)) = join(C,A). [para(220(a,1),79(a,1)),flip(a)].
% 1.49/1.78 260 join(meet(A,B),join(B,C)) = join(B,C). [para(131(a,1),224(a,1,1))].
% 1.49/1.78 285 join(A,meet(B,A)) = A. [para(109(a,1),260(a,1,2)),rewrite([79(2),109(3)])].
% 1.49/1.78 312 meet(meet(A,B),meet(A,meet(B,join(A,C)))) = meet(A,B). [para(150(a,1),100(a,1,2,1))].
% 1.49/1.78 337 join(A,meet(B,meet(C,A))) = A. [para(285(a,1),243(a,1,2)),rewrite([131(2),79(3),285(5)])].
% 1.49/1.78 339 meet(A,meet(B,meet(C,A))) = meet(B,meet(C,A)). [para(337(a,1),134(a,1,2)),rewrite([131(3)])].
% 1.49/1.78 371 meet(meet(A,B),meet(A,meet(B,C))) = meet(A,meet(B,C)). [para(150(a,1),141(a,1,2,2)),rewrite([131(4)])].
% 1.49/1.78 386 meet(A,meet(B,join(A,C))) = meet(A,B). [back_rewrite(312),rewrite([371(5)])].
% 1.49/1.78 427 meet(meet(A,B),meet(C,join(A,D))) = meet(C,meet(A,B)). [para(224(a,1),386(a,1,2,2)),rewrite([131(6)])].
% 1.49/1.78 435 join(meet(A,B),meet(A,C)) = meet(A,join(C,B)). [para(143(a,1),79(a,1)),rewrite([131(4)]),flip(a)].
% 1.49/1.78 983 meet(meet(A,B),meet(B,join(C,A))) = meet(A,B). [para(141(a,1),339(a,1,2)),rewrite([131(2),191(3),131(2)]),flip(a)].
% 1.49/1.78 1052 join(meet(A,meet(B,C)),meet(B,D)) = meet(B,join(D,meet(A,meet(B,C)))). [para(221(a,1),435(a,1,1))].
% 1.49/1.78 1405 meet(meet(A,B),meet(B,meet(A,C))) = meet(B,meet(A,C)). [para(150(a,1),983(a,1,2,2)),rewrite([131(2),131(3),131(4),131(6)])].
% 1.49/1.78 2485 meet(meet(A,B),join(C,meet(A,meet(B,D)))) = meet(A,join(meet(B,D),meet(C,meet(A,B)))). [para(371(a,1),143(a,1,2)),rewrite([1052(5)]),flip(a)].
% 1.49/1.78 2492 meet(meet(A,B),meet(C,A)) = meet(C,meet(A,B)). [para(371(a,1),135(a,1,1)),rewrite([427(7),2485(10),427(11),221(6),1405(6),371(7)])].
% 1.49/1.78 2526 meet(meet(A,B),meet(B,C)) = meet(A,meet(B,C)). [para(2492(a,1),131(a,1)),flip(a)].
% 1.49/1.78 2527 meet(A,meet(B,C)) = meet(C,meet(A,B)). [para(131(a,1),2492(a,1,1)),rewrite([131(2),2526(3),131(3)])].
% 1.49/1.78 2528 $F # answer(prove_associativity_of_meet). [resolve(2527,a,156,a(flip))].
% 1.49/1.78
% 1.49/1.78 % SZS output end Refutation
% 1.49/1.78 ============================== end of proof ==========================
% 1.49/1.78
% 1.49/1.78 ============================== STATISTICS ============================
% 1.49/1.78
% 1.49/1.78 Given=148. Generated=26558. Kept=2526. proofs=1.
% 1.49/1.78 Usable=115. Sos=1664. Demods=1768. Limbo=1, Disabled=748. Hints=0.
% 1.49/1.78 Megabytes=3.14.
% 1.49/1.78 User_CPU=0.78, System_CPU=0.02, Wall_clock=1.
% 1.49/1.78
% 1.49/1.78 ============================== end of statistics =====================
% 1.49/1.78
% 1.49/1.78 ============================== end of search =========================
% 1.49/1.78
% 1.49/1.78 THEOREM PROVED
% 1.49/1.78 % SZS status Unsatisfiable
% 1.49/1.78
% 1.49/1.78 Exiting with 1 proof.
% 1.49/1.78
% 1.49/1.78 Process 19583 exit (max_proofs) Thu Jun 30 04:48:47 2022
% 1.49/1.78 Prover9 interrupted
%------------------------------------------------------------------------------