TSTP Solution File: LAT235-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT235-1 : TPTP v8.1.0. Released v3.1.0.
% 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 : Sun Jul 17 06:26:18 EDT 2022
% Result : Unsatisfiable 1.48s 1.75s
% Output : Refutation 1.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT235-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % 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 : Wed Jun 29 11:20:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.48/1.75 ============================== Prover9 ===============================
% 1.48/1.75 Prover9 (32) version 2009-11A, November 2009.
% 1.48/1.75 Process 11570 was started by sandbox on n025.cluster.edu,
% 1.48/1.75 Wed Jun 29 11:20:08 2022
% 1.48/1.75 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11417_n025.cluster.edu".
% 1.48/1.75 ============================== end of head ===========================
% 1.48/1.75
% 1.48/1.75 ============================== INPUT =================================
% 1.48/1.75
% 1.48/1.75 % Reading from file /tmp/Prover9_11417_n025.cluster.edu
% 1.48/1.75
% 1.48/1.75 set(prolog_style_variables).
% 1.48/1.75 set(auto2).
% 1.48/1.75 % set(auto2) -> set(auto).
% 1.48/1.75 % set(auto) -> set(auto_inference).
% 1.48/1.75 % set(auto) -> set(auto_setup).
% 1.48/1.75 % set(auto_setup) -> set(predicate_elim).
% 1.48/1.75 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.48/1.75 % set(auto) -> set(auto_limits).
% 1.48/1.75 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.48/1.75 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.48/1.75 % set(auto) -> set(auto_denials).
% 1.48/1.75 % set(auto) -> set(auto_process).
% 1.48/1.75 % set(auto2) -> assign(new_constants, 1).
% 1.48/1.75 % set(auto2) -> assign(fold_denial_max, 3).
% 1.48/1.75 % set(auto2) -> assign(max_weight, "200.000").
% 1.48/1.75 % set(auto2) -> assign(max_hours, 1).
% 1.48/1.75 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.48/1.75 % set(auto2) -> assign(max_seconds, 0).
% 1.48/1.75 % set(auto2) -> assign(max_minutes, 5).
% 1.48/1.75 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.48/1.75 % set(auto2) -> set(sort_initial_sos).
% 1.48/1.75 % set(auto2) -> assign(sos_limit, -1).
% 1.48/1.75 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.48/1.75 % set(auto2) -> assign(max_megs, 400).
% 1.48/1.75 % set(auto2) -> assign(stats, some).
% 1.48/1.75 % set(auto2) -> clear(echo_input).
% 1.48/1.75 % set(auto2) -> set(quiet).
% 1.48/1.75 % set(auto2) -> clear(print_initial_clauses).
% 1.48/1.75 % set(auto2) -> clear(print_given).
% 1.48/1.75 assign(lrs_ticks,-1).
% 1.48/1.75 assign(sos_limit,10000).
% 1.48/1.75 assign(order,kbo).
% 1.48/1.75 set(lex_order_vars).
% 1.48/1.75 clear(print_given).
% 1.48/1.75
% 1.48/1.75 % formulas(sos). % not echoed (14 formulas)
% 1.48/1.75
% 1.48/1.75 ============================== end of input ==========================
% 1.48/1.75
% 1.48/1.75 % From the command line: assign(max_seconds, 300).
% 1.48/1.75
% 1.48/1.75 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.48/1.75
% 1.48/1.75 % Formulas that are not ordinary clauses:
% 1.48/1.75
% 1.48/1.75 ============================== end of process non-clausal formulas ===
% 1.48/1.75
% 1.48/1.75 ============================== PROCESS INITIAL CLAUSES ===============
% 1.48/1.75
% 1.48/1.75 ============================== PREDICATE ELIMINATION =================
% 1.48/1.75
% 1.48/1.75 ============================== end predicate elimination =============
% 1.48/1.75
% 1.48/1.75 Auto_denials:
% 1.48/1.75 % copying label prove_distributivity to answer in negative clause
% 1.48/1.75
% 1.48/1.75 Term ordering decisions:
% 1.48/1.75
% 1.48/1.75 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 1.48/1.75 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. complement=0.
% 1.48/1.75
% 1.48/1.75 ============================== end of process initial clauses ========
% 1.48/1.75
% 1.48/1.75 ============================== CLAUSES FOR SEARCH ====================
% 1.48/1.75
% 1.48/1.75 ============================== end of clauses for search =============
% 1.48/1.75
% 1.48/1.75 ============================== SEARCH ================================
% 1.48/1.75
% 1.48/1.75 % Starting search at 0.01 seconds.
% 1.48/1.75
% 1.48/1.75 ============================== PROOF =================================
% 1.48/1.75 % SZS status Unsatisfiable
% 1.48/1.75 % SZS output start Refutation
% 1.48/1.75
% 1.48/1.75 % Proof 1 at 0.73 (+ 0.02) seconds: prove_distributivity.
% 1.48/1.75 % Length of proof is 73.
% 1.48/1.75 % Level of proof is 23.
% 1.48/1.75 % Maximum clause weight is 25.000.
% 1.48/1.75 % Given clauses 249.
% 1.48/1.75
% 1.48/1.75 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 1.48/1.75 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 1.48/1.75 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 1.48/1.75 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 1.48/1.75 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 1.48/1.75 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 1.48/1.75 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 1.48/1.75 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 1.48/1.75 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 1.48/1.75 10 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 1.48/1.75 11 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(10),rewrite([8(2)]),flip(a)].
% 1.48/1.75 12 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 1.48/1.75 13 join(A,join(B,C)) = join(C,join(A,B)). [copy(12),rewrite([9(2)]),flip(a)].
% 1.48/1.75 14 meet(A,join(B,meet(C,D))) = meet(A,join(B,meet(C,join(B,meet(D,join(B,C)))))) # label(equation_H34) # label(axiom). [assumption].
% 1.48/1.75 15 meet(A,join(B,meet(C,join(B,meet(D,join(B,C)))))) = meet(A,join(B,meet(C,D))). [copy(14),flip(a)].
% 1.48/1.75 16 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 1.48/1.75 17 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(16),rewrite([9(5)])].
% 1.48/1.75 18 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 1.48/1.75 19 meet(a,b) = a. [back_rewrite(3),rewrite([8(3)])].
% 1.48/1.75 20 meet(A,one) = A. [para(4(a,1),6(a,1,2))].
% 1.48/1.75 21 join(A,zero) = A. [para(5(a,1),7(a,1,2))].
% 1.48/1.75 22 meet(A,meet(A,B)) = meet(A,B). [para(11(a,1),1(a,1)),rewrite([8(1),8(2),11(2,R),1(1),8(3)])].
% 1.48/1.75 23 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),11(a,2,2)),rewrite([8(2)])].
% 1.48/1.75 24 meet(A,meet(B,join(A,C))) = meet(A,B). [para(6(a,1),11(a,2,2)),rewrite([8(2),8(4)])].
% 1.48/1.75 25 join(A,join(A,B)) = join(A,B). [para(13(a,1),2(a,1)),rewrite([9(1),9(2),13(2,R),2(1),9(3)])].
% 1.48/1.75 26 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),13(a,2,2)),rewrite([9(2)])].
% 1.48/1.75 27 join(A,join(B,meet(A,C))) = join(A,B). [para(7(a,1),13(a,2,2)),rewrite([9(2),9(4)])].
% 1.48/1.75 28 join(A,meet(B,join(A,meet(C,join(A,B))))) = join(A,meet(B,C)). [para(15(a,1),1(a,1)),rewrite([8(8),15(8),1(5)]),flip(a)].
% 1.48/1.75 36 meet(A,zero) != zero | one != A | complement(A) = zero. [para(21(a,1),18(b,1)),flip(b)].
% 1.48/1.75 37 meet(A,zero) = zero. [para(5(a,1),22(a,1,2)),rewrite([5(4)])].
% 1.48/1.75 38 one != A | complement(A) = zero. [back_rewrite(36),rewrite([37(2)]),xx(a)].
% 1.48/1.75 39 meet(A,meet(B,complement(A))) = zero. [back_rewrite(23),rewrite([37(5)])].
% 1.48/1.75 41 meet(A,meet(B,meet(C,join(A,D)))) = meet(A,meet(B,C)). [para(24(a,1),11(a,2,2)),rewrite([8(3),11(3,R),8(2),11(6),8(5),11(6,R),8(5)])].
% 1.48/1.75 43 complement(join(A,one)) = zero. [hyper(38,a,7,a(flip)),rewrite([8(3),20(3),9(2)])].
% 1.48/1.75 45 join(A,one) = one. [para(43(a,1),4(a,1,2)),rewrite([9(4),13(4),9(3),21(3),9(2)])].
% 1.48/1.75 46 join(A,join(B,complement(A))) = one. [back_rewrite(26),rewrite([45(5)])].
% 1.48/1.75 61 join(A,meet(complement(A),join(A,B))) = join(A,meet(B,complement(A))). [para(4(a,1),28(a,1,2,2,2,2)),rewrite([20(3),8(6)])].
% 1.48/1.75 62 join(A,meet(B,join(A,meet(C,join(B,A))))) = join(A,meet(B,C)). [para(28(a,1),9(a,2)),rewrite([9(1),9(5)])].
% 1.48/1.75 65 join(A,meet(one,join(A,B))) = join(A,B). [para(45(a,1),28(a,1,2,2,2,2)),rewrite([20(3),8(6),20(6)])].
% 1.48/1.75 67 join(A,meet(join(B,complement(A)),join(A,C))) = join(A,meet(C,join(B,complement(A)))). [para(46(a,1),28(a,1,2,2,2,2)),rewrite([20(4),8(8)])].
% 1.48/1.75 68 join(A,meet(join(B,meet(A,C)),join(A,meet(D,join(A,B))))) = join(A,meet(D,join(B,meet(A,C)))). [para(27(a,1),28(a,1,2,2,2,2)),rewrite([8(10)])].
% 1.48/1.75 73 join(A,join(B,meet(one,join(A,C)))) = join(A,join(C,B)). [para(65(a,1),13(a,2,2)),rewrite([9(4),13(7),9(6),13(7,R),9(6)])].
% 1.48/1.75 75 join(A,meet(meet(one,join(A,B)),join(A,meet(C,join(A,B))))) = join(A,meet(C,meet(one,join(A,B)))). [para(65(a,1),28(a,1,2,2,2,2)),rewrite([8(12)])].
% 1.48/1.75 76 join(A,meet(B,join(A,B))) = join(A,B). [para(65(a,1),28(a,1,2,2)),rewrite([20(5)])].
% 1.48/1.75 79 join(A,meet(one,join(B,complement(A)))) = one. [para(46(a,1),76(a,1,2,2)),rewrite([8(4),46(8)])].
% 1.48/1.75 80 join(A,meet(join(A,B),join(B,meet(A,C)))) = join(A,B). [para(27(a,1),76(a,1,2,2)),rewrite([8(4),27(8)])].
% 1.48/1.75 84 join(A,meet(one,complement(A))) = one. [para(2(a,1),79(a,1,2,2))].
% 1.48/1.75 91 meet(one,complement(A)) = complement(A). [hyper(18,a,39,a,b,84,a),flip(a)].
% 1.48/1.75 95 meet(A,meet(B,meet(meet(A,B),join(C,meet(A,B))))) = meet(A,B). [para(1(a,1),41(a,2)),rewrite([9(3),11(6,R),8(5),11(5,R),8(4)])].
% 1.48/1.75 190 join(join(A,B),meet(A,join(join(A,B),meet(C,join(A,B))))) = join(join(A,B),meet(A,C)). [para(25(a,1),62(a,1,2,2,2,2))].
% 1.48/1.75 344 join(A,meet(join(B,complement(A)),join(C,complement(A)))) = one. [para(46(a,1),67(a,1,2,2)),rewrite([8(4),79(5)]),flip(a)].
% 1.48/1.75 428 join(A,meet(one,join(B,meet(A,C)))) = join(A,B). [para(65(a,1),68(a,1,2,2)),rewrite([8(4),80(5)]),flip(a)].
% 1.48/1.75 820 join(complement(A),meet(one,join(A,meet(B,complement(A))))) = one. [para(61(a,1),428(a,1,2,2)),rewrite([9(9),4(9)])].
% 1.48/1.75 969 join(A,meet(B,meet(one,join(A,C)))) = join(A,meet(B,join(A,C))). [para(11(a,1),75(a,2,2)),rewrite([75(8),20(8),8(7)])].
% 1.48/1.75 972 join(A,join(B,meet(C,join(A,B)))) = join(A,B). [para(75(a,1),27(a,1,2)),rewrite([969(8),13(7,R),73(7),9(8),65(8)])].
% 1.48/1.75 1148 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(972(a,1),13(a,1)),rewrite([9(5)]),flip(a)].
% 1.48/1.75 1183 join(join(A,B),meet(A,C)) = join(A,B). [back_rewrite(190),rewrite([1148(5),6(3),9(2),25(2)]),flip(a)].
% 1.48/1.75 1198 join(complement(join(A,B)),meet(one,join(A,B))) = one. [para(1183(a,1),820(a,1,2,2))].
% 1.48/1.75 1271 meet(one,join(A,B)) = complement(complement(join(A,B))). [para(1198(a,1),18(b,1)),rewrite([11(6),8(5),91(5),5(4)]),flip(c),xx(a),xx(b)].
% 1.48/1.75 1705 complement(complement(A)) = A. [para(2(a,1),1271(a,1,2)),rewrite([8(2),20(2),2(1)]),flip(a)].
% 1.48/1.75 1750 join(complement(A),meet(join(A,B),join(A,C))) = one. [para(1705(a,1),344(a,1,2,1,2)),rewrite([9(2),1705(4),9(3)])].
% 1.48/1.75 1822 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(95(a,1),11(a,1)),rewrite([8(7),22(7)]),flip(a)].
% 1.48/1.75 2372 meet(meet(A,B),join(A,C)) = meet(A,B). [para(1183(a,1),1822(a,1,2))].
% 1.48/1.75 2391 meet(meet(A,B),join(B,C)) = meet(A,B). [para(8(a,1),2372(a,1,1)),rewrite([8(4)])].
% 1.48/1.75 2419 meet(a,join(A,b)) = a. [para(19(a,1),2391(a,1,1)),rewrite([9(3),19(7)])].
% 1.48/1.75 2456 join(A,join(a,b)) = join(A,b). [para(2419(a,1),972(a,1,2,2)),rewrite([9(3)])].
% 1.48/1.75 2478 join(a,b) = b. [para(2456(a,1),2(a,1)),rewrite([9(5),2456(5),2(3)]),flip(a)].
% 1.48/1.75 2490 join(complement(a),meet(b,join(A,a))) = one. [para(2478(a,1),1750(a,1,2,1)),rewrite([9(5)])].
% 1.48/1.75 2597 join(b,complement(a)) = one. [para(6(a,1),2490(a,1,2)),rewrite([9(4)])].
% 1.48/1.75 2618 join(b,meet(complement(a),complement(b))) = one. [para(2597(a,1),61(a,1,2,2)),rewrite([8(5),91(5),4(4)]),flip(a)].
% 1.48/1.75 2628 meet(complement(a),complement(b)) = complement(b). [hyper(18,a,39,a,b,2618,a),flip(a)].
% 1.48/1.75 2633 join(complement(a),complement(b)) = complement(a). [para(2628(a,1),7(a,1,2))].
% 1.48/1.75 2634 $F # answer(prove_distributivity). [resolve(2633,a,17,a)].
% 1.48/1.75
% 1.48/1.75 % SZS output end Refutation
% 1.48/1.75 ============================== end of proof ==========================
% 1.48/1.75
% 1.48/1.75 ============================== STATISTICS ============================
% 1.48/1.75
% 1.48/1.75 Given=249. Generated=23912. Kept=2629. proofs=1.
% 1.48/1.75 Usable=165. Sos=1185. Demods=1112. Limbo=0, Disabled=1292. Hints=0.
% 1.48/1.75 Megabytes=3.59.
% 1.48/1.75 User_CPU=0.73, System_CPU=0.02, Wall_clock=0.
% 1.48/1.75
% 1.48/1.75 ============================== end of statistics =====================
% 1.48/1.75
% 1.48/1.75 ============================== end of search =========================
% 1.48/1.75
% 1.48/1.75 THEOREM PROVED
% 1.48/1.75 % SZS status Unsatisfiable
% 1.48/1.75
% 1.48/1.75 Exiting with 1 proof.
% 1.48/1.75
% 1.48/1.75 Process 11570 exit (max_proofs) Wed Jun 29 11:20:08 2022
% 1.48/1.75 Prover9 interrupted
%------------------------------------------------------------------------------