TSTP Solution File: LAT254-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT254-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 06:26:24 EDT 2022
% Result : Unsatisfiable 2.02s 2.33s
% Output : Refutation 2.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LAT254-1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Thu Jun 30 15:13:04 EDT 2022
% 0.11/0.32 % CPUTime :
% 2.02/2.33 ============================== Prover9 ===============================
% 2.02/2.33 Prover9 (32) version 2009-11A, November 2009.
% 2.02/2.33 Process 13784 was started by sandbox on n010.cluster.edu,
% 2.02/2.33 Thu Jun 30 15:13:04 2022
% 2.02/2.33 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13631_n010.cluster.edu".
% 2.02/2.33 ============================== end of head ===========================
% 2.02/2.33
% 2.02/2.33 ============================== INPUT =================================
% 2.02/2.33
% 2.02/2.33 % Reading from file /tmp/Prover9_13631_n010.cluster.edu
% 2.02/2.33
% 2.02/2.33 set(prolog_style_variables).
% 2.02/2.33 set(auto2).
% 2.02/2.33 % set(auto2) -> set(auto).
% 2.02/2.33 % set(auto) -> set(auto_inference).
% 2.02/2.33 % set(auto) -> set(auto_setup).
% 2.02/2.33 % set(auto_setup) -> set(predicate_elim).
% 2.02/2.33 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.02/2.33 % set(auto) -> set(auto_limits).
% 2.02/2.33 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.02/2.33 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.02/2.33 % set(auto) -> set(auto_denials).
% 2.02/2.33 % set(auto) -> set(auto_process).
% 2.02/2.33 % set(auto2) -> assign(new_constants, 1).
% 2.02/2.33 % set(auto2) -> assign(fold_denial_max, 3).
% 2.02/2.33 % set(auto2) -> assign(max_weight, "200.000").
% 2.02/2.33 % set(auto2) -> assign(max_hours, 1).
% 2.02/2.33 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.02/2.33 % set(auto2) -> assign(max_seconds, 0).
% 2.02/2.33 % set(auto2) -> assign(max_minutes, 5).
% 2.02/2.33 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.02/2.33 % set(auto2) -> set(sort_initial_sos).
% 2.02/2.33 % set(auto2) -> assign(sos_limit, -1).
% 2.02/2.33 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.02/2.33 % set(auto2) -> assign(max_megs, 400).
% 2.02/2.33 % set(auto2) -> assign(stats, some).
% 2.02/2.33 % set(auto2) -> clear(echo_input).
% 2.02/2.33 % set(auto2) -> set(quiet).
% 2.02/2.33 % set(auto2) -> clear(print_initial_clauses).
% 2.02/2.33 % set(auto2) -> clear(print_given).
% 2.02/2.33 assign(lrs_ticks,-1).
% 2.02/2.33 assign(sos_limit,10000).
% 2.02/2.33 assign(order,kbo).
% 2.02/2.33 set(lex_order_vars).
% 2.02/2.33 clear(print_given).
% 2.02/2.33
% 2.02/2.33 % formulas(sos). % not echoed (14 formulas)
% 2.02/2.33
% 2.02/2.33 ============================== end of input ==========================
% 2.02/2.33
% 2.02/2.33 % From the command line: assign(max_seconds, 300).
% 2.02/2.33
% 2.02/2.33 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.02/2.33
% 2.02/2.33 % Formulas that are not ordinary clauses:
% 2.02/2.33
% 2.02/2.33 ============================== end of process non-clausal formulas ===
% 2.02/2.33
% 2.02/2.33 ============================== PROCESS INITIAL CLAUSES ===============
% 2.02/2.33
% 2.02/2.33 ============================== PREDICATE ELIMINATION =================
% 2.02/2.33
% 2.02/2.33 ============================== end predicate elimination =============
% 2.02/2.33
% 2.02/2.33 Auto_denials:
% 2.02/2.33 % copying label prove_distributivity to answer in negative clause
% 2.02/2.33
% 2.02/2.33 Term ordering decisions:
% 2.02/2.33
% 2.02/2.33 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 2.02/2.33 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. complement=0.
% 2.02/2.33
% 2.02/2.33 ============================== end of process initial clauses ========
% 2.02/2.33
% 2.02/2.33 ============================== CLAUSES FOR SEARCH ====================
% 2.02/2.33
% 2.02/2.33 ============================== end of clauses for search =============
% 2.02/2.33
% 2.02/2.33 ============================== SEARCH ================================
% 2.02/2.33
% 2.02/2.33 % Starting search at 0.01 seconds.
% 2.02/2.33
% 2.02/2.33 ============================== PROOF =================================
% 2.02/2.33 % SZS status Unsatisfiable
% 2.02/2.33 % SZS output start Refutation
% 2.02/2.33
% 2.02/2.33 % Proof 1 at 1.37 (+ 0.02) seconds: prove_distributivity.
% 2.02/2.33 % Length of proof is 87.
% 2.02/2.33 % Level of proof is 24.
% 2.02/2.33 % Maximum clause weight is 23.000.
% 2.02/2.33 % Given clauses 286.
% 2.02/2.33
% 2.02/2.33 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 2.02/2.33 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 2.02/2.33 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 2.02/2.33 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 2.02/2.33 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 2.02/2.33 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 2.02/2.33 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 2.02/2.33 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 2.02/2.33 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 2.02/2.33 10 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 2.02/2.33 11 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(10),rewrite([8(2)]),flip(a)].
% 2.02/2.33 12 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 2.02/2.33 13 join(A,join(B,C)) = join(C,join(A,B)). [copy(12),rewrite([9(2)]),flip(a)].
% 2.02/2.33 14 meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(meet(A,join(B,meet(A,C))),meet(C,D))) # label(equation_H79) # label(axiom). [assumption].
% 2.02/2.33 15 meet(A,join(meet(A,join(B,meet(A,C))),meet(C,D))) = meet(A,join(B,meet(C,join(A,D)))). [copy(14),flip(a)].
% 2.02/2.33 16 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 2.02/2.33 17 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(16),rewrite([9(5)])].
% 2.02/2.33 18 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 2.02/2.33 19 meet(a,b) = a. [back_rewrite(3),rewrite([8(3)])].
% 2.02/2.33 20 meet(A,one) = A. [para(4(a,1),6(a,1,2))].
% 2.02/2.33 21 join(A,zero) = A. [para(5(a,1),7(a,1,2))].
% 2.02/2.33 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)])].
% 2.02/2.33 23 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),11(a,2,2)),rewrite([8(2)])].
% 2.02/2.33 24 meet(A,meet(B,join(A,C))) = meet(A,B). [para(6(a,1),11(a,2,2)),rewrite([8(2),8(4)])].
% 2.02/2.33 26 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),13(a,2,2)),rewrite([9(2)])].
% 2.02/2.33 27 join(A,join(B,meet(A,C))) = join(A,B). [para(7(a,1),13(a,2,2)),rewrite([9(2),9(4)])].
% 2.02/2.33 28 meet(A,join(B,meet(A,join(C,meet(A,B))))) = meet(A,join(C,meet(B,join(A,B)))). [para(1(a,1),15(a,1,2,2)),rewrite([9(4)])].
% 2.02/2.33 29 meet(A,join(meet(A,B),meet(B,join(A,C)))) = meet(A,join(meet(A,B),meet(B,C))). [para(2(a,1),15(a,1,2,1,2)),rewrite([22(2)]),flip(a)].
% 2.02/2.33 31 meet(A,join(meet(B,C),meet(A,join(meet(A,B),meet(B,C))))) = meet(A,B). [para(2(a,1),15(a,2,2)),rewrite([9(4),29(5),9(6),24(10)])].
% 2.02/2.33 33 meet(A,join(meet(A,B),meet(C,complement(A)))) = meet(A,join(B,meet(complement(A),join(A,C)))). [para(5(a,1),15(a,1,2,1,2,2)),rewrite([21(2),8(3)])].
% 2.02/2.33 34 meet(A,join(zero,meet(A,join(B,meet(A,C))))) = meet(A,join(B,meet(C,join(A,complement(C))))). [para(5(a,1),15(a,1,2,2)),rewrite([9(5)])].
% 2.02/2.33 48 meet(A,join(B,meet(one,join(A,C)))) = A. [para(20(a,1),15(a,1,2,1,2,2)),rewrite([9(1),6(2),8(2),20(2),6(2)]),flip(a)].
% 2.02/2.33 49 meet(A,join(B,meet(C,join(A,one)))) = meet(A,join(B,meet(C,join(A,C)))). [para(20(a,1),15(a,1,2,2)),rewrite([9(4),28(5)]),flip(a)].
% 2.02/2.33 50 meet(A,zero) != zero | one != A | complement(A) = zero. [para(21(a,1),18(b,1)),flip(b)].
% 2.02/2.33 51 meet(A,zero) = zero. [para(5(a,1),22(a,1,2)),rewrite([5(4)])].
% 2.02/2.33 54 one != A | complement(A) = zero. [back_rewrite(50),rewrite([51(2)]),xx(a)].
% 2.02/2.33 55 meet(A,meet(B,complement(A))) = zero. [back_rewrite(23),rewrite([51(5)])].
% 2.02/2.33 56 complement(one) = zero. [hyper(18,a,51,a,b,21,a)].
% 2.02/2.33 58 meet(A,join(zero,meet(A,join(B,meet(A,C))))) = meet(A,join(B,meet(A,C))). [para(51(a,1),15(a,1,2,2)),rewrite([9(5),21(8),8(7)])].
% 2.02/2.33 59 meet(A,join(B,meet(C,join(A,complement(C))))) = meet(A,join(B,meet(A,C))). [back_rewrite(34),rewrite([58(6)]),flip(a)].
% 2.02/2.33 65 complement(join(A,one)) = zero. [hyper(54,a,7,a(flip)),rewrite([8(3),20(3),9(2)])].
% 2.02/2.33 67 join(A,one) = one. [para(65(a,1),4(a,1,2)),rewrite([9(4),13(4),9(3),21(3),9(2)])].
% 2.02/2.33 68 meet(A,join(B,meet(C,join(A,C)))) = meet(A,join(B,C)). [back_rewrite(49),rewrite([67(2),20(2)]),flip(a)].
% 2.02/2.33 69 join(A,join(B,complement(A))) = one. [back_rewrite(26),rewrite([67(5)])].
% 2.02/2.33 72 meet(A,join(B,meet(A,join(C,meet(A,B))))) = meet(A,join(B,C)). [back_rewrite(28),rewrite([68(9),9(6)])].
% 2.02/2.33 74 zero != A | complement(A) = one. [para(67(a,1),18(b,1)),rewrite([20(2)]),flip(a),xx(b)].
% 2.02/2.33 112 complement(meet(zero,join(A,B))) = one. [hyper(74,a,48,a(flip)),rewrite([9(4),21(4),8(3),20(3)])].
% 2.02/2.33 117 join(one,meet(zero,join(A,B))) = one. [para(112(a,1),4(a,1,2)),rewrite([9(5)])].
% 2.02/2.33 119 meet(A,meet(zero,join(B,C))) = zero. [para(112(a,1),55(a,1,2,2)),rewrite([20(5),8(4)])].
% 2.02/2.33 121 meet(zero,join(A,B)) = zero. [para(117(a,1),18(b,1)),rewrite([119(5),56(8)]),flip(c),xx(a),xx(b)].
% 2.02/2.33 200 meet(A,join(complement(A),meet(A,B))) = meet(A,join(B,complement(A))). [para(1(a,1),33(a,1,2,2)),rewrite([9(3),4(7),20(7)])].
% 2.02/2.33 201 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(2(a,1),33(a,2,2)),rewrite([24(4),5(2),24(9),5(7)])].
% 2.02/2.33 203 meet(A,join(meet(B,complement(A)),meet(A,C))) = meet(A,join(C,meet(complement(A),join(A,B)))). [para(9(a,1),33(a,1,2))].
% 2.02/2.33 212 meet(A,join(one,meet(complement(A),join(A,B)))) = A. [para(20(a,1),33(a,1,2,1)),rewrite([6(4)]),flip(a)].
% 2.02/2.33 214 meet(A,join(meet(B,complement(A)),meet(complement(A),join(A,C)))) = zero. [para(55(a,1),33(a,1,2,1)),rewrite([201(5)]),flip(a)].
% 2.02/2.33 250 meet(A,join(zero,complement(A))) = zero. [para(1(a,1),201(a,1,2,2))].
% 2.02/2.33 257 join(zero,complement(A)) = complement(A). [hyper(18,a,250,a,b,69,a),flip(a)].
% 2.02/2.33 358 meet(A,join(one,complement(A))) = A. [para(4(a,1),212(a,1,2,2,2)),rewrite([20(4)])].
% 2.02/2.33 967 meet(A,join(B,meet(A,B))) = meet(A,B). [para(7(a,1),59(a,1,2)),flip(a)].
% 2.02/2.33 991 meet(A,join(meet(A,B),meet(B,C))) = meet(A,B). [para(967(a,1),15(a,1,2,1)),rewrite([7(7)])].
% 2.02/2.33 996 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(967(a,1),31(a,1,2,1)),rewrite([967(5),991(5)])].
% 2.02/2.33 1109 meet(A,join(meet(B,C),meet(B,A))) = meet(B,A). [para(996(a,1),8(a,2)),rewrite([8(2),8(4),8(5)])].
% 2.02/2.33 1110 meet(A,join(meet(B,C),meet(A,C))) = meet(A,C). [para(8(a,1),996(a,1,2,1))].
% 2.02/2.33 1193 meet(b,join(a,meet(A,a))) = a. [para(19(a,1),1109(a,1,2,2)),rewrite([8(3),9(5),19(9)])].
% 2.02/2.33 1242 join(a,b) = b. [para(1193(a,1),7(a,1,2)),rewrite([9(3)])].
% 2.02/2.33 1262 meet(A,join(a,meet(A,b))) = meet(A,b). [para(1193(a,1),991(a,1,2,2)),rewrite([9(4)])].
% 2.02/2.33 1267 join(a,join(b,meet(A,a))) = b. [para(1242(a,1),27(a,2)),rewrite([8(4)])].
% 2.02/2.33 1269 meet(zero,b) = zero. [para(1242(a,1),121(a,1,2))].
% 2.02/2.33 1304 join(b,meet(A,a)) = b. [para(1267(a,1),13(a,1)),rewrite([1242(6),9(5)]),flip(a)].
% 2.02/2.33 1314 meet(one,b) = b. [para(1304(a,1),212(a,1,2,2,2)),rewrite([8(6),5(6),21(4),8(3)])].
% 2.02/2.33 1329 meet(one,join(b,meet(A,b))) = b. [para(1314(a,1),991(a,1,2,1)),rewrite([8(4),1314(9)])].
% 2.02/2.33 1436 meet(one,join(zero,b)) = b. [para(1269(a,1),1329(a,1,2,2)),rewrite([9(4)])].
% 2.02/2.33 1460 meet(A,join(zero,b)) = meet(A,b). [para(1436(a,1),11(a,1,2)),rewrite([20(7),8(6)]),flip(a)].
% 2.02/2.33 1472 join(zero,b) = b. [para(1460(a,1),1(a,1)),rewrite([8(5),1460(5),1(3)]),flip(a)].
% 2.02/2.33 1478 meet(A,join(meet(A,b),meet(B,b))) = meet(A,b). [para(1460(a,1),991(a,1,2,1)),rewrite([1472(5),8(4),1472(9)])].
% 2.02/2.33 1524 meet(A,join(meet(B,complement(A)),meet(A,C))) = meet(A,join(C,meet(B,complement(A)))). [para(55(a,1),72(a,1,2,2,2,2)),rewrite([21(4),9(8)])].
% 2.02/2.33 1573 meet(A,join(B,meet(complement(A),join(A,C)))) = meet(A,join(B,meet(C,complement(A)))). [back_rewrite(203),rewrite([1524(5)]),flip(a)].
% 2.02/2.33 1637 meet(A,join(meet(B,complement(A)),meet(C,complement(A)))) = zero. [back_rewrite(214),rewrite([1573(7)])].
% 2.02/2.33 1765 meet(A,join(a,meet(b,join(A,B)))) = meet(A,b). [para(1262(a,1),15(a,1,2,1)),rewrite([8(4),1478(6)]),flip(a)].
% 2.02/2.33 1964 meet(A,join(meet(B,C),meet(C,A))) = meet(C,A). [para(1110(a,1),8(a,2)),rewrite([8(2),8(4),8(5)])].
% 2.02/2.33 2379 meet(A,join(complement(A),meet(B,complement(A)))) = zero. [para(1(a,1),1637(a,1,2,1))].
% 2.02/2.33 2437 meet(a,complement(b)) = zero. [para(2379(a,1),1765(a,1,2,2)),rewrite([21(5),8(4),8(8),5(8)])].
% 2.02/2.33 2515 meet(one,join(A,meet(B,A))) = A. [para(20(a,1),1964(a,1,2,2)),rewrite([9(3),20(6)])].
% 2.02/2.33 2536 join(one,complement(A)) = one. [para(358(a,1),2515(a,1,2,2)),rewrite([9(5),69(5),1(3)]),flip(a)].
% 2.02/2.33 4208 meet(a,join(complement(a),complement(b))) = zero. [para(2437(a,1),200(a,1,2,2)),rewrite([9(5),257(5),5(4),9(7)]),flip(a)].
% 2.02/2.33 4246 join(a,join(complement(a),complement(b))) != one # answer(prove_distributivity). [ur(18,a,4208,a,c,17,a(flip))].
% 2.02/2.33 4436 $F # answer(prove_distributivity). [para(13(a,1),4246(a,1)),rewrite([4(6),9(4),2536(4)]),xx(a)].
% 2.02/2.33
% 2.02/2.33 % SZS output end Refutation
% 2.02/2.33 ============================== end of proof ==========================
% 2.02/2.33
% 2.02/2.33 ============================== STATISTICS ============================
% 2.02/2.33
% 2.02/2.33 Given=286. Generated=38311. Kept=4431. proofs=1.
% 2.02/2.33 Usable=215. Sos=2817. Demods=2921. Limbo=0, Disabled=1413. Hints=0.
% 2.02/2.33 Megabytes=7.22.
% 2.02/2.33 User_CPU=1.37, System_CPU=0.02, Wall_clock=2.
% 2.02/2.33
% 2.02/2.33 ============================== end of statistics =====================
% 2.02/2.33
% 2.02/2.33 ============================== end of search =========================
% 2.02/2.33
% 2.02/2.33 THEOREM PROVED
% 2.02/2.33 % SZS status Unsatisfiable
% 2.02/2.33
% 2.02/2.33 Exiting with 1 proof.
% 2.02/2.33
% 2.02/2.33 Process 13784 exit (max_proofs) Thu Jun 30 15:13:06 2022
% 2.02/2.33 Prover9 interrupted
%------------------------------------------------------------------------------