TSTP Solution File: LAT250-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT250-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 06:26:23 EDT 2022
% Result : Unsatisfiable 1.28s 1.58s
% Output : Refutation 1.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT250-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n029.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 : Tue Jun 28 18:21:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.28/1.58 ============================== Prover9 ===============================
% 1.28/1.58 Prover9 (32) version 2009-11A, November 2009.
% 1.28/1.58 Process 19717 was started by sandbox on n029.cluster.edu,
% 1.28/1.58 Tue Jun 28 18:21:22 2022
% 1.28/1.58 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19564_n029.cluster.edu".
% 1.28/1.58 ============================== end of head ===========================
% 1.28/1.58
% 1.28/1.58 ============================== INPUT =================================
% 1.28/1.58
% 1.28/1.58 % Reading from file /tmp/Prover9_19564_n029.cluster.edu
% 1.28/1.58
% 1.28/1.58 set(prolog_style_variables).
% 1.28/1.58 set(auto2).
% 1.28/1.58 % set(auto2) -> set(auto).
% 1.28/1.58 % set(auto) -> set(auto_inference).
% 1.28/1.58 % set(auto) -> set(auto_setup).
% 1.28/1.58 % set(auto_setup) -> set(predicate_elim).
% 1.28/1.58 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.28/1.58 % set(auto) -> set(auto_limits).
% 1.28/1.58 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.28/1.58 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.28/1.58 % set(auto) -> set(auto_denials).
% 1.28/1.58 % set(auto) -> set(auto_process).
% 1.28/1.58 % set(auto2) -> assign(new_constants, 1).
% 1.28/1.58 % set(auto2) -> assign(fold_denial_max, 3).
% 1.28/1.58 % set(auto2) -> assign(max_weight, "200.000").
% 1.28/1.58 % set(auto2) -> assign(max_hours, 1).
% 1.28/1.58 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.28/1.58 % set(auto2) -> assign(max_seconds, 0).
% 1.28/1.58 % set(auto2) -> assign(max_minutes, 5).
% 1.28/1.58 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.28/1.58 % set(auto2) -> set(sort_initial_sos).
% 1.28/1.58 % set(auto2) -> assign(sos_limit, -1).
% 1.28/1.58 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.28/1.58 % set(auto2) -> assign(max_megs, 400).
% 1.28/1.58 % set(auto2) -> assign(stats, some).
% 1.28/1.58 % set(auto2) -> clear(echo_input).
% 1.28/1.58 % set(auto2) -> set(quiet).
% 1.28/1.58 % set(auto2) -> clear(print_initial_clauses).
% 1.28/1.58 % set(auto2) -> clear(print_given).
% 1.28/1.58 assign(lrs_ticks,-1).
% 1.28/1.58 assign(sos_limit,10000).
% 1.28/1.58 assign(order,kbo).
% 1.28/1.58 set(lex_order_vars).
% 1.28/1.58 clear(print_given).
% 1.28/1.58
% 1.28/1.58 % formulas(sos). % not echoed (14 formulas)
% 1.28/1.58
% 1.28/1.58 ============================== end of input ==========================
% 1.28/1.58
% 1.28/1.58 % From the command line: assign(max_seconds, 300).
% 1.28/1.58
% 1.28/1.58 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.28/1.58
% 1.28/1.58 % Formulas that are not ordinary clauses:
% 1.28/1.58
% 1.28/1.58 ============================== end of process non-clausal formulas ===
% 1.28/1.58
% 1.28/1.58 ============================== PROCESS INITIAL CLAUSES ===============
% 1.28/1.58
% 1.28/1.58 ============================== PREDICATE ELIMINATION =================
% 1.28/1.58
% 1.28/1.58 ============================== end predicate elimination =============
% 1.28/1.58
% 1.28/1.58 Auto_denials:
% 1.28/1.58 % copying label prove_distributivity to answer in negative clause
% 1.28/1.58
% 1.28/1.58 Term ordering decisions:
% 1.28/1.58
% 1.28/1.58 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 1.28/1.58 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. complement=0.
% 1.28/1.58
% 1.28/1.58 ============================== end of process initial clauses ========
% 1.28/1.58
% 1.28/1.58 ============================== CLAUSES FOR SEARCH ====================
% 1.28/1.58
% 1.28/1.58 ============================== end of clauses for search =============
% 1.28/1.58
% 1.28/1.58 ============================== SEARCH ================================
% 1.28/1.58
% 1.28/1.58 % Starting search at 0.01 seconds.
% 1.28/1.58
% 1.28/1.58 ============================== PROOF =================================
% 1.28/1.58 % SZS status Unsatisfiable
% 1.28/1.58 % SZS output start Refutation
% 1.28/1.58
% 1.28/1.58 % Proof 1 at 0.59 (+ 0.01) seconds: prove_distributivity.
% 1.28/1.58 % Length of proof is 70.
% 1.28/1.58 % Level of proof is 16.
% 1.28/1.58 % Maximum clause weight is 35.000.
% 1.28/1.58 % Given clauses 181.
% 1.28/1.58
% 1.28/1.58 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 1.28/1.58 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 1.28/1.58 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 1.28/1.58 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 1.28/1.58 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 1.28/1.58 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 1.28/1.58 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 1.28/1.58 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 1.28/1.58 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 1.28/1.58 10 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 1.28/1.58 11 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(10),rewrite([8(2)]),flip(a)].
% 1.28/1.58 12 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 1.28/1.58 13 join(A,join(B,C)) = join(C,join(A,B)). [copy(12),rewrite([9(2)]),flip(a)].
% 1.28/1.58 14 meet(A,join(B,C)) = meet(A,join(B,meet(A,join(C,meet(A,B))))) # label(equation_H68) # label(axiom). [assumption].
% 1.28/1.58 15 meet(A,join(B,meet(A,join(C,meet(A,B))))) = meet(A,join(B,C)). [copy(14),flip(a)].
% 1.28/1.58 16 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 1.28/1.58 17 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(16),rewrite([9(5)])].
% 1.28/1.58 18 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 1.28/1.58 19 meet(a,b) = a. [back_rewrite(3),rewrite([8(3)])].
% 1.28/1.58 20 meet(A,one) = A. [para(4(a,1),6(a,1,2))].
% 1.28/1.58 21 join(A,zero) = A. [para(5(a,1),7(a,1,2))].
% 1.28/1.58 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)])].
% 1.28/1.58 23 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),11(a,2,2)),rewrite([8(2)])].
% 1.28/1.58 24 meet(A,meet(B,join(A,C))) = meet(A,B). [para(6(a,1),11(a,2,2)),rewrite([8(2),8(4)])].
% 1.28/1.58 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)])].
% 1.28/1.58 26 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),13(a,2,2)),rewrite([9(2)])].
% 1.28/1.58 28 meet(A,join(complement(A),meet(A,B))) = meet(A,join(B,complement(A))). [para(5(a,1),15(a,1,2,2,2,2)),rewrite([21(3),9(6)])].
% 1.28/1.58 29 meet(A,join(B,meet(A,join(C,meet(B,A))))) = meet(A,join(B,C)). [para(15(a,1),8(a,2)),rewrite([8(1),8(5)])].
% 1.28/1.58 31 meet(A,join(join(B,meet(A,join(C,meet(A,B)))),meet(A,join(D,meet(A,join(B,C)))))) = meet(A,join(B,join(D,meet(A,join(C,meet(A,B)))))). [para(15(a,1),15(a,1,2,2,2,2)),rewrite([9(15),13(15,R),9(14)])].
% 1.28/1.58 38 meet(A,zero) != zero | one != A | complement(A) = zero. [para(21(a,1),18(b,1)),flip(b)].
% 1.28/1.58 40 meet(A,zero) = zero. [para(5(a,1),22(a,1,2)),rewrite([5(4)])].
% 1.28/1.58 41 meet(A,join(meet(A,B),meet(A,join(C,meet(A,B))))) = meet(A,join(C,meet(A,B))). [para(22(a,1),15(a,1,2,2,2,2)),rewrite([9(8)])].
% 1.28/1.58 42 one != A | complement(A) = zero. [back_rewrite(38),rewrite([40(2)]),xx(a)].
% 1.28/1.58 43 meet(A,meet(B,complement(A))) = zero. [back_rewrite(23),rewrite([40(5)])].
% 1.28/1.58 45 meet(A,join(zero,meet(A,B))) = meet(A,B). [para(40(a,1),15(a,1,2,2,2,2)),rewrite([21(3),9(6),21(6)])].
% 1.28/1.58 47 meet(A,join(meet(B,join(A,C)),meet(A,join(D,meet(A,B))))) = meet(A,join(D,meet(B,join(A,C)))). [para(24(a,1),15(a,1,2,2,2,2)),rewrite([9(10)])].
% 1.28/1.58 49 complement(join(A,one)) = zero. [hyper(42,a,7,a(flip)),rewrite([8(3),20(3),9(2)])].
% 1.28/1.58 50 join(A,one) = one. [para(49(a,1),4(a,1,2)),rewrite([9(4),13(4),9(3),21(3),9(2)])].
% 1.28/1.58 51 join(A,join(B,complement(A))) = one. [back_rewrite(26),rewrite([50(5)])].
% 1.28/1.58 55 meet(A,meet(B,meet(C,complement(A)))) = zero. [para(43(a,1),11(a,2,2)),rewrite([8(3),11(3,R),8(2),40(6)])].
% 1.28/1.58 58 meet(A,join(B,complement(A))) != zero | join(B,complement(A)) = complement(A). [para(51(a,1),18(b,1)),flip(c),xx(b)].
% 1.28/1.58 77 meet(A,join(zero,complement(A))) = zero. [para(40(a,1),28(a,1,2,2)),rewrite([21(3),5(2)]),flip(a)].
% 1.28/1.58 79 meet(A,join(complement(A),meet(B,join(A,C)))) = meet(A,join(B,complement(A))). [para(24(a,1),28(a,1,2,2)),rewrite([28(4),9(7)]),flip(a)].
% 1.28/1.58 80 meet(A,join(complement(A),meet(B,complement(A)))) = zero. [para(43(a,1),28(a,1,2,2)),rewrite([21(3),5(2),9(5)]),flip(a)].
% 1.28/1.58 85 join(zero,complement(A)) = complement(A). [hyper(18,a,77,a,b,51,a),flip(a)].
% 1.28/1.58 88 meet(join(A,B),join(A,meet(join(A,B),join(A,C)))) = meet(join(A,B),join(A,C)). [para(6(a,1),29(a,1,2,2,2,2)),rewrite([9(3)])].
% 1.28/1.58 89 meet(A,join(B,meet(A,B))) = meet(A,B). [para(7(a,1),29(a,1,2,2,2)),rewrite([2(4)])].
% 1.28/1.58 92 meet(b,join(a,meet(b,join(A,a)))) = meet(b,join(A,a)). [para(19(a,1),29(a,1,2,2,2,2)),rewrite([9(11)])].
% 1.28/1.58 140 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(1(a,1),31(a,1,2,2,2,2)),rewrite([8(4),6(4),9(3),1(4),25(3),13(5),9(4),13(5,R),9(4),7(7),1(3),8(5),6(5),9(4),1(5),13(4),9(3),13(4,R),9(3),25(5)]),flip(a)].
% 1.28/1.58 259 meet(A,join(zero,meet(B,meet(C,complement(A))))) = zero. [para(55(a,1),89(a,1,2,2)),rewrite([9(5),55(10)])].
% 1.28/1.58 474 meet(one,join(A,B)) = join(A,B). [para(4(a,1),140(a,1,2,2)),rewrite([50(3),8(3)])].
% 1.28/1.58 486 meet(one,complement(A)) = complement(A). [para(85(a,1),474(a,1,2)),rewrite([85(6)])].
% 1.28/1.58 487 join(one,complement(A)) = one. [para(486(a,1),7(a,1,2))].
% 1.28/1.58 945 meet(complement(A),join(A,complement(complement(A)))) = zero. [para(80(a,1),79(a,1,2,2)),rewrite([21(5),5(4)]),flip(a)].
% 1.28/1.58 954 join(A,complement(complement(A))) = complement(complement(A)). [hyper(58,a,945,a)].
% 1.28/1.58 961 meet(A,complement(complement(A))) = A. [para(954(a,1),6(a,1,2))].
% 1.28/1.58 976 meet(complement(A),join(zero,meet(A,B))) = zero. [para(961(a,1),259(a,1,2,2,2)),rewrite([8(3)])].
% 1.28/1.58 1499 meet(b,join(a,meet(b,join(a,b)))) = b. [para(6(a,1),92(a,2)),rewrite([9(6)])].
% 1.28/1.58 1515 meet(b,join(a,b)) = b. [para(1499(a,1),15(a,2)),rewrite([8(11),19(11),9(10),1499(11)])].
% 1.28/1.58 1524 meet(b,join(A,b)) = b. [para(1499(a,1),41(a,1,2,1)),rewrite([1515(10),1515(8),7(7),1(3),1515(9),1515(7)]),flip(a)].
% 1.28/1.58 1533 meet(b,meet(join(A,b),join(B,b))) = b. [para(1524(a,1),24(a,2)),rewrite([9(5)])].
% 1.28/1.58 1535 meet(b,join(A,meet(join(B,b),join(C,b)))) = b. [para(1524(a,1),47(a,1,2,2,2,2)),rewrite([9(5),1524(10),9(8),6(9),9(6)]),flip(a)].
% 1.28/1.58 1572 meet(one,b) = b. [para(1533(a,1),28(a,1,2,2)),rewrite([9(5),4(5),8(3),9(12),1535(13)])].
% 1.28/1.58 1581 join(zero,b) = b. [para(1572(a,1),45(a,1,2,2)),rewrite([474(5),1572(6)])].
% 1.28/1.58 1609 meet(b,join(zero,meet(A,b))) = meet(A,b). [para(1581(a,1),88(a,1,1)),rewrite([1581(5),9(5),21(5),8(4),1581(9),9(9),21(9),8(8)])].
% 1.28/1.58 1664 meet(complement(b),join(zero,meet(A,b))) = zero. [para(1609(a,1),976(a,1,2,2))].
% 1.28/1.58 1738 meet(a,complement(b)) = zero. [para(19(a,1),1664(a,1,2,2)),rewrite([9(5),21(5),8(4)])].
% 1.28/1.58 1749 meet(a,join(complement(a),complement(b))) = zero. [para(1738(a,1),28(a,1,2,2)),rewrite([9(5),85(5),5(4),9(7)]),flip(a)].
% 1.28/1.58 1774 join(a,join(complement(a),complement(b))) != one # answer(prove_distributivity). [ur(18,a,1749,a,c,17,a(flip))].
% 1.28/1.58 1828 $F # answer(prove_distributivity). [para(13(a,1),1774(a,1)),rewrite([4(6),9(4),487(4)]),xx(a)].
% 1.28/1.58
% 1.28/1.58 % SZS output end Refutation
% 1.28/1.58 ============================== end of proof ==========================
% 1.28/1.58
% 1.28/1.58 ============================== STATISTICS ============================
% 1.28/1.58
% 1.28/1.58 Given=181. Generated=12922. Kept=1823. proofs=1.
% 1.28/1.58 Usable=154. Sos=1299. Demods=1373. Limbo=0, Disabled=384. Hints=0.
% 1.28/1.58 Megabytes=3.85.
% 1.28/1.58 User_CPU=0.59, System_CPU=0.01, Wall_clock=1.
% 1.28/1.58
% 1.28/1.58 ============================== end of statistics =====================
% 1.28/1.58
% 1.28/1.58 ============================== end of search =========================
% 1.28/1.58
% 1.28/1.58 THEOREM PROVED
% 1.28/1.58 % SZS status Unsatisfiable
% 1.28/1.58
% 1.28/1.58 Exiting with 1 proof.
% 1.28/1.58
% 1.28/1.58 Process 19717 exit (max_proofs) Tue Jun 28 18:21:23 2022
% 1.28/1.58 Prover9 interrupted
%------------------------------------------------------------------------------