TSTP Solution File: LAT249-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT249-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 3.66s 3.94s
% Output : Refutation 3.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT249-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n011.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 29 16:28:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.66/3.94 ============================== Prover9 ===============================
% 3.66/3.94 Prover9 (32) version 2009-11A, November 2009.
% 3.66/3.94 Process 21418 was started by sandbox2 on n011.cluster.edu,
% 3.66/3.94 Wed Jun 29 16:28:33 2022
% 3.66/3.94 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21265_n011.cluster.edu".
% 3.66/3.94 ============================== end of head ===========================
% 3.66/3.94
% 3.66/3.94 ============================== INPUT =================================
% 3.66/3.94
% 3.66/3.94 % Reading from file /tmp/Prover9_21265_n011.cluster.edu
% 3.66/3.94
% 3.66/3.94 set(prolog_style_variables).
% 3.66/3.94 set(auto2).
% 3.66/3.94 % set(auto2) -> set(auto).
% 3.66/3.94 % set(auto) -> set(auto_inference).
% 3.66/3.94 % set(auto) -> set(auto_setup).
% 3.66/3.94 % set(auto_setup) -> set(predicate_elim).
% 3.66/3.94 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.66/3.94 % set(auto) -> set(auto_limits).
% 3.66/3.94 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.66/3.94 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.66/3.94 % set(auto) -> set(auto_denials).
% 3.66/3.94 % set(auto) -> set(auto_process).
% 3.66/3.94 % set(auto2) -> assign(new_constants, 1).
% 3.66/3.94 % set(auto2) -> assign(fold_denial_max, 3).
% 3.66/3.94 % set(auto2) -> assign(max_weight, "200.000").
% 3.66/3.94 % set(auto2) -> assign(max_hours, 1).
% 3.66/3.94 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.66/3.94 % set(auto2) -> assign(max_seconds, 0).
% 3.66/3.94 % set(auto2) -> assign(max_minutes, 5).
% 3.66/3.94 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.66/3.94 % set(auto2) -> set(sort_initial_sos).
% 3.66/3.94 % set(auto2) -> assign(sos_limit, -1).
% 3.66/3.94 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.66/3.94 % set(auto2) -> assign(max_megs, 400).
% 3.66/3.94 % set(auto2) -> assign(stats, some).
% 3.66/3.94 % set(auto2) -> clear(echo_input).
% 3.66/3.94 % set(auto2) -> set(quiet).
% 3.66/3.94 % set(auto2) -> clear(print_initial_clauses).
% 3.66/3.94 % set(auto2) -> clear(print_given).
% 3.66/3.94 assign(lrs_ticks,-1).
% 3.66/3.94 assign(sos_limit,10000).
% 3.66/3.94 assign(order,kbo).
% 3.66/3.94 set(lex_order_vars).
% 3.66/3.94 clear(print_given).
% 3.66/3.94
% 3.66/3.94 % formulas(sos). % not echoed (14 formulas)
% 3.66/3.94
% 3.66/3.94 ============================== end of input ==========================
% 3.66/3.94
% 3.66/3.94 % From the command line: assign(max_seconds, 300).
% 3.66/3.94
% 3.66/3.94 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.66/3.94
% 3.66/3.94 % Formulas that are not ordinary clauses:
% 3.66/3.94
% 3.66/3.94 ============================== end of process non-clausal formulas ===
% 3.66/3.94
% 3.66/3.94 ============================== PROCESS INITIAL CLAUSES ===============
% 3.66/3.94
% 3.66/3.94 ============================== PREDICATE ELIMINATION =================
% 3.66/3.94
% 3.66/3.94 ============================== end predicate elimination =============
% 3.66/3.94
% 3.66/3.94 Auto_denials:
% 3.66/3.94 % copying label prove_distributivity to answer in negative clause
% 3.66/3.94
% 3.66/3.94 Term ordering decisions:
% 3.66/3.94
% 3.66/3.94 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 3.66/3.94 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. complement=0.
% 3.66/3.94
% 3.66/3.94 ============================== end of process initial clauses ========
% 3.66/3.94
% 3.66/3.94 ============================== CLAUSES FOR SEARCH ====================
% 3.66/3.94
% 3.66/3.94 ============================== end of clauses for search =============
% 3.66/3.94
% 3.66/3.94 ============================== SEARCH ================================
% 3.66/3.94
% 3.66/3.94 % Starting search at 0.01 seconds.
% 3.66/3.94
% 3.66/3.94 ============================== PROOF =================================
% 3.66/3.94 % SZS status Unsatisfiable
% 3.66/3.94 % SZS output start Refutation
% 3.66/3.94
% 3.66/3.94 % Proof 1 at 2.92 (+ 0.03) seconds: prove_distributivity.
% 3.66/3.94 % Length of proof is 77.
% 3.66/3.94 % Level of proof is 19.
% 3.66/3.94 % Maximum clause weight is 47.000.
% 3.66/3.94 % Given clauses 316.
% 3.66/3.94
% 3.66/3.94 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 3.66/3.94 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 3.66/3.94 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 3.66/3.94 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 3.66/3.94 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 3.66/3.94 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 3.66/3.94 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 3.66/3.94 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 3.66/3.94 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 3.66/3.94 10 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 3.66/3.94 11 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(10),rewrite([8(2)]),flip(a)].
% 3.66/3.94 12 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 3.66/3.94 13 join(A,join(B,C)) = join(C,join(A,B)). [copy(12),rewrite([9(2)]),flip(a)].
% 3.66/3.94 14 meet(A,join(B,C)) = meet(A,join(B,meet(A,join(C,meet(A,join(B,meet(A,C))))))) # label(equation_H64) # label(axiom). [assumption].
% 3.66/3.94 15 meet(A,join(B,meet(A,join(C,meet(A,join(B,meet(A,C))))))) = meet(A,join(B,C)). [copy(14),flip(a)].
% 3.66/3.94 16 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 3.66/3.94 17 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(16),rewrite([9(5)])].
% 3.66/3.94 18 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 3.66/3.94 19 meet(a,b) = a. [back_rewrite(3),rewrite([8(3)])].
% 3.66/3.94 20 meet(A,one) = A. [para(4(a,1),6(a,1,2))].
% 3.66/3.94 21 join(A,zero) = A. [para(5(a,1),7(a,1,2))].
% 3.66/3.94 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)])].
% 3.66/3.94 23 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),11(a,2,2)),rewrite([8(2)])].
% 3.66/3.94 24 meet(A,meet(B,join(A,C))) = meet(A,B). [para(6(a,1),11(a,2,2)),rewrite([8(2),8(4)])].
% 3.66/3.94 26 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),13(a,2,2)),rewrite([9(2)])].
% 3.66/3.94 27 join(A,join(B,meet(A,C))) = join(A,B). [para(7(a,1),13(a,2,2)),rewrite([9(2),9(4)])].
% 3.66/3.94 29 meet(A,join(meet(A,B),meet(A,join(B,meet(A,B))))) = meet(A,join(B,meet(A,B))). [para(2(a,1),15(a,1,2,2,2,2,2)),rewrite([22(3),9(8)])].
% 3.66/3.94 30 meet(A,join(B,meet(A,join(complement(A),meet(A,B))))) = meet(A,join(B,complement(A))). [para(5(a,1),15(a,1,2,2,2,2,2,2)),rewrite([21(3)])].
% 3.66/3.94 31 meet(A,meet(B,join(C,meet(A,join(D,meet(A,join(C,meet(A,D)))))))) = meet(A,meet(B,join(C,D))). [para(15(a,1),11(a,2,2)),rewrite([8(7),11(11,R),8(10)])].
% 3.66/3.94 32 meet(A,join(B,meet(A,join(join(C,meet(A,join(D,meet(A,join(C,meet(A,D)))))),meet(A,join(B,meet(A,join(C,D)))))))) = meet(A,join(B,join(C,meet(A,join(D,meet(A,join(C,meet(A,D)))))))). [para(15(a,1),15(a,1,2,2,2,2,2,2))].
% 3.66/3.94 33 meet(A,join(B,meet(A,join(C,join(meet(A,join(B,C)),meet(A,join(B,meet(A,C)))))))) = meet(A,join(B,join(C,meet(A,join(B,meet(A,C)))))). [para(15(a,1),15(a,1,2,2,2,2)),rewrite([9(7),13(7,R),9(6)])].
% 3.66/3.94 34 meet(A,join(B,meet(A,join(meet(A,join(B,C)),meet(A,join(C,meet(A,join(B,meet(A,C))))))))) = meet(A,join(B,C)). [para(15(a,1),15(a,2)),rewrite([22(11),15(12),9(8)])].
% 3.66/3.94 39 meet(A,zero) != zero | one != A | complement(A) = zero. [para(21(a,1),18(b,1)),flip(b)].
% 3.66/3.94 41 meet(A,zero) = zero. [para(5(a,1),22(a,1,2)),rewrite([5(4)])].
% 3.66/3.94 42 meet(A,join(B,meet(A,join(meet(A,C),meet(A,join(B,meet(A,C))))))) = meet(A,join(B,meet(A,C))). [para(22(a,1),15(a,1,2,2,2,2,2,2))].
% 3.66/3.94 43 one != A | complement(A) = zero. [back_rewrite(39),rewrite([41(2)]),xx(a)].
% 3.66/3.94 44 meet(A,meet(B,complement(A))) = zero. [back_rewrite(23),rewrite([41(5)])].
% 3.66/3.94 46 meet(A,join(B,meet(A,join(zero,meet(A,B))))) = meet(A,B). [para(41(a,1),15(a,1,2,2,2,2,2,2)),rewrite([21(3),21(8)])].
% 3.66/3.94 50 complement(join(A,one)) = zero. [hyper(43,a,7,a(flip)),rewrite([8(3),20(3),9(2)])].
% 3.66/3.94 51 join(A,one) = one. [para(50(a,1),4(a,1,2)),rewrite([9(4),13(4),9(3),21(3),9(2)])].
% 3.66/3.94 52 join(A,join(B,complement(A))) = one. [back_rewrite(26),rewrite([51(5)])].
% 3.66/3.94 56 meet(A,meet(B,meet(C,complement(A)))) = zero. [para(44(a,1),11(a,2,2)),rewrite([8(3),11(3,R),8(2),41(6)])].
% 3.66/3.94 57 meet(A,join(B,meet(A,join(meet(C,complement(A)),meet(A,B))))) = meet(A,join(B,meet(C,complement(A)))). [para(44(a,1),15(a,1,2,2,2,2,2,2)),rewrite([21(4)])].
% 3.66/3.94 59 meet(A,join(B,complement(A))) != zero | join(B,complement(A)) = complement(A). [para(52(a,1),18(b,1)),flip(c),xx(b)].
% 3.66/3.94 61 meet(A,join(B,meet(A,C))) != zero | join(A,B) != one | join(B,meet(A,C)) = complement(A). [para(27(a,1),18(b,1)),flip(c)].
% 3.66/3.94 106 meet(A,join(B,meet(A,join(complement(A),meet(B,A))))) = meet(A,join(B,complement(A))). [para(30(a,1),8(a,2)),rewrite([8(2),8(6)])].
% 3.66/3.94 117 meet(A,join(zero,complement(A))) = zero. [para(41(a,1),30(a,1,2,2,2,2)),rewrite([21(4),5(3),2(3),41(2)]),flip(a)].
% 3.66/3.94 129 join(zero,complement(A)) = complement(A). [hyper(18,a,117,a,b,52,a),flip(a)].
% 3.66/3.94 139 meet(A,meet(B,join(C,meet(A,join(meet(D,join(A,E)),meet(A,join(C,meet(A,D)))))))) = meet(A,meet(B,join(C,meet(D,join(A,E))))). [para(24(a,1),31(a,1,2,2,2,2,2,2,2))].
% 3.66/3.94 184 meet(A,join(meet(A,B),meet(A,join(B,meet(A,join(B,meet(A,B))))))) = meet(A,join(B,join(meet(A,B),meet(A,join(B,meet(A,B)))))). [para(29(a,1),32(a,1,2,2,2,2)),rewrite([22(4),29(7),9(9),13(9,R),2(8),22(12),29(15),13(14,R),9(13)])].
% 3.66/3.94 228 meet(A,join(B,join(meet(A,C),meet(A,join(B,meet(A,C)))))) = meet(A,join(B,meet(A,C))). [para(22(a,1),33(a,1,2,2,2,2,2,2,2)),rewrite([2(8),42(8),22(6)]),flip(a)].
% 3.66/3.94 265 meet(A,join(meet(A,B),meet(A,join(B,meet(A,join(B,meet(A,B))))))) = meet(A,join(B,meet(A,B))). [back_rewrite(184),rewrite([228(15)])].
% 3.66/3.94 292 meet(A,join(B,meet(A,join(B,meet(A,B))))) = meet(A,B). [para(2(a,1),34(a,1,2,2,2,1,2)),rewrite([265(8),2(6)])].
% 3.66/3.94 293 meet(A,join(B,meet(A,B))) = meet(A,B). [para(2(a,1),34(a,2,2)),rewrite([2(1),292(6),2(3),22(2)])].
% 3.66/3.94 332 meet(A,join(meet(A,B),meet(B,join(A,C)))) = meet(A,B). [para(24(a,1),293(a,1,2,2)),rewrite([9(4),24(8)])].
% 3.66/3.94 333 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(44(a,1),293(a,1,2,2)),rewrite([9(4),44(8)])].
% 3.66/3.94 334 meet(A,join(zero,meet(B,meet(C,complement(A))))) = zero. [para(56(a,1),293(a,1,2,2)),rewrite([9(5),56(10)])].
% 3.66/3.94 419 meet(A,join(zero,meet(A,B))) = meet(A,B). [para(46(a,1),15(a,1,2,2)),rewrite([9(6),21(6)])].
% 3.66/3.94 421 meet(A,meet(B,join(zero,meet(A,C)))) = meet(A,meet(B,C)). [para(46(a,1),31(a,1,2,2,2)),rewrite([9(7),21(7)])].
% 3.66/3.94 636 meet(A,join(meet(B,complement(A)),meet(C,complement(A)))) = zero. [para(44(a,1),57(a,1,2,2,2,2)),rewrite([9(6),333(7),9(4),333(5)]),flip(a)].
% 3.66/3.94 1458 meet(complement(A),join(A,complement(complement(A)))) = zero. [para(5(a,1),106(a,1,2,2,2,2)),rewrite([21(6),5(5),21(3),8(2),5(2)]),flip(a)].
% 3.66/3.94 1463 meet(meet(A,B),join(A,complement(meet(A,B)))) = meet(A,B). [para(22(a,1),106(a,1,2,2,2,2)),rewrite([9(6),4(6),8(4),11(4),8(3),20(3),8(2),7(3),8(2),22(2)]),flip(a)].
% 3.66/3.94 1563 join(A,complement(complement(A))) = complement(complement(A)). [hyper(59,a,1458,a)].
% 3.66/3.94 1572 meet(A,complement(complement(A))) = A. [para(1563(a,1),6(a,1,2))].
% 3.66/3.94 1588 meet(complement(A),join(zero,meet(A,B))) = zero. [para(1572(a,1),334(a,1,2,2,2)),rewrite([8(3)])].
% 3.66/3.94 1590 meet(complement(A),join(A,meet(B,complement(complement(A))))) = zero. [para(1572(a,1),636(a,1,2,1))].
% 3.66/3.94 1812 complement(complement(A)) = A. [para(1590(a,1),61(a,1)),rewrite([9(5),4(5),5(10),21(8)]),flip(c),xx(a),xx(b)].
% 3.66/3.94 1831 meet(complement(A),join(A,B)) != zero | join(A,B) = A. [para(1812(a,1),59(a,1,2,2)),rewrite([9(2),1812(7),9(6),1812(8)])].
% 3.66/3.94 2186 meet(a,join(complement(a),complement(b))) != zero # answer(prove_distributivity). [ur(1831,b,17,a),rewrite([1812(3)])].
% 3.66/3.94 4411 meet(complement(meet(A,B)),join(zero,meet(A,B))) = zero. [para(1463(a,1),1588(a,1,2,2))].
% 3.66/3.94 4562 meet(A,meet(B,complement(meet(B,join(A,C))))) = zero. [para(4411(a,1),139(a,2,2)),rewrite([419(10),9(8),332(9),421(8),8(4),41(7)])].
% 3.66/3.94 5080 meet(meet(A,B),complement(meet(A,join(B,C)))) = zero. [para(4562(a,1),11(a,1)),rewrite([8(5),8(6)]),flip(a)].
% 3.66/3.94 5663 meet(meet(A,B),complement(meet(B,join(A,C)))) = zero. [para(8(a,1),5080(a,1,1))].
% 3.66/3.94 6219 meet(a,complement(meet(b,join(A,a)))) = zero. [para(19(a,1),5663(a,1,1)),rewrite([9(4)])].
% 3.66/3.94 6367 meet(a,complement(b)) = zero. [para(6(a,1),6219(a,1,2,1))].
% 3.66/3.94 6386 meet(a,join(complement(a),complement(b))) = zero. [para(6367(a,1),30(a,1,2,2,2,2)),rewrite([9(8),129(8),5(7),9(5),129(5),6367(4),9(7)]),flip(a)].
% 3.66/3.94 6387 $F # answer(prove_distributivity). [resolve(6386,a,2186,a)].
% 3.66/3.94
% 3.66/3.94 % SZS output end Refutation
% 3.66/3.94 ============================== end of proof ==========================
% 3.66/3.94
% 3.66/3.94 ============================== STATISTICS ============================
% 3.66/3.94
% 3.66/3.94 Given=316. Generated=45414. Kept=6382. proofs=1.
% 3.66/3.94 Usable=242. Sos=4459. Demods=4471. Limbo=2, Disabled=1692. Hints=0.
% 3.66/3.94 Megabytes=19.18.
% 3.66/3.94 User_CPU=2.92, System_CPU=0.03, Wall_clock=3.
% 3.66/3.94
% 3.66/3.94 ============================== end of statistics =====================
% 3.66/3.94
% 3.66/3.94 ============================== end of search =========================
% 3.66/3.94
% 3.66/3.94 THEOREM PROVED
% 3.66/3.94 % SZS status Unsatisfiable
% 3.66/3.94
% 3.66/3.94 Exiting with 1 proof.
% 3.66/3.94
% 3.66/3.94 Process 21418 exit (max_proofs) Wed Jun 29 16:28:36 2022
% 3.66/3.94 Prover9 interrupted
%------------------------------------------------------------------------------