TSTP Solution File: LAT251-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT251-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 1.25s 1.58s
% Output : Refutation 1.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT251-1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n006.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 : Thu Jun 30 06:43:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.25/1.58 ============================== Prover9 ===============================
% 1.25/1.58 Prover9 (32) version 2009-11A, November 2009.
% 1.25/1.58 Process 23807 was started by sandbox on n006.cluster.edu,
% 1.25/1.58 Thu Jun 30 06:43:53 2022
% 1.25/1.58 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23653_n006.cluster.edu".
% 1.25/1.58 ============================== end of head ===========================
% 1.25/1.58
% 1.25/1.58 ============================== INPUT =================================
% 1.25/1.58
% 1.25/1.58 % Reading from file /tmp/Prover9_23653_n006.cluster.edu
% 1.25/1.58
% 1.25/1.58 set(prolog_style_variables).
% 1.25/1.58 set(auto2).
% 1.25/1.58 % set(auto2) -> set(auto).
% 1.25/1.58 % set(auto) -> set(auto_inference).
% 1.25/1.58 % set(auto) -> set(auto_setup).
% 1.25/1.58 % set(auto_setup) -> set(predicate_elim).
% 1.25/1.58 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.25/1.58 % set(auto) -> set(auto_limits).
% 1.25/1.58 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.25/1.58 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.25/1.58 % set(auto) -> set(auto_denials).
% 1.25/1.58 % set(auto) -> set(auto_process).
% 1.25/1.58 % set(auto2) -> assign(new_constants, 1).
% 1.25/1.58 % set(auto2) -> assign(fold_denial_max, 3).
% 1.25/1.58 % set(auto2) -> assign(max_weight, "200.000").
% 1.25/1.58 % set(auto2) -> assign(max_hours, 1).
% 1.25/1.58 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.25/1.58 % set(auto2) -> assign(max_seconds, 0).
% 1.25/1.58 % set(auto2) -> assign(max_minutes, 5).
% 1.25/1.58 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.25/1.58 % set(auto2) -> set(sort_initial_sos).
% 1.25/1.58 % set(auto2) -> assign(sos_limit, -1).
% 1.25/1.58 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.25/1.58 % set(auto2) -> assign(max_megs, 400).
% 1.25/1.58 % set(auto2) -> assign(stats, some).
% 1.25/1.58 % set(auto2) -> clear(echo_input).
% 1.25/1.58 % set(auto2) -> set(quiet).
% 1.25/1.58 % set(auto2) -> clear(print_initial_clauses).
% 1.25/1.58 % set(auto2) -> clear(print_given).
% 1.25/1.58 assign(lrs_ticks,-1).
% 1.25/1.58 assign(sos_limit,10000).
% 1.25/1.58 assign(order,kbo).
% 1.25/1.58 set(lex_order_vars).
% 1.25/1.58 clear(print_given).
% 1.25/1.58
% 1.25/1.58 % formulas(sos). % not echoed (14 formulas)
% 1.25/1.58
% 1.25/1.58 ============================== end of input ==========================
% 1.25/1.58
% 1.25/1.58 % From the command line: assign(max_seconds, 300).
% 1.25/1.58
% 1.25/1.58 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.25/1.58
% 1.25/1.58 % Formulas that are not ordinary clauses:
% 1.25/1.58
% 1.25/1.58 ============================== end of process non-clausal formulas ===
% 1.25/1.58
% 1.25/1.58 ============================== PROCESS INITIAL CLAUSES ===============
% 1.25/1.58
% 1.25/1.58 ============================== PREDICATE ELIMINATION =================
% 1.25/1.58
% 1.25/1.58 ============================== end predicate elimination =============
% 1.25/1.58
% 1.25/1.58 Auto_denials:
% 1.25/1.58 % copying label prove_distributivity to answer in negative clause
% 1.25/1.58
% 1.25/1.58 Term ordering decisions:
% 1.25/1.58
% 1.25/1.58 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 1.25/1.58 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. complement=0.
% 1.25/1.58
% 1.25/1.58 ============================== end of process initial clauses ========
% 1.25/1.58
% 1.25/1.58 ============================== CLAUSES FOR SEARCH ====================
% 1.25/1.58
% 1.25/1.58 ============================== end of clauses for search =============
% 1.25/1.58
% 1.25/1.58 ============================== SEARCH ================================
% 1.25/1.58
% 1.25/1.58 % Starting search at 0.01 seconds.
% 1.25/1.58
% 1.25/1.58 ============================== PROOF =================================
% 1.25/1.58 % SZS status Unsatisfiable
% 1.25/1.58 % SZS output start Refutation
% 1.25/1.58
% 1.25/1.58 % Proof 1 at 0.57 (+ 0.02) seconds: prove_distributivity.
% 1.25/1.58 % Length of proof is 59.
% 1.25/1.58 % Level of proof is 15.
% 1.25/1.58 % Maximum clause weight is 37.000.
% 1.25/1.58 % Given clauses 181.
% 1.25/1.58
% 1.25/1.58 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 1.25/1.58 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 1.25/1.58 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 1.25/1.58 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 1.25/1.58 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 1.25/1.58 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 1.25/1.58 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 1.25/1.58 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 1.25/1.58 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 1.25/1.58 10 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 1.25/1.58 11 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(10),rewrite([8(2)]),flip(a)].
% 1.25/1.58 12 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 1.25/1.58 13 join(A,join(B,C)) = join(C,join(A,B)). [copy(12),rewrite([9(2)]),flip(a)].
% 1.25/1.58 14 meet(A,join(B,C)) = join(meet(A,join(C,meet(A,B))),meet(A,join(B,meet(A,C)))) # label(equation_H69) # label(axiom). [assumption].
% 1.25/1.58 15 join(meet(A,join(B,meet(A,C))),meet(A,join(C,meet(A,B)))) = meet(A,join(B,C)). [copy(14),rewrite([9(9)]),flip(a)].
% 1.25/1.58 16 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 1.25/1.58 17 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(16),rewrite([9(5)])].
% 1.25/1.58 18 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 1.25/1.58 19 meet(a,b) = a. [back_rewrite(3),rewrite([8(3)])].
% 1.25/1.58 20 meet(A,one) = A. [para(4(a,1),6(a,1,2))].
% 1.25/1.58 21 join(A,zero) = A. [para(5(a,1),7(a,1,2))].
% 1.25/1.58 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)])].
% 1.25/1.58 23 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),11(a,2,2)),rewrite([8(2)])].
% 1.25/1.58 24 meet(A,meet(B,join(A,C))) = meet(A,B). [para(6(a,1),11(a,2,2)),rewrite([8(2),8(4)])].
% 1.25/1.58 26 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),13(a,2,2)),rewrite([9(2)])].
% 1.25/1.58 28 meet(A,join(B,meet(A,B))) = meet(A,B). [para(15(a,1),2(a,1)),rewrite([2(1)]),flip(a)].
% 1.25/1.58 29 join(meet(A,B),meet(A,join(complement(A),meet(A,B)))) = meet(A,join(B,complement(A))). [para(5(a,1),15(a,1,1,2,2)),rewrite([21(2)])].
% 1.25/1.58 31 join(meet(A,join(B,meet(A,C))),meet(A,join(C,meet(B,A)))) = meet(A,join(B,C)). [para(8(a,1),15(a,1,1)),rewrite([8(3),8(4)])].
% 1.25/1.58 32 join(meet(A,join(B,C)),meet(A,join(join(C,meet(A,B)),meet(A,join(B,meet(A,C)))))) = meet(A,join(join(C,meet(A,B)),meet(A,join(B,meet(A,C))))). [para(15(a,1),15(a,1,1,2)),rewrite([22(3),22(8),9(16)])].
% 1.25/1.58 39 meet(A,zero) != zero | one != A | complement(A) = zero. [para(21(a,1),18(b,1)),flip(b)].
% 1.25/1.58 41 meet(A,zero) = zero. [para(5(a,1),22(a,1,2)),rewrite([5(4)])].
% 1.25/1.58 42 join(meet(A,join(B,meet(A,C))),meet(A,join(meet(A,C),meet(A,B)))) = meet(A,join(B,meet(A,C))). [para(22(a,1),15(a,1,1,2,2))].
% 1.25/1.58 43 one != A | complement(A) = zero. [back_rewrite(39),rewrite([41(2)]),xx(a)].
% 1.25/1.58 44 meet(A,meet(B,complement(A))) = zero. [back_rewrite(23),rewrite([41(5)])].
% 1.25/1.58 48 join(meet(A,join(B,meet(A,C))),meet(A,join(meet(C,join(A,D)),meet(A,B)))) = meet(A,join(B,meet(C,join(A,D)))). [para(24(a,1),15(a,1,1,2,2))].
% 1.25/1.58 51 complement(join(A,one)) = zero. [hyper(43,a,7,a(flip)),rewrite([8(3),20(3),9(2)])].
% 1.25/1.58 52 join(A,one) = one. [para(51(a,1),4(a,1,2)),rewrite([9(4),13(4),9(3),21(3),9(2)])].
% 1.25/1.58 53 join(A,join(B,complement(A))) = one. [back_rewrite(26),rewrite([52(5)])].
% 1.25/1.58 61 meet(A,join(B,complement(A))) != zero | join(B,complement(A)) = complement(A). [para(53(a,1),18(b,1)),flip(c),xx(b)].
% 1.25/1.58 87 join(meet(A,B),meet(B,join(complement(B),meet(A,B)))) = meet(B,join(A,complement(B))). [para(8(a,1),29(a,1,1)),rewrite([8(3)])].
% 1.25/1.58 94 meet(A,join(complement(A),meet(A,B))) = meet(A,join(B,complement(A))). [para(22(a,1),29(a,1,1)),rewrite([22(4),29(6),9(6)]),flip(a)].
% 1.25/1.58 96 meet(A,join(zero,complement(A))) = zero. [para(41(a,1),29(a,1,1)),rewrite([41(4),21(4),5(3),2(3)]),flip(a)].
% 1.25/1.58 109 join(zero,complement(A)) = complement(A). [hyper(18,a,96,a,b,53,a),flip(a)].
% 1.25/1.58 132 meet(meet(A,B),join(A,C)) = meet(A,B). [para(22(a,1),31(a,1,2,2,2)),rewrite([8(3),11(3),8(2),11(3,R),8(2),7(4),8(2),22(2),7(6)]),flip(a)].
% 1.25/1.58 415 meet(a,join(b,meet(A,a))) = a. [para(19(a,1),42(a,1,2,2,2)),rewrite([8(4),8(9),9(11),6(12),9(8),7(8),8(5)]),flip(a)].
% 1.25/1.58 600 meet(a,join(b,meet(A,join(B,a)))) = a. [para(19(a,1),48(a,1,2,2,2)),rewrite([8(4),415(6),9(4),9(7),6(8),2(3),9(5)]),flip(a)].
% 1.25/1.58 601 meet(A,join(B,meet(one,join(A,C)))) = A. [para(20(a,1),48(a,1,1,2,2)),rewrite([9(1),6(2),7(7)]),flip(a)].
% 1.25/1.58 709 meet(a,join(b,meet(A,B))) = a. [para(132(a,1),600(a,1,2,2))].
% 1.25/1.58 733 meet(one,join(A,B)) = join(A,B). [para(32(a,1),601(a,1,2)),rewrite([8(2),20(2),8(4),20(4),8(6),20(6),9(5),28(8),11(5,R),1(4),8(5),20(5)])].
% 1.25/1.58 740 meet(one,complement(A)) = complement(A). [para(109(a,1),733(a,1,2)),rewrite([109(6)])].
% 1.25/1.58 805 join(one,complement(A)) = one. [para(740(a,1),7(a,1,2))].
% 1.25/1.58 809 meet(a,join(b,complement(A))) = a. [para(740(a,1),709(a,1,2,2))].
% 1.25/1.58 1575 meet(complement(A),join(A,complement(complement(A)))) = zero. [para(5(a,1),87(a,1,1)),rewrite([5(6),21(6),5(5),2(3)]),flip(a)].
% 1.25/1.58 1665 join(A,complement(complement(A))) = complement(complement(A)). [hyper(61,a,1575,a)].
% 1.25/1.58 1687 meet(a,complement(complement(b))) = a. [para(1665(a,1),809(a,1,2))].
% 1.25/1.58 1774 meet(a,complement(b)) = zero. [para(1687(a,1),44(a,1,2)),rewrite([8(4)])].
% 1.25/1.58 1964 meet(a,join(complement(a),complement(b))) = zero. [para(1774(a,1),94(a,1,2,2)),rewrite([9(5),109(5),5(4),9(7)]),flip(a)].
% 1.25/1.58 1980 join(a,join(complement(a),complement(b))) != one # answer(prove_distributivity). [ur(18,a,1964,a,c,17,a(flip))].
% 1.25/1.58 2035 $F # answer(prove_distributivity). [para(13(a,1),1980(a,1)),rewrite([4(6),9(4),805(4)]),xx(a)].
% 1.25/1.58
% 1.25/1.58 % SZS output end Refutation
% 1.25/1.58 ============================== end of proof ==========================
% 1.25/1.58
% 1.25/1.58 ============================== STATISTICS ============================
% 1.25/1.58
% 1.25/1.58 Given=181. Generated=14181. Kept=2030. proofs=1.
% 1.25/1.58 Usable=136. Sos=1258. Demods=1196. Limbo=0, Disabled=650. Hints=0.
% 1.25/1.58 Megabytes=3.51.
% 1.25/1.58 User_CPU=0.57, System_CPU=0.02, Wall_clock=1.
% 1.25/1.58
% 1.25/1.58 ============================== end of statistics =====================
% 1.25/1.58
% 1.25/1.58 ============================== end of search =========================
% 1.25/1.58
% 1.25/1.58 THEOREM PROVED
% 1.25/1.58 % SZS status Unsatisfiable
% 1.25/1.58
% 1.25/1.58 Exiting with 1 proof.
% 1.25/1.58
% 1.25/1.58 Process 23807 exit (max_proofs) Thu Jun 30 06:43:54 2022
% 1.25/1.58 Prover9 interrupted
%------------------------------------------------------------------------------