TSTP Solution File: LAT240-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT240-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 06:26:20 EDT 2022
% Result : Unsatisfiable 2.26s 2.58s
% Output : Refutation 2.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT240-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.32 % Computer : n019.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Wed Jun 29 17:47:38 EDT 2022
% 0.12/0.32 % CPUTime :
% 2.26/2.58 ============================== Prover9 ===============================
% 2.26/2.58 Prover9 (32) version 2009-11A, November 2009.
% 2.26/2.58 Process 32030 was started by sandbox on n019.cluster.edu,
% 2.26/2.58 Wed Jun 29 17:47:39 2022
% 2.26/2.58 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31873_n019.cluster.edu".
% 2.26/2.58 ============================== end of head ===========================
% 2.26/2.58
% 2.26/2.58 ============================== INPUT =================================
% 2.26/2.58
% 2.26/2.58 % Reading from file /tmp/Prover9_31873_n019.cluster.edu
% 2.26/2.58
% 2.26/2.58 set(prolog_style_variables).
% 2.26/2.58 set(auto2).
% 2.26/2.58 % set(auto2) -> set(auto).
% 2.26/2.58 % set(auto) -> set(auto_inference).
% 2.26/2.58 % set(auto) -> set(auto_setup).
% 2.26/2.58 % set(auto_setup) -> set(predicate_elim).
% 2.26/2.58 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.26/2.58 % set(auto) -> set(auto_limits).
% 2.26/2.58 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.26/2.58 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.26/2.58 % set(auto) -> set(auto_denials).
% 2.26/2.58 % set(auto) -> set(auto_process).
% 2.26/2.58 % set(auto2) -> assign(new_constants, 1).
% 2.26/2.58 % set(auto2) -> assign(fold_denial_max, 3).
% 2.26/2.58 % set(auto2) -> assign(max_weight, "200.000").
% 2.26/2.58 % set(auto2) -> assign(max_hours, 1).
% 2.26/2.58 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.26/2.58 % set(auto2) -> assign(max_seconds, 0).
% 2.26/2.58 % set(auto2) -> assign(max_minutes, 5).
% 2.26/2.58 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.26/2.58 % set(auto2) -> set(sort_initial_sos).
% 2.26/2.58 % set(auto2) -> assign(sos_limit, -1).
% 2.26/2.58 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.26/2.58 % set(auto2) -> assign(max_megs, 400).
% 2.26/2.58 % set(auto2) -> assign(stats, some).
% 2.26/2.58 % set(auto2) -> clear(echo_input).
% 2.26/2.58 % set(auto2) -> set(quiet).
% 2.26/2.58 % set(auto2) -> clear(print_initial_clauses).
% 2.26/2.58 % set(auto2) -> clear(print_given).
% 2.26/2.58 assign(lrs_ticks,-1).
% 2.26/2.58 assign(sos_limit,10000).
% 2.26/2.58 assign(order,kbo).
% 2.26/2.58 set(lex_order_vars).
% 2.26/2.58 clear(print_given).
% 2.26/2.58
% 2.26/2.58 % formulas(sos). % not echoed (14 formulas)
% 2.26/2.58
% 2.26/2.58 ============================== end of input ==========================
% 2.26/2.58
% 2.26/2.58 % From the command line: assign(max_seconds, 300).
% 2.26/2.58
% 2.26/2.58 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.26/2.58
% 2.26/2.58 % Formulas that are not ordinary clauses:
% 2.26/2.58
% 2.26/2.58 ============================== end of process non-clausal formulas ===
% 2.26/2.58
% 2.26/2.58 ============================== PROCESS INITIAL CLAUSES ===============
% 2.26/2.58
% 2.26/2.58 ============================== PREDICATE ELIMINATION =================
% 2.26/2.58
% 2.26/2.58 ============================== end predicate elimination =============
% 2.26/2.58
% 2.26/2.58 Auto_denials:
% 2.26/2.58 % copying label prove_distributivity to answer in negative clause
% 2.26/2.58
% 2.26/2.58 Term ordering decisions:
% 2.26/2.58
% 2.26/2.58 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 2.26/2.58 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. complement=0.
% 2.26/2.58
% 2.26/2.58 ============================== end of process initial clauses ========
% 2.26/2.58
% 2.26/2.58 ============================== CLAUSES FOR SEARCH ====================
% 2.26/2.58
% 2.26/2.58 ============================== end of clauses for search =============
% 2.26/2.58
% 2.26/2.58 ============================== SEARCH ================================
% 2.26/2.58
% 2.26/2.58 % Starting search at 0.01 seconds.
% 2.26/2.58
% 2.26/2.58 Low Water (keep): wt=64.000, iters=3409
% 2.26/2.58
% 2.26/2.58 ============================== PROOF =================================
% 2.26/2.58 % SZS status Unsatisfiable
% 2.26/2.58 % SZS output start Refutation
% 2.26/2.58
% 2.26/2.58 % Proof 1 at 1.58 (+ 0.03) seconds: prove_distributivity.
% 2.26/2.58 % Length of proof is 61.
% 2.26/2.58 % Level of proof is 14.
% 2.26/2.58 % Maximum clause weight is 31.000.
% 2.26/2.58 % Given clauses 341.
% 2.26/2.58
% 2.26/2.58 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 2.26/2.58 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 2.26/2.58 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 2.26/2.58 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 2.26/2.58 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 2.26/2.58 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 2.26/2.58 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 2.26/2.58 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 2.26/2.58 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 2.26/2.58 10 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 2.26/2.58 11 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(10),rewrite([8(2)]),flip(a)].
% 2.26/2.58 12 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 2.26/2.58 13 join(A,join(B,C)) = join(C,join(A,B)). [copy(12),rewrite([9(2)]),flip(a)].
% 2.26/2.58 14 meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,meet(C,join(A,meet(C,join(B,D)))))) # label(equation_H50) # label(axiom). [assumption].
% 2.26/2.58 15 meet(A,join(B,meet(C,join(A,meet(C,join(B,D)))))) = meet(A,join(B,meet(C,join(A,D)))). [copy(14),flip(a)].
% 2.26/2.58 16 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 2.26/2.58 17 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(16),rewrite([9(5)])].
% 2.26/2.58 18 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 2.26/2.58 19 meet(a,b) = a. [back_rewrite(3),rewrite([8(3)])].
% 2.26/2.58 20 meet(A,one) = A. [para(4(a,1),6(a,1,2))].
% 2.26/2.58 21 join(A,zero) = A. [para(5(a,1),7(a,1,2))].
% 2.26/2.58 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)])].
% 2.26/2.58 23 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),11(a,2,2)),rewrite([8(2)])].
% 2.26/2.58 24 meet(A,meet(B,join(A,C))) = meet(A,B). [para(6(a,1),11(a,2,2)),rewrite([8(2),8(4)])].
% 2.26/2.58 26 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),13(a,2,2)),rewrite([9(2)])].
% 2.26/2.58 29 meet(A,join(B,meet(C,join(A,meet(B,C))))) = meet(A,join(B,meet(C,join(A,B)))). [para(2(a,1),15(a,1,2,2,2,2,2)),rewrite([8(1)])].
% 2.26/2.58 31 meet(A,join(B,meet(C,join(A,meet(C,join(A,B)))))) = meet(A,join(B,meet(A,C))). [para(2(a,1),15(a,2,2,2,2)),rewrite([9(1),8(7)])].
% 2.26/2.58 34 meet(A,join(B,meet(C,join(A,meet(B,D))))) = meet(A,join(B,meet(C,join(A,B)))). [para(7(a,1),15(a,1,2,2,2,2,2)),rewrite([8(1),29(5)]),flip(a)].
% 2.26/2.58 35 meet(A,meet(B,join(C,meet(D,join(A,meet(D,join(C,E))))))) = meet(A,meet(B,join(C,meet(D,join(A,E))))). [para(15(a,1),11(a,2,2)),rewrite([8(6),11(12,R),8(11)])].
% 2.26/2.58 36 meet(A,join(B,meet(C,join(A,meet(D,join(C,meet(D,join(B,E)))))))) = meet(A,join(B,meet(C,join(A,meet(D,join(C,E)))))). [para(15(a,1),15(a,1,2,2,2,2)),rewrite([15(8)]),flip(a)].
% 2.26/2.58 39 meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(A,C))). [para(21(a,1),15(a,1,2,2,2,2,2)),rewrite([8(1),34(5),21(6),8(5)])].
% 2.26/2.58 40 meet(A,zero) != zero | one != A | complement(A) = zero. [para(21(a,1),18(b,1)),flip(b)].
% 2.26/2.58 41 meet(A,join(B,meet(C,join(A,meet(B,D))))) = meet(A,join(B,meet(A,C))). [back_rewrite(34),rewrite([39(9)])].
% 2.26/2.58 42 meet(A,zero) = zero. [para(5(a,1),22(a,1,2)),rewrite([5(4)])].
% 2.26/2.58 43 one != A | complement(A) = zero. [back_rewrite(40),rewrite([42(2)]),xx(a)].
% 2.26/2.58 44 meet(A,meet(B,complement(A))) = zero. [back_rewrite(23),rewrite([42(5)])].
% 2.26/2.58 48 complement(join(A,one)) = zero. [hyper(43,a,7,a(flip)),rewrite([8(3),20(3),9(2)])].
% 2.26/2.58 50 join(A,one) = one. [para(48(a,1),4(a,1,2)),rewrite([9(4),13(4),9(3),21(3),9(2)])].
% 2.26/2.58 51 join(A,join(B,complement(A))) = one. [back_rewrite(26),rewrite([50(5)])].
% 2.26/2.58 53 meet(A,join(B,meet(C,join(A,C)))) = meet(A,join(B,C)). [para(50(a,1),15(a,1,2,2,2,2,2)),rewrite([20(2),50(6),20(6)])].
% 2.26/2.58 93 meet(A,join(complement(A),meet(A,B))) = meet(A,join(B,complement(A))). [para(4(a,1),31(a,1,2,2,2,2,2)),rewrite([20(3),53(5),9(2)]),flip(a)].
% 2.26/2.58 94 meet(A,join(B,meet(A,B))) = meet(A,B). [para(7(a,1),31(a,1,2)),flip(a)].
% 2.26/2.58 97 meet(A,join(one,meet(A,B))) = A. [para(50(a,1),31(a,1,2,2,2,2,2)),rewrite([20(3),53(5),9(2),50(2),20(2)]),flip(a)].
% 2.26/2.58 107 meet(A,join(one,meet(B,join(A,meet(B,C))))) = A. [para(97(a,1),15(a,1,2,2,2,2)),rewrite([53(5),9(2),50(2),20(2)]),flip(a)].
% 2.26/2.58 110 meet(A,join(meet(A,B),meet(B,join(A,C)))) = meet(A,B). [para(24(a,1),94(a,1,2,2)),rewrite([9(4),24(8)])].
% 2.26/2.58 111 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(44(a,1),94(a,1,2,2)),rewrite([9(4),44(8)])].
% 2.26/2.58 116 meet(A,join(zero,complement(A))) = zero. [para(1(a,1),111(a,1,2,2))].
% 2.26/2.58 119 join(zero,complement(A)) = complement(A). [hyper(18,a,116,a,b,51,a),flip(a)].
% 2.26/2.58 203 meet(A,join(one,meet(B,join(A,meet(C,join(B,meet(C,D))))))) = meet(A,join(one,meet(B,join(A,C)))). [para(97(a,1),36(a,1,2,2,2,2,2,2)),rewrite([53(5)]),flip(a)].
% 2.26/2.58 228 meet(A,join(one,meet(B,join(A,C)))) = A. [para(107(a,1),15(a,1,2,2,2,2)),rewrite([53(5),9(2),50(2),20(2),203(8)]),flip(a)].
% 2.26/2.58 320 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [para(53(a,1),41(a,1)),rewrite([7(2)]),flip(a)].
% 2.26/2.58 321 meet(A,join(join(A,B),meet(A,C))) = A. [para(6(a,1),320(a,2)),rewrite([8(3),24(4)])].
% 2.26/2.58 471 meet(one,join(A,B)) = join(A,B). [para(321(a,1),228(a,1,2,2)),rewrite([9(3),50(3),8(3)])].
% 2.26/2.58 510 meet(one,complement(A)) = complement(A). [para(119(a,1),471(a,1,2)),rewrite([119(6)])].
% 2.26/2.58 514 join(one,complement(A)) = one. [para(510(a,1),7(a,1,2))].
% 2.26/2.58 2265 meet(complement(A),join(zero,meet(A,join(B,complement(A))))) = zero. [para(93(a,1),110(a,1,2,2)),rewrite([8(3),5(3),8(9),5(9)])].
% 2.26/2.58 4233 meet(A,meet(complement(B),join(zero,meet(A,B)))) = zero. [para(2265(a,1),35(a,2,2)),rewrite([119(5),5(4),21(4),8(3),42(8)])].
% 2.26/2.58 4299 meet(a,complement(b)) = zero. [para(19(a,1),4233(a,1,2,2,2)),rewrite([9(6),21(6),8(5),22(6)])].
% 2.26/2.58 4423 meet(a,join(complement(a),complement(b))) = zero. [para(4299(a,1),93(a,1,2,2)),rewrite([9(5),119(5),5(4),9(7)]),flip(a)].
% 2.26/2.58 4572 join(a,join(complement(a),complement(b))) != one # answer(prove_distributivity). [ur(18,a,4423,a,c,17,a(flip))].
% 2.26/2.58 4617 $F # answer(prove_distributivity). [para(13(a,1),4572(a,1)),rewrite([4(6),9(4),514(4)]),xx(a)].
% 2.26/2.58
% 2.26/2.58 % SZS output end Refutation
% 2.26/2.58 ============================== end of proof ==========================
% 2.26/2.58
% 2.26/2.58 ============================== STATISTICS ============================
% 2.26/2.58
% 2.26/2.58 Given=341. Generated=45710. Kept=4612. proofs=1.
% 2.26/2.58 Usable=274. Sos=3496. Demods=3528. Limbo=0, Disabled=856. Hints=0.
% 2.26/2.58 Megabytes=10.18.
% 2.26/2.58 User_CPU=1.58, System_CPU=0.03, Wall_clock=2.
% 2.26/2.58
% 2.26/2.58 ============================== end of statistics =====================
% 2.26/2.58
% 2.26/2.58 ============================== end of search =========================
% 2.26/2.58
% 2.26/2.58 THEOREM PROVED
% 2.26/2.58 % SZS status Unsatisfiable
% 2.26/2.58
% 2.26/2.58 Exiting with 1 proof.
% 2.26/2.58
% 2.26/2.58 Process 32030 exit (max_proofs) Wed Jun 29 17:47:41 2022
% 2.26/2.58 Prover9 interrupted
%------------------------------------------------------------------------------