TSTP Solution File: LAT237-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT237-1 : 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 06:26:19 EDT 2022
% Result : Unsatisfiable 1.51s 1.79s
% Output : Refutation 1.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT237-1 : TPTP v8.1.0. Released v3.1.0.
% 0.00/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n019.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 : Tue Jun 28 22:56:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.51/1.79 ============================== Prover9 ===============================
% 1.51/1.79 Prover9 (32) version 2009-11A, November 2009.
% 1.51/1.79 Process 13453 was started by sandbox on n019.cluster.edu,
% 1.51/1.79 Tue Jun 28 22:56:54 2022
% 1.51/1.79 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13296_n019.cluster.edu".
% 1.51/1.79 ============================== end of head ===========================
% 1.51/1.79
% 1.51/1.79 ============================== INPUT =================================
% 1.51/1.79
% 1.51/1.79 % Reading from file /tmp/Prover9_13296_n019.cluster.edu
% 1.51/1.79
% 1.51/1.79 set(prolog_style_variables).
% 1.51/1.79 set(auto2).
% 1.51/1.79 % set(auto2) -> set(auto).
% 1.51/1.79 % set(auto) -> set(auto_inference).
% 1.51/1.79 % set(auto) -> set(auto_setup).
% 1.51/1.79 % set(auto_setup) -> set(predicate_elim).
% 1.51/1.79 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.51/1.79 % set(auto) -> set(auto_limits).
% 1.51/1.79 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.51/1.79 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.51/1.79 % set(auto) -> set(auto_denials).
% 1.51/1.79 % set(auto) -> set(auto_process).
% 1.51/1.79 % set(auto2) -> assign(new_constants, 1).
% 1.51/1.79 % set(auto2) -> assign(fold_denial_max, 3).
% 1.51/1.79 % set(auto2) -> assign(max_weight, "200.000").
% 1.51/1.79 % set(auto2) -> assign(max_hours, 1).
% 1.51/1.79 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.51/1.79 % set(auto2) -> assign(max_seconds, 0).
% 1.51/1.79 % set(auto2) -> assign(max_minutes, 5).
% 1.51/1.79 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.51/1.79 % set(auto2) -> set(sort_initial_sos).
% 1.51/1.79 % set(auto2) -> assign(sos_limit, -1).
% 1.51/1.79 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.51/1.79 % set(auto2) -> assign(max_megs, 400).
% 1.51/1.79 % set(auto2) -> assign(stats, some).
% 1.51/1.79 % set(auto2) -> clear(echo_input).
% 1.51/1.79 % set(auto2) -> set(quiet).
% 1.51/1.79 % set(auto2) -> clear(print_initial_clauses).
% 1.51/1.79 % set(auto2) -> clear(print_given).
% 1.51/1.79 assign(lrs_ticks,-1).
% 1.51/1.79 assign(sos_limit,10000).
% 1.51/1.79 assign(order,kbo).
% 1.51/1.79 set(lex_order_vars).
% 1.51/1.79 clear(print_given).
% 1.51/1.79
% 1.51/1.79 % formulas(sos). % not echoed (14 formulas)
% 1.51/1.79
% 1.51/1.79 ============================== end of input ==========================
% 1.51/1.79
% 1.51/1.79 % From the command line: assign(max_seconds, 300).
% 1.51/1.79
% 1.51/1.79 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.51/1.79
% 1.51/1.79 % Formulas that are not ordinary clauses:
% 1.51/1.79
% 1.51/1.79 ============================== end of process non-clausal formulas ===
% 1.51/1.79
% 1.51/1.79 ============================== PROCESS INITIAL CLAUSES ===============
% 1.51/1.79
% 1.51/1.79 ============================== PREDICATE ELIMINATION =================
% 1.51/1.79
% 1.51/1.79 ============================== end predicate elimination =============
% 1.51/1.79
% 1.51/1.79 Auto_denials:
% 1.51/1.79 % copying label prove_distributivity to answer in negative clause
% 1.51/1.79
% 1.51/1.79 Term ordering decisions:
% 1.51/1.79
% 1.51/1.79 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 1.51/1.79 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. complement=0.
% 1.51/1.79
% 1.51/1.79 ============================== end of process initial clauses ========
% 1.51/1.79
% 1.51/1.79 ============================== CLAUSES FOR SEARCH ====================
% 1.51/1.79
% 1.51/1.79 ============================== end of clauses for search =============
% 1.51/1.79
% 1.51/1.79 ============================== SEARCH ================================
% 1.51/1.79
% 1.51/1.79 % Starting search at 0.01 seconds.
% 1.51/1.79
% 1.51/1.79 ============================== PROOF =================================
% 1.51/1.79 % SZS status Unsatisfiable
% 1.51/1.79 % SZS output start Refutation
% 1.51/1.79
% 1.51/1.79 % Proof 1 at 0.80 (+ 0.02) seconds: prove_distributivity.
% 1.51/1.79 % Length of proof is 59.
% 1.51/1.79 % Level of proof is 16.
% 1.51/1.79 % Maximum clause weight is 25.000.
% 1.51/1.79 % Given clauses 221.
% 1.51/1.79
% 1.51/1.79 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 1.51/1.79 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 1.51/1.79 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 1.51/1.79 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 1.51/1.79 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 1.51/1.79 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 1.51/1.79 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 1.51/1.79 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 1.51/1.79 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 1.51/1.79 10 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 1.51/1.79 11 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(10),rewrite([8(2)]),flip(a)].
% 1.51/1.79 12 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 1.51/1.79 13 join(A,join(B,C)) = join(C,join(A,B)). [copy(12),rewrite([9(2)]),flip(a)].
% 1.51/1.79 14 meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,meet(C,join(D,meet(C,join(A,B)))))) # label(equation_H40) # label(axiom). [assumption].
% 1.51/1.79 15 meet(A,join(B,meet(C,join(D,meet(C,join(A,B)))))) = meet(A,join(B,meet(C,join(A,D)))). [copy(14),flip(a)].
% 1.51/1.79 16 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 1.51/1.79 17 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(16),rewrite([9(5)])].
% 1.51/1.79 18 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 1.51/1.79 19 meet(a,b) = a. [back_rewrite(3),rewrite([8(3)])].
% 1.51/1.79 20 meet(A,one) = A. [para(4(a,1),6(a,1,2))].
% 1.51/1.79 21 join(A,zero) = A. [para(5(a,1),7(a,1,2))].
% 1.51/1.79 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)])].
% 1.51/1.79 23 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),11(a,2,2)),rewrite([8(2)])].
% 1.51/1.79 26 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),13(a,2,2)),rewrite([9(2)])].
% 1.51/1.79 28 meet(A,join(B,meet(join(A,B),join(A,join(B,C))))) = meet(A,join(B,meet(join(A,B),join(A,C)))). [para(1(a,1),15(a,1,2,2,2,2)),rewrite([13(3),9(2),13(3,R),9(2)])].
% 1.51/1.79 29 meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(A,C))). [para(2(a,1),15(a,1,2,2,2)),rewrite([22(3),15(10),2(5),8(5)])].
% 1.51/1.79 30 meet(A,join(complement(A),meet(B,join(A,C)))) = meet(A,join(B,complement(A))). [para(4(a,1),15(a,1,2,2,2,2,2)),rewrite([20(3),9(2),6(3),9(2)]),flip(a)].
% 1.51/1.79 39 meet(A,zero) != zero | one != A | complement(A) = zero. [para(21(a,1),18(b,1)),flip(b)].
% 1.51/1.79 40 meet(A,zero) = zero. [para(5(a,1),22(a,1,2)),rewrite([5(4)])].
% 1.51/1.79 41 one != A | complement(A) = zero. [back_rewrite(39),rewrite([40(2)]),xx(a)].
% 1.51/1.79 42 meet(A,meet(B,complement(A))) = zero. [back_rewrite(23),rewrite([40(5)])].
% 1.51/1.79 46 complement(join(A,one)) = zero. [hyper(41,a,7,a(flip)),rewrite([8(3),20(3),9(2)])].
% 1.51/1.79 48 join(A,one) = one. [para(46(a,1),4(a,1,2)),rewrite([9(4),13(4),9(3),21(3),9(2)])].
% 1.51/1.79 49 join(A,join(B,complement(A))) = one. [back_rewrite(26),rewrite([48(5)])].
% 1.51/1.79 51 meet(A,join(one,meet(B,join(A,C)))) = A. [para(48(a,1),15(a,1,2,2,2,2,2)),rewrite([20(3),9(2),6(3),9(2),48(2),20(2)]),flip(a)].
% 1.51/1.79 55 meet(A,meet(B,meet(C,complement(A)))) = zero. [para(42(a,1),11(a,2,2)),rewrite([8(3),11(3,R),8(2),40(6)])].
% 1.51/1.79 56 join(A,join(B,join(C,complement(A)))) = one. [para(49(a,1),13(a,2,2)),rewrite([9(3),13(3,R),9(2),48(6)])].
% 1.51/1.79 57 meet(A,join(join(B,complement(A)),meet(C,join(A,D)))) = meet(A,join(B,join(C,complement(A)))). [para(49(a,1),15(a,1,2,2,2,2,2)),rewrite([20(4),9(3),6(4),9(3),13(3,R),9(2)]),flip(a)].
% 1.51/1.79 58 meet(A,join(B,complement(A))) != zero | join(B,complement(A)) = complement(A). [para(49(a,1),18(b,1)),flip(c),xx(b)].
% 1.51/1.79 76 meet(A,join(B,join(one,complement(A)))) = A. [para(49(a,1),28(a,1,2,2,1)),rewrite([9(6),13(6,R),9(5),56(7),1(5),9(4),13(4,R),48(3),48(2),20(2),49(5),57(7)]),flip(a)].
% 1.51/1.79 86 meet(A,join(complement(A),meet(A,B))) = meet(A,join(B,complement(A))). [para(4(a,1),29(a,1,2,2,2)),rewrite([20(3),9(2)]),flip(a)].
% 1.51/1.79 87 meet(A,join(B,meet(A,B))) = meet(A,B). [para(7(a,1),29(a,1,2)),flip(a)].
% 1.51/1.79 89 meet(A,meet(B,join(C,meet(D,join(A,C))))) = meet(A,meet(B,join(C,meet(A,D)))). [para(29(a,1),11(a,2,2)),rewrite([8(4),11(9,R),8(8)])].
% 1.51/1.79 96 meet(A,join(join(one,complement(B)),meet(A,B))) = A. [para(76(a,1),29(a,1,2,2)),rewrite([9(4),49(4),20(2)]),flip(a)].
% 1.51/1.79 105 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(42(a,1),87(a,1,2,2)),rewrite([9(4),42(8)])].
% 1.51/1.79 106 meet(A,join(zero,meet(B,meet(C,complement(A))))) = zero. [para(55(a,1),87(a,1,2,2)),rewrite([9(5),55(10)])].
% 1.51/1.79 116 meet(A,join(zero,complement(A))) = zero. [para(1(a,1),105(a,1,2,2))].
% 1.51/1.79 119 join(zero,complement(A)) = complement(A). [hyper(18,a,116,a,b,49,a),flip(a)].
% 1.51/1.79 217 join(one,complement(A)) = one. [para(96(a,1),51(a,1,2,2)),rewrite([9(5),48(5),8(5),6(5)]),flip(a)].
% 1.51/1.79 771 meet(A,join(complement(A),meet(B,complement(A)))) = zero. [para(42(a,1),86(a,1,2,2)),rewrite([21(3),5(2),9(5)]),flip(a)].
% 1.51/1.79 889 meet(complement(A),join(A,complement(complement(A)))) = zero. [para(771(a,1),30(a,1,2,2)),rewrite([21(5),5(4)]),flip(a)].
% 1.51/1.79 902 join(A,complement(complement(A))) = complement(complement(A)). [hyper(58,a,889,a)].
% 1.51/1.79 943 meet(A,complement(complement(A))) = A. [para(902(a,1),6(a,1,2))].
% 1.51/1.79 972 meet(complement(A),join(zero,meet(A,B))) = zero. [para(943(a,1),106(a,1,2,2,2)),rewrite([8(3)])].
% 1.51/1.79 1205 meet(A,meet(complement(B),join(zero,meet(A,B)))) = zero. [para(972(a,1),89(a,1,2)),rewrite([40(2)]),flip(a)].
% 1.51/1.79 2561 meet(a,complement(b)) = zero. [para(19(a,1),1205(a,1,2,2,2)),rewrite([9(6),21(6),8(5),22(6)])].
% 1.51/1.79 2636 meet(a,join(complement(a),complement(b))) = zero. [para(2561(a,1),86(a,1,2,2)),rewrite([9(5),119(5),5(4),9(7)]),flip(a)].
% 1.51/1.79 2707 join(a,join(complement(a),complement(b))) != one # answer(prove_distributivity). [ur(18,a,2636,a,c,17,a(flip))].
% 1.51/1.79 2759 $F # answer(prove_distributivity). [para(13(a,1),2707(a,1)),rewrite([4(6),9(4),217(4)]),xx(a)].
% 1.51/1.79
% 1.51/1.79 % SZS output end Refutation
% 1.51/1.79 ============================== end of proof ==========================
% 1.51/1.79
% 1.51/1.79 ============================== STATISTICS ============================
% 1.51/1.79
% 1.51/1.79 Given=221. Generated=21511. Kept=2754. proofs=1.
% 1.51/1.79 Usable=181. Sos=2030. Demods=2046. Limbo=0, Disabled=557. Hints=0.
% 1.51/1.79 Megabytes=5.31.
% 1.51/1.79 User_CPU=0.80, System_CPU=0.02, Wall_clock=1.
% 1.51/1.79
% 1.51/1.79 ============================== end of statistics =====================
% 1.51/1.79
% 1.51/1.79 ============================== end of search =========================
% 1.51/1.79
% 1.51/1.79 THEOREM PROVED
% 1.51/1.79 % SZS status Unsatisfiable
% 1.51/1.79
% 1.51/1.79 Exiting with 1 proof.
% 1.51/1.79
% 1.51/1.79 Process 13453 exit (max_proofs) Tue Jun 28 22:56:55 2022
% 1.51/1.79 Prover9 interrupted
%------------------------------------------------------------------------------