TSTP Solution File: LAT044-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT044-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 06:25:17 EDT 2022
% Result : Unsatisfiable 5.92s 6.22s
% Output : Refutation 5.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT044-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Thu Jun 30 00:27:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 5.92/6.22 ============================== Prover9 ===============================
% 5.92/6.22 Prover9 (32) version 2009-11A, November 2009.
% 5.92/6.22 Process 3499 was started by sandbox on n023.cluster.edu,
% 5.92/6.22 Thu Jun 30 00:27:45 2022
% 5.92/6.22 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3346_n023.cluster.edu".
% 5.92/6.22 ============================== end of head ===========================
% 5.92/6.22
% 5.92/6.22 ============================== INPUT =================================
% 5.92/6.22
% 5.92/6.22 % Reading from file /tmp/Prover9_3346_n023.cluster.edu
% 5.92/6.22
% 5.92/6.22 set(prolog_style_variables).
% 5.92/6.22 set(auto2).
% 5.92/6.22 % set(auto2) -> set(auto).
% 5.92/6.22 % set(auto) -> set(auto_inference).
% 5.92/6.22 % set(auto) -> set(auto_setup).
% 5.92/6.22 % set(auto_setup) -> set(predicate_elim).
% 5.92/6.22 % set(auto_setup) -> assign(eq_defs, unfold).
% 5.92/6.22 % set(auto) -> set(auto_limits).
% 5.92/6.22 % set(auto_limits) -> assign(max_weight, "100.000").
% 5.92/6.22 % set(auto_limits) -> assign(sos_limit, 20000).
% 5.92/6.22 % set(auto) -> set(auto_denials).
% 5.92/6.22 % set(auto) -> set(auto_process).
% 5.92/6.22 % set(auto2) -> assign(new_constants, 1).
% 5.92/6.22 % set(auto2) -> assign(fold_denial_max, 3).
% 5.92/6.22 % set(auto2) -> assign(max_weight, "200.000").
% 5.92/6.22 % set(auto2) -> assign(max_hours, 1).
% 5.92/6.22 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 5.92/6.22 % set(auto2) -> assign(max_seconds, 0).
% 5.92/6.22 % set(auto2) -> assign(max_minutes, 5).
% 5.92/6.22 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 5.92/6.22 % set(auto2) -> set(sort_initial_sos).
% 5.92/6.22 % set(auto2) -> assign(sos_limit, -1).
% 5.92/6.22 % set(auto2) -> assign(lrs_ticks, 3000).
% 5.92/6.22 % set(auto2) -> assign(max_megs, 400).
% 5.92/6.22 % set(auto2) -> assign(stats, some).
% 5.92/6.22 % set(auto2) -> clear(echo_input).
% 5.92/6.22 % set(auto2) -> set(quiet).
% 5.92/6.22 % set(auto2) -> clear(print_initial_clauses).
% 5.92/6.22 % set(auto2) -> clear(print_given).
% 5.92/6.22 assign(lrs_ticks,-1).
% 5.92/6.22 assign(sos_limit,10000).
% 5.92/6.22 assign(order,kbo).
% 5.92/6.22 set(lex_order_vars).
% 5.92/6.22 clear(print_given).
% 5.92/6.22
% 5.92/6.22 % formulas(sos). % not echoed (15 formulas)
% 5.92/6.22
% 5.92/6.22 ============================== end of input ==========================
% 5.92/6.22
% 5.92/6.22 % From the command line: assign(max_seconds, 300).
% 5.92/6.22
% 5.92/6.22 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 5.92/6.22
% 5.92/6.22 % Formulas that are not ordinary clauses:
% 5.92/6.22
% 5.92/6.22 ============================== end of process non-clausal formulas ===
% 5.92/6.22
% 5.92/6.22 ============================== PROCESS INITIAL CLAUSES ===============
% 5.92/6.22
% 5.92/6.22 ============================== PREDICATE ELIMINATION =================
% 5.92/6.22
% 5.92/6.22 ============================== end predicate elimination =============
% 5.92/6.22
% 5.92/6.22 Auto_denials:
% 5.92/6.22 % copying label prove_weak_orthomodular_law to answer in negative clause
% 5.92/6.22
% 5.92/6.22 Term ordering decisions:
% 5.92/6.22
% 5.92/6.22 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 5.92/6.22 Function symbol KB weights: n0=1. n1=1. a=1. b=1. join=1. meet=1. complement=0.
% 5.92/6.22
% 5.92/6.22 ============================== end of process initial clauses ========
% 5.92/6.22
% 5.92/6.22 ============================== CLAUSES FOR SEARCH ====================
% 5.92/6.22
% 5.92/6.22 ============================== end of clauses for search =============
% 5.92/6.22
% 5.92/6.22 ============================== SEARCH ================================
% 5.92/6.22
% 5.92/6.22 % Starting search at 0.01 seconds.
% 5.92/6.22
% 5.92/6.22 Low Water (keep): wt=59.000, iters=3335
% 5.92/6.22
% 5.92/6.22 Low Water (keep): wt=45.000, iters=3363
% 5.92/6.22
% 5.92/6.22 Low Water (keep): wt=41.000, iters=3405
% 5.92/6.22
% 5.92/6.22 Low Water (keep): wt=39.000, iters=3355
% 5.92/6.22
% 5.92/6.22 ============================== PROOF =================================
% 5.92/6.22 % SZS status Unsatisfiable
% 5.92/6.22 % SZS output start Refutation
% 5.92/6.22
% 5.92/6.22 % Proof 1 at 5.14 (+ 0.08) seconds: prove_weak_orthomodular_law.
% 5.92/6.22 % Length of proof is 70.
% 5.92/6.22 % Level of proof is 20.
% 5.92/6.22 % Maximum clause weight is 21.000.
% 5.92/6.22 % Given clauses 580.
% 5.92/6.22
% 5.92/6.22 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 5.92/6.22 3 complement(complement(A)) = A # label(invertability3) # label(axiom). [assumption].
% 5.92/6.22 4 join(complement(A),A) = n1 # label(invertability1) # label(axiom). [assumption].
% 5.92/6.22 5 meet(complement(A),A) = n0 # label(invertability2) # label(axiom). [assumption].
% 5.92/6.22 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 5.92/6.22 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 5.92/6.22 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 5.92/6.22 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 5.92/6.22 10 complement(join(A,B)) = meet(complement(A),complement(B)) # label(compatibility1) # label(axiom). [assumption].
% 5.92/6.22 11 complement(meet(A,B)) = join(complement(A),complement(B)) # label(compatibility2) # label(axiom). [assumption].
% 5.92/6.22 12 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 5.92/6.22 13 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(12),rewrite([8(2)]),flip(a)].
% 5.92/6.22 14 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 5.92/6.22 15 join(A,join(B,C)) = join(C,join(A,B)). [copy(14),rewrite([9(2)]),flip(a)].
% 5.92/6.22 16 join(A,meet(complement(A),join(A,B))) = join(A,B) # label(orthomodular_law) # label(axiom). [assumption].
% 5.92/6.22 17 join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) != n1 # label(prove_weak_orthomodular_law) # label(negated_conjecture) # answer(prove_weak_orthomodular_law). [assumption].
% 5.92/6.22 18 join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))) != n1 # answer(prove_weak_orthomodular_law). [copy(17),rewrite([9(13)])].
% 5.92/6.22 19 meet(A,complement(A)) = n0. [back_rewrite(5),rewrite([8(2)])].
% 5.92/6.22 20 join(A,complement(A)) = n1. [back_rewrite(4),rewrite([9(2)])].
% 5.92/6.22 21 meet(meet(complement(A),complement(B)),complement(C)) = meet(complement(A),meet(complement(B),complement(C))). [para(10(a,1),10(a,2,1)),rewrite([9(2),15(2),9(1),15(2,R),9(1),10(3),10(3)]),flip(a)].
% 5.92/6.22 22 join(join(complement(A),complement(B)),complement(C)) = join(complement(A),join(complement(B),complement(C))). [para(11(a,1),11(a,2,1)),rewrite([8(2),13(2),8(1),13(2,R),8(1),11(3),11(3)]),flip(a)].
% 5.92/6.22 27 join(A,n0) = A. [para(2(a,1),16(a,1,2,2)),rewrite([8(2),19(2),2(3)])].
% 5.92/6.22 31 join(meet(A,B),meet(join(complement(A),complement(B)),join(C,meet(A,B)))) = join(C,meet(A,B)). [para(11(a,1),16(a,1,2,1)),rewrite([9(6),9(10)])].
% 5.92/6.22 32 join(A,join(B,meet(complement(A),join(A,C)))) = join(A,join(C,B)). [para(16(a,1),15(a,2,2)),rewrite([9(4),15(7),9(6),15(7,R),9(6)])].
% 5.92/6.22 33 complement(n1) = n0. [para(19(a,1),10(a,2)),rewrite([20(2)])].
% 5.92/6.22 35 complement(n0) = n1. [para(19(a,1),11(a,1,1)),rewrite([3(5),9(4),20(4)])].
% 5.92/6.22 36 meet(A,meet(B,join(complement(A),complement(B)))) = n0. [para(11(a,1),19(a,1,2)),rewrite([8(5),13(5),8(4),13(5,R),8(4)])].
% 5.92/6.22 38 meet(A,n1) = A. [para(20(a,1),6(a,1,2))].
% 5.92/6.22 39 join(join(A,B),meet(complement(A),complement(B))) = n1. [para(10(a,1),20(a,1,2))].
% 5.92/6.22 42 meet(meet(A,complement(B)),complement(C)) = meet(A,meet(complement(B),complement(C))). [para(3(a,1),21(a,1,1,1)),rewrite([3(6)])].
% 5.92/6.22 49 join(n0,complement(A)) = complement(A). [para(33(a,1),11(a,2,1)),rewrite([8(2),38(2)]),flip(a)].
% 5.92/6.22 52 meet(n1,complement(A)) = complement(A). [para(35(a,1),10(a,2,1)),rewrite([9(2),27(2)]),flip(a)].
% 5.92/6.22 60 join(complement(A),join(complement(B),meet(A,B))) = n1. [para(22(a,1),20(a,1)),rewrite([10(6),3(4),3(4)])].
% 5.92/6.22 64 meet(n0,complement(A)) = n0. [para(49(a,1),6(a,1,2))].
% 5.92/6.22 67 meet(n0,meet(complement(A),complement(B))) = n0. [para(10(a,1),64(a,1,2))].
% 5.92/6.22 73 join(n1,complement(A)) = n1. [para(52(a,1),7(a,1,2))].
% 5.92/6.22 77 join(n1,join(complement(A),complement(B))) = n1. [para(11(a,1),73(a,1,2))].
% 5.92/6.22 85 meet(n0,meet(join(complement(A),complement(B)),complement(C))) = n0. [para(11(a,1),67(a,1,2,1))].
% 5.92/6.22 93 join(n1,join(meet(complement(A),complement(B)),complement(C))) = n1. [para(10(a,1),77(a,1,2,1))].
% 5.92/6.22 137 meet(n1,join(A,B)) = join(A,B). [para(39(a,1),6(a,1,2)),rewrite([8(3)])].
% 5.92/6.22 157 join(meet(complement(A),complement(B)),join(complement(C),meet(C,join(A,B)))) = n1. [para(10(a,1),60(a,1,1)),rewrite([8(6)])].
% 5.92/6.22 167 join(n0,meet(A,B)) = meet(A,B). [para(2(a,1),31(a,1,2,2)),rewrite([13(6),8(5),13(6,R),8(5),36(6),9(3),2(6)])].
% 5.92/6.22 170 join(meet(A,B),meet(A,join(complement(A),complement(B)))) = A. [para(7(a,1),31(a,1,2,2)),rewrite([8(5),7(8)])].
% 5.92/6.22 196 join(A,join(B,join(C,meet(complement(A),join(A,D))))) = join(A,join(B,join(D,C))). [para(32(a,1),15(a,2,2)),rewrite([9(5),15(5,R),9(4),9(7),15(9,R),9(8),15(8),9(7),15(8,R),9(7)])].
% 5.92/6.22 214 meet(n0,meet(join(A,complement(B)),complement(C))) = n0. [para(3(a,1),85(a,1,2,1,1))].
% 5.92/6.22 218 meet(meet(A,B),complement(C)) = meet(A,meet(B,complement(C))). [para(3(a,1),42(a,1,1,2)),rewrite([3(5)])].
% 5.92/6.22 227 meet(n0,meet(join(A,B),complement(C))) = n0. [para(3(a,1),214(a,1,2,1,2))].
% 5.92/6.22 231 meet(n0,meet(complement(A),join(B,C))) = n0. [para(8(a,1),227(a,1,2))].
% 5.92/6.22 236 join(n1,join(meet(A,complement(B)),complement(C))) = n1. [para(3(a,1),93(a,1,2,1,1))].
% 5.92/6.22 253 join(n1,join(meet(A,B),complement(C))) = n1. [para(3(a,1),236(a,1,2,1,2))].
% 5.92/6.22 258 join(n1,join(meet(A,B),meet(complement(C),complement(D)))) = n1. [para(10(a,1),253(a,1,2,2))].
% 5.92/6.22 383 join(meet(A,complement(B)),meet(complement(B),join(B,complement(A)))) = complement(B). [para(3(a,1),170(a,1,2,2,1)),rewrite([8(2)])].
% 5.92/6.22 448 meet(meet(A,B),join(complement(C),complement(D))) = meet(A,meet(B,join(complement(C),complement(D)))). [para(11(a,1),218(a,1,2)),rewrite([11(7)])].
% 5.92/6.22 456 meet(n0,meet(complement(A),meet(complement(B),join(C,D)))) = n0. [para(231(a,1),218(a,1,1)),rewrite([64(3),218(7),13(7)]),flip(a)].
% 5.92/6.22 534 join(n1,join(meet(A,B),meet(C,complement(D)))) = n1. [para(3(a,1),258(a,1,2,2,1))].
% 5.92/6.22 552 join(n1,join(meet(A,B),meet(C,D))) = n1. [para(3(a,1),534(a,1,2,2,2))].
% 5.92/6.22 555 join(n1,join(join(A,B),meet(C,D))) = n1. [para(137(a,1),552(a,1,2,1))].
% 5.92/6.22 3126 meet(join(A,complement(B)),join(A,meet(B,complement(A)))) = A. [para(383(a,1),10(a,1,1)),rewrite([3(2),11(3),3(3),9(2),11(7),3(4),10(5),3(5),8(4)]),flip(a)].
% 5.92/6.22 3143 meet(join(A,B),join(A,meet(complement(A),complement(B)))) = A. [para(3(a,1),3126(a,1,1,2)),rewrite([8(4)])].
% 5.92/6.22 3230 meet(join(A,B),join(B,meet(complement(A),complement(B)))) = B. [para(9(a,1),3143(a,1,1)),rewrite([8(4)])].
% 5.92/6.22 3274 join(n0,join(join(A,B),meet(C,D))) = join(join(A,B),meet(C,D)). [para(555(a,1),3230(a,1,1)),rewrite([33(6),10(9),10(7),11(10),448(12),456(13),9(6),137(7)])].
% 5.92/6.22 4434 join(A,join(join(B,C),meet(D,E))) = join(A,join(B,join(C,meet(D,E)))). [para(11(a,1),196(a,1,2,2,2,1)),rewrite([9(6),15(10,R),9(9),15(9,R),9(8),31(8),9(6),15(8,R)]),flip(a)].
% 5.92/6.22 4642 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [back_rewrite(3274),rewrite([4434(5),15(5,R),9(4),15(4,R),9(3),167(3)]),flip(a)].
% 5.92/6.22 5293 join(complement(b),join(meet(a,b),meet(complement(a),join(a,b)))) != n1 # answer(prove_weak_orthomodular_law). [back_rewrite(18),rewrite([4642(13)])].
% 5.92/6.22 7809 join(A,join(meet(A,B),meet(C,D))) = join(A,meet(C,D)). [para(7(a,1),4642(a,1,1)),flip(a)].
% 5.92/6.22 10530 join(A,meet(complement(B),join(B,complement(A)))) = join(A,complement(B)). [para(383(a,1),7809(a,1,2)),flip(a)].
% 5.92/6.22 10870 meet(complement(A),join(B,meet(A,complement(B)))) = meet(B,complement(A)). [para(10530(a,1),10(a,1,1)),rewrite([10(3),3(3),8(2),11(8),3(5),10(6),3(6),8(5)]),flip(a)].
% 5.92/6.22 10957 meet(A,join(B,meet(complement(A),complement(B)))) = meet(A,B). [para(3(a,1),10870(a,1,1)),rewrite([3(7),8(6)])].
% 5.92/6.22 11033 join(complement(A),join(meet(B,A),meet(complement(B),join(B,A)))) = n1. [para(10957(a,1),157(a,1,2,2)),rewrite([8(4),11(5),3(3),3(3),8(5),15(7),9(6),15(7,R),9(6)])].
% 5.92/6.22 11034 $F # answer(prove_weak_orthomodular_law). [resolve(11033,a,5293,a)].
% 5.92/6.22
% 5.92/6.22 % SZS output end Refutation
% 5.92/6.22 ============================== end of proof ==========================
% 5.92/6.22
% 5.92/6.22 ============================== STATISTICS ============================
% 5.92/6.22
% 5.92/6.22 Given=580. Generated=159603. Kept=11030. proofs=1.
% 5.92/6.22 Usable=363. Sos=5736. Demods=6154. Limbo=56, Disabled=4889. Hints=0.
% 5.92/6.22 Megabytes=12.50.
% 5.92/6.22 User_CPU=5.14, System_CPU=0.08, Wall_clock=5.
% 5.92/6.22
% 5.92/6.22 ============================== end of statistics =====================
% 5.92/6.22
% 5.92/6.22 ============================== end of search =========================
% 5.92/6.22
% 5.92/6.22 THEOREM PROVED
% 5.92/6.22 % SZS status Unsatisfiable
% 5.92/6.22
% 5.92/6.22 Exiting with 1 proof.
% 5.92/6.22
% 5.92/6.22 Process 3499 exit (max_proofs) Thu Jun 30 00:27:50 2022
% 5.92/6.23 Prover9 interrupted
%------------------------------------------------------------------------------