TSTP Solution File: MVA008-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : MVA008-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 : Mon Jul 18 00:55:34 EDT 2022
% Result : Unsatisfiable 99.35s 99.66s
% Output : Refutation 99.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : MVA008-1 : TPTP v8.1.0. Released v8.1.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.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 May 31 17:27:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 99.35/99.66 ============================== Prover9 ===============================
% 99.35/99.66 Prover9 (32) version 2009-11A, November 2009.
% 99.35/99.66 Process 26885 was started by sandbox2 on n025.cluster.edu,
% 99.35/99.66 Tue May 31 17:27:14 2022
% 99.35/99.66 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_26732_n025.cluster.edu".
% 99.35/99.66 ============================== end of head ===========================
% 99.35/99.66
% 99.35/99.66 ============================== INPUT =================================
% 99.35/99.66
% 99.35/99.66 % Reading from file /tmp/Prover9_26732_n025.cluster.edu
% 99.35/99.66
% 99.35/99.66 set(prolog_style_variables).
% 99.35/99.66 set(auto2).
% 99.35/99.66 % set(auto2) -> set(auto).
% 99.35/99.66 % set(auto) -> set(auto_inference).
% 99.35/99.66 % set(auto) -> set(auto_setup).
% 99.35/99.66 % set(auto_setup) -> set(predicate_elim).
% 99.35/99.66 % set(auto_setup) -> assign(eq_defs, unfold).
% 99.35/99.66 % set(auto) -> set(auto_limits).
% 99.35/99.66 % set(auto_limits) -> assign(max_weight, "100.000").
% 99.35/99.66 % set(auto_limits) -> assign(sos_limit, 20000).
% 99.35/99.66 % set(auto) -> set(auto_denials).
% 99.35/99.66 % set(auto) -> set(auto_process).
% 99.35/99.66 % set(auto2) -> assign(new_constants, 1).
% 99.35/99.66 % set(auto2) -> assign(fold_denial_max, 3).
% 99.35/99.66 % set(auto2) -> assign(max_weight, "200.000").
% 99.35/99.66 % set(auto2) -> assign(max_hours, 1).
% 99.35/99.66 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 99.35/99.66 % set(auto2) -> assign(max_seconds, 0).
% 99.35/99.66 % set(auto2) -> assign(max_minutes, 5).
% 99.35/99.66 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 99.35/99.66 % set(auto2) -> set(sort_initial_sos).
% 99.35/99.66 % set(auto2) -> assign(sos_limit, -1).
% 99.35/99.66 % set(auto2) -> assign(lrs_ticks, 3000).
% 99.35/99.66 % set(auto2) -> assign(max_megs, 400).
% 99.35/99.66 % set(auto2) -> assign(stats, some).
% 99.35/99.66 % set(auto2) -> clear(echo_input).
% 99.35/99.66 % set(auto2) -> set(quiet).
% 99.35/99.66 % set(auto2) -> clear(print_initial_clauses).
% 99.35/99.66 % set(auto2) -> clear(print_given).
% 99.35/99.66 assign(lrs_ticks,-1).
% 99.35/99.66 assign(sos_limit,10000).
% 99.35/99.66 assign(order,kbo).
% 99.35/99.66 set(lex_order_vars).
% 99.35/99.66 clear(print_given).
% 99.35/99.66
% 99.35/99.66 % formulas(sos). % not echoed (19 formulas)
% 99.35/99.66
% 99.35/99.66 ============================== end of input ==========================
% 99.35/99.66
% 99.35/99.66 % From the command line: assign(max_seconds, 300).
% 99.35/99.66
% 99.35/99.66 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 99.35/99.66
% 99.35/99.66 % Formulas that are not ordinary clauses:
% 99.35/99.66
% 99.35/99.66 ============================== end of process non-clausal formulas ===
% 99.35/99.66
% 99.35/99.66 ============================== PROCESS INITIAL CLAUSES ===============
% 99.35/99.66
% 99.35/99.66 ============================== PREDICATE ELIMINATION =================
% 99.35/99.66
% 99.35/99.66 ============================== end predicate elimination =============
% 99.35/99.66
% 99.35/99.66 Auto_denials:
% 99.35/99.66 % copying label goal to answer in negative clause
% 99.35/99.66
% 99.35/99.66 Term ordering decisions:
% 99.35/99.66 Function symbol KB weights: unit=1. x=1. join=1. meet=1. op=1. ld=1. rd=1. at=1.
% 99.35/99.66
% 99.35/99.66 ============================== end of process initial clauses ========
% 99.35/99.66
% 99.35/99.66 ============================== CLAUSES FOR SEARCH ====================
% 99.35/99.66
% 99.35/99.66 ============================== end of clauses for search =============
% 99.35/99.66
% 99.35/99.66 ============================== SEARCH ================================
% 99.35/99.66
% 99.35/99.66 % Starting search at 0.01 seconds.
% 99.35/99.66
% 99.35/99.66 Low Water (keep): wt=29.000, iters=3350
% 99.35/99.66
% 99.35/99.66 Low Water (keep): wt=25.000, iters=3471
% 99.35/99.66
% 99.35/99.66 Low Water (keep): wt=23.000, iters=3361
% 99.35/99.66
% 99.35/99.66 Low Water (keep): wt=21.000, iters=3352
% 99.35/99.66
% 99.35/99.66 Low Water (keep): wt=19.000, iters=3334
% 99.35/99.66
% 99.35/99.66 Low Water (keep): wt=17.000, iters=3335
% 99.35/99.66
% 99.35/99.66 Low Water (displace): id=4831, wt=75.000
% 99.35/99.66
% 99.35/99.66 Low Water (displace): id=5207, wt=65.000
% 99.35/99.66
% 99.35/99.66 Low Water (displace): id=5165, wt=57.000
% 99.35/99.66
% 99.35/99.66 Low Water (displace): id=2660, wt=53.000
% 99.35/99.66
% 99.35/99.66 Low Water (displace): id=11808, wt=15.000
% 99.35/99.66
% 99.35/99.66 Low Water (displace): id=11861, wt=13.000
% 99.35/99.66
% 99.35/99.66 Low Water (keep): wt=15.000, iters=3337
% 99.35/99.66
% 99.35/99.66 ============================== PROOF =================================
% 99.35/99.66 % SZS status Unsatisfiable
% 99.35/99.66 % SZS output start Refutation
% 99.35/99.66
% 99.35/99.66 % Proof 1 at 94.89 (+ 3.71) seconds: goal.
% 99.35/99.66 % Length of proof is 195.
% 99.35/99.66 % Level of proof is 32.
% 99.35/99.66 % Maximum clause weight is 25.000.
% 99.35/99.66 % Given clauses 5458.
% 99.35/99.66
% 99.35/99.66 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 99.35/99.66 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 99.35/99.66 3 op(unit,A) = A # label(left_monoid_unit) # label(axiom). [assumption].
% 99.35/99.66 4 op(A,unit) = A # label(right_monoid_unit) # label(axiom). [assumption].
% 99.35/99.66 5 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 99.35/99.66 6 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 99.35/99.66 7 join(meet(A,B),A) = A # label(absorption_a) # label(axiom). [assumption].
% 99.35/99.66 8 join(A,meet(A,B)) = A. [copy(7),rewrite([6(2)])].
% 99.35/99.66 9 meet(join(A,B),A) = A # label(absorption_b) # label(axiom). [assumption].
% 99.35/99.66 10 meet(A,join(A,B)) = A. [copy(9),rewrite([5(2)])].
% 99.35/99.66 11 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 99.35/99.66 12 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(11),rewrite([5(2)]),flip(a)].
% 99.35/99.66 13 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 99.35/99.66 14 join(A,join(B,C)) = join(C,join(A,B)). [copy(13),rewrite([6(2)]),flip(a)].
% 99.35/99.66 15 join(op(A,meet(ld(A,B),C)),B) = B # label(residual_a) # label(axiom). [assumption].
% 99.35/99.66 16 join(A,op(B,meet(C,ld(B,A)))) = A. [copy(15),rewrite([5(2),6(4)])].
% 99.35/99.66 17 join(op(meet(A,rd(B,C)),C),B) = B # label(residual_b) # label(axiom). [assumption].
% 99.35/99.66 18 join(A,op(meet(B,rd(A,C)),C)) = A. [copy(17),rewrite([6(4)])].
% 99.35/99.66 19 meet(ld(A,join(op(A,B),C)),B) = B # label(residual_c) # label(axiom). [assumption].
% 99.35/99.66 20 meet(A,ld(B,join(C,op(B,A)))) = A. [copy(19),rewrite([6(2),5(4)])].
% 99.35/99.66 21 meet(rd(join(op(A,B),C),B),A) = A # label(residual_d) # label(axiom). [assumption].
% 99.35/99.66 22 meet(A,rd(join(B,op(A,C)),C)) = A. [copy(21),rewrite([6(2),5(4)])].
% 99.35/99.66 23 op(op(A,B),C) = op(A,op(B,C)) # label(monoid_associativity) # label(axiom). [assumption].
% 99.35/99.66 24 join(A,B) = rd(A,ld(join(A,B),A)) # label(generalized_mv_algebra_a) # label(axiom). [assumption].
% 99.35/99.66 25 rd(A,ld(join(A,B),A)) = join(A,B). [copy(24),flip(a)].
% 99.35/99.66 26 join(A,B) = ld(rd(A,join(A,B)),A) # label(generalized_mv_algebra_b) # label(axiom). [assumption].
% 99.35/99.66 27 ld(rd(A,join(A,B)),A) = join(A,B). [copy(26),flip(a)].
% 99.35/99.66 28 at(A,B) = op(op(A,ld(A,unit)),ld(ld(B,unit),unit)) # label(definition_of_at) # label(axiom). [assumption].
% 99.35/99.66 29 at(A,B) = op(A,op(ld(A,unit),ld(ld(B,unit),unit))). [copy(28),rewrite([23(9)])].
% 99.35/99.66 30 at(op(x,ld(x,unit)),unit) != op(x,ld(x,unit)) # label(goal) # label(negated_conjecture) # answer(goal). [assumption].
% 99.35/99.66 31 op(x,op(ld(x,unit),op(ld(op(x,ld(x,unit)),unit),ld(ld(unit,unit),unit)))) != op(x,ld(x,unit)) # answer(goal). [copy(30),rewrite([29(7),23(19)])].
% 99.35/99.66 33 meet(A,meet(B,join(A,C))) = meet(A,B). [para(10(a,1),12(a,2,2)),rewrite([5(2),5(4)])].
% 99.35/99.66 34 join(A,join(A,B)) = join(A,B). [para(14(a,1),2(a,1)),rewrite([6(1),6(2),14(2,R),2(1),6(3)])].
% 99.35/99.66 36 join(A,op(B,ld(B,A))) = A. [para(1(a,1),16(a,1,2,2))].
% 99.35/99.66 39 join(A,op(rd(A,B),B)) = A. [para(1(a,1),18(a,1,2,1))].
% 99.35/99.66 42 meet(A,ld(B,op(B,A))) = A. [para(2(a,1),20(a,1,2,2))].
% 99.35/99.66 46 meet(A,ld(meet(B,rd(C,A)),C)) = A. [para(18(a,1),20(a,1,2,2))].
% 99.35/99.66 47 meet(A,rd(op(A,B),B)) = A. [para(2(a,1),22(a,1,2,1))].
% 99.35/99.66 48 meet(unit,rd(join(A,B),B)) = unit. [para(3(a,1),22(a,1,2,1,2))].
% 99.35/99.66 51 meet(A,rd(B,meet(C,ld(A,B)))) = A. [para(16(a,1),22(a,1,2,1))].
% 99.35/99.66 52 join(A,op(B,op(C,meet(D,ld(op(B,C),A))))) = A. [para(23(a,1),16(a,1,2))].
% 99.35/99.66 53 meet(A,ld(op(B,C),join(D,op(B,op(C,A))))) = A. [para(23(a,1),20(a,1,2,2,2))].
% 99.35/99.66 54 meet(op(A,B),rd(join(C,op(A,op(B,D))),D)) = op(A,B). [para(23(a,1),22(a,1,2,1,2))].
% 99.35/99.66 55 rd(A,ld(A,A)) = A. [para(2(a,1),25(a,1,2,1)),rewrite([2(3)])].
% 99.35/99.66 57 ld(rd(A,A),A) = A. [para(2(a,1),27(a,1,1,2)),rewrite([2(3)])].
% 99.35/99.66 58 join(A,op(rd(A,join(A,B)),meet(C,join(A,B)))) = A. [para(27(a,1),16(a,1,2,2,2))].
% 99.35/99.66 61 join(A,op(meet(A,B),ld(A,A))) = A. [para(55(a,1),18(a,1,2,1,2)),rewrite([5(1)])].
% 99.35/99.66 62 join(A,op(rd(A,A),meet(A,B))) = A. [para(57(a,1),16(a,1,2,2,2)),rewrite([5(2)])].
% 99.35/99.66 63 join(A,ld(unit,A)) = A. [para(3(a,1),36(a,1,2))].
% 99.35/99.66 66 join(A,op(B,op(C,ld(op(B,C),A)))) = A. [para(23(a,1),36(a,1,2))].
% 99.35/99.66 70 join(A,rd(A,unit)) = A. [para(4(a,1),39(a,1,2))].
% 99.35/99.66 72 meet(A,ld(rd(B,A),B)) = A. [para(39(a,1),20(a,1,2,2))].
% 99.35/99.66 76 meet(A,ld(unit,A)) = A. [para(3(a,1),42(a,1,2,2))].
% 99.35/99.66 77 meet(unit,ld(A,A)) = unit. [para(4(a,1),42(a,1,2,2))].
% 99.35/99.66 79 meet(A,ld(op(B,C),op(B,op(C,A)))) = A. [para(23(a,1),42(a,1,2,2))].
% 99.35/99.66 81 meet(unit,meet(ld(A,A),join(B,unit))) = unit. [para(77(a,1),33(a,2)),rewrite([6(4)])].
% 99.35/99.66 88 meet(unit,rd(A,A)) = unit. [para(3(a,1),47(a,1,2,1))].
% 99.35/99.66 89 meet(A,rd(A,unit)) = A. [para(4(a,1),47(a,1,2,1))].
% 99.35/99.66 97 meet(unit,rd(join(A,B),A)) = unit. [para(6(a,1),48(a,1,2,1))].
% 99.35/99.66 98 meet(unit,rd(A,meet(A,B))) = unit. [para(8(a,1),48(a,1,2,1))].
% 99.35/99.66 101 meet(unit,rd(A,op(B,meet(C,ld(B,A))))) = unit. [para(16(a,1),48(a,1,2,1))].
% 99.35/99.66 102 meet(unit,rd(A,op(meet(B,rd(A,C)),C))) = unit. [para(18(a,1),48(a,1,2,1))].
% 99.35/99.66 103 meet(unit,rd(A,op(B,ld(B,A)))) = unit. [para(36(a,1),48(a,1,2,1))].
% 99.35/99.66 105 meet(unit,rd(A,op(rd(A,B),B))) = unit. [para(39(a,1),48(a,1,2,1))].
% 99.35/99.66 106 meet(unit,rd(A,rd(A,unit))) = unit. [para(70(a,1),48(a,1,2,1))].
% 99.35/99.66 122 meet(unit,rd(join(A,join(B,C)),C)) = unit. [para(14(a,2),97(a,1,2,1))].
% 99.35/99.66 130 meet(ld(A,A),ld(meet(A,B),A)) = ld(A,A). [para(55(a,1),46(a,1,2,1,2)),rewrite([5(2)])].
% 99.35/99.66 131 meet(meet(A,B),ld(unit,A)) = meet(A,B). [para(98(a,1),46(a,1,2,1))].
% 99.35/99.66 132 meet(ld(unit,A),rd(A,unit)) = rd(A,unit). [para(106(a,1),46(a,1,2,1)),rewrite([5(5)])].
% 99.35/99.66 155 meet(unit,join(A,unit)) = unit. [para(81(a,1),12(a,1)),rewrite([77(6),5(5)]),flip(a)].
% 99.35/99.66 163 meet(ld(A,B),op(C,meet(D,ld(op(A,C),B)))) = op(C,meet(D,ld(op(A,C),B))). [para(52(a,1),20(a,1,2,2)),rewrite([5(6)])].
% 99.35/99.66 164 meet(A,rd(B,op(C,meet(D,ld(op(A,C),B))))) = A. [para(52(a,1),22(a,1,2,1))].
% 99.35/99.66 182 meet(ld(unit,A),op(B,ld(B,A))) = op(B,ld(B,A)). [para(103(a,1),46(a,1,2,1)),rewrite([5(5)])].
% 99.35/99.66 188 meet(ld(unit,A),op(rd(A,B),B)) = op(rd(A,B),B). [para(105(a,1),46(a,1,2,1)),rewrite([5(5)])].
% 99.35/99.66 192 meet(unit,ld(op(A,B),join(C,op(A,B)))) = unit. [para(4(a,1),53(a,1,2,2,2,2))].
% 99.35/99.66 193 meet(A,ld(op(meet(B,rd(C,op(D,A))),D),C)) = A. [para(18(a,1),53(a,1,2,2))].
% 99.35/99.66 208 meet(unit,rd(join(A,B),meet(B,C))) = unit. [para(8(a,1),122(a,1,2,1,2))].
% 99.35/99.66 212 meet(unit,rd(join(A,B),op(meet(C,rd(B,D)),D))) = unit. [para(18(a,1),122(a,1,2,1,2))].
% 99.35/99.66 213 meet(unit,rd(join(A,B),op(C,ld(C,B)))) = unit. [para(36(a,1),122(a,1,2,1,2))].
% 99.35/99.66 217 meet(unit,rd(join(A,B),op(rd(B,C),C))) = unit. [para(39(a,1),122(a,1,2,1,2))].
% 99.35/99.66 237 meet(meet(A,B),ld(unit,B)) = meet(A,B). [para(5(a,1),131(a,1,1)),rewrite([5(5)])].
% 99.35/99.66 240 meet(rd(A,B),op(meet(C,rd(A,op(D,B))),D)) = op(meet(C,rd(A,op(D,B))),D). [para(18(a,1),54(a,1,2,1)),rewrite([5(6)])].
% 99.35/99.66 252 meet(rd(A,unit),ld(unit,ld(unit,A))) = rd(A,unit). [para(132(a,1),131(a,1,1)),rewrite([132(12)])].
% 99.35/99.66 277 join(join(A,B),meet(B,C)) = join(A,B). [para(208(a,1),18(a,1,2,1)),rewrite([3(4)])].
% 99.35/99.66 289 meet(meet(A,B),ld(unit,join(A,C))) = meet(A,B). [para(208(a,1),46(a,1,2,1)),rewrite([6(3)])].
% 99.35/99.66 359 join(A,rd(A,join(A,unit))) = A. [para(155(a,1),58(a,1,2,2)),rewrite([4(5)])].
% 99.35/99.66 365 meet(unit,rd(A,rd(A,join(A,unit)))) = unit. [para(359(a,1),48(a,1,2,1))].
% 99.35/99.66 414 meet(A,ld(unit,ld(unit,A))) = A. [para(76(a,1),237(a,1,1)),rewrite([76(8)])].
% 99.35/99.66 456 ld(unit,A) = A. [para(414(a,1),16(a,1,2,2)),rewrite([3(4),6(3),63(3)]),flip(a)].
% 99.35/99.66 460 meet(meet(A,B),join(A,C)) = meet(A,B). [back_rewrite(289),rewrite([456(4)])].
% 99.35/99.66 461 rd(A,unit) = A. [back_rewrite(252),rewrite([456(5),456(4),5(3),89(3)]),flip(a)].
% 99.35/99.66 463 meet(A,op(rd(A,B),B)) = op(rd(A,B),B). [back_rewrite(188),rewrite([456(2)])].
% 99.35/99.66 464 meet(A,op(B,ld(B,A))) = op(B,ld(B,A)). [back_rewrite(182),rewrite([456(2)])].
% 99.35/99.66 465 op(x,op(ld(x,unit),ld(op(x,ld(x,unit)),unit))) != op(x,ld(x,unit)) # answer(goal). [back_rewrite(31),rewrite([456(14),456(14),4(13)])].
% 99.35/99.66 468 meet(unit,ld(meet(A,B),B)) = unit. [para(461(a,1),46(a,1,2,1,2))].
% 99.35/99.66 475 meet(unit,ld(meet(A,B),A)) = unit. [para(5(a,1),468(a,1,2,1))].
% 99.35/99.66 478 meet(unit,ld(A,ld(B,join(C,op(B,A))))) = unit. [para(20(a,1),468(a,1,2,1))].
% 99.35/99.66 482 meet(unit,ld(A,ld(B,op(B,A)))) = unit. [para(42(a,1),468(a,1,2,1))].
% 99.35/99.66 483 meet(unit,ld(A,rd(op(A,B),B))) = unit. [para(47(a,1),468(a,1,2,1))].
% 99.35/99.66 487 meet(unit,ld(A,ld(rd(B,A),B))) = unit. [para(72(a,1),468(a,1,2,1))].
% 99.35/99.66 489 meet(unit,ld(A,rd(B,meet(C,ld(A,B))))) = unit. [para(51(a,1),468(a,1,2,1))].
% 99.35/99.66 509 meet(unit,ld(meet(A,meet(B,C)),C)) = unit. [para(12(a,2),475(a,1,2,1))].
% 99.35/99.66 529 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(34(a,1),277(a,1,1)),rewrite([5(3),34(6)])].
% 99.35/99.66 530 join(A,meet(B,op(C,ld(C,A)))) = A. [para(36(a,1),277(a,1,1)),rewrite([5(3),36(7)])].
% 99.35/99.66 576 meet(A,rd(A,join(A,unit))) = rd(A,join(A,unit)). [para(365(a,1),46(a,1,2,1)),rewrite([456(5),5(4)])].
% 99.35/99.66 588 meet(meet(A,B),join(B,C)) = meet(A,B). [para(5(a,1),460(a,1,1)),rewrite([5(4)])].
% 99.35/99.66 615 join(A,ld(B,op(B,A))) = ld(B,op(B,A)). [para(482(a,1),16(a,1,2,2)),rewrite([4(4),6(3)])].
% 99.35/99.66 621 join(A,rd(op(A,B),B)) = rd(op(A,B),B). [para(483(a,1),16(a,1,2,2)),rewrite([4(4),6(3)])].
% 99.35/99.66 639 join(A,ld(rd(B,A),B)) = ld(rd(B,A),B). [para(487(a,1),16(a,1,2,2)),rewrite([4(4),6(3)])].
% 99.35/99.66 698 meet(unit,ld(meet(A,B),ld(C,op(C,B)))) = unit. [para(42(a,1),509(a,1,2,1,2))].
% 99.35/99.66 699 meet(unit,ld(meet(A,unit),ld(B,B))) = unit. [para(77(a,1),509(a,1,2,1,2))].
% 99.35/99.66 701 meet(unit,ld(meet(A,B),rd(op(B,C),C))) = unit. [para(47(a,1),509(a,1,2,1,2))].
% 99.35/99.66 954 join(ld(A,A),meet(B,unit)) = ld(A,A). [para(699(a,1),16(a,1,2,2)),rewrite([4(5)])].
% 99.35/99.66 1310 join(unit,ld(A,A)) = ld(A,A). [para(1(a,1),954(a,1,2)),rewrite([6(3)])].
% 99.35/99.66 1555 meet(A,op(meet(B,rd(A,C)),C)) = op(meet(B,rd(A,C)),C). [para(102(a,1),46(a,1,2,1)),rewrite([456(5),5(4)])].
% 99.35/99.66 2555 meet(unit,ld(op(A,ld(A,B)),B)) = unit. [para(36(a,1),192(a,1,2,2))].
% 99.35/99.66 3389 join(A,op(rd(A,A),op(rd(A,B),B))) = A. [para(463(a,1),62(a,1,2,2))].
% 99.35/99.66 3401 join(A,op(B,op(ld(B,A),ld(A,A)))) = A. [para(464(a,1),61(a,1,2,1)),rewrite([23(4)])].
% 99.35/99.66 3648 meet(unit,ld(op(A,ld(op(B,A),C)),ld(B,C))) = unit. [para(66(a,1),478(a,1,2,2,2))].
% 99.35/99.66 3949 meet(unit,rd(rd(A,meet(B,ld(C,A))),C)) = unit. [para(489(a,1),101(a,1,2,2,2)),rewrite([4(6)])].
% 99.35/99.66 4799 meet(ld(A,A),join(A,unit)) = ld(A,A). [para(576(a,1),130(a,1,2,1)),rewrite([27(5)])].
% 99.35/99.66 4820 join(join(A,unit),ld(A,A)) = join(A,unit). [para(4799(a,1),529(a,1,2))].
% 99.35/99.66 4902 join(A,ld(A,A)) = join(A,unit). [para(4820(a,1),6(a,1)),rewrite([14(6),6(5),14(6,R),6(5),1310(5)]),flip(a)].
% 99.35/99.66 5169 meet(meet(A,B),ld(C,op(C,A))) = meet(A,B). [para(615(a,1),460(a,1,2))].
% 99.35/99.66 5211 meet(meet(A,B),rd(op(A,C),C)) = meet(A,B). [para(621(a,1),460(a,1,2))].
% 99.35/99.66 5294 meet(meet(A,B),ld(rd(C,B),C)) = meet(A,B). [para(639(a,1),588(a,1,2))].
% 99.35/99.66 6113 meet(unit,ld(A,op(A,ld(B,B)))) = unit. [para(77(a,1),698(a,1,2,1)),rewrite([456(6)])].
% 99.35/99.66 6130 meet(unit,ld(A,op(A,join(B,unit)))) = unit. [para(155(a,1),698(a,1,2,1)),rewrite([456(7)])].
% 99.35/99.66 6328 join(A,op(A,ld(B,B))) = op(A,ld(B,B)). [para(6113(a,1),16(a,1,2,2)),rewrite([4(4),6(3)])].
% 99.35/99.66 6332 meet(A,op(A,ld(B,B))) = A. [para(6113(a,1),51(a,1,2,2)),rewrite([461(4)])].
% 99.35/99.66 6355 op(A,ld(A,A)) = A. [para(6332(a,1),61(a,1,2,1)),rewrite([6328(3)])].
% 99.35/99.66 6358 meet(A,join(B,op(A,ld(C,C)))) = A. [para(6332(a,1),588(a,1,1)),rewrite([6(3),6332(7)])].
% 99.35/99.66 6382 meet(ld(A,A),ld(op(B,A),op(B,A))) = ld(A,A). [para(6355(a,1),79(a,1,2,2,2))].
% 99.35/99.66 6502 meet(A,op(A,join(B,unit))) = A. [para(6130(a,1),51(a,1,2,2)),rewrite([461(5)])].
% 99.35/99.66 6593 meet(A,rd(A,ld(B,B))) = rd(A,ld(B,B)). [para(39(a,1),6358(a,1,2)),rewrite([5(3)])].
% 99.35/99.66 7074 meet(A,ld(rd(B,A),join(B,C))) = A. [para(217(a,1),193(a,1,2,1,1)),rewrite([3(3),6(2)])].
% 99.35/99.66 7090 meet(A,ld(rd(unit,A),ld(B,B))) = A. [para(1310(a,1),7074(a,1,2,2))].
% 99.35/99.66 7108 join(ld(A,A),op(rd(unit,B),B)) = ld(A,A). [para(7090(a,1),16(a,1,2,2))].
% 99.35/99.66 7180 meet(unit,rd(op(rd(A,A),B),B)) = unit. [para(88(a,1),701(a,1,2,1)),rewrite([456(6)])].
% 99.35/99.66 7469 meet(A,op(rd(B,B),A)) = A. [para(7180(a,1),46(a,1,2,1)),rewrite([456(4)])].
% 99.35/99.66 7488 meet(A,join(B,op(rd(C,C),A))) = A. [para(7469(a,1),588(a,1,1)),rewrite([6(3),7469(7)])].
% 99.35/99.66 7784 meet(A,ld(rd(B,B),A)) = ld(rd(B,B),A). [para(36(a,1),7488(a,1,2)),rewrite([5(3)])].
% 99.35/99.66 8106 meet(A,ld(meet(B,rd(C,A)),join(C,D))) = A. [para(212(a,1),193(a,1,2,1,1)),rewrite([3(4),6(3)])].
% 99.35/99.66 9510 meet(A,rd(join(B,C),ld(A,C))) = A. [para(213(a,1),240(a,1,2,1)),rewrite([3(5),5(4),213(10),3(6)])].
% 99.35/99.66 9523 meet(A,rd(B,ld(A,op(C,ld(C,B))))) = A. [para(36(a,1),9510(a,1,2,1))].
% 99.35/99.66 9524 meet(A,rd(B,ld(A,op(rd(B,C),C)))) = A. [para(39(a,1),9510(a,1,2,1))].
% 99.35/99.66 11078 op(rd(A,A),rd(A,B)) = rd(A,B). [para(3389(a,1),54(a,1,2,1)),rewrite([5(5),7469(5)]),flip(a)].
% 99.35/99.66 11081 op(rd(A,A),join(A,B)) = join(A,B). [para(25(a,1),11078(a,1,2)),rewrite([25(6)])].
% 99.35/99.66 11082 ld(rd(A,A),rd(A,B)) = rd(A,B). [para(11078(a,1),42(a,1,2,2)),rewrite([7784(5)])].
% 99.35/99.66 11099 meet(rd(A,A),join(A,unit)) = rd(A,A). [para(11081(a,1),6502(a,1,2))].
% 99.35/99.66 11118 join(join(A,unit),rd(A,A)) = join(A,unit). [para(11099(a,1),529(a,1,2))].
% 99.35/99.66 11184 op(ld(A,B),ld(B,B)) = ld(A,B). [para(3401(a,1),20(a,1,2,2)),rewrite([5(5),6332(5)]),flip(a)].
% 99.35/99.66 11186 op(join(A,B),ld(A,A)) = join(A,B). [para(27(a,1),11184(a,1,1)),rewrite([27(6)])].
% 99.35/99.66 11196 op(join(A,B),ld(B,B)) = join(A,B). [para(6(a,1),11186(a,1,1)),rewrite([6(4)])].
% 99.35/99.66 11242 op(join(A,unit),rd(A,A)) = join(A,unit). [para(11118(a,1),11196(a,1,1)),rewrite([11082(5),11118(8)])].
% 99.35/99.66 11283 meet(rd(A,A),ld(join(A,unit),join(A,unit))) = rd(A,A). [para(11242(a,1),42(a,1,2,2))].
% 99.35/99.66 11624 meet(A,rd(op(A,B),meet(B,C))) = A. [para(5169(a,1),51(a,1,2,2))].
% 99.35/99.66 11642 meet(A,rd(op(A,B),op(C,ld(C,B)))) = A. [para(464(a,1),11624(a,1,2,2))].
% 99.35/99.66 11862 meet(A,ld(meet(B,C),op(B,A))) = A. [para(5211(a,1),46(a,1,2,1))].
% 99.35/99.66 11876 meet(A,ld(meet(B,C),op(C,A))) = A. [para(5(a,1),11862(a,1,2,1))].
% 99.35/99.66 11933 meet(A,op(ld(meet(B,C),B),A)) = A. [para(475(a,1),11876(a,1,2,1)),rewrite([456(5)])].
% 99.35/99.66 12738 join(A,ld(ld(meet(B,C),B),A)) = A. [para(11933(a,1),530(a,1,2))].
% 99.35/99.66 13327 join(A,ld(ld(op(B,ld(B,C)),C),A)) = A. [para(464(a,1),12738(a,1,2,1,1))].
% 99.35/99.66 14021 meet(unit,rd(rd(A,meet(B,C)),rd(A,C))) = unit. [para(5294(a,1),3949(a,1,2,1,2))].
% 99.35/99.66 15772 meet(A,ld(rd(B,ld(C,C)),op(B,A))) = A. [para(6593(a,1),11862(a,1,2,1))].
% 99.35/99.66 15793 join(op(rd(unit,A),A),ld(B,B)) = ld(B,B). [para(7108(a,1),6(a,1)),flip(a)].
% 99.35/99.66 15911 meet(A,ld(meet(B,C),join(D,op(B,A)))) = A. [para(5211(a,1),8106(a,1,2,1)),rewrite([6(3)])].
% 99.35/99.66 16276 meet(A,rd(A,op(B,ld(B,unit)))) = A. [para(4(a,1),11642(a,1,2,1))].
% 99.35/99.66 16285 meet(ld(A,unit),ld(op(B,A),B)) = ld(A,unit). [para(16276(a,1),193(a,1,2,1,1))].
% 99.35/99.66 17188 meet(A,ld(rd(unit,ld(B,B)),A)) = A. [para(3(a,1),15772(a,1,2,2))].
% 99.35/99.66 17190 join(A,op(rd(unit,ld(B,B)),A)) = A. [para(17188(a,1),16(a,1,2,2))].
% 99.35/99.66 17228 ld(op(rd(unit,A),A),op(rd(unit,A),A)) = unit. [para(15793(a,1),4902(a,1)),rewrite([6(12),39(12)])].
% 99.35/99.66 17292 meet(A,ld(meet(B,rd(unit,ld(C,C))),A)) = A. [para(17190(a,1),15911(a,1,2,2)),rewrite([5(4)])].
% 99.35/99.66 18071 meet(A,ld(op(B,ld(B,unit)),A)) = A. [para(9523(a,1),17292(a,1,2,1))].
% 99.35/99.66 18072 meet(A,ld(op(rd(unit,B),B),A)) = A. [para(9524(a,1),17292(a,1,2,1))].
% 99.35/99.66 18074 join(A,op(B,op(ld(B,unit),A))) = A. [para(18071(a,1),16(a,1,2,2)),rewrite([23(4)])].
% 99.35/99.66 18082 join(A,op(rd(unit,B),op(B,A))) = A. [para(18072(a,1),16(a,1,2,2)),rewrite([23(4)])].
% 99.35/99.66 18091 meet(unit,ld(op(ld(A,unit),B),ld(A,B))) = unit. [para(18074(a,1),478(a,1,2,2,2))].
% 99.35/99.66 18099 meet(unit,ld(op(A,B),ld(rd(unit,A),B))) = unit. [para(18082(a,1),478(a,1,2,2,2))].
% 99.35/99.66 18120 meet(rd(A,B),rd(A,meet(C,B))) = rd(A,B). [para(14021(a,1),1555(a,1,2,1)),rewrite([3(5),5(4),14021(10),3(7)])].
% 99.35/99.66 18349 meet(ld(A,unit),rd(ld(A,B),B)) = ld(A,unit). [para(18091(a,1),164(a,1,2,2,2)),rewrite([4(5)])].
% 99.35/99.66 18359 meet(A,ld(B,ld(rd(unit,B),A))) = A. [para(18099(a,1),163(a,1,2,2)),rewrite([4(6),5(5),18099(12),4(7)])].
% 99.35/99.66 19279 meet(A,rd(ld(B,C),ld(op(B,A),C))) = A. [para(3648(a,1),164(a,1,2,2,2)),rewrite([4(5)])].
% 99.35/99.66 19542 ld(A,A) = unit. [para(17228(a,1),6382(a,1,2)),rewrite([5(3),77(3)]),flip(a)].
% 99.35/99.66 19569 rd(A,A) = unit. [back_rewrite(11283),rewrite([19542(6),5(3),88(3)]),flip(a)].
% 99.35/99.66 19634 join(unit,ld(op(A,ld(A,B)),B)) = ld(op(A,ld(A,B)),B). [para(19542(a,1),13327(a,1,2)),rewrite([6(5)])].
% 99.35/99.66 19673 meet(ld(A,unit),rd(unit,A)) = rd(unit,A). [para(19542(a,1),18359(a,1,2,2)),rewrite([5(5)])].
% 99.35/99.66 19681 rd(unit,A) = ld(A,unit). [para(19542(a,1),18349(a,1,2,1)),rewrite([19673(5)])].
% 99.35/99.66 19724 meet(A,ld(ld(op(B,A),B),unit)) = A. [para(19542(a,1),19279(a,1,2,1)),rewrite([19681(4)])].
% 99.35/99.66 20129 meet(unit,rd(meet(A,B),B)) = rd(meet(A,B),B). [para(19569(a,1),18120(a,1,2)),rewrite([5(4)])].
% 99.35/99.66 23021 ld(op(A,B),A) = ld(B,unit). [para(19724(a,1),51(a,1,2,2)),rewrite([19681(4),5(5),16285(5)]),flip(a)].
% 99.35/99.66 23023 meet(unit,ld(ld(op(A,ld(A,B)),B),unit)) = unit. [para(23021(a,1),3648(a,1,2))].
% 99.35/99.66 23388 ld(ld(op(A,ld(A,B)),B),unit) = unit. [para(2555(a,1),20129(a,1,2,1)),rewrite([19681(6),23023(7),2555(6),19681(6)]),flip(a)].
% 99.35/99.66 23390 ld(op(A,ld(A,B)),B) = unit. [para(23388(a,1),36(a,1,2,2)),rewrite([4(6),19634(5)])].
% 99.35/99.66 23391 $F # answer(goal). [back_rewrite(465),rewrite([23390(11),4(6)]),xx(a)].
% 99.35/99.66
% 99.35/99.66 % SZS output end Refutation
% 99.35/99.66 ============================== end of proof ==========================
% 99.35/99.66
% 99.35/99.66 ============================== STATISTICS ============================
% 99.35/99.66
% 99.35/99.66 Given=5458. Generated=7068103. Kept=23378. proofs=1.
% 99.35/99.66 Usable=2694. Sos=8022. Demods=10717. Limbo=1, Disabled=12680. Hints=0.
% 99.35/99.66 Megabytes=20.36.
% 99.35/99.66 User_CPU=94.89, System_CPU=3.71, Wall_clock=98.
% 99.35/99.66
% 99.35/99.66 ============================== end of statistics =====================
% 99.35/99.66
% 99.35/99.66 ============================== end of search =========================
% 99.35/99.66
% 99.35/99.66 THEOREM PROVED
% 99.35/99.66 % SZS status Unsatisfiable
% 99.35/99.66
% 99.35/99.66 Exiting with 1 proof.
% 99.35/99.66
% 99.35/99.66 Process 26885 exit (max_proofs) Tue May 31 17:28:52 2022
% 99.35/99.66 Prover9 interrupted
%------------------------------------------------------------------------------