TSTP Solution File: BOO076-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO076-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 : Thu Jul 14 23:48:08 EDT 2022
% Result : Unsatisfiable 43.76s 44.03s
% Output : Refutation 43.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : BOO076-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 1 19:31:34 EDT 2022
% 0.12/0.34 % CPUTime :
% 43.76/44.03 ============================== Prover9 ===============================
% 43.76/44.03 Prover9 (32) version 2009-11A, November 2009.
% 43.76/44.03 Process 25392 was started by sandbox2 on n027.cluster.edu,
% 43.76/44.03 Wed Jun 1 19:31:34 2022
% 43.76/44.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25237_n027.cluster.edu".
% 43.76/44.03 ============================== end of head ===========================
% 43.76/44.03
% 43.76/44.03 ============================== INPUT =================================
% 43.76/44.03
% 43.76/44.03 % Reading from file /tmp/Prover9_25237_n027.cluster.edu
% 43.76/44.03
% 43.76/44.03 set(prolog_style_variables).
% 43.76/44.03 set(auto2).
% 43.76/44.03 % set(auto2) -> set(auto).
% 43.76/44.03 % set(auto) -> set(auto_inference).
% 43.76/44.03 % set(auto) -> set(auto_setup).
% 43.76/44.03 % set(auto_setup) -> set(predicate_elim).
% 43.76/44.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 43.76/44.03 % set(auto) -> set(auto_limits).
% 43.76/44.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 43.76/44.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 43.76/44.03 % set(auto) -> set(auto_denials).
% 43.76/44.03 % set(auto) -> set(auto_process).
% 43.76/44.03 % set(auto2) -> assign(new_constants, 1).
% 43.76/44.03 % set(auto2) -> assign(fold_denial_max, 3).
% 43.76/44.03 % set(auto2) -> assign(max_weight, "200.000").
% 43.76/44.03 % set(auto2) -> assign(max_hours, 1).
% 43.76/44.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 43.76/44.03 % set(auto2) -> assign(max_seconds, 0).
% 43.76/44.03 % set(auto2) -> assign(max_minutes, 5).
% 43.76/44.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 43.76/44.03 % set(auto2) -> set(sort_initial_sos).
% 43.76/44.03 % set(auto2) -> assign(sos_limit, -1).
% 43.76/44.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 43.76/44.03 % set(auto2) -> assign(max_megs, 400).
% 43.76/44.03 % set(auto2) -> assign(stats, some).
% 43.76/44.03 % set(auto2) -> clear(echo_input).
% 43.76/44.03 % set(auto2) -> set(quiet).
% 43.76/44.03 % set(auto2) -> clear(print_initial_clauses).
% 43.76/44.03 % set(auto2) -> clear(print_given).
% 43.76/44.03 assign(lrs_ticks,-1).
% 43.76/44.03 assign(sos_limit,10000).
% 43.76/44.03 assign(order,kbo).
% 43.76/44.03 set(lex_order_vars).
% 43.76/44.03 clear(print_given).
% 43.76/44.03
% 43.76/44.03 % formulas(sos). % not echoed (2 formulas)
% 43.76/44.03
% 43.76/44.03 ============================== end of input ==========================
% 43.76/44.03
% 43.76/44.03 % From the command line: assign(max_seconds, 300).
% 43.76/44.03
% 43.76/44.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 43.76/44.03
% 43.76/44.03 % Formulas that are not ordinary clauses:
% 43.76/44.03
% 43.76/44.03 ============================== end of process non-clausal formulas ===
% 43.76/44.03
% 43.76/44.03 ============================== PROCESS INITIAL CLAUSES ===============
% 43.76/44.03
% 43.76/44.03 ============================== PREDICATE ELIMINATION =================
% 43.76/44.03
% 43.76/44.03 ============================== end predicate elimination =============
% 43.76/44.03
% 43.76/44.03 Auto_denials:
% 43.76/44.03 % copying label prove_meredith_2_basis_2 to answer in negative clause
% 43.76/44.03
% 43.76/44.03 Term ordering decisions:
% 43.76/44.03 Function symbol KB weights: a=1. b=1. c=1. nand=1.
% 43.76/44.03
% 43.76/44.03 ============================== end of process initial clauses ========
% 43.76/44.03
% 43.76/44.03 ============================== CLAUSES FOR SEARCH ====================
% 43.76/44.03
% 43.76/44.03 ============================== end of clauses for search =============
% 43.76/44.03
% 43.76/44.03 ============================== SEARCH ================================
% 43.76/44.03
% 43.76/44.03 % Starting search at 0.01 seconds.
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=61.000, iters=3412
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=59.000, iters=3387
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=57.000, iters=3357
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=51.000, iters=3355
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=49.000, iters=3405
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=47.000, iters=3358
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=45.000, iters=3546
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=43.000, iters=3453
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=41.000, iters=3361
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=39.000, iters=3370
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=37.000, iters=3387
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=35.000, iters=3353
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=33.000, iters=3346
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=31.000, iters=3345
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=29.000, iters=3379
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=27.000, iters=3336
% 43.76/44.03
% 43.76/44.03 Low Water (displace): id=2979, wt=125.000
% 43.76/44.03
% 43.76/44.03 Low Water (displace): id=4708, wt=123.000
% 43.76/44.03
% 43.76/44.03 Low Water (displace): id=2934, wt=121.000
% 43.76/44.03
% 43.76/44.03 Low Water (displace): id=14530, wt=25.000
% 43.76/44.03
% 43.76/44.03 Low Water (displace): id=14584, wt=23.000
% 43.76/44.03
% 43.76/44.03 Low Water (displace): id=14693, wt=21.000
% 43.76/44.03
% 43.76/44.03 Low Water (displace): id=14700, wt=19.000
% 43.76/44.03
% 43.76/44.03 Low Water (keep): wt=25.000, iters=3340
% 43.76/44.03
% 43.76/44.03 ============================== PROOF =================================
% 43.76/44.03 % SZS status Unsatisfiable
% 43.76/44.03 % SZS output start Refutation
% 43.76/44.03
% 43.76/44.03 % Proof 1 at 42.53 (+ 0.54) seconds: prove_meredith_2_basis_2.
% 43.76/44.03 % Length of proof is 149.
% 43.76/44.03 % Level of proof is 30.
% 43.76/44.03 % Maximum clause weight is 129.000.
% 43.76/44.03 % Given clauses 553.
% 43.76/44.03
% 43.76/44.03 1 nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,A))) = B # label(sh_1) # label(axiom). [assumption].
% 43.76/44.03 2 nand(a,nand(b,nand(a,c))) != nand(nand(nand(c,b),b),a) # label(prove_meredith_2_basis_2) # label(negated_conjecture) # answer(prove_meredith_2_basis_2). [assumption].
% 43.76/44.03 3 nand(nand(nand(c,b),b),a) != nand(a,nand(b,nand(a,c))) # answer(prove_meredith_2_basis_2). [copy(2),flip(a)].
% 43.76/44.03 4 nand(nand(nand(A,nand(B,C)),nand(A,nand(A,nand(B,C)))),nand(nand(C,nand(nand(A,C),C)),nand(D,nand(A,nand(B,C))))) = nand(C,nand(nand(A,C),C)). [para(1(a,1),1(a,1,1,2,1))].
% 43.76/44.03 5 nand(nand(nand(A,nand(B,C)),nand(nand(D,nand(A,nand(B,C))),nand(A,nand(B,C)))),nand(D,A)) = D. [para(1(a,1),1(a,1,2,2))].
% 43.76/44.03 6 nand(nand(nand(A,B),nand(nand(nand(B,nand(nand(C,B),B)),nand(A,B)),nand(A,B))),C) = nand(B,nand(nand(C,B),B)). [para(1(a,1),1(a,1,2))].
% 43.76/44.03 7 nand(nand(nand(nand(A,nand(nand(B,A),A)),nand(C,nand(B,nand(D,A)))),nand(nand(A,nand(nand(B,A),A)),nand(nand(A,nand(nand(B,A),A)),nand(C,nand(B,nand(D,A)))))),nand(nand(nand(B,nand(D,A)),nand(B,nand(B,nand(D,A)))),nand(E,nand(nand(A,nand(nand(B,A),A)),nand(C,nand(B,nand(D,A))))))) = nand(nand(B,nand(D,A)),nand(B,nand(B,nand(D,A)))). [para(4(a,1),1(a,1,1,2,1))].
% 43.76/44.03 8 nand(nand(nand(A,nand(B,nand(C,D))),nand(nand(nand(nand(B,nand(C,D)),nand(B,nand(B,nand(C,D)))),nand(A,nand(B,nand(C,D)))),nand(A,nand(B,nand(C,D))))),nand(D,nand(nand(B,D),D))) = nand(nand(B,nand(C,D)),nand(B,nand(B,nand(C,D)))). [para(4(a,1),1(a,1,2))].
% 43.76/44.03 15 nand(nand(nand(A,B),nand(nand(C,nand(A,B)),nand(A,B))),nand(C,A)) = C. [para(5(a,1),1(a,1,2,2))].
% 43.76/44.03 17 nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,nand(nand(A,C),C)))) = B. [para(1(a,1),5(a,1,1,1)),rewrite([1(6),1(7)])].
% 43.76/44.03 19 nand(nand(nand(A,B),nand(A,nand(A,B))),nand(nand(nand(B,C),nand(nand(A,nand(B,C)),nand(B,C))),nand(D,nand(A,B)))) = nand(nand(B,C),nand(nand(A,nand(B,C)),nand(B,C))). [para(5(a,1),4(a,1,1,1,2)),rewrite([15(12),15(21)])].
% 43.76/44.03 36 nand(nand(A,nand(nand(nand(B,nand(nand(B,B),B)),A),A)),B) = nand(B,nand(nand(B,B),B)). [para(1(a,1),17(a,1,2))].
% 43.76/44.03 40 nand(A,nand(nand(A,A),A)) = nand(A,A). [para(17(a,1),4(a,1,2)),rewrite([17(8)]),flip(a)].
% 43.76/44.03 42 nand(nand(nand(nand(A,nand(B,C)),nand(A,nand(A,nand(B,C)))),nand(nand(D,nand(nand(A,nand(B,C)),nand(A,nand(A,nand(B,C))))),nand(nand(A,nand(B,C)),nand(A,nand(A,nand(B,C)))))),nand(D,nand(nand(nand(C,nand(nand(A,C),C)),nand(E,nand(A,nand(B,C)))),nand(nand(C,nand(nand(A,C),C)),nand(nand(C,nand(nand(A,C),C)),nand(E,nand(A,nand(B,C)))))))) = D. [para(4(a,1),17(a,1,2,2,2,1))].
% 43.76/44.03 43 nand(nand(A,nand(nand(nand(nand(B,B),nand(B,nand(B,B))),A),A)),nand(B,B)) = nand(nand(B,B),nand(B,nand(B,B))). [para(4(a,1),17(a,1,2)),rewrite([40(3),40(4),40(10),40(12),40(13)])].
% 43.76/44.03 52 nand(nand(A,nand(nand(nand(B,B),A),A)),B) = nand(B,B). [back_rewrite(36),rewrite([40(3),40(8)])].
% 43.76/44.03 54 nand(nand(A,A),nand(A,nand(B,A))) = A. [para(40(a,1),1(a,1,1))].
% 43.76/44.03 55 nand(nand(A,A),nand(A,A)) = A. [para(40(a,1),1(a,1,2)),rewrite([40(3)])].
% 43.76/44.03 59 nand(nand(nand(A,B),nand(A,B)),nand(nand(A,B),A)) = nand(A,B). [para(40(a,1),15(a,1,1))].
% 43.76/44.03 64 nand(nand(A,nand(nand(B,A),A)),nand(B,B)) = B. [back_rewrite(43),rewrite([54(4),54(9)])].
% 43.76/44.03 65 nand(nand(A,nand(nand(nand(nand(B,C),nand(nand(nand(C,nand(nand(nand(D,A),C),C)),nand(B,C)),nand(B,C))),A),A)),nand(C,nand(nand(nand(D,A),C),C))) = nand(nand(B,C),nand(nand(nand(C,nand(nand(nand(D,A),C),C)),nand(B,C)),nand(B,C))). [para(6(a,1),1(a,1,2))].
% 43.76/44.03 71 nand(nand(nand(A,nand(B,C)),nand(nand(nand(nand(B,C),nand(B,nand(B,C))),nand(A,nand(B,C))),nand(A,nand(B,C)))),nand(nand(C,D),nand(nand(B,nand(C,D)),nand(C,D)))) = nand(nand(B,C),nand(B,nand(B,C))). [para(15(a,1),6(a,1,1,2,1,1,2,1)),rewrite([15(29)])].
% 43.76/44.03 95 nand(nand(nand(nand(A,nand(nand(B,A),A)),nand(C,nand(B,nand(D,A)))),nand(nand(A,nand(nand(B,A),A)),nand(nand(A,nand(nand(B,A),A)),nand(C,nand(B,nand(D,A)))))),nand(nand(nand(B,nand(D,A)),nand(B,nand(B,nand(D,A)))),nand(nand(B,nand(D,A)),nand(B,nand(B,nand(D,A)))))) = nand(nand(B,nand(D,A)),nand(B,nand(B,nand(D,A)))). [para(4(a,1),64(a,1,1,2,1))].
% 43.76/44.03 100 nand(nand(nand(A,nand(nand(B,A),A)),nand(nand(C,nand(A,nand(nand(B,A),A))),nand(A,nand(nand(B,A),A)))),nand(C,B)) = C. [para(64(a,1),17(a,1,2,2,2,1)),rewrite([54(16)])].
% 43.76/44.03 138 nand(nand(nand(A,nand(B,nand(nand(C,nand(nand(A,C),C)),nand(D,nand(A,A))))),nand(A,nand(A,nand(B,nand(nand(C,nand(nand(A,C),C)),nand(D,nand(A,A))))))),nand(nand(nand(nand(C,nand(nand(A,C),C)),nand(D,nand(A,A))),nand(nand(C,nand(nand(A,C),C)),nand(nand(C,nand(nand(A,C),C)),nand(D,nand(A,A))))),nand(E,nand(A,nand(B,nand(nand(C,nand(nand(A,C),C)),nand(D,nand(A,A)))))))) = nand(nand(nand(C,nand(nand(A,C),C)),nand(D,nand(A,A))),nand(nand(C,nand(nand(A,C),C)),nand(nand(C,nand(nand(A,C),C)),nand(D,nand(A,A))))). [para(64(a,1),7(a,1,1,1,1,2,1)),rewrite([54(4),64(14),54(12),64(14),54(12),64(41),54(39)])].
% 43.76/44.03 150 nand(A,nand(nand(nand(nand(B,A),nand(B,A)),A),A)) = nand(B,A). [para(52(a,1),6(a,1,1,2,1)),rewrite([40(7),55(7)]),flip(a)].
% 43.76/44.03 185 nand(nand(A,A),nand(B,A)) = A. [para(150(a,1),1(a,1,2)),rewrite([40(3)])].
% 43.76/44.03 195 nand(nand(nand(A,B),nand(nand(C,nand(A,B)),nand(A,B))),nand(C,B)) = C. [para(150(a,1),15(a,1,1,1)),rewrite([150(7),150(9)])].
% 43.76/44.03 199 nand(nand(A,B),nand(nand(nand(A,A),nand(A,B)),nand(A,B))) = A. [para(15(a,1),150(a,1,2,1,1,1)),rewrite([15(9),15(15)])].
% 43.76/44.03 208 nand(nand(nand(nand(nand(nand(A,B),nand(A,B)),B),B),nand(nand(A,B),nand(nand(nand(nand(A,B),nand(A,B)),B),B))),nand(B,B)) = B. [para(150(a,1),64(a,1,1,2,1))].
% 43.76/44.03 212 nand(nand(nand(nand(nand(nand(A,nand(B,B)),nand(A,nand(B,B))),nand(B,B)),nand(B,B)),nand(nand(A,nand(B,B)),nand(nand(nand(nand(A,nand(B,B)),nand(A,nand(B,B))),nand(B,B)),nand(B,B)))),B) = nand(B,B). [para(150(a,1),52(a,1,1,2,1))].
% 43.76/44.03 215 nand(nand(nand(A,B),nand(A,B)),nand(nand(A,B),B)) = nand(A,B). [para(150(a,1),59(a,1,1,1)),rewrite([150(7),150(9),150(12)])].
% 43.76/44.03 217 nand(nand(nand(nand(nand(A,B),nand(A,B)),B),B),nand(nand(nand(nand(A,B),nand(A,B)),nand(nand(nand(nand(A,B),nand(A,B)),B),B)),nand(nand(nand(nand(A,B),nand(A,B)),B),B))) = nand(A,B). [para(150(a,1),150(a,1,2,1,1,1)),rewrite([150(12),150(27)])].
% 43.76/44.03 248 nand(nand(nand(A,nand(nand(B,A),A)),nand(nand(nand(B,nand(C,A)),nand(B,nand(B,nand(C,A)))),nand(A,nand(nand(B,A),A)))),nand(nand(nand(D,nand(B,nand(C,A))),nand(nand(nand(nand(B,nand(C,A)),nand(B,nand(B,nand(C,A)))),nand(D,nand(B,nand(C,A)))),nand(D,nand(B,nand(C,A))))),A)) = nand(nand(D,nand(B,nand(C,A))),nand(nand(nand(nand(B,nand(C,A)),nand(B,nand(B,nand(C,A)))),nand(D,nand(B,nand(C,A)))),nand(D,nand(B,nand(C,A))))). [para(8(a,1),15(a,1,1,2,1))].
% 43.76/44.03 290 nand(nand(nand(A,nand(B,C)),nand(A,nand(A,nand(B,C)))),nand(nand(C,nand(nand(A,C),C)),nand(B,C))) = nand(C,nand(nand(A,C),C)). [para(185(a,1),4(a,1,2,2))].
% 43.76/44.03 295 nand(nand(A,nand(nand(nand(nand(B,A),nand(nand(C,nand(B,A)),nand(B,A))),A),A)),C) = nand(nand(B,A),nand(nand(C,nand(B,A)),nand(B,A))). [para(185(a,1),6(a,1,1,1)),rewrite([185(9),185(10)])].
% 43.76/44.03 296 nand(nand(A,A),nand(B,nand(nand(A,B),B))) = A. [para(6(a,1),185(a,1,2))].
% 43.76/44.03 299 nand(nand(nand(nand(nand(A,B),nand(nand(C,nand(A,B)),nand(A,B))),nand(D,nand(C,B))),nand(nand(nand(A,B),nand(nand(C,nand(A,B)),nand(A,B))),nand(nand(nand(A,B),nand(nand(C,nand(A,B)),nand(A,B))),nand(D,nand(C,B))))),nand(nand(nand(C,B),nand(C,nand(C,B))),nand(E,nand(nand(nand(A,B),nand(nand(C,nand(A,B)),nand(A,B))),nand(D,nand(C,B)))))) = nand(nand(C,B),nand(C,nand(C,B))). [para(185(a,1),7(a,1,1,1,2,2,2)),rewrite([185(24),185(29),185(30),185(39),185(45),185(46)])].
% 43.76/44.03 309 nand(nand(nand(A,B),nand(A,B)),B) = nand(A,B). [para(185(a,1),185(a,1,2))].
% 43.76/44.03 317 nand(nand(nand(A,B),B),nand(nand(A,B),nand(nand(A,B),B))) = nand(A,B). [back_rewrite(217),rewrite([309(4),309(9),215(8),309(7)])].
% 43.76/44.03 318 nand(nand(A,nand(B,B)),B) = nand(B,B). [back_rewrite(212),rewrite([309(7),309(13),317(12)])].
% 43.76/44.03 319 nand(nand(A,B),nand(B,B)) = B. [back_rewrite(208),rewrite([309(4),309(7),317(7)])].
% 43.76/44.03 325 nand(A,nand(nand(B,A),A)) = nand(B,A). [back_rewrite(150),rewrite([309(4)])].
% 43.76/44.03 336 nand(nand(nand(nand(A,nand(B,C)),nand(D,nand(A,C))),nand(nand(A,nand(B,C)),nand(nand(A,nand(B,C)),nand(D,nand(A,C))))),nand(nand(nand(A,C),nand(A,nand(A,C))),nand(E,nand(nand(A,nand(B,C)),nand(D,nand(A,C)))))) = nand(nand(A,C),nand(A,nand(A,C))). [back_rewrite(299),rewrite([325(6),325(11),325(13),325(24)])].
% 43.76/44.03 337 nand(nand(A,A),nand(A,B)) = A. [back_rewrite(296),rewrite([325(4)])].
% 43.76/44.03 338 nand(nand(nand(A,nand(B,C)),C),A) = nand(A,nand(B,C)). [back_rewrite(295),rewrite([325(6),325(5),325(10)])].
% 43.76/44.03 339 nand(nand(nand(A,nand(B,C)),nand(A,nand(A,nand(B,C)))),nand(nand(A,C),nand(B,C))) = nand(A,C). [back_rewrite(290),rewrite([325(9),325(13)])].
% 43.76/44.03 365 nand(nand(nand(A,B),nand(nand(nand(A,nand(C,B)),nand(A,nand(A,nand(C,B)))),nand(A,B))),nand(nand(nand(nand(A,nand(C,B)),nand(A,nand(A,nand(C,B)))),nand(D,nand(A,nand(C,B)))),B)) = nand(nand(nand(A,nand(C,B)),nand(A,nand(A,nand(C,B)))),nand(D,nand(A,nand(C,B)))). [back_rewrite(248),rewrite([325(3),325(10),325(28),325(40)])].
% 43.76/44.03 374 nand(nand(A,B),nand(A,nand(A,B))) = A. [back_rewrite(199),rewrite([337(4)])].
% 43.76/44.03 375 nand(nand(A,nand(B,C)),nand(A,C)) = A. [back_rewrite(195),rewrite([325(6)])].
% 43.76/44.03 387 nand(A,nand(nand(A,B),nand(C,nand(A,nand(D,nand(nand(A,B),nand(E,nand(A,A)))))))) = nand(A,B). [back_rewrite(138),rewrite([325(3),325(9),374(14),325(3),325(7),325(8),374(11),325(4),325(13),325(17),325(18),374(21)])].
% 43.76/44.03 408 nand(nand(A,nand(B,C)),nand(A,B)) = A. [back_rewrite(100),rewrite([325(3),325(4),325(6),325(6)])].
% 43.76/44.03 411 nand(nand(A,B),nand(A,A)) = A. [back_rewrite(95),rewrite([325(3),325(8),325(9),374(13),374(7),374(7),374(9)])].
% 43.76/44.03 417 nand(nand(A,nand(B,nand(A,C))),nand(A,nand(C,D))) = A. [back_rewrite(71),rewrite([374(6),325(9),325(9),374(10)])].
% 43.76/44.03 420 nand(nand(nand(nand(nand(A,B),C),nand(D,C)),B),nand(nand(A,B),C)) = nand(nand(nand(A,B),C),nand(D,C)). [back_rewrite(65),rewrite([325(5),325(8),325(7),325(9),325(13),325(16)])].
% 43.76/44.03 426 nand(nand(A,B),nand(A,nand(B,C))) = A. [back_rewrite(42),rewrite([374(6),374(6),374(7),325(3),325(4),325(9),325(10),374(14)])].
% 43.76/44.03 437 nand(A,nand(nand(A,nand(B,C)),nand(D,nand(A,B)))) = nand(A,nand(B,C)). [back_rewrite(19),rewrite([374(4),325(6),325(12)])].
% 43.76/44.03 444 nand(nand(A,B),nand(A,nand(C,B))) = A. [back_rewrite(1),rewrite([325(3)])].
% 43.76/44.03 447 nand(A,nand(nand(A,nand(B,nand(A,nand(C,D)))),D)) = nand(A,nand(B,nand(A,nand(C,D)))). [back_rewrite(365),rewrite([374(7),374(4),374(6),374(12)])].
% 43.76/44.03 457 nand(A,nand(nand(A,B),nand(C,B))) = nand(A,B). [back_rewrite(339),rewrite([374(6)])].
% 43.76/44.03 458 nand(nand(A,nand(B,C)),nand(A,nand(D,nand(nand(A,nand(B,C)),nand(E,nand(A,C)))))) = A. [back_rewrite(336),rewrite([374(14),374(6),374(14)])].
% 43.76/44.03 477 nand(nand(A,B),A) = nand(A,nand(A,B)). [para(375(a,1),325(a,1,2))].
% 43.76/44.03 490 nand(A,nand(nand(A,nand(B,C)),B)) = nand(A,nand(B,C)). [para(408(a,1),375(a,1,1))].
% 43.76/44.03 498 nand(nand(A,A),nand(nand(B,nand(A,A)),nand(A,C))) = nand(B,nand(A,A)). [para(318(a,1),426(a,1,1))].
% 43.76/44.03 502 nand(A,nand(nand(A,B),nand(B,C))) = nand(A,B). [para(426(a,1),375(a,1,1))].
% 43.76/44.03 508 nand(nand(nand(A,nand(nand(B,C),nand(B,C))),C),nand(nand(B,C),nand(B,C))) = nand(A,nand(nand(B,C),nand(B,C))). [para(318(a,1),444(a,1,2))].
% 43.76/44.03 510 nand(nand(A,B),B) = nand(B,nand(A,B)). [para(319(a,1),477(a,1,1)),rewrite([319(6)]),flip(a)].
% 43.76/44.03 528 nand(nand(b,nand(c,b)),a) != nand(a,nand(b,nand(a,c))) # answer(prove_meredith_2_basis_2). [back_rewrite(3),rewrite([510(5)])].
% 43.76/44.03 529 nand(A,B) = nand(B,A). [para(319(a,1),338(a,1,1,1,2)),rewrite([319(3),319(4)])].
% 43.76/44.03 531 nand(nand(nand(A,B),nand(C,D)),nand(B,nand(D,nand(nand(A,B),nand(C,D))))) = nand(D,nand(nand(A,B),nand(C,D))). [para(338(a,1),375(a,1,1)),rewrite([529(7),529(8),529(13)])].
% 43.76/44.03 534 nand(A,nand(B,nand(A,B))) = nand(A,A). [para(408(a,1),338(a,1,1)),flip(a)].
% 43.76/44.03 536 nand(A,nand(B,nand(A,nand(C,B)))) = nand(A,nand(C,B)). [para(338(a,1),309(a,2)),rewrite([529(3),529(4),529(7),529(8),529(10),457(10)])].
% 43.76/44.03 542 nand(a,nand(b,nand(b,c))) != nand(a,nand(b,nand(a,c))) # answer(prove_meredith_2_basis_2). [back_rewrite(528),rewrite([529(4),529(7)])].
% 43.76/44.03 550 nand(nand(nand(A,B),nand(A,B)),nand(B,nand(C,nand(nand(A,B),nand(A,B))))) = nand(C,nand(nand(A,B),nand(A,B))). [back_rewrite(508),rewrite([529(5),529(9)])].
% 43.76/44.03 553 nand(A,nand(B,nand(A,nand(B,C)))) = nand(A,nand(B,C)). [back_rewrite(490),rewrite([529(3)])].
% 43.76/44.03 563 nand(A,nand(B,nand(A,nand(C,nand(A,nand(D,B)))))) = nand(A,nand(C,nand(A,nand(D,B)))). [back_rewrite(447),rewrite([529(5)])].
% 43.76/44.03 566 nand(nand(A,nand(B,C)),nand(C,nand(nand(A,nand(B,C)),nand(A,D)))) = nand(nand(A,nand(B,C)),nand(A,D)). [back_rewrite(420),rewrite([529(2),529(3),529(5),529(7),529(8),529(10),529(11)])].
% 43.76/44.03 580 nand(nand(A,B),nand(A,nand(C,B))) = A. [back_rewrite(375),rewrite([529(4)])].
% 43.76/44.03 585 nand(nand(A,B),nand(B,nand(A,C))) = B. [para(529(a,1),426(a,1,1))].
% 43.76/44.03 591 nand(A,nand(B,nand(B,A))) = nand(A,A). [para(534(a,1),529(a,2)),rewrite([529(1),529(3)])].
% 43.76/44.03 596 nand(nand(A,nand(B,nand(B,C))),nand(A,nand(C,C))) = A. [para(534(a,1),580(a,1,2,2)),rewrite([529(1)])].
% 43.76/44.03 606 nand(nand(A,B),nand(B,nand(C,A))) = B. [para(319(a,1),585(a,1,2,2)),rewrite([529(2),529(3),529(4)])].
% 43.76/44.03 610 nand(A,nand(nand(B,A),nand(B,C))) = nand(B,A). [para(585(a,1),580(a,1,2)),rewrite([529(4)])].
% 43.76/44.03 618 nand(A,nand(nand(B,C),nand(B,A))) = nand(B,A). [para(426(a,1),606(a,1,2)),rewrite([529(2),529(4),529(5)])].
% 43.76/44.03 632 nand(nand(A,B),nand(B,nand(C,nand(B,nand(A,D))))) = B. [para(585(a,1),502(a,1,2,1)),rewrite([529(4),585(10)])].
% 43.76/44.03 659 nand(nand(nand(A,B),nand(A,C)),nand(nand(C,D),nand(A,C))) = nand(A,C). [para(618(a,1),618(a,1,2,2)),rewrite([618(11)])].
% 43.76/44.03 676 nand(A,nand(nand(A,A),nand(B,C))) = nand(A,A). [para(337(a,1),417(a,1,1))].
% 43.76/44.03 719 nand(A,nand(nand(A,nand(B,C)),nand(B,nand(A,nand(B,C))))) = nand(A,A). [para(536(a,1),534(a,1,2,2)),rewrite([529(1),529(4),529(6)])].
% 43.76/44.03 722 nand(A,nand(B,B)) = nand(A,nand(A,B)). [para(591(a,1),536(a,1,2))].
% 43.76/44.03 730 nand(A,nand(B,nand(A,nand(C,nand(A,B))))) = nand(A,A). [para(417(a,1),536(a,1,2)),flip(a)].
% 43.76/44.03 738 nand(A,nand(A,nand(B,B))) = nand(A,B). [para(319(a,1),722(a,1,2)),flip(a)].
% 43.76/44.03 741 nand(A,nand(B,B)) = nand(A,nand(B,A)). [para(722(a,1),529(a,2)),rewrite([529(2),529(3)])].
% 43.76/44.03 743 nand(nand(A,nand(B,B)),nand(A,nand(C,nand(B,C)))) = A. [para(722(a,1),580(a,1,2,2)),rewrite([529(3)])].
% 43.76/44.03 744 nand(nand(A,nand(B,C)),nand(A,nand(B,nand(C,C)))) = A. [para(722(a,2),580(a,1,2,2))].
% 43.76/44.03 784 nand(A,nand(nand(A,nand(B,C)),nand(B,B))) = nand(A,A). [back_rewrite(719),rewrite([741(6,R)])].
% 43.76/44.03 785 nand(nand(A,nand(B,B)),nand(nand(A,C),nand(A,B))) = nand(A,B). [para(738(a,1),618(a,1,2,2)),rewrite([738(9)])].
% 43.76/44.03 1110 nand(A,nand(B,nand(C,nand(A,B)))) = nand(A,nand(B,B)). [para(730(a,1),553(a,1,2)),rewrite([529(3)]),flip(a)].
% 43.76/44.03 1374 nand(A,nand(B,nand(B,B))) = nand(A,A). [para(744(a,1),744(a,1,2)),rewrite([529(2),529(6),580(6),529(3)]),flip(a)].
% 43.76/44.03 1377 nand(nand(A,A),nand(B,nand(B,B))) = A. [para(1374(a,2),319(a,1))].
% 43.76/44.03 1401 nand(A,nand(B,nand(C,nand(C,C)))) = nand(A,nand(A,B)). [para(1374(a,2),722(a,1,2))].
% 43.76/44.03 1458 nand(A,nand(nand(B,nand(B,B)),nand(B,nand(B,B)))) = nand(B,nand(B,B)). [para(1377(a,1),319(a,1,1))].
% 43.76/44.03 1459 nand(nand(A,nand(A,A)),nand(B,B)) = B. [para(1377(a,1),529(a,1)),flip(a)].
% 43.76/44.03 1462 nand(A,nand(nand(B,nand(B,B)),nand(A,C))) = nand(A,C). [para(1377(a,1),536(a,1,2,2,2)),rewrite([1377(9)])].
% 43.76/44.03 1463 nand(A,nand(A,A)) = nand(B,nand(B,B)). [para(1377(a,1),722(a,2,2)),rewrite([1458(7),529(4)])].
% 43.76/44.03 1465 nand(nand(A,nand(B,nand(B,B))),nand(C,nand(C,C))) = A. [para(1377(a,1),596(a,1,1,2,2)),rewrite([529(2),1458(9)])].
% 43.76/44.03 1468 nand(A,nand(A,A)) = c_0. [new_symbol(1463)].
% 43.76/44.03 1471 nand(c_0,nand(A,c_0)) = A. [back_rewrite(1465),rewrite([1468(2),1468(4),529(4)])].
% 43.76/44.03 1473 nand(A,nand(c_0,nand(A,B))) = nand(A,B). [back_rewrite(1462),rewrite([1468(2)])].
% 43.76/44.03 1475 nand(c_0,nand(A,A)) = A. [back_rewrite(1459),rewrite([1468(2)])].
% 43.76/44.03 1476 nand(A,nand(c_0,c_0)) = c_0. [back_rewrite(1458),rewrite([1468(2),1468(3),1468(6)])].
% 43.76/44.03 1491 nand(A,nand(B,c_0)) = nand(A,nand(A,B)). [back_rewrite(1401),rewrite([1468(2)])].
% 43.76/44.03 1504 nand(A,c_0) = nand(A,A). [back_rewrite(1374),rewrite([1468(2)])].
% 43.76/44.03 1598 nand(nand(c_0,nand(A,B)),nand(B,nand(C,nand(c_0,nand(A,B))))) = nand(C,nand(c_0,nand(A,B))). [back_rewrite(550),rewrite([1504(3,R),529(3),1504(6,R),529(6),1504(12,R),529(12)])].
% 43.76/44.03 1701 nand(A,nand(c_0,nand(B,nand(B,A)))) = c_0. [para(1475(a,1),596(a,1,2)),rewrite([529(5)])].
% 43.76/44.03 1706 nand(A,nand(c_0,nand(B,nand(A,B)))) = c_0. [para(1475(a,1),743(a,1,1))].
% 43.76/44.03 1721 nand(c_0,nand(c_0,nand(A,B))) = nand(A,B). [para(676(a,1),458(a,1,2,2)),rewrite([1504(3,R),529(3),1504(7,R),529(7),741(8,R),1476(8),529(5)])].
% 43.76/44.03 1805 nand(nand(A,B),nand(C,nand(c_0,nand(A,B)))) = nand(c_0,nand(A,B)). [para(498(a,1),437(a,1,2)),rewrite([1504(4,R),529(4),1504(9,R),529(9)])].
% 43.76/44.03 1841 nand(nand(c_0,nand(A,B)),nand(B,nand(A,B))) = nand(A,B). [para(337(a,1),531(a,1,2,2)),rewrite([1504(4,R),529(4),1805(6),1504(9,R),529(9),1504(13,R),529(13),1805(15),1504(13,R),529(11),1721(11)])].
% 43.76/44.03 1847 nand(nand(A,nand(B,C)),nand(c_0,nand(B,C))) = nand(B,C). [para(426(a,1),531(a,1,2,2)),rewrite([529(3),591(5),1504(3,R),529(3),1841(6),529(3),529(6),591(8),1504(6,R),529(6)]),flip(a)].
% 43.76/44.03 2006 nand(nand(A,c_0),nand(B,nand(c_0,nand(A,C)))) = A. [para(387(a,1),1473(a,1,2)),rewrite([529(2),529(4),1504(5,R),529(4),1471(4),529(2),529(5),1476(9),529(7),1471(7),529(4)]),flip(a)].
% 43.76/44.03 2165 nand(A,nand(B,c_0)) = nand(A,nand(B,A)). [para(1491(a,1),529(a,2)),rewrite([529(3),529(4)])].
% 43.76/44.03 2171 nand(nand(A,B),nand(c_0,nand(B,nand(A,C)))) = nand(B,nand(A,B)). [para(585(a,1),1491(a,2,2)),rewrite([529(5),529(8)])].
% 43.76/44.03 2484 nand(nand(A,nand(B,C)),nand(c_0,nand(A,nand(A,C)))) = c_0. [para(580(a,1),1701(a,1,2,2,2)),rewrite([529(5)])].
% 43.76/44.03 2491 nand(nand(c_0,nand(A,nand(A,B))),nand(c_0,nand(B,C))) = c_0. [para(1701(a,1),610(a,1,2,1)),rewrite([1701(13)])].
% 43.76/44.03 2535 nand(A,nand(c_0,nand(nand(A,B),nand(c_0,nand(B,C))))) = c_0. [para(502(a,1),1706(a,1,2,2,2)),rewrite([529(6),1491(6,R),529(5)])].
% 43.76/44.03 3006 nand(A,nand(nand(c_0,nand(B,C)),nand(A,B))) = nand(A,A). [para(2006(a,1),730(a,1,2,2,2))].
% 43.76/44.03 3681 nand(A,nand(B,nand(A,nand(C,nand(B,B))))) = nand(A,A). [para(319(a,1),784(a,1,2,2)),rewrite([529(2),529(4)])].
% 43.76/44.03 3683 nand(A,nand(nand(B,B),nand(A,nand(B,C)))) = nand(A,A). [para(529(a,1),784(a,1,2))].
% 43.76/44.03 4358 nand(A,nand(c_0,nand(B,nand(C,nand(A,B))))) = nand(A,B). [para(417(a,1),1110(a,1,2)),rewrite([529(2),529(5),1504(8,R),529(6)]),flip(a)].
% 43.76/44.03 7022 nand(nand(A,nand(B,C)),nand(c_0,nand(A,nand(C,A)))) = c_0. [para(529(a,1),2484(a,1,1)),rewrite([529(2),529(4)])].
% 43.76/44.03 7188 nand(nand(A,nand(B,nand(B,C))),nand(A,nand(C,D))) = A. [para(2491(a,1),596(a,1,1,2,2)),rewrite([529(6),1721(6),1504(10,R),529(8),1721(8)])].
% 43.76/44.03 8269 nand(A,nand(c_0,nand(B,nand(c_0,nand(C,nand(A,B)))))) = c_0. [para(563(a,1),2535(a,1,2))].
% 43.76/44.03 9631 nand(nand(c_0,nand(A,B)),nand(c_0,nand(A,C))) = nand(C,nand(c_0,nand(A,B))). [para(3006(a,1),1110(a,1,2,2)),rewrite([529(4),319(6),529(4),529(8),529(9),1504(10,R),529(10)]),flip(a)].
% 43.76/44.03 10223 nand(A,nand(c_0,nand(B,nand(C,nand(A,A))))) = nand(A,B). [para(3681(a,1),1110(a,1,2,2)),rewrite([411(5),1504(8,R),529(6)]),flip(a)].
% 43.76/44.03 10342 nand(nand(A,A),nand(c_0,nand(B,nand(A,C)))) = nand(B,nand(A,A)). [para(3683(a,1),1110(a,1,2,2)),rewrite([411(5),529(2),1504(8,R),529(7)]),flip(a)].
% 43.76/44.03 11305 nand(A,nand(B,nand(C,nand(A,A)))) = nand(A,nand(B,c_0)). [para(3681(a,1),4358(a,1,2,2,2)),rewrite([411(6),529(2)]),flip(a)].
% 43.76/44.03 12573 nand(A,nand(c_0,nand(B,nand(C,nand(A,C))))) = nand(A,B). [para(7188(a,1),1110(a,1,2)),rewrite([529(2),529(5),1504(8,R),529(6)]),flip(a)].
% 43.76/44.03 13365 nand(A,nand(B,nand(c_0,nand(C,nand(A,B))))) = nand(A,A). [para(8269(a,1),534(a,1,2,2)),rewrite([529(9),1721(9)])].
% 43.76/44.03 14636 nand(nand(c_0,nand(A,B)),nand(c_0,nand(C,nand(D,nand(A,B))))) = nand(C,nand(c_0,nand(A,B))). [para(10223(a,1),566(a,1,2,2)),rewrite([529(7),1598(9),1504(15,R),529(13),1721(13)]),flip(a)].
% 43.76/44.03 14965 nand(nand(c_0,nand(A,B)),nand(C,nand(D,nand(A,B)))) = nand(nand(c_0,nand(A,B)),nand(C,c_0)). [para(1847(a,1),11305(a,1,2,2,2))].
% 43.76/44.03 15372 nand(nand(A,nand(B,C)),nand(c_0,nand(D,nand(A,nand(A,C))))) = nand(D,nand(A,nand(B,C))). [para(7022(a,1),12573(a,1,2,2,2,2)),rewrite([529(5),529(9),1721(9),529(11)])].
% 43.76/44.03 15500 nand(A,nand(c_0,nand(B,nand(A,nand(A,C))))) = nand(B,nand(c_0,nand(A,C))). [para(13365(a,1),618(a,1,2)),rewrite([529(3),1504(8,R),529(8),529(9),14636(9),529(7)]),flip(a)].
% 43.76/44.03 16884 nand(A,nand(B,nand(c_0,nand(A,C)))) = nand(A,nand(B,nand(A,nand(A,C)))). [para(632(a,1),785(a,1,2)),rewrite([1504(7,R),529(5),15500(6),529(5)])].
% 43.76/44.03 17649 nand(nand(nand(A,B),nand(C,A)),nand(c_0,nand(C,D))) = nand(D,nand(c_0,nand(C,A))). [para(659(a,1),2171(a,1,2,2)),rewrite([529(3),529(7),529(9),14965(9),529(6),9631(7),529(6),529(10),2165(13,R),529(10)]),flip(a)].
% 43.76/44.03 20380 nand(A,nand(c_0,nand(B,C))) = nand(C,nand(c_0,nand(B,A))). [para(659(a,1),10342(a,1,2,2)),rewrite([1504(3,R),529(3),529(5),9631(7),529(6),1504(10,R),529(10),17649(11)])].
% 43.76/44.03 20433 nand(A,nand(B,nand(c_0,nand(A,C)))) = nand(A,nand(C,B)). [para(20380(a,1),722(a,2,2)),rewrite([1504(7,R),529(5),1721(5),529(4)]),flip(a)].
% 43.76/44.03 20709 nand(A,nand(B,nand(A,nand(A,C)))) = nand(A,nand(B,C)). [back_rewrite(16884),rewrite([20433(5),529(1)]),flip(a)].
% 43.76/44.03 21626 nand(A,nand(B,nand(B,C))) = nand(A,nand(B,nand(A,C))). [para(20709(a,1),319(a,1,1)),rewrite([1504(9,R),529(7),15372(8)]),flip(a)].
% 43.76/44.03 21627 $F # answer(prove_meredith_2_basis_2). [resolve(21626,a,542,a)].
% 43.76/44.03
% 43.76/44.03 % SZS output end Refutation
% 43.76/44.03 ============================== end of proof ==========================
% 43.76/44.03
% 43.76/44.03 ============================== STATISTICS ============================
% 43.76/44.03
% 43.76/44.03 Given=553. Generated=897716. Kept=21625. proofs=1.
% 43.76/44.03 Usable=325. Sos=9028. Demods=8823. Limbo=0, Disabled=12273. Hints=0.
% 43.76/44.03 Megabytes=20.16.
% 43.76/44.03 User_CPU=42.53, System_CPU=0.54, Wall_clock=43.
% 43.76/44.03
% 43.76/44.03 ============================== end of statistics =====================
% 43.76/44.03
% 43.76/44.03 ============================== end of search =========================
% 43.76/44.03
% 43.76/44.03 THEOREM PROVED
% 43.76/44.03 % SZS status Unsatisfiable
% 43.76/44.03
% 43.76/44.03 Exiting with 1 proof.
% 43.76/44.03
% 43.76/44.03 Process 25392 exit (max_proofs) Wed Jun 1 19:32:17 2022
% 43.76/44.03 Prover9 interrupted
%------------------------------------------------------------------------------