TSTP Solution File: BOO039-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO039-1 : TPTP v8.1.0. Released v2.5.0.
% 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 : Thu Jul 14 23:48:05 EDT 2022
% Result : Unsatisfiable 42.74s 43.02s
% Output : Refutation 42.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO039-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n019.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 : Wed Jun 1 19:42:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 42.74/43.02 ============================== Prover9 ===============================
% 42.74/43.02 Prover9 (32) version 2009-11A, November 2009.
% 42.74/43.02 Process 29267 was started by sandbox on n019.cluster.edu,
% 42.74/43.02 Wed Jun 1 19:42:26 2022
% 42.74/43.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29114_n019.cluster.edu".
% 42.74/43.02 ============================== end of head ===========================
% 42.74/43.02
% 42.74/43.02 ============================== INPUT =================================
% 42.74/43.02
% 42.74/43.02 % Reading from file /tmp/Prover9_29114_n019.cluster.edu
% 42.74/43.02
% 42.74/43.02 set(prolog_style_variables).
% 42.74/43.02 set(auto2).
% 42.74/43.02 % set(auto2) -> set(auto).
% 42.74/43.02 % set(auto) -> set(auto_inference).
% 42.74/43.02 % set(auto) -> set(auto_setup).
% 42.74/43.02 % set(auto_setup) -> set(predicate_elim).
% 42.74/43.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 42.74/43.02 % set(auto) -> set(auto_limits).
% 42.74/43.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 42.74/43.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 42.74/43.02 % set(auto) -> set(auto_denials).
% 42.74/43.02 % set(auto) -> set(auto_process).
% 42.74/43.02 % set(auto2) -> assign(new_constants, 1).
% 42.74/43.02 % set(auto2) -> assign(fold_denial_max, 3).
% 42.74/43.02 % set(auto2) -> assign(max_weight, "200.000").
% 42.74/43.02 % set(auto2) -> assign(max_hours, 1).
% 42.74/43.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 42.74/43.02 % set(auto2) -> assign(max_seconds, 0).
% 42.74/43.02 % set(auto2) -> assign(max_minutes, 5).
% 42.74/43.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 42.74/43.02 % set(auto2) -> set(sort_initial_sos).
% 42.74/43.02 % set(auto2) -> assign(sos_limit, -1).
% 42.74/43.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 42.74/43.02 % set(auto2) -> assign(max_megs, 400).
% 42.74/43.02 % set(auto2) -> assign(stats, some).
% 42.74/43.02 % set(auto2) -> clear(echo_input).
% 42.74/43.02 % set(auto2) -> set(quiet).
% 42.74/43.02 % set(auto2) -> clear(print_initial_clauses).
% 42.74/43.02 % set(auto2) -> clear(print_given).
% 42.74/43.02 assign(lrs_ticks,-1).
% 42.74/43.02 assign(sos_limit,10000).
% 42.74/43.02 assign(order,kbo).
% 42.74/43.02 set(lex_order_vars).
% 42.74/43.02 clear(print_given).
% 42.74/43.02
% 42.74/43.02 % formulas(sos). % not echoed (2 formulas)
% 42.74/43.02
% 42.74/43.02 ============================== end of input ==========================
% 42.74/43.02
% 42.74/43.02 % From the command line: assign(max_seconds, 300).
% 42.74/43.02
% 42.74/43.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 42.74/43.02
% 42.74/43.02 % Formulas that are not ordinary clauses:
% 42.74/43.02
% 42.74/43.02 ============================== end of process non-clausal formulas ===
% 42.74/43.02
% 42.74/43.02 ============================== PROCESS INITIAL CLAUSES ===============
% 42.74/43.02
% 42.74/43.02 ============================== PREDICATE ELIMINATION =================
% 42.74/43.02
% 42.74/43.02 ============================== end predicate elimination =============
% 42.74/43.02
% 42.74/43.02 Auto_denials:
% 42.74/43.02 % copying label prove_meredith_2_basis to answer in negative clause
% 42.74/43.02
% 42.74/43.02 Term ordering decisions:
% 42.74/43.02 Function symbol KB weights: a=1. b=1. c=1. nand=1.
% 42.74/43.02
% 42.74/43.02 ============================== end of process initial clauses ========
% 42.74/43.02
% 42.74/43.02 ============================== CLAUSES FOR SEARCH ====================
% 42.74/43.02
% 42.74/43.02 ============================== end of clauses for search =============
% 42.74/43.02
% 42.74/43.02 ============================== SEARCH ================================
% 42.74/43.02
% 42.74/43.02 % Starting search at 0.01 seconds.
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=61.000, iters=3412
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=59.000, iters=3387
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=57.000, iters=3357
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=51.000, iters=3355
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=49.000, iters=3405
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=47.000, iters=3358
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=45.000, iters=3546
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=43.000, iters=3453
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=41.000, iters=3361
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=39.000, iters=3370
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=37.000, iters=3387
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=35.000, iters=3353
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=33.000, iters=3346
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=31.000, iters=3345
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=29.000, iters=3379
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=27.000, iters=3336
% 42.74/43.02
% 42.74/43.02 Low Water (displace): id=2980, wt=125.000
% 42.74/43.02
% 42.74/43.02 Low Water (displace): id=4709, wt=123.000
% 42.74/43.02
% 42.74/43.02 Low Water (displace): id=2935, wt=121.000
% 42.74/43.02
% 42.74/43.02 Low Water (displace): id=14531, wt=25.000
% 42.74/43.02
% 42.74/43.02 Low Water (displace): id=14585, wt=23.000
% 42.74/43.02
% 42.74/43.02 Low Water (displace): id=14694, wt=21.000
% 42.74/43.02
% 42.74/43.02 Low Water (displace): id=14701, wt=19.000
% 42.74/43.02
% 42.74/43.02 Low Water (keep): wt=25.000, iters=3340
% 42.74/43.02
% 42.74/43.02 ============================== PROOF =================================
% 42.74/43.02 % SZS status Unsatisfiable
% 42.74/43.02 % SZS output start Refutation
% 42.74/43.02
% 42.74/43.02 % Proof 1 at 41.52 (+ 0.51) seconds: prove_meredith_2_basis.
% 42.74/43.02 % Length of proof is 150.
% 42.74/43.02 % Level of proof is 30.
% 42.74/43.02 % Maximum clause weight is 129.000.
% 42.74/43.02 % Given clauses 554.
% 42.74/43.02
% 42.74/43.02 1 nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,A))) = B # label(sh_1) # label(axiom). [assumption].
% 42.74/43.02 2 nand(nand(a,a),nand(b,a)) != a | nand(a,nand(b,nand(a,c))) != nand(nand(nand(c,b),b),a) # label(prove_meredith_2_basis) # label(negated_conjecture) # answer(prove_meredith_2_basis). [assumption].
% 42.74/43.02 3 nand(nand(a,a),nand(b,a)) != a | nand(nand(nand(c,b),b),a) != nand(a,nand(b,nand(a,c))) # answer(prove_meredith_2_basis). [copy(2),flip(b)].
% 42.74/43.02 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))].
% 42.74/43.02 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))].
% 42.74/43.02 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))].
% 42.74/43.02 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))].
% 42.74/43.02 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))].
% 42.74/43.02 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))].
% 42.74/43.02 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)])].
% 42.74/43.02 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)])].
% 42.74/43.02 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))].
% 42.74/43.02 40 nand(A,nand(nand(A,A),A)) = nand(A,A). [para(17(a,1),4(a,1,2)),rewrite([17(8)]),flip(a)].
% 42.74/43.02 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))].
% 42.74/43.02 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)])].
% 42.74/43.02 52 nand(nand(A,nand(nand(nand(B,B),A),A)),B) = nand(B,B). [back_rewrite(36),rewrite([40(3),40(8)])].
% 42.74/43.02 54 nand(nand(A,A),nand(A,nand(B,A))) = A. [para(40(a,1),1(a,1,1))].
% 42.74/43.02 55 nand(nand(A,A),nand(A,A)) = A. [para(40(a,1),1(a,1,2)),rewrite([40(3)])].
% 42.74/43.02 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))].
% 42.74/43.02 64 nand(nand(A,nand(nand(B,A),A)),nand(B,B)) = B. [back_rewrite(43),rewrite([54(4),54(9)])].
% 42.74/43.02 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))].
% 42.74/43.02 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)])].
% 42.74/43.02 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))].
% 42.74/43.02 100 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)])].
% 42.74/43.02 138 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)])].
% 42.74/43.02 150 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)].
% 42.74/43.02 185 nand(nand(A,A),nand(B,A)) = A. [para(150(a,1),1(a,1,2)),rewrite([40(3)])].
% 42.74/43.02 195 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)])].
% 42.74/43.02 199 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)])].
% 42.74/43.02 208 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))].
% 42.74/43.02 212 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))].
% 42.74/43.02 215 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)])].
% 42.74/43.02 217 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)])].
% 42.74/43.02 223 nand(nand(nand(c,b),b),a) != nand(a,nand(b,nand(a,c))) # answer(prove_meredith_2_basis). [back_rewrite(3),rewrite([185(7)]),xx(a)].
% 42.74/43.02 249 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))].
% 42.74/43.02 291 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))].
% 42.74/43.02 296 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)])].
% 42.74/43.02 297 nand(nand(A,A),nand(B,nand(nand(A,B),B))) = A. [para(6(a,1),185(a,1,2))].
% 42.74/43.02 300 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)])].
% 42.74/43.02 310 nand(nand(nand(A,B),nand(A,B)),B) = nand(A,B). [para(185(a,1),185(a,1,2))].
% 42.74/43.02 318 nand(nand(nand(A,B),B),nand(nand(A,B),nand(nand(A,B),B))) = nand(A,B). [back_rewrite(217),rewrite([310(4),310(9),215(8),310(7)])].
% 42.74/43.02 319 nand(nand(A,nand(B,B)),B) = nand(B,B). [back_rewrite(212),rewrite([310(7),310(13),318(12)])].
% 42.74/43.02 320 nand(nand(A,B),nand(B,B)) = B. [back_rewrite(208),rewrite([310(4),310(7),318(7)])].
% 42.74/43.02 326 nand(A,nand(nand(B,A),A)) = nand(B,A). [back_rewrite(150),rewrite([310(4)])].
% 42.74/43.02 337 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(300),rewrite([326(6),326(11),326(13),326(24)])].
% 42.74/43.02 338 nand(nand(A,A),nand(A,B)) = A. [back_rewrite(297),rewrite([326(4)])].
% 42.74/43.02 339 nand(nand(nand(A,nand(B,C)),C),A) = nand(A,nand(B,C)). [back_rewrite(296),rewrite([326(6),326(5),326(10)])].
% 42.74/43.02 340 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(291),rewrite([326(9),326(13)])].
% 42.74/43.02 366 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(249),rewrite([326(3),326(10),326(28),326(40)])].
% 42.74/43.02 375 nand(nand(A,B),nand(A,nand(A,B))) = A. [back_rewrite(199),rewrite([338(4)])].
% 42.74/43.02 376 nand(nand(A,nand(B,C)),nand(A,C)) = A. [back_rewrite(195),rewrite([326(6)])].
% 42.74/43.02 388 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([326(3),326(9),375(14),326(3),326(7),326(8),375(11),326(4),326(13),326(17),326(18),375(21)])].
% 42.74/43.02 409 nand(nand(A,nand(B,C)),nand(A,B)) = A. [back_rewrite(100),rewrite([326(3),326(4),326(6),326(6)])].
% 42.74/43.02 412 nand(nand(A,B),nand(A,A)) = A. [back_rewrite(95),rewrite([326(3),326(8),326(9),375(13),375(7),375(7),375(9)])].
% 42.74/43.02 418 nand(nand(A,nand(B,nand(A,C))),nand(A,nand(C,D))) = A. [back_rewrite(71),rewrite([375(6),326(9),326(9),375(10)])].
% 42.74/43.02 421 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([326(5),326(8),326(7),326(9),326(13),326(16)])].
% 42.74/43.02 427 nand(nand(A,B),nand(A,nand(B,C))) = A. [back_rewrite(42),rewrite([375(6),375(6),375(7),326(3),326(4),326(9),326(10),375(14)])].
% 42.74/43.02 438 nand(A,nand(nand(A,nand(B,C)),nand(D,nand(A,B)))) = nand(A,nand(B,C)). [back_rewrite(19),rewrite([375(4),326(6),326(12)])].
% 42.74/43.02 445 nand(nand(A,B),nand(A,nand(C,B))) = A. [back_rewrite(1),rewrite([326(3)])].
% 42.74/43.02 448 nand(A,nand(nand(A,nand(B,nand(A,nand(C,D)))),D)) = nand(A,nand(B,nand(A,nand(C,D)))). [back_rewrite(366),rewrite([375(7),375(4),375(6),375(12)])].
% 42.74/43.02 458 nand(A,nand(nand(A,B),nand(C,B))) = nand(A,B). [back_rewrite(340),rewrite([375(6)])].
% 42.74/43.02 459 nand(nand(A,nand(B,C)),nand(A,nand(D,nand(nand(A,nand(B,C)),nand(E,nand(A,C)))))) = A. [back_rewrite(337),rewrite([375(14),375(6),375(14)])].
% 42.74/43.02 478 nand(nand(A,B),A) = nand(A,nand(A,B)). [para(376(a,1),326(a,1,2))].
% 42.74/43.02 491 nand(A,nand(nand(A,nand(B,C)),B)) = nand(A,nand(B,C)). [para(409(a,1),376(a,1,1))].
% 42.74/43.02 499 nand(nand(A,A),nand(nand(B,nand(A,A)),nand(A,C))) = nand(B,nand(A,A)). [para(319(a,1),427(a,1,1))].
% 42.74/43.02 503 nand(A,nand(nand(A,B),nand(B,C))) = nand(A,B). [para(427(a,1),376(a,1,1))].
% 42.74/43.02 509 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(319(a,1),445(a,1,2))].
% 42.74/43.02 511 nand(nand(A,B),B) = nand(B,nand(A,B)). [para(320(a,1),478(a,1,1)),rewrite([320(6)]),flip(a)].
% 42.74/43.02 529 nand(nand(b,nand(c,b)),a) != nand(a,nand(b,nand(a,c))) # answer(prove_meredith_2_basis). [back_rewrite(223),rewrite([511(5)])].
% 42.74/43.02 530 nand(A,B) = nand(B,A). [para(320(a,1),339(a,1,1,1,2)),rewrite([320(3),320(4)])].
% 42.74/43.02 532 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(339(a,1),376(a,1,1)),rewrite([530(7),530(8),530(13)])].
% 42.74/43.02 535 nand(A,nand(B,nand(A,B))) = nand(A,A). [para(409(a,1),339(a,1,1)),flip(a)].
% 42.74/43.02 537 nand(A,nand(B,nand(A,nand(C,B)))) = nand(A,nand(C,B)). [para(339(a,1),310(a,2)),rewrite([530(3),530(4),530(7),530(8),530(10),458(10)])].
% 42.74/43.02 543 nand(a,nand(b,nand(b,c))) != nand(a,nand(b,nand(a,c))) # answer(prove_meredith_2_basis). [back_rewrite(529),rewrite([530(4),530(7)])].
% 42.74/43.02 551 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(509),rewrite([530(5),530(9)])].
% 42.74/43.02 554 nand(A,nand(B,nand(A,nand(B,C)))) = nand(A,nand(B,C)). [back_rewrite(491),rewrite([530(3)])].
% 42.74/43.02 564 nand(A,nand(B,nand(A,nand(C,nand(A,nand(D,B)))))) = nand(A,nand(C,nand(A,nand(D,B)))). [back_rewrite(448),rewrite([530(5)])].
% 42.74/43.02 567 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(421),rewrite([530(2),530(3),530(5),530(7),530(8),530(10),530(11)])].
% 42.74/43.02 581 nand(nand(A,B),nand(A,nand(C,B))) = A. [back_rewrite(376),rewrite([530(4)])].
% 42.74/43.02 586 nand(nand(A,B),nand(B,nand(A,C))) = B. [para(530(a,1),427(a,1,1))].
% 42.74/43.02 592 nand(A,nand(B,nand(B,A))) = nand(A,A). [para(535(a,1),530(a,2)),rewrite([530(1),530(3)])].
% 42.74/43.02 597 nand(nand(A,nand(B,nand(B,C))),nand(A,nand(C,C))) = A. [para(535(a,1),581(a,1,2,2)),rewrite([530(1)])].
% 42.74/43.02 607 nand(nand(A,B),nand(B,nand(C,A))) = B. [para(320(a,1),586(a,1,2,2)),rewrite([530(2),530(3),530(4)])].
% 42.74/43.02 611 nand(A,nand(nand(B,A),nand(B,C))) = nand(B,A). [para(586(a,1),581(a,1,2)),rewrite([530(4)])].
% 42.74/43.02 619 nand(A,nand(nand(B,C),nand(B,A))) = nand(B,A). [para(427(a,1),607(a,1,2)),rewrite([530(2),530(4),530(5)])].
% 42.74/43.02 633 nand(nand(A,B),nand(B,nand(C,nand(B,nand(A,D))))) = B. [para(586(a,1),503(a,1,2,1)),rewrite([530(4),586(10)])].
% 42.74/43.02 660 nand(nand(nand(A,B),nand(A,C)),nand(nand(C,D),nand(A,C))) = nand(A,C). [para(619(a,1),619(a,1,2,2)),rewrite([619(11)])].
% 42.74/43.02 677 nand(A,nand(nand(A,A),nand(B,C))) = nand(A,A). [para(338(a,1),418(a,1,1))].
% 42.74/43.02 720 nand(A,nand(nand(A,nand(B,C)),nand(B,nand(A,nand(B,C))))) = nand(A,A). [para(537(a,1),535(a,1,2,2)),rewrite([530(1),530(4),530(6)])].
% 42.74/43.02 723 nand(A,nand(B,B)) = nand(A,nand(A,B)). [para(592(a,1),537(a,1,2))].
% 42.74/43.02 731 nand(A,nand(B,nand(A,nand(C,nand(A,B))))) = nand(A,A). [para(418(a,1),537(a,1,2)),flip(a)].
% 42.74/43.02 739 nand(A,nand(A,nand(B,B))) = nand(A,B). [para(320(a,1),723(a,1,2)),flip(a)].
% 42.74/43.02 742 nand(A,nand(B,B)) = nand(A,nand(B,A)). [para(723(a,1),530(a,2)),rewrite([530(2),530(3)])].
% 42.74/43.02 744 nand(nand(A,nand(B,B)),nand(A,nand(C,nand(B,C)))) = A. [para(723(a,1),581(a,1,2,2)),rewrite([530(3)])].
% 42.74/43.02 745 nand(nand(A,nand(B,C)),nand(A,nand(B,nand(C,C)))) = A. [para(723(a,2),581(a,1,2,2))].
% 42.74/43.02 785 nand(A,nand(nand(A,nand(B,C)),nand(B,B))) = nand(A,A). [back_rewrite(720),rewrite([742(6,R)])].
% 42.74/43.02 786 nand(nand(A,nand(B,B)),nand(nand(A,C),nand(A,B))) = nand(A,B). [para(739(a,1),619(a,1,2,2)),rewrite([739(9)])].
% 42.74/43.02 1111 nand(A,nand(B,nand(C,nand(A,B)))) = nand(A,nand(B,B)). [para(731(a,1),554(a,1,2)),rewrite([530(3)]),flip(a)].
% 42.74/43.02 1375 nand(A,nand(B,nand(B,B))) = nand(A,A). [para(745(a,1),745(a,1,2)),rewrite([530(2),530(6),581(6),530(3)]),flip(a)].
% 42.74/43.02 1378 nand(nand(A,A),nand(B,nand(B,B))) = A. [para(1375(a,2),320(a,1))].
% 42.74/43.02 1402 nand(A,nand(B,nand(C,nand(C,C)))) = nand(A,nand(A,B)). [para(1375(a,2),723(a,1,2))].
% 42.74/43.02 1459 nand(A,nand(nand(B,nand(B,B)),nand(B,nand(B,B)))) = nand(B,nand(B,B)). [para(1378(a,1),320(a,1,1))].
% 42.74/43.02 1460 nand(nand(A,nand(A,A)),nand(B,B)) = B. [para(1378(a,1),530(a,1)),flip(a)].
% 42.74/43.02 1463 nand(A,nand(nand(B,nand(B,B)),nand(A,C))) = nand(A,C). [para(1378(a,1),537(a,1,2,2,2)),rewrite([1378(9)])].
% 42.74/43.02 1464 nand(A,nand(A,A)) = nand(B,nand(B,B)). [para(1378(a,1),723(a,2,2)),rewrite([1459(7),530(4)])].
% 42.74/43.02 1466 nand(nand(A,nand(B,nand(B,B))),nand(C,nand(C,C))) = A. [para(1378(a,1),597(a,1,1,2,2)),rewrite([530(2),1459(9)])].
% 42.74/43.02 1469 nand(A,nand(A,A)) = c_0. [new_symbol(1464)].
% 42.74/43.02 1472 nand(c_0,nand(A,c_0)) = A. [back_rewrite(1466),rewrite([1469(2),1469(4),530(4)])].
% 42.74/43.02 1474 nand(A,nand(c_0,nand(A,B))) = nand(A,B). [back_rewrite(1463),rewrite([1469(2)])].
% 42.74/43.02 1476 nand(c_0,nand(A,A)) = A. [back_rewrite(1460),rewrite([1469(2)])].
% 42.74/43.02 1477 nand(A,nand(c_0,c_0)) = c_0. [back_rewrite(1459),rewrite([1469(2),1469(3),1469(6)])].
% 42.74/43.02 1492 nand(A,nand(B,c_0)) = nand(A,nand(A,B)). [back_rewrite(1402),rewrite([1469(2)])].
% 42.74/43.02 1505 nand(A,c_0) = nand(A,A). [back_rewrite(1375),rewrite([1469(2)])].
% 42.74/43.02 1599 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(551),rewrite([1505(3,R),530(3),1505(6,R),530(6),1505(12,R),530(12)])].
% 42.74/43.02 1702 nand(A,nand(c_0,nand(B,nand(B,A)))) = c_0. [para(1476(a,1),597(a,1,2)),rewrite([530(5)])].
% 42.74/43.02 1707 nand(A,nand(c_0,nand(B,nand(A,B)))) = c_0. [para(1476(a,1),744(a,1,1))].
% 42.74/43.02 1722 nand(c_0,nand(c_0,nand(A,B))) = nand(A,B). [para(677(a,1),459(a,1,2,2)),rewrite([1505(3,R),530(3),1505(7,R),530(7),742(8,R),1477(8),530(5)])].
% 42.74/43.02 1806 nand(nand(A,B),nand(C,nand(c_0,nand(A,B)))) = nand(c_0,nand(A,B)). [para(499(a,1),438(a,1,2)),rewrite([1505(4,R),530(4),1505(9,R),530(9)])].
% 42.74/43.02 1842 nand(nand(c_0,nand(A,B)),nand(B,nand(A,B))) = nand(A,B). [para(338(a,1),532(a,1,2,2)),rewrite([1505(4,R),530(4),1806(6),1505(9,R),530(9),1505(13,R),530(13),1806(15),1505(13,R),530(11),1722(11)])].
% 42.74/43.02 1848 nand(nand(A,nand(B,C)),nand(c_0,nand(B,C))) = nand(B,C). [para(427(a,1),532(a,1,2,2)),rewrite([530(3),592(5),1505(3,R),530(3),1842(6),530(3),530(6),592(8),1505(6,R),530(6)]),flip(a)].
% 42.74/43.02 2007 nand(nand(A,c_0),nand(B,nand(c_0,nand(A,C)))) = A. [para(388(a,1),1474(a,1,2)),rewrite([530(2),530(4),1505(5,R),530(4),1472(4),530(2),530(5),1477(9),530(7),1472(7),530(4)]),flip(a)].
% 42.74/43.02 2166 nand(A,nand(B,c_0)) = nand(A,nand(B,A)). [para(1492(a,1),530(a,2)),rewrite([530(3),530(4)])].
% 42.74/43.02 2172 nand(nand(A,B),nand(c_0,nand(B,nand(A,C)))) = nand(B,nand(A,B)). [para(586(a,1),1492(a,2,2)),rewrite([530(5),530(8)])].
% 42.74/43.02 2485 nand(nand(A,nand(B,C)),nand(c_0,nand(A,nand(A,C)))) = c_0. [para(581(a,1),1702(a,1,2,2,2)),rewrite([530(5)])].
% 42.74/43.02 2492 nand(nand(c_0,nand(A,nand(A,B))),nand(c_0,nand(B,C))) = c_0. [para(1702(a,1),611(a,1,2,1)),rewrite([1702(13)])].
% 42.74/43.02 2536 nand(A,nand(c_0,nand(nand(A,B),nand(c_0,nand(B,C))))) = c_0. [para(503(a,1),1707(a,1,2,2,2)),rewrite([530(6),1492(6,R),530(5)])].
% 42.74/43.02 3007 nand(A,nand(nand(c_0,nand(B,C)),nand(A,B))) = nand(A,A). [para(2007(a,1),731(a,1,2,2,2))].
% 42.74/43.02 3682 nand(A,nand(B,nand(A,nand(C,nand(B,B))))) = nand(A,A). [para(320(a,1),785(a,1,2,2)),rewrite([530(2),530(4)])].
% 42.74/43.02 3684 nand(A,nand(nand(B,B),nand(A,nand(B,C)))) = nand(A,A). [para(530(a,1),785(a,1,2))].
% 42.74/43.02 4359 nand(A,nand(c_0,nand(B,nand(C,nand(A,B))))) = nand(A,B). [para(418(a,1),1111(a,1,2)),rewrite([530(2),530(5),1505(8,R),530(6)]),flip(a)].
% 42.74/43.02 7023 nand(nand(A,nand(B,C)),nand(c_0,nand(A,nand(C,A)))) = c_0. [para(530(a,1),2485(a,1,1)),rewrite([530(2),530(4)])].
% 42.74/43.02 7189 nand(nand(A,nand(B,nand(B,C))),nand(A,nand(C,D))) = A. [para(2492(a,1),597(a,1,1,2,2)),rewrite([530(6),1722(6),1505(10,R),530(8),1722(8)])].
% 42.74/43.02 8270 nand(A,nand(c_0,nand(B,nand(c_0,nand(C,nand(A,B)))))) = c_0. [para(564(a,1),2536(a,1,2))].
% 42.74/43.02 9632 nand(nand(c_0,nand(A,B)),nand(c_0,nand(A,C))) = nand(C,nand(c_0,nand(A,B))). [para(3007(a,1),1111(a,1,2,2)),rewrite([530(4),320(6),530(4),530(8),530(9),1505(10,R),530(10)]),flip(a)].
% 42.74/43.02 10224 nand(A,nand(c_0,nand(B,nand(C,nand(A,A))))) = nand(A,B). [para(3682(a,1),1111(a,1,2,2)),rewrite([412(5),1505(8,R),530(6)]),flip(a)].
% 42.74/43.02 10343 nand(nand(A,A),nand(c_0,nand(B,nand(A,C)))) = nand(B,nand(A,A)). [para(3684(a,1),1111(a,1,2,2)),rewrite([412(5),530(2),1505(8,R),530(7)]),flip(a)].
% 42.74/43.02 11306 nand(A,nand(B,nand(C,nand(A,A)))) = nand(A,nand(B,c_0)). [para(3682(a,1),4359(a,1,2,2,2)),rewrite([412(6),530(2)]),flip(a)].
% 42.74/43.02 12574 nand(A,nand(c_0,nand(B,nand(C,nand(A,C))))) = nand(A,B). [para(7189(a,1),1111(a,1,2)),rewrite([530(2),530(5),1505(8,R),530(6)]),flip(a)].
% 42.74/43.02 13366 nand(A,nand(B,nand(c_0,nand(C,nand(A,B))))) = nand(A,A). [para(8270(a,1),535(a,1,2,2)),rewrite([530(9),1722(9)])].
% 42.74/43.02 14637 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(10224(a,1),567(a,1,2,2)),rewrite([530(7),1599(9),1505(15,R),530(13),1722(13)]),flip(a)].
% 42.74/43.02 14966 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(1848(a,1),11306(a,1,2,2,2))].
% 42.74/43.02 15373 nand(nand(A,nand(B,C)),nand(c_0,nand(D,nand(A,nand(A,C))))) = nand(D,nand(A,nand(B,C))). [para(7023(a,1),12574(a,1,2,2,2,2)),rewrite([530(5),530(9),1722(9),530(11)])].
% 42.74/43.02 15501 nand(A,nand(c_0,nand(B,nand(A,nand(A,C))))) = nand(B,nand(c_0,nand(A,C))). [para(13366(a,1),619(a,1,2)),rewrite([530(3),1505(8,R),530(8),530(9),14637(9),530(7)]),flip(a)].
% 42.74/43.02 16885 nand(A,nand(B,nand(c_0,nand(A,C)))) = nand(A,nand(B,nand(A,nand(A,C)))). [para(633(a,1),786(a,1,2)),rewrite([1505(7,R),530(5),15501(6),530(5)])].
% 42.74/43.02 17650 nand(nand(nand(A,B),nand(C,A)),nand(c_0,nand(C,D))) = nand(D,nand(c_0,nand(C,A))). [para(660(a,1),2172(a,1,2,2)),rewrite([530(3),530(7),530(9),14966(9),530(6),9632(7),530(6),530(10),2166(13,R),530(10)]),flip(a)].
% 42.74/43.02 20381 nand(A,nand(c_0,nand(B,C))) = nand(C,nand(c_0,nand(B,A))). [para(660(a,1),10343(a,1,2,2)),rewrite([1505(3,R),530(3),530(5),9632(7),530(6),1505(10,R),530(10),17650(11)])].
% 42.74/43.02 20434 nand(A,nand(B,nand(c_0,nand(A,C)))) = nand(A,nand(C,B)). [para(20381(a,1),723(a,2,2)),rewrite([1505(7,R),530(5),1722(5),530(4)]),flip(a)].
% 42.74/43.02 20710 nand(A,nand(B,nand(A,nand(A,C)))) = nand(A,nand(B,C)). [back_rewrite(16885),rewrite([20434(5),530(1)]),flip(a)].
% 42.74/43.02 21627 nand(A,nand(B,nand(B,C))) = nand(A,nand(B,nand(A,C))). [para(20710(a,1),320(a,1,1)),rewrite([1505(9,R),530(7),15373(8)]),flip(a)].
% 42.74/43.02 21628 $F # answer(prove_meredith_2_basis). [resolve(21627,a,543,a)].
% 42.74/43.02
% 42.74/43.02 % SZS output end Refutation
% 42.74/43.02 ============================== end of proof ==========================
% 42.74/43.02
% 42.74/43.02 ============================== STATISTICS ============================
% 42.74/43.02
% 42.74/43.02 Given=554. Generated=897717. Kept=21626. proofs=1.
% 42.74/43.02 Usable=325. Sos=9028. Demods=8823. Limbo=0, Disabled=12274. Hints=0.
% 42.74/43.02 Megabytes=20.19.
% 42.74/43.02 User_CPU=41.52, System_CPU=0.51, Wall_clock=42.
% 42.74/43.02
% 42.74/43.02 ============================== end of statistics =====================
% 42.74/43.02
% 42.74/43.02 ============================== end of search =========================
% 42.74/43.02
% 42.74/43.02 THEOREM PROVED
% 42.74/43.02 % SZS status Unsatisfiable
% 42.74/43.02
% 42.74/43.02 Exiting with 1 proof.
% 42.74/43.02
% 42.74/43.02 Process 29267 exit (max_proofs) Wed Jun 1 19:43:08 2022
% 42.74/43.02 Prover9 interrupted
%------------------------------------------------------------------------------