%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : SWX217-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %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 : 300s
% DateTime : Tue May 5 07:08:07 PM UTC 2026
% Result : Unsatisfiable 1.73s 2.18s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX217-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : woody %s
% 0.16/0.34 % Computer : n023.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 12:16:38 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.59/1.01 ********************************************************************************
% 0.59/1.01 * W A L D M E I S T E R \| \ / \|/ *
% 0.59/1.01 * |/ | \/ | *
% 0.59/1.01 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.59/1.01 * A. Jaeger and B. Loechner | | *
% 0.59/1.01 * <waldmeister@informatik.uni-kl.de> | *
% 0.59/1.01 ********************************************************************************
% 0.59/1.01
% 0.59/1.01
% 0.59/1.01 Goals:
% 0.59/1.01 ------
% 0.59/1.01
% 0.59/1.01 ( 1) true ?= false
% 0.59/1.01 using narrowing to prove btrue ?= eq2(sat_comm(x2,x1),bfalse)
% 0.59/1.01
% 0.59/1.01 Detected structure: Orkus
% 0.59/1.01 ********************************************************************************
% 0.59/1.01 ****************************** COMPLETION - PROOF ******************************
% 0.59/1.01 ********************************************************************************
% 0.59/1.01
% 1.73/2.18 joined goal: 1 btrue ?= eq2(sat_comm(x2,x1),bfalse) to false
% 1.73/2.18 goal joined
% 1.73/2.18 % SZS status Unsatisfiable
% 1.73/2.18 #START OF PROOF
% 1.73/2.18 % SZS output start CNFRefutation
% 1.73/2.18 cnf('0.1.0.0',axiom,
% 1.73/2.18 ( X1 = addNat(zero,X1) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.1.1.0',plain,
% 1.73/2.18 ( X1 = addNat(zero,X1) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.1.0.0']),
% 1.73/2.18 [weight('<0,0,0,[0,0,0,1]>')]).
% 1.73/2.18 cnf('0.1.2.0',plain,
% 1.73/2.18 ( addNat(zero,X1) = X1 ),
% 1.73/2.18 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_1]).
% 1.73/2.18 cnf('0.2.0.0',axiom,
% 1.73/2.18 ( X1 = append(nil,X1) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.2.1.0',plain,
% 1.73/2.18 ( X1 = append(nil,X1) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.2.0.0']),
% 1.73/2.18 [weight('<1,0,0,[0,0,0,2]>')]).
% 1.73/2.18 cnf('0.2.2.0',plain,
% 1.73/2.18 ( append(nil,X1) = X1 ),
% 1.73/2.18 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_2]).
% 1.73/2.18 cnf('0.3.0.0',axiom,
% 1.73/2.18 ( suc(half(X1)) = half(suc(suc(X1))) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.3.1.0',plain,
% 1.73/2.18 ( suc(half(X1)) = half(suc(suc(X1))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.3.0.0']),
% 1.73/2.18 [weight('<2,0,0,[0,0,0,3]>')]).
% 1.73/2.18 cnf('0.3.2.0',plain,
% 1.73/2.18 ( half(suc(suc(X1))) = suc(half(X1)) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_3]).
% 1.73/2.18 cnf('0.4.0.0',axiom,
% 1.73/2.18 ( suc(addNat(X1,X2)) = addNat(suc(X1),X2) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.4.1.0',plain,
% 1.73/2.18 ( suc(addNat(X1,X2)) = addNat(suc(X1),X2) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.4.0.0']),
% 1.73/2.18 [weight('<3,0,0,[0,0,0,4]>')]).
% 1.73/2.18 cnf('0.4.2.0',plain,
% 1.73/2.18 ( suc(addNat(X1,X2)) = addNat(suc(X1),X2) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_4]).
% 1.73/2.18 cnf('0.5.0.0',axiom,
% 1.73/2.18 ( suc(double(rd(X1))) = rd(cons(i,X1)) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.5.1.0',plain,
% 1.73/2.18 ( suc(double(rd(X1))) = rd(cons(i,X1)) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.5.0.0']),
% 1.73/2.18 [weight('<4,0,0,[0,0,0,5]>')]).
% 1.73/2.18 cnf('0.5.2.0',plain,
% 1.73/2.18 ( suc(double(rd(X1))) = rd(cons(i,X1)) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_5]).
% 1.73/2.18 cnf('0.7.0.0',axiom,
% 1.73/2.18 ( bfalse = eq(zero,suc(X1)) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.7.1.0',plain,
% 1.73/2.18 ( bfalse = eq(zero,suc(X1)) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.7.0.0']),
% 1.73/2.18 [weight('<6,0,0,[0,0,0,7]>')]).
% 1.73/2.18 cnf('0.7.2.0',plain,
% 1.73/2.18 ( eq(zero,suc(X1)) = bfalse ),
% 1.73/2.18 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_7]).
% 1.73/2.18 cnf('0.8.0.0',axiom,
% 1.73/2.18 ( bfalse = notb(btrue) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.8.1.0',plain,
% 1.73/2.18 ( bfalse = notb(btrue) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.8.0.0']),
% 1.73/2.18 [weight('<7,0,0,[0,0,0,8]>')]).
% 1.73/2.18 cnf('0.8.2.0',plain,
% 1.73/2.18 ( notb(btrue) = bfalse ),
% 1.73/2.18 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_8]).
% 1.73/2.18 cnf('0.13.0.0',axiom,
% 1.73/2.18 ( zero = rd(nil) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.13.1.0',plain,
% 1.73/2.18 ( zero = rd(nil) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.13.0.0']),
% 1.73/2.18 [weight('<12,0,0,[0,0,0,13]>')]).
% 1.73/2.18 cnf('0.13.2.0',plain,
% 1.73/2.18 ( rd(nil) = zero ),
% 1.73/2.18 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_13]).
% 1.73/2.18 cnf('0.14.0.0',axiom,
% 1.73/2.18 ( zero = half(suc(zero)) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.14.1.0',plain,
% 1.73/2.18 ( zero = half(suc(zero)) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.14.0.0']),
% 1.73/2.18 [weight('<13,0,0,[0,0,0,14]>')]).
% 1.73/2.18 cnf('0.14.2.0',plain,
% 1.73/2.18 ( half(suc(zero)) = zero ),
% 1.73/2.18 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_14]).
% 1.73/2.18 cnf('0.15.0.0',axiom,
% 1.73/2.18 ( zero = half(zero) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.15.1.0',plain,
% 1.73/2.18 ( zero = half(zero) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.15.0.0']),
% 1.73/2.18 [weight('<14,0,0,[0,0,0,15]>')]).
% 1.73/2.18 cnf('0.15.2.0',plain,
% 1.73/2.18 ( half(zero) = zero ),
% 1.73/2.18 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_15]).
% 1.73/2.18 cnf('0.17.0.0',axiom,
% 1.73/2.18 ( btrue = evenNat(zero) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.17.1.0',plain,
% 1.73/2.18 ( btrue = evenNat(zero) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.17.0.0']),
% 1.73/2.18 [weight('<16,0,0,[0,0,0,17]>')]).
% 1.73/2.18 cnf('0.17.2.0',plain,
% 1.73/2.18 ( evenNat(zero) = btrue ),
% 1.73/2.18 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_17]).
% 1.73/2.18 cnf('0.18.0.0',axiom,
% 1.73/2.18 ( btrue = notb(bfalse) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.18.1.0',plain,
% 1.73/2.18 ( btrue = notb(bfalse) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.18.0.0']),
% 1.73/2.18 [weight('<17,0,0,[0,0,0,18]>')]).
% 1.73/2.18 cnf('0.18.2.0',plain,
% 1.73/2.18 ( notb(bfalse) = btrue ),
% 1.73/2.18 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_18]).
% 1.73/2.18 cnf('0.20.0.0',axiom,
% 1.73/2.18 ( btrue = eq2(X1,X1) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.20.1.0',plain,
% 1.73/2.18 ( btrue = eq2(X1,X1) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.20.0.0']),
% 1.73/2.18 [weight('<19,0,0,[0,0,0,20]>')]).
% 1.73/2.18 cnf('0.20.2.0',plain,
% 1.73/2.18 ( eq2(X1,X1) = btrue ),
% 1.73/2.18 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_20]).
% 1.73/2.18 cnf('0.21.0.0',axiom,
% 1.73/2.18 ( rd(cons(o,X1)) = double(rd(X1)) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.21.1.0',plain,
% 1.73/2.18 ( rd(cons(o,X1)) = double(rd(X1)) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.21.0.0']),
% 1.73/2.18 [weight('<20,0,0,[0,0,0,21]>')]).
% 1.73/2.18 cnf('0.21.2.0',plain,
% 1.73/2.18 ( rd(cons(o,X1)) = double(rd(X1)) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_21]).
% 1.73/2.18 cnf('0.22.0.0',axiom,
% 1.73/2.18 ( rd(append(shw(X1),shw(X2))) = x(X1,X2) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.22.1.0',plain,
% 1.73/2.18 ( rd(append(shw(X1),shw(X2))) = x(X1,X2) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.22.0.0']),
% 1.73/2.18 [weight('<21,0,0,[0,0,0,22]>')]).
% 1.73/2.18 cnf('0.22.2.0',plain,
% 1.73/2.18 ( rd(append(shw(X1),shw(X2))) = x(X1,X2) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_22]).
% 1.73/2.18 cnf('0.23.0.0',axiom,
% 1.73/2.18 ( shw(suc(X1)) = aux(X1,evenNat(suc(X1))) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.23.1.0',plain,
% 1.73/2.18 ( shw(suc(X1)) = aux(X1,evenNat(suc(X1))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.23.0.0']),
% 1.73/2.18 [weight('<22,0,0,[0,0,0,23]>')]).
% 1.73/2.18 cnf('0.23.2.0',plain,
% 1.73/2.18 ( aux(X1,evenNat(suc(X1))) = shw(suc(X1)) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_23]).
% 1.73/2.18 cnf('0.24.0.0',axiom,
% 1.73/2.18 ( shw(zero) = nil ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.24.1.0',plain,
% 1.73/2.18 ( shw(zero) = nil ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.24.0.0']),
% 1.73/2.18 [weight('<23,0,0,[0,0,0,24]>')]).
% 1.73/2.18 cnf('0.24.2.0',plain,
% 1.73/2.18 ( shw(zero) = nil ),
% 1.73/2.18 inference(orient,[status(thm)],['0.24.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_24]).
% 1.73/2.18 cnf('0.25.0.0',axiom,
% 1.73/2.18 ( eq(X1,X2) = eq(suc(X1),suc(X2)) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.25.1.0',plain,
% 1.73/2.18 ( eq(X1,X2) = eq(suc(X1),suc(X2)) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.25.0.0']),
% 1.73/2.18 [weight('<24,0,0,[0,0,0,25]>')]).
% 1.73/2.18 cnf('0.25.2.0',plain,
% 1.73/2.18 ( eq(suc(X1),suc(X2)) = eq(X1,X2) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_25]).
% 1.73/2.18 cnf('0.26.0.0',axiom,
% 1.73/2.18 ( eq(x(X1,X2),x(X2,X1)) = sat_comm(X1,X2) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.26.1.0',plain,
% 1.73/2.18 ( eq(x(X1,X2),x(X2,X1)) = sat_comm(X1,X2) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.26.0.0']),
% 1.73/2.18 [weight('<25,0,0,[0,0,0,26]>')]).
% 1.73/2.18 cnf('0.26.2.0',plain,
% 1.73/2.18 ( eq(x(X1,X2),x(X2,X1)) = sat_comm(X1,X2) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_26]).
% 1.73/2.18 cnf('0.27.0.0',axiom,
% 1.73/2.18 ( cons(X1,append(X2,X3)) = append(cons(X1,X2),X3) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.27.1.0',plain,
% 1.73/2.18 ( cons(X1,append(X2,X3)) = append(cons(X1,X2),X3) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.27.0.0']),
% 1.73/2.18 [weight('<26,0,0,[0,0,0,27]>')]).
% 1.73/2.18 cnf('0.27.2.0',plain,
% 1.73/2.18 ( cons(X1,append(X2,X3)) = append(cons(X1,X2),X3) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_27]).
% 1.73/2.18 cnf('0.28.0.0',axiom,
% 1.73/2.18 ( cons(o,shw(half(suc(X1)))) = aux(X1,btrue) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.28.1.0',plain,
% 1.73/2.18 ( cons(o,shw(half(suc(X1)))) = aux(X1,btrue) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.28.0.0']),
% 1.73/2.18 [weight('<27,0,0,[0,0,0,28]>')]).
% 1.73/2.18 cnf('0.28.2.0',plain,
% 1.73/2.18 ( cons(o,shw(half(suc(X1)))) = aux(X1,btrue) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_28]).
% 1.73/2.18 cnf('0.29.0.0',axiom,
% 1.73/2.18 ( cons(i,shw(half(suc(X1)))) = aux(X1,bfalse) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.29.1.0',plain,
% 1.73/2.18 ( cons(i,shw(half(suc(X1)))) = aux(X1,bfalse) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.29.0.0']),
% 1.73/2.18 [weight('<28,0,0,[0,0,0,29]>')]).
% 1.73/2.18 cnf('0.29.2.0',plain,
% 1.73/2.18 ( cons(i,shw(half(suc(X1)))) = aux(X1,bfalse) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_29]).
% 1.73/2.18 cnf('0.30.0.0',axiom,
% 1.73/2.18 ( evenNat(suc(X1)) = notb(evenNat(X1)) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.30.1.0',plain,
% 1.73/2.18 ( evenNat(suc(X1)) = notb(evenNat(X1)) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.30.0.0']),
% 1.73/2.18 [weight('<29,0,0,[0,0,0,30]>')]).
% 1.73/2.18 cnf('0.30.2.0',plain,
% 1.73/2.18 ( evenNat(suc(X1)) = notb(evenNat(X1)) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.30.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_30]).
% 1.73/2.18 cnf('0.31.0.0',axiom,
% 1.73/2.18 ( addNat(X1,X1) = double(X1) ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.31.1.0',plain,
% 1.73/2.18 ( addNat(X1,X1) = double(X1) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.31.0.0']),
% 1.73/2.18 [weight('<30,0,0,[0,0,0,31]>')]).
% 1.73/2.18 cnf('0.31.2.0',plain,
% 1.73/2.18 ( addNat(X1,X1) = double(X1) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_31]).
% 1.73/2.18 cnf('0.32.0.0',axiom,
% 1.73/2.18 ( eq1(X1,X1) = true ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.32.1.0',plain,
% 1.73/2.18 ( eq1(X1,X1) = true ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.32.0.0']),
% 1.73/2.18 [weight('<31,0,0,[0,0,0,32]>')]).
% 1.73/2.18 cnf('0.32.2.0',plain,
% 1.73/2.18 ( eq1(X1,X1) = true ),
% 1.73/2.18 inference(orient,[status(thm)],['0.32.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_32]).
% 1.73/2.18 cnf('0.33.0.0',axiom,
% 1.73/2.18 ( eq1(btrue,eq2(sat_comm(X2,X1),bfalse)) = false ),
% 1.73/2.18 file('/tmp/WALDMEISTER_10589_n023')).
% 1.73/2.18 cnf('0.33.1.0',plain,
% 1.73/2.18 ( eq1(btrue,eq2(sat_comm(X2,X1),bfalse)) = false ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.33.0.0']),
% 1.73/2.18 [weight('<32,0,0,[0,0,0,33]>')]).
% 1.73/2.18 cnf('0.33.2.0',plain,
% 1.73/2.18 ( eq1(btrue,eq2(sat_comm(X1,X2),bfalse)) = false ),
% 1.73/2.18 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_33]).
% 1.73/2.18 cnf('0.34.0.0',plain,
% 1.73/2.18 ( double(zero) = zero ),
% 1.73/2.18 inference(cp,[status(thm)],['0.31.2.0','0.1.2.0',theory(equality)]),
% 1.73/2.18 [pos('L','L')]).
% 1.73/2.18 cnf('0.34.1.0',plain,
% 1.73/2.18 ( double(zero) = zero ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.34.0.0']),
% 1.73/2.18 [weight('<11,31,1,[1,0,0,0]>')]).
% 1.73/2.18 cnf('0.34.2.0',plain,
% 1.73/2.18 ( double(zero) = zero ),
% 1.73/2.18 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_34]).
% 1.73/2.18 cnf('0.36.0.0',plain,
% 1.73/2.18 ( x(zero,X1) = rd(append(nil,shw(X1))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.22.2.0','0.24.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1.1','L')]).
% 1.73/2.18 cnf('0.36.0.1',plain,
% 1.73/2.18 ( x(zero,X1) = rd(shw(X1)) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.36.0.0','0.2.2.0',theory(equality)]),
% 1.73/2.18 [pos('R.1','L')]).
% 1.73/2.18 cnf('0.36.1.0',plain,
% 1.73/2.18 ( x(zero,X1) = rd(shw(X1)) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.36.0.1']),
% 1.73/2.18 [weight('<27,24,22,[0,0,0,2]>')]).
% 1.73/2.18 cnf('0.36.2.0',plain,
% 1.73/2.18 ( rd(shw(X1)) = x(zero,X1) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_36]).
% 1.73/2.18 cnf('0.39.0.0',plain,
% 1.73/2.18 ( aux(zero,bfalse) = cons(i,shw(zero)) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.29.2.0','0.14.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.2.1','L')]).
% 1.73/2.18 cnf('0.39.0.1',plain,
% 1.73/2.18 ( aux(zero,bfalse) = cons(i,nil) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.39.0.0','0.24.2.0',theory(equality)]),
% 1.73/2.18 [pos('R.2','L')]).
% 1.73/2.18 cnf('0.39.1.0',plain,
% 1.73/2.18 ( aux(zero,bfalse) = cons(i,nil) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.39.0.1']),
% 1.73/2.18 [weight('<27,29,14,[1,0,0,3]>')]).
% 1.73/2.18 cnf('0.39.2.0',plain,
% 1.73/2.18 ( cons(i,nil) = aux(zero,bfalse) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_39]).
% 1.73/2.18 cnf('0.41.0.0',plain,
% 1.73/2.18 ( addNat(suc(zero),X1) = suc(X1) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.4.2.0','0.1.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.41.1.0',plain,
% 1.73/2.18 ( addNat(suc(zero),X1) = suc(X1) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.41.0.0']),
% 1.73/2.18 [weight('<34,4,1,[1,0,0,1]>')]).
% 1.73/2.18 cnf('0.41.2.0',plain,
% 1.73/2.18 ( addNat(suc(zero),X1) = suc(X1) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.41.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_41]).
% 1.73/2.18 cnf('0.42.0.0',plain,
% 1.73/2.18 ( suc(suc(zero)) = double(suc(zero)) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.41.2.0','0.31.2.0',theory(equality)]),
% 1.73/2.18 [pos('L','L')]).
% 1.73/2.18 cnf('0.42.1.0',plain,
% 1.73/2.18 ( suc(suc(zero)) = double(suc(zero)) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.42.0.0']),
% 1.73/2.18 [weight('<27,41,31,[1,0,0,0]>')]).
% 1.73/2.18 cnf('0.42.2.0',plain,
% 1.73/2.18 ( suc(suc(zero)) = double(suc(zero)) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.42.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_42]).
% 1.73/2.18 cnf('0.44.0.0',plain,
% 1.73/2.18 ( suc(half(zero)) = half(double(suc(zero))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.3.2.0','0.42.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.44.0.1',plain,
% 1.73/2.18 ( suc(zero) = half(double(suc(zero))) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.44.0.0','0.15.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.44.1.0',plain,
% 1.73/2.18 ( suc(zero) = half(double(suc(zero))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.44.0.1']),
% 1.73/2.18 [weight('<34,42,3,[0,0,0,1]>')]).
% 1.73/2.18 cnf('0.44.2.0',plain,
% 1.73/2.18 ( half(double(suc(zero))) = suc(zero) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.44.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_44]).
% 1.73/2.18 cnf('0.45.0.0',plain,
% 1.73/2.18 ( rd(cons(i,nil)) = suc(double(zero)) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.5.2.0','0.13.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1.1','L')]).
% 1.73/2.18 cnf('0.45.1.0',plain,
% 1.73/2.18 ( rd(cons(i,nil)) = suc(double(zero)) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.45.0.0']),
% 1.73/2.18 [weight('<39,13,5,[0,0,0,2]>')]).
% 1.73/2.18 cnf('0.45.1.1',plain,
% 1.73/2.18 ( rd(aux(zero,bfalse)) = suc(double(zero)) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.45.1.0','0.39.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.45.1.2',plain,
% 1.73/2.18 ( rd(aux(zero,bfalse)) = suc(zero) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.45.1.1','0.34.2.0',theory(equality)]),
% 1.73/2.18 [pos('R.1','L')]).
% 1.73/2.18 cnf('0.45.2.0',plain,
% 1.73/2.18 ( rd(aux(zero,bfalse)) = suc(zero) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.45.1.2',theory(equality)]),
% 1.73/2.18 [u,rule_45]).
% 1.73/2.18 cnf('0.49.0.0',plain,
% 1.73/2.18 ( suc(half(suc(zero))) = half(suc(double(suc(zero)))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.3.2.0','0.42.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1.1','L')]).
% 1.73/2.18 cnf('0.49.0.1',plain,
% 1.73/2.18 ( suc(zero) = half(suc(double(suc(zero)))) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.49.0.0','0.14.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.49.1.0',plain,
% 1.73/2.18 ( suc(zero) = half(suc(double(suc(zero)))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.49.0.1']),
% 1.73/2.18 [weight('<47,42,3,[0,0,0,2]>')]).
% 1.73/2.18 cnf('0.49.2.0',plain,
% 1.73/2.18 ( half(suc(double(suc(zero)))) = suc(zero) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.49.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_49]).
% 1.73/2.18 cnf('0.50.0.0',plain,
% 1.73/2.18 ( aux(X1,evenNat(suc(X1))) = shw(suc(X1)) ),
% 1.73/2.18 inference(interreduction_right,[status(thm)],['0.23.2.0'])).
% 1.73/2.18 cnf('0.50.0.1',plain,
% 1.73/2.18 ( aux(X1,notb(evenNat(X1))) = shw(suc(X1)) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.50.0.0','0.30.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.2','L')]).
% 1.73/2.18 cnf('0.50.1.0',plain,
% 1.73/2.18 ( aux(X1,notb(evenNat(X1))) = shw(suc(X1)) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.50.0.1']),
% 1.73/2.18 [weight('<53,23,30,[0,0,0,0]>')]).
% 1.73/2.18 cnf('0.50.2.0',plain,
% 1.73/2.18 ( aux(X1,notb(evenNat(X1))) = shw(suc(X1)) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.50.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_50]).
% 1.73/2.18 cnf('0.51.0.0',plain,
% 1.73/2.18 ( shw(suc(zero)) = aux(zero,notb(btrue)) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.50.2.0','0.17.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.2.1','L')]).
% 1.73/2.18 cnf('0.51.0.1',plain,
% 1.73/2.18 ( shw(suc(zero)) = aux(zero,bfalse) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.51.0.0','0.8.2.0',theory(equality)]),
% 1.73/2.18 [pos('R.2','L')]).
% 1.73/2.18 cnf('0.51.1.0',plain,
% 1.73/2.18 ( shw(suc(zero)) = aux(zero,bfalse) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.51.0.1']),
% 1.73/2.18 [weight('<27,50,17,[1,0,0,3]>')]).
% 1.73/2.18 cnf('0.51.2.0',plain,
% 1.73/2.18 ( shw(suc(zero)) = aux(zero,bfalse) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.51.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_51]).
% 1.73/2.18 cnf('0.54.0.0',plain,
% 1.73/2.18 ( append(cons(X1,nil),X2) = cons(X1,X2) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.27.2.0','0.2.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.2','L')]).
% 1.73/2.18 cnf('0.54.1.0',plain,
% 1.73/2.18 ( append(cons(X1,nil),X2) = cons(X1,X2) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.54.0.0']),
% 1.73/2.18 [weight('<53,27,2,[1,0,0,2]>')]).
% 1.73/2.18 cnf('0.54.2.0',plain,
% 1.73/2.18 ( append(cons(X1,nil),X2) = cons(X1,X2) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.54.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_54]).
% 1.73/2.18 cnf('0.55.0.0',plain,
% 1.73/2.18 ( addNat(suc(suc(zero)),X1) = suc(suc(X1)) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.4.2.0','0.41.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.55.1.0',plain,
% 1.73/2.18 ( addNat(suc(suc(zero)),X1) = suc(suc(X1)) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.55.0.0']),
% 1.73/2.18 [weight('<53,41,4,[0,0,0,1]>')]).
% 1.73/2.18 cnf('0.55.1.1',plain,
% 1.73/2.18 ( addNat(double(suc(zero)),X1) = suc(suc(X1)) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.55.1.0','0.42.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.55.2.0',plain,
% 1.73/2.18 ( addNat(double(suc(zero)),X1) = suc(suc(X1)) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.55.1.1',theory(equality)]),
% 1.73/2.18 [u,rule_55]).
% 1.73/2.18 cnf('0.57.0.0',plain,
% 1.73/2.18 ( cons(i,X1) = append(aux(zero,bfalse),X1) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.54.2.0','0.39.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.57.1.0',plain,
% 1.73/2.18 ( cons(i,X1) = append(aux(zero,bfalse),X1) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.57.0.0']),
% 1.73/2.18 [weight('<53,54,39,[1,0,0,1]>')]).
% 1.73/2.18 cnf('0.57.2.0',plain,
% 1.73/2.18 ( append(aux(zero,bfalse),X1) = cons(i,X1) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.57.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_57]).
% 1.73/2.18 cnf('0.70.0.0',plain,
% 1.73/2.18 ( suc(suc(double(suc(zero)))) = double(double(suc(zero))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.55.2.0','0.31.2.0',theory(equality)]),
% 1.73/2.18 [pos('L','L')]).
% 1.73/2.18 cnf('0.70.1.0',plain,
% 1.73/2.18 ( suc(suc(double(suc(zero)))) = double(double(suc(zero))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.70.0.0']),
% 1.73/2.18 [weight('<59,55,31,[1,0,0,0]>')]).
% 1.73/2.18 cnf('0.70.2.0',plain,
% 1.73/2.18 ( suc(suc(double(suc(zero)))) = double(double(suc(zero))) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.70.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_70]).
% 1.73/2.18 cnf('0.72.0.0',plain,
% 1.73/2.18 ( suc(half(double(suc(zero)))) = half(double(double(suc(zero)))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.3.2.0','0.70.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.72.0.1',plain,
% 1.73/2.18 ( suc(suc(zero)) = half(double(double(suc(zero)))) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.72.0.0','0.44.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.72.0.2',plain,
% 1.73/2.18 ( double(suc(zero)) = half(double(double(suc(zero)))) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.72.0.1','0.42.2.0',theory(equality)]),
% 1.73/2.18 [pos('L','L')]).
% 1.73/2.18 cnf('0.72.1.0',plain,
% 1.73/2.18 ( double(suc(zero)) = half(double(double(suc(zero)))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.72.0.2']),
% 1.73/2.18 [weight('<53,70,3,[0,0,0,1]>')]).
% 1.73/2.18 cnf('0.72.2.0',plain,
% 1.73/2.18 ( half(double(double(suc(zero)))) = double(suc(zero)) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.72.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_72]).
% 1.73/2.18 cnf('0.76.0.0',plain,
% 1.73/2.18 ( rd(cons(i,shw(X1))) = suc(double(x(zero,X1))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.5.2.0','0.36.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1.1','L')]).
% 1.73/2.18 cnf('0.76.1.0',plain,
% 1.73/2.18 ( rd(cons(i,shw(X1))) = suc(double(x(zero,X1))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.76.0.0']),
% 1.73/2.18 [weight('<65,36,5,[0,0,0,2]>')]).
% 1.73/2.18 cnf('0.76.2.0',plain,
% 1.73/2.18 ( suc(double(x(zero,X1))) = rd(cons(i,shw(X1))) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.76.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_76]).
% 1.73/2.18 cnf('0.77.0.0',plain,
% 1.73/2.18 ( aux(double(suc(zero)),btrue) = cons(o,shw(suc(zero))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.28.2.0','0.49.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.2.1','L')]).
% 1.73/2.18 cnf('0.77.1.0',plain,
% 1.73/2.18 ( aux(double(suc(zero)),btrue) = cons(o,shw(suc(zero))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.77.0.0']),
% 1.73/2.18 [weight('<65,49,28,[0,0,0,3]>')]).
% 1.73/2.18 cnf('0.77.1.1',plain,
% 1.73/2.18 ( aux(double(suc(zero)),btrue) = cons(o,aux(zero,bfalse)) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.77.1.0','0.51.2.0',theory(equality)]),
% 1.73/2.18 [pos('R.2','L')]).
% 1.73/2.18 cnf('0.77.2.0',plain,
% 1.73/2.18 ( cons(o,aux(zero,bfalse)) = aux(double(suc(zero)),btrue) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.77.1.1',theory(equality)]),
% 1.73/2.18 [x,rule_77]).
% 1.73/2.18 cnf('0.78.0.0',plain,
% 1.73/2.18 ( aux(double(suc(zero)),bfalse) = cons(i,shw(suc(zero))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.29.2.0','0.49.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.2.1','L')]).
% 1.73/2.18 cnf('0.78.1.0',plain,
% 1.73/2.18 ( aux(double(suc(zero)),bfalse) = cons(i,shw(suc(zero))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.78.0.0']),
% 1.73/2.18 [weight('<65,49,29,[0,0,0,3]>')]).
% 1.73/2.18 cnf('0.78.1.1',plain,
% 1.73/2.18 ( aux(double(suc(zero)),bfalse) = cons(i,aux(zero,bfalse)) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.78.1.0','0.51.2.0',theory(equality)]),
% 1.73/2.18 [pos('R.2','L')]).
% 1.73/2.18 cnf('0.78.2.0',plain,
% 1.73/2.18 ( cons(i,aux(zero,bfalse)) = aux(double(suc(zero)),bfalse) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.78.1.1',theory(equality)]),
% 1.73/2.18 [x,rule_78]).
% 1.73/2.18 cnf('0.80.0.0',plain,
% 1.73/2.18 ( suc(half(suc(double(suc(zero))))) = half(suc(double(double(suc(zero))))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.3.2.0','0.70.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1.1','L')]).
% 1.73/2.18 cnf('0.80.0.1',plain,
% 1.73/2.18 ( suc(suc(zero)) = half(suc(double(double(suc(zero))))) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.80.0.0','0.49.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.80.0.2',plain,
% 1.73/2.18 ( double(suc(zero)) = half(suc(double(double(suc(zero))))) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.80.0.1','0.42.2.0',theory(equality)]),
% 1.73/2.18 [pos('L','L')]).
% 1.73/2.18 cnf('0.80.1.0',plain,
% 1.73/2.18 ( double(suc(zero)) = half(suc(double(double(suc(zero))))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.80.0.2']),
% 1.73/2.18 [weight('<69,70,3,[0,0,0,2]>')]).
% 1.73/2.18 cnf('0.80.2.0',plain,
% 1.73/2.18 ( half(suc(double(double(suc(zero))))) = double(suc(zero)) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.80.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_80]).
% 1.73/2.18 cnf('0.81.0.0',plain,
% 1.73/2.18 ( double(rd(aux(zero,bfalse))) = rd(aux(double(suc(zero)),btrue)) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.21.2.0','0.77.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.81.0.1',plain,
% 1.73/2.18 ( double(suc(zero)) = rd(aux(double(suc(zero)),btrue)) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.81.0.0','0.45.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.81.1.0',plain,
% 1.73/2.18 ( double(suc(zero)) = rd(aux(double(suc(zero)),btrue)) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.81.0.1']),
% 1.73/2.18 [weight('<69,77,21,[0,0,0,1]>')]).
% 1.73/2.18 cnf('0.81.2.0',plain,
% 1.73/2.18 ( rd(aux(double(suc(zero)),btrue)) = double(suc(zero)) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.81.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_81]).
% 1.73/2.18 cnf('0.93.0.0',plain,
% 1.73/2.18 ( aux(suc(X1),btrue) = cons(o,shw(suc(half(X1)))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.28.2.0','0.3.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.2.1','L')]).
% 1.73/2.18 cnf('0.93.1.0',plain,
% 1.73/2.18 ( aux(suc(X1),btrue) = cons(o,shw(suc(half(X1)))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.93.0.0']),
% 1.73/2.18 [weight('<76,28,3,[1,0,0,3]>')]).
% 1.73/2.18 cnf('0.93.2.0',plain,
% 1.73/2.18 ( cons(o,shw(suc(half(X1)))) = aux(suc(X1),btrue) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.93.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_93]).
% 1.73/2.18 cnf('0.94.0.0',plain,
% 1.73/2.18 ( aux(suc(zero),btrue) = cons(o,shw(suc(zero))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.93.2.0','0.15.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.2.1.1','L')]).
% 1.73/2.18 cnf('0.94.0.1',plain,
% 1.73/2.18 ( aux(suc(zero),btrue) = cons(o,aux(zero,bfalse)) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.94.0.0','0.51.2.0',theory(equality)]),
% 1.73/2.18 [pos('R.2','L')]).
% 1.73/2.18 cnf('0.94.0.2',plain,
% 1.73/2.18 ( aux(suc(zero),btrue) = aux(double(suc(zero)),btrue) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.94.0.1','0.77.2.0',theory(equality)]),
% 1.73/2.18 [pos('R','L')]).
% 1.73/2.18 cnf('0.94.1.0',plain,
% 1.73/2.18 ( aux(suc(zero),btrue) = aux(double(suc(zero)),btrue) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.94.0.2']),
% 1.73/2.18 [weight('<59,93,15,[1,0,0,4]>')]).
% 1.73/2.18 cnf('0.94.2.0',plain,
% 1.73/2.18 ( aux(double(suc(zero)),btrue) = aux(suc(zero),btrue) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.94.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_94]).
% 1.73/2.18 cnf('0.95.0.0',plain,
% 1.73/2.18 ( rd(aux(double(suc(zero)),btrue)) = double(suc(zero)) ),
% 1.73/2.18 inference(interreduction_right,[status(thm)],['0.81.2.0'])).
% 1.73/2.18 cnf('0.95.0.1',plain,
% 1.73/2.18 ( rd(aux(suc(zero),btrue)) = double(suc(zero)) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.95.0.0','0.94.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.95.1.0',plain,
% 1.73/2.18 ( rd(aux(suc(zero),btrue)) = double(suc(zero)) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.95.0.1']),
% 1.73/2.18 [weight('<53,81,94,[0,0,0,0]>')]).
% 1.73/2.18 cnf('0.95.2.0',plain,
% 1.73/2.18 ( rd(aux(suc(zero),btrue)) = double(suc(zero)) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.95.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_95]).
% 1.73/2.18 cnf('0.96.0.0',plain,
% 1.73/2.18 ( cons(o,aux(zero,bfalse)) = aux(double(suc(zero)),btrue) ),
% 1.73/2.18 inference(interreduction_right,[status(thm)],['0.77.2.0'])).
% 1.73/2.18 cnf('0.96.0.1',plain,
% 1.73/2.18 ( cons(o,aux(zero,bfalse)) = aux(suc(zero),btrue) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.96.0.0','0.94.2.0',theory(equality)]),
% 1.73/2.18 [pos('R','L')]).
% 1.73/2.18 cnf('0.96.1.0',plain,
% 1.73/2.18 ( cons(o,aux(zero,bfalse)) = aux(suc(zero),btrue) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.96.0.1']),
% 1.73/2.18 [weight('<59,77,94,[0,0,0,0]>')]).
% 1.73/2.18 cnf('0.96.2.0',plain,
% 1.73/2.18 ( cons(o,aux(zero,bfalse)) = aux(suc(zero),btrue) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.96.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_96]).
% 1.73/2.18 cnf('0.97.0.0',plain,
% 1.73/2.18 ( double(rd(shw(half(suc(X1))))) = rd(aux(X1,btrue)) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.21.2.0','0.28.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.97.1.0',plain,
% 1.73/2.18 ( double(rd(shw(half(suc(X1))))) = rd(aux(X1,btrue)) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.97.0.0']),
% 1.73/2.18 [weight('<76,28,21,[0,0,0,1]>')]).
% 1.73/2.18 cnf('0.97.1.1',plain,
% 1.73/2.18 ( double(x(zero,half(suc(X1)))) = rd(aux(X1,btrue)) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.97.1.0','0.36.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.97.2.0',plain,
% 1.73/2.18 ( double(x(zero,half(suc(X1)))) = rd(aux(X1,btrue)) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.97.1.1',theory(equality)]),
% 1.73/2.18 [u,rule_97]).
% 1.73/2.18 cnf('0.98.0.0',plain,
% 1.73/2.18 ( rd(cons(i,shw(half(suc(X1))))) = suc(rd(aux(X1,btrue))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.76.2.0','0.97.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.98.0.1',plain,
% 1.73/2.18 ( rd(aux(X1,bfalse)) = suc(rd(aux(X1,btrue))) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.98.0.0','0.29.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.98.1.0',plain,
% 1.73/2.18 ( rd(aux(X1,bfalse)) = suc(rd(aux(X1,btrue))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.98.0.1']),
% 1.73/2.18 [weight('<59,97,76,[0,0,0,1]>')]).
% 1.73/2.18 cnf('0.98.2.0',plain,
% 1.73/2.18 ( suc(rd(aux(X1,btrue))) = rd(aux(X1,bfalse)) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.98.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_98]).
% 1.73/2.18 cnf('0.99.0.0',plain,
% 1.73/2.18 ( rd(aux(suc(zero),bfalse)) = suc(double(suc(zero))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.98.2.0','0.95.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.99.1.0',plain,
% 1.73/2.18 ( rd(aux(suc(zero),bfalse)) = suc(double(suc(zero))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.99.0.0']),
% 1.73/2.18 [weight('<59,98,95,[1,0,0,1]>')]).
% 1.73/2.18 cnf('0.99.2.0',plain,
% 1.73/2.18 ( rd(aux(suc(zero),bfalse)) = suc(double(suc(zero))) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.99.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_99]).
% 1.73/2.18 cnf('0.100.0.0',plain,
% 1.73/2.18 ( aux(suc(X1),bfalse) = cons(i,shw(suc(half(X1)))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.29.2.0','0.3.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.2.1','L')]).
% 1.73/2.18 cnf('0.100.1.0',plain,
% 1.73/2.18 ( aux(suc(X1),bfalse) = cons(i,shw(suc(half(X1)))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.100.0.0']),
% 1.73/2.18 [weight('<76,29,3,[1,0,0,3]>')]).
% 1.73/2.18 cnf('0.100.2.0',plain,
% 1.73/2.18 ( cons(i,shw(suc(half(X1)))) = aux(suc(X1),bfalse) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.100.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_100]).
% 1.73/2.18 cnf('0.101.0.0',plain,
% 1.73/2.18 ( aux(suc(zero),bfalse) = cons(i,shw(suc(zero))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.100.2.0','0.15.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.2.1.1','L')]).
% 1.73/2.18 cnf('0.101.0.1',plain,
% 1.73/2.18 ( aux(suc(zero),bfalse) = cons(i,aux(zero,bfalse)) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.101.0.0','0.51.2.0',theory(equality)]),
% 1.73/2.18 [pos('R.2','L')]).
% 1.73/2.18 cnf('0.101.0.2',plain,
% 1.73/2.18 ( aux(suc(zero),bfalse) = aux(double(suc(zero)),bfalse) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.101.0.1','0.78.2.0',theory(equality)]),
% 1.73/2.18 [pos('R','L')]).
% 1.73/2.18 cnf('0.101.1.0',plain,
% 1.73/2.18 ( aux(suc(zero),bfalse) = aux(double(suc(zero)),bfalse) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.101.0.2']),
% 1.73/2.18 [weight('<59,100,15,[1,0,0,4]>')]).
% 1.73/2.18 cnf('0.101.2.0',plain,
% 1.73/2.18 ( aux(double(suc(zero)),bfalse) = aux(suc(zero),bfalse) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.101.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_101]).
% 1.73/2.18 cnf('0.102.0.0',plain,
% 1.73/2.18 ( cons(i,aux(zero,bfalse)) = aux(double(suc(zero)),bfalse) ),
% 1.73/2.18 inference(interreduction_right,[status(thm)],['0.78.2.0'])).
% 1.73/2.18 cnf('0.102.0.1',plain,
% 1.73/2.18 ( cons(i,aux(zero,bfalse)) = aux(suc(zero),bfalse) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.102.0.0','0.101.2.0',theory(equality)]),
% 1.73/2.18 [pos('R','L')]).
% 1.73/2.18 cnf('0.102.1.0',plain,
% 1.73/2.18 ( cons(i,aux(zero,bfalse)) = aux(suc(zero),bfalse) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.102.0.1']),
% 1.73/2.18 [weight('<59,78,101,[0,0,0,0]>')]).
% 1.73/2.18 cnf('0.102.2.0',plain,
% 1.73/2.18 ( cons(i,aux(zero,bfalse)) = aux(suc(zero),bfalse) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.102.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_102]).
% 1.73/2.18 cnf('0.104.0.0',plain,
% 1.73/2.18 ( eq(suc(zero),X1) = eq(double(suc(zero)),suc(X1)) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.25.2.0','0.42.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.104.1.0',plain,
% 1.73/2.18 ( eq(suc(zero),X1) = eq(double(suc(zero)),suc(X1)) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.104.0.0']),
% 1.73/2.18 [weight('<76,42,25,[0,0,0,1]>')]).
% 1.73/2.18 cnf('0.104.2.0',plain,
% 1.73/2.18 ( eq(double(suc(zero)),suc(X1)) = eq(suc(zero),X1) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.104.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_104]).
% 1.73/2.18 cnf('0.109.0.0',plain,
% 1.73/2.18 ( addNat(suc(double(suc(zero))),X1) = suc(suc(suc(X1))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.4.2.0','0.55.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.109.1.0',plain,
% 1.73/2.18 ( addNat(suc(double(suc(zero))),X1) = suc(suc(suc(X1))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.109.0.0']),
% 1.73/2.18 [weight('<76,55,4,[0,0,0,1]>')]).
% 1.73/2.18 cnf('0.109.2.0',plain,
% 1.73/2.18 ( addNat(suc(double(suc(zero))),X1) = suc(suc(suc(X1))) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.109.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_109]).
% 1.73/2.18 cnf('0.126.0.0',plain,
% 1.73/2.18 ( suc(suc(suc(suc(double(suc(zero)))))) = double(suc(double(suc(zero)))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.109.2.0','0.31.2.0',theory(equality)]),
% 1.73/2.18 [pos('L','L')]).
% 1.73/2.18 cnf('0.126.0.1',plain,
% 1.73/2.18 ( suc(suc(double(double(suc(zero))))) = double(suc(double(suc(zero)))) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.126.0.0','0.70.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1.1','L')]).
% 1.73/2.18 cnf('0.126.1.0',plain,
% 1.73/2.18 ( suc(suc(double(double(suc(zero))))) = double(suc(double(suc(zero)))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.126.0.1']),
% 1.73/2.18 [weight('<83,109,31,[1,0,0,0]>')]).
% 1.73/2.18 cnf('0.126.2.0',plain,
% 1.73/2.18 ( suc(suc(double(double(suc(zero))))) = double(suc(double(suc(zero)))) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.126.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_126]).
% 1.73/2.18 cnf('0.157.0.0',plain,
% 1.73/2.18 ( aux(double(double(suc(zero))),bfalse) = cons(i,shw(double(suc(zero)))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.29.2.0','0.80.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.2.1','L')]).
% 1.73/2.18 cnf('0.157.1.0',plain,
% 1.73/2.18 ( aux(double(double(suc(zero))),bfalse) = cons(i,shw(double(suc(zero)))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.157.0.0']),
% 1.73/2.18 [weight('<90,80,29,[0,0,0,3]>')]).
% 1.73/2.18 cnf('0.157.2.0',plain,
% 1.73/2.18 ( cons(i,shw(double(suc(zero)))) = aux(double(double(suc(zero))),bfalse) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.157.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_157]).
% 1.73/2.18 cnf('0.162.0.0',plain,
% 1.73/2.18 ( aux(suc(double(suc(zero))),bfalse) = cons(i,shw(suc(suc(zero)))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.100.2.0','0.44.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.2.1.1','L')]).
% 1.73/2.18 cnf('0.162.0.1',plain,
% 1.73/2.18 ( aux(suc(double(suc(zero))),bfalse) = cons(i,shw(double(suc(zero)))) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.162.0.0','0.42.2.0',theory(equality)]),
% 1.73/2.18 [pos('R.2.1','L')]).
% 1.73/2.18 cnf('0.162.1.0',plain,
% 1.73/2.18 ( aux(suc(double(suc(zero))),bfalse) = cons(i,shw(double(suc(zero)))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.162.0.1']),
% 1.73/2.18 [weight('<90,100,44,[1,0,0,4]>')]).
% 1.73/2.18 cnf('0.162.1.1',plain,
% 1.73/2.18 ( aux(suc(double(suc(zero))),bfalse) = aux(double(double(suc(zero))),bfalse) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.162.1.0','0.157.2.0',theory(equality)]),
% 1.73/2.18 [pos('R','L')]).
% 1.73/2.18 cnf('0.162.2.0',plain,
% 1.73/2.18 ( aux(suc(double(suc(zero))),bfalse) = aux(double(double(suc(zero))),bfalse) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.162.1.1',theory(equality)]),
% 1.73/2.18 [u,rule_162]).
% 1.73/2.18 cnf('0.163.0.0',plain,
% 1.73/2.18 ( shw(suc(suc(X1))) = aux(suc(X1),notb(notb(evenNat(X1)))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.50.2.0','0.30.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.2.1','L')]).
% 1.73/2.18 cnf('0.163.1.0',plain,
% 1.73/2.18 ( shw(suc(suc(X1))) = aux(suc(X1),notb(notb(evenNat(X1)))) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.163.0.0']),
% 1.73/2.18 [weight('<95,50,30,[1,0,0,3]>')]).
% 1.73/2.18 cnf('0.163.2.0',plain,
% 1.73/2.18 ( aux(suc(X1),notb(notb(evenNat(X1)))) = shw(suc(suc(X1))) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.163.1.0',theory(equality)]),
% 1.73/2.18 [x,rule_163]).
% 1.73/2.18 cnf('0.164.0.0',plain,
% 1.73/2.18 ( shw(suc(suc(zero))) = aux(suc(zero),notb(notb(btrue))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.163.2.0','0.17.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.2.1.1','L')]).
% 1.73/2.18 cnf('0.164.0.1',plain,
% 1.73/2.18 ( shw(double(suc(zero))) = aux(suc(zero),notb(notb(btrue))) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.164.0.0','0.42.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1','L')]).
% 1.73/2.18 cnf('0.164.0.2',plain,
% 1.73/2.18 ( shw(double(suc(zero))) = aux(suc(zero),notb(bfalse)) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.164.0.1','0.8.2.0',theory(equality)]),
% 1.73/2.18 [pos('R.2.1','L')]).
% 1.73/2.18 cnf('0.164.0.3',plain,
% 1.73/2.18 ( shw(double(suc(zero))) = aux(suc(zero),btrue) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.164.0.2','0.18.2.0',theory(equality)]),
% 1.73/2.18 [pos('R.2','L')]).
% 1.73/2.18 cnf('0.164.1.0',plain,
% 1.73/2.18 ( shw(double(suc(zero))) = aux(suc(zero),btrue) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.164.0.3']),
% 1.73/2.18 [weight('<44,163,17,[1,0,0,5]>')]).
% 1.73/2.18 cnf('0.164.2.0',plain,
% 1.73/2.18 ( shw(double(suc(zero))) = aux(suc(zero),btrue) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.164.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_164]).
% 1.73/2.18 cnf('0.170.0.0',plain,
% 1.73/2.18 ( cons(i,shw(double(suc(zero)))) = aux(double(double(suc(zero))),bfalse) ),
% 1.73/2.18 inference(interreduction_right,[status(thm)],['0.157.2.0'])).
% 1.73/2.18 cnf('0.170.0.1',plain,
% 1.73/2.18 ( cons(i,aux(suc(zero),btrue)) = aux(double(double(suc(zero))),bfalse) ),
% 1.73/2.18 inference(reduction,[status(thm)],['0.170.0.0','0.164.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.2','L')]).
% 1.73/2.18 cnf('0.170.1.0',plain,
% 1.73/2.18 ( cons(i,aux(suc(zero),btrue)) = aux(double(double(suc(zero))),bfalse) ),
% 1.73/2.18 inference(weigh,[status(thm)],['0.170.0.1']),
% 1.73/2.18 [weight('<90,157,164,[0,0,0,0]>')]).
% 1.73/2.18 cnf('0.170.2.0',plain,
% 1.73/2.18 ( cons(i,aux(suc(zero),btrue)) = aux(double(double(suc(zero))),bfalse) ),
% 1.73/2.18 inference(orient,[status(thm)],['0.170.1.0',theory(equality)]),
% 1.73/2.18 [u,rule_170]).
% 1.73/2.18 cnf('0.178.0.0',plain,
% 1.73/2.18 ( x(suc(zero),X1) = rd(append(aux(zero,bfalse),shw(X1))) ),
% 1.73/2.18 inference(cp,[status(thm)],['0.22.2.0','0.51.2.0',theory(equality)]),
% 1.73/2.18 [pos('L.1.1','L')]).
% 1.73/2.18 cnf('0.178.1.0',plain,
% 1.73/2.18 ( x(suc(zero),X1) = rd(append(aux(zero,bfalse),shw(X1))) ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.178.0.0']),
% 1.73/2.19 [weight('<95,51,22,[0,0,0,2]>')]).
% 1.73/2.19 cnf('0.178.1.1',plain,
% 1.73/2.19 ( x(suc(zero),X1) = rd(cons(i,shw(X1))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.178.1.0','0.57.2.0',theory(equality)]),
% 1.73/2.19 [pos('R.1','L')]).
% 1.73/2.19 cnf('0.178.2.0',plain,
% 1.73/2.19 ( rd(cons(i,shw(X1))) = x(suc(zero),X1) ),
% 1.73/2.19 inference(orient,[status(thm)],['0.178.1.1',theory(equality)]),
% 1.73/2.19 [x,rule_178]).
% 1.73/2.19 cnf('0.182.0.0',plain,
% 1.73/2.19 ( x(suc(zero),suc(zero)) = rd(cons(i,aux(zero,bfalse))) ),
% 1.73/2.19 inference(cp,[status(thm)],['0.178.2.0','0.51.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.1.2','L')]).
% 1.73/2.19 cnf('0.182.0.1',plain,
% 1.73/2.19 ( x(suc(zero),suc(zero)) = rd(aux(suc(zero),bfalse)) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.182.0.0','0.102.2.0',theory(equality)]),
% 1.73/2.19 [pos('R.1','L')]).
% 1.73/2.19 cnf('0.182.0.2',plain,
% 1.73/2.19 ( x(suc(zero),suc(zero)) = suc(double(suc(zero))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.182.0.1','0.99.2.0',theory(equality)]),
% 1.73/2.19 [pos('R','L')]).
% 1.73/2.19 cnf('0.182.1.0',plain,
% 1.73/2.19 ( x(suc(zero),suc(zero)) = suc(double(suc(zero))) ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.182.0.2']),
% 1.73/2.19 [weight('<59,178,51,[1,0,0,3]>')]).
% 1.73/2.19 cnf('0.182.2.0',plain,
% 1.73/2.19 ( x(suc(zero),suc(zero)) = suc(double(suc(zero))) ),
% 1.73/2.19 inference(orient,[status(thm)],['0.182.1.0',theory(equality)]),
% 1.73/2.19 [u,rule_182]).
% 1.73/2.19 cnf('0.185.0.0',plain,
% 1.73/2.19 ( x(suc(zero),half(suc(X1))) = rd(aux(X1,bfalse)) ),
% 1.73/2.19 inference(cp,[status(thm)],['0.178.2.0','0.29.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.1','L')]).
% 1.73/2.19 cnf('0.185.1.0',plain,
% 1.73/2.19 ( x(suc(zero),half(suc(X1))) = rd(aux(X1,bfalse)) ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.185.0.0']),
% 1.73/2.19 [weight('<76,178,29,[1,0,0,1]>')]).
% 1.73/2.19 cnf('0.185.2.0',plain,
% 1.73/2.19 ( x(suc(zero),half(suc(X1))) = rd(aux(X1,bfalse)) ),
% 1.73/2.19 inference(orient,[status(thm)],['0.185.1.0',theory(equality)]),
% 1.73/2.19 [u,rule_185]).
% 1.73/2.19 cnf('0.202.0.0',plain,
% 1.73/2.19 ( eq(X1,addNat(X2,X3)) = eq(suc(X1),addNat(suc(X2),X3)) ),
% 1.73/2.19 inference(cp,[status(thm)],['0.25.2.0','0.4.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.2','L')]).
% 1.73/2.19 cnf('0.202.1.0',plain,
% 1.73/2.19 ( eq(X1,addNat(X2,X3)) = eq(suc(X1),addNat(suc(X2),X3)) ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.202.0.0']),
% 1.73/2.19 [weight('<103,25,4,[1,0,0,3]>')]).
% 1.73/2.19 cnf('0.202.2.0',plain,
% 1.73/2.19 ( eq(suc(X1),addNat(suc(X2),X3)) = eq(X1,addNat(X2,X3)) ),
% 1.73/2.19 inference(orient,[status(thm)],['0.202.1.0',theory(equality)]),
% 1.73/2.19 [x,rule_202]).
% 1.73/2.19 cnf('0.209.0.0',plain,
% 1.73/2.19 ( append(cons(X1,aux(zero,bfalse)),X2) = cons(X1,cons(i,X2)) ),
% 1.73/2.19 inference(cp,[status(thm)],['0.27.2.0','0.57.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.2','L')]).
% 1.73/2.19 cnf('0.209.1.0',plain,
% 1.73/2.19 ( append(cons(X1,aux(zero,bfalse)),X2) = cons(X1,cons(i,X2)) ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.209.0.0']),
% 1.73/2.19 [weight('<103,57,27,[0,0,0,2]>')]).
% 1.73/2.19 cnf('0.209.2.0',plain,
% 1.73/2.19 ( append(cons(X1,aux(zero,bfalse)),X2) = cons(X1,cons(i,X2)) ),
% 1.73/2.19 inference(orient,[status(thm)],['0.209.1.0',theory(equality)]),
% 1.73/2.19 [u,rule_209]).
% 1.73/2.19 cnf('0.210.0.0',plain,
% 1.73/2.19 ( cons(o,cons(i,X1)) = append(aux(suc(zero),btrue),X1) ),
% 1.73/2.19 inference(cp,[status(thm)],['0.209.2.0','0.96.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.1','L')]).
% 1.73/2.19 cnf('0.210.1.0',plain,
% 1.73/2.19 ( cons(o,cons(i,X1)) = append(aux(suc(zero),btrue),X1) ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.210.0.0']),
% 1.73/2.19 [weight('<83,209,96,[1,0,0,1]>')]).
% 1.73/2.19 cnf('0.210.2.0',plain,
% 1.73/2.19 ( append(aux(suc(zero),btrue),X1) = cons(o,cons(i,X1)) ),
% 1.73/2.19 inference(orient,[status(thm)],['0.210.1.0',theory(equality)]),
% 1.73/2.19 [x,rule_210]).
% 1.73/2.19 cnf('0.218.0.0',plain,
% 1.73/2.19 ( rd(cons(i,aux(suc(zero),btrue))) = suc(double(double(suc(zero)))) ),
% 1.73/2.19 inference(cp,[status(thm)],['0.5.2.0','0.95.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.1.1','L')]).
% 1.73/2.19 cnf('0.218.1.0',plain,
% 1.73/2.19 ( rd(cons(i,aux(suc(zero),btrue))) = suc(double(double(suc(zero)))) ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.218.0.0']),
% 1.73/2.19 [weight('<103,95,5,[0,0,0,2]>')]).
% 1.73/2.19 cnf('0.218.1.1',plain,
% 1.73/2.19 ( rd(aux(double(double(suc(zero))),bfalse)) = suc(double(double(suc(zero)))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.218.1.0','0.170.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.1','L')]).
% 1.73/2.19 cnf('0.218.2.0',plain,
% 1.73/2.19 ( rd(aux(double(double(suc(zero))),bfalse)) = suc(double(double(suc(zero)))) ),
% 1.73/2.19 inference(orient,[status(thm)],['0.218.1.1',theory(equality)]),
% 1.73/2.19 [u,rule_218]).
% 1.73/2.19 cnf('0.311.0.0',plain,
% 1.73/2.19 ( eq(suc(double(suc(zero))),X1) = eq(double(double(suc(zero))),suc(X1)) ),
% 1.73/2.19 inference(cp,[status(thm)],['0.25.2.0','0.70.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.1','L')]).
% 1.73/2.19 cnf('0.311.1.0',plain,
% 1.73/2.19 ( eq(suc(double(suc(zero))),X1) = eq(double(double(suc(zero))),suc(X1)) ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.311.0.0']),
% 1.73/2.19 [weight('<111,70,25,[0,0,0,1]>')]).
% 1.73/2.19 cnf('0.311.2.0',plain,
% 1.73/2.19 ( eq(double(double(suc(zero))),suc(X1)) = eq(suc(double(suc(zero))),X1) ),
% 1.73/2.19 inference(orient,[status(thm)],['0.311.1.0',theory(equality)]),
% 1.73/2.19 [x,rule_311]).
% 1.73/2.19 cnf('0.312.0.0',plain,
% 1.73/2.19 ( eq(X1,suc(double(suc(zero)))) = eq(suc(X1),double(double(suc(zero)))) ),
% 1.73/2.19 inference(cp,[status(thm)],['0.25.2.0','0.70.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.2','L')]).
% 1.73/2.19 cnf('0.312.1.0',plain,
% 1.73/2.19 ( eq(X1,suc(double(suc(zero)))) = eq(suc(X1),double(double(suc(zero)))) ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.312.0.0']),
% 1.73/2.19 [weight('<111,70,25,[0,0,0,3]>')]).
% 1.73/2.19 cnf('0.312.2.0',plain,
% 1.73/2.19 ( eq(suc(X1),double(double(suc(zero)))) = eq(X1,suc(double(suc(zero)))) ),
% 1.73/2.19 inference(orient,[status(thm)],['0.312.1.0',theory(equality)]),
% 1.73/2.19 [x,rule_312]).
% 1.73/2.19 cnf('0.382.0.0',plain,
% 1.73/2.19 ( x(double(suc(zero)),X1) = rd(append(aux(suc(zero),btrue),shw(X1))) ),
% 1.73/2.19 inference(cp,[status(thm)],['0.22.2.0','0.164.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.1.1','L')]).
% 1.73/2.19 cnf('0.382.1.0',plain,
% 1.73/2.19 ( x(double(suc(zero)),X1) = rd(append(aux(suc(zero),btrue),shw(X1))) ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.382.0.0']),
% 1.73/2.19 [weight('<125,164,22,[0,0,0,2]>')]).
% 1.73/2.19 cnf('0.382.1.1',plain,
% 1.73/2.19 ( x(double(suc(zero)),X1) = rd(cons(o,cons(i,shw(X1)))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.382.1.0','0.210.2.0',theory(equality)]),
% 1.73/2.19 [pos('R.1','L')]).
% 1.73/2.19 cnf('0.382.1.2',plain,
% 1.73/2.19 ( x(double(suc(zero)),X1) = double(rd(cons(i,shw(X1)))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.382.1.1','0.21.2.0',theory(equality)]),
% 1.73/2.19 [pos('R','L')]).
% 1.73/2.19 cnf('0.382.1.3',plain,
% 1.73/2.19 ( x(double(suc(zero)),X1) = double(x(suc(zero),X1)) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.382.1.2','0.178.2.0',theory(equality)]),
% 1.73/2.19 [pos('R.1','L')]).
% 1.73/2.19 cnf('0.382.2.0',plain,
% 1.73/2.19 ( double(x(suc(zero),X1)) = x(double(suc(zero)),X1) ),
% 1.73/2.19 inference(orient,[status(thm)],['0.382.1.3',theory(equality)]),
% 1.73/2.19 [x,rule_382]).
% 1.73/2.19 cnf('0.385.0.0',plain,
% 1.73/2.19 ( x(double(suc(zero)),suc(zero)) = double(suc(double(suc(zero)))) ),
% 1.73/2.19 inference(cp,[status(thm)],['0.382.2.0','0.182.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.1','L')]).
% 1.73/2.19 cnf('0.385.1.0',plain,
% 1.73/2.19 ( x(double(suc(zero)),suc(zero)) = double(suc(double(suc(zero)))) ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.385.0.0']),
% 1.73/2.19 [weight('<83,382,182,[1,0,0,1]>')]).
% 1.73/2.19 cnf('0.385.2.0',plain,
% 1.73/2.19 ( x(double(suc(zero)),suc(zero)) = double(suc(double(suc(zero)))) ),
% 1.73/2.19 inference(orient,[status(thm)],['0.385.1.0',theory(equality)]),
% 1.73/2.19 [u,rule_385]).
% 1.73/2.19 cnf('0.679.0.0',plain,
% 1.73/2.19 ( eq(X1,suc(double(double(suc(zero))))) = eq(suc(X1),double(suc(double(suc(zero))))) ),
% 1.73/2.19 inference(cp,[status(thm)],['0.25.2.0','0.126.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.2','L')]).
% 1.73/2.19 cnf('0.679.1.0',plain,
% 1.73/2.19 ( eq(X1,suc(double(double(suc(zero))))) = eq(suc(X1),double(suc(double(suc(zero))))) ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.679.0.0']),
% 1.73/2.19 [weight('<143,126,25,[0,0,0,3]>')]).
% 1.73/2.19 cnf('0.679.2.0',plain,
% 1.73/2.19 ( eq(suc(X1),double(suc(double(suc(zero))))) = eq(X1,suc(double(double(suc(zero))))) ),
% 1.73/2.19 inference(orient,[status(thm)],['0.679.1.0',theory(equality)]),
% 1.73/2.19 [x,rule_679]).
% 1.73/2.19 cnf('0.1265.0.0',plain,
% 1.73/2.19 ( eq(X1,addNat(X2,suc(X2))) = eq(suc(X1),double(suc(X2))) ),
% 1.73/2.19 inference(cp,[status(thm)],['0.202.2.0','0.31.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.2','L')]).
% 1.73/2.19 cnf('0.1265.1.0',plain,
% 1.73/2.19 ( eq(X1,addNat(X2,suc(X2))) = eq(suc(X1),double(suc(X2))) ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.1265.0.0']),
% 1.73/2.19 [weight('<168,202,31,[1,0,0,3]>')]).
% 1.73/2.19 cnf('0.1265.2.0',plain,
% 1.73/2.19 ( eq(X1,addNat(X2,suc(X2))) = eq(suc(X1),double(suc(X2))) ),
% 1.73/2.19 inference(activate,[status(thm)],['0.1265.1.0']),
% 1.73/2.19 [equation_2]).
% 1.73/2.19 cnf('0.3639.0.0',plain,
% 1.73/2.19 ( sat_comm(suc(zero),half(suc(X1))) = eq(rd(aux(X1,bfalse)),x(half(suc(X1)),suc(zero))) ),
% 1.73/2.19 inference(cp,[status(thm)],['0.26.2.0','0.185.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.1','L')]).
% 1.73/2.19 cnf('0.3639.1.0',plain,
% 1.73/2.19 ( sat_comm(suc(zero),half(suc(X1))) = eq(rd(aux(X1,bfalse)),x(half(suc(X1)),suc(zero))) ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.3639.0.0']),
% 1.73/2.19 [weight('<?,185,26,[0,0,0,1]>')]).
% 1.73/2.19 cnf('0.3639.2.0',plain,
% 1.73/2.19 ( eq(rd(aux(X1,bfalse)),x(half(suc(X1)),suc(zero))) = sat_comm(suc(zero),half(suc(X1))) ),
% 1.73/2.19 inference(orient,[status(thm)],['0.3639.1.0',theory(equality)]),
% 1.73/2.19 [x,rule_3627]).
% 1.73/2.19 cnf('0.3640.0.0',plain,
% 1.73/2.19 ( sat_comm(suc(zero),half(suc(suc(double(suc(zero)))))) = eq(rd(aux(suc(double(suc(zero))),bfalse)),x(half(double(double(suc(zero)))),suc(zero))) ),
% 1.73/2.19 inference(cp,[status(thm)],['0.3639.2.0','0.70.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.2.1.1','L')]).
% 1.73/2.19 cnf('0.3640.0.1',plain,
% 1.73/2.19 ( sat_comm(suc(zero),suc(half(double(suc(zero))))) = eq(rd(aux(suc(double(suc(zero))),bfalse)),x(half(double(double(suc(zero)))),suc(zero))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3640.0.0','0.3.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.2','L')]).
% 1.73/2.19 cnf('0.3640.0.2',plain,
% 1.73/2.19 ( sat_comm(suc(zero),suc(suc(zero))) = eq(rd(aux(suc(double(suc(zero))),bfalse)),x(half(double(double(suc(zero)))),suc(zero))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3640.0.1','0.44.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.2.1','L')]).
% 1.73/2.19 cnf('0.3640.0.3',plain,
% 1.73/2.19 ( sat_comm(suc(zero),double(suc(zero))) = eq(rd(aux(suc(double(suc(zero))),bfalse)),x(half(double(double(suc(zero)))),suc(zero))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3640.0.2','0.42.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.2','L')]).
% 1.73/2.19 cnf('0.3640.0.4',plain,
% 1.73/2.19 ( sat_comm(suc(zero),double(suc(zero))) = eq(rd(aux(double(double(suc(zero))),bfalse)),x(half(double(double(suc(zero)))),suc(zero))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3640.0.3','0.162.2.0',theory(equality)]),
% 1.73/2.19 [pos('R.1.1','L')]).
% 1.73/2.19 cnf('0.3640.0.5',plain,
% 1.73/2.19 ( sat_comm(suc(zero),double(suc(zero))) = eq(suc(double(double(suc(zero)))),x(half(double(double(suc(zero)))),suc(zero))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3640.0.4','0.218.2.0',theory(equality)]),
% 1.73/2.19 [pos('R.1','L')]).
% 1.73/2.19 cnf('0.3640.0.6',plain,
% 1.73/2.19 ( sat_comm(suc(zero),double(suc(zero))) = eq(suc(double(double(suc(zero)))),x(double(suc(zero)),suc(zero))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3640.0.5','0.72.2.0',theory(equality)]),
% 1.73/2.19 [pos('R.2.1','L')]).
% 1.73/2.19 cnf('0.3640.0.7',plain,
% 1.73/2.19 ( sat_comm(suc(zero),double(suc(zero))) = eq(suc(double(double(suc(zero)))),double(suc(double(suc(zero))))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3640.0.6','0.385.2.0',theory(equality)]),
% 1.73/2.19 [pos('R.2','L')]).
% 1.73/2.19 cnf('0.3640.0.8',plain,
% 1.73/2.19 ( sat_comm(suc(zero),double(suc(zero))) = eq(double(double(suc(zero))),suc(double(double(suc(zero))))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3640.0.7','0.679.2.0',theory(equality)]),
% 1.73/2.19 [pos('R','L')]).
% 1.73/2.19 cnf('0.3640.0.9',plain,
% 1.73/2.19 ( sat_comm(suc(zero),double(suc(zero))) = eq(suc(double(suc(zero))),double(double(suc(zero)))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3640.0.8','0.311.2.0',theory(equality)]),
% 1.73/2.19 [pos('R','L')]).
% 1.73/2.19 cnf('0.3640.0.10',plain,
% 1.73/2.19 ( sat_comm(suc(zero),double(suc(zero))) = eq(double(suc(zero)),suc(double(suc(zero)))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3640.0.9','0.312.2.0',theory(equality)]),
% 1.73/2.19 [pos('R','L')]).
% 1.73/2.19 cnf('0.3640.0.11',plain,
% 1.73/2.19 ( sat_comm(suc(zero),double(suc(zero))) = eq(suc(zero),double(suc(zero))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3640.0.10','0.104.2.0',theory(equality)]),
% 1.73/2.19 [pos('R','L')]).
% 1.73/2.19 cnf('0.3640.1.0',plain,
% 1.73/2.19 ( sat_comm(suc(zero),double(suc(zero))) = eq(suc(zero),double(suc(zero))) ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.3640.0.11']),
% 1.73/2.19 [weight('<90,3639,70,[1,0,0,7]>')]).
% 1.73/2.19 cnf('0.3640.1.1',plain,
% 1.73/2.19 ( sat_comm(suc(zero),double(suc(zero))) = eq(zero,addNat(zero,suc(zero))) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3640.1.0','0.1265.2.0',theory(equality)]),
% 1.73/2.19 [pos('R','R')]).
% 1.73/2.19 cnf('0.3640.1.2',plain,
% 1.73/2.19 ( sat_comm(suc(zero),double(suc(zero))) = eq(zero,suc(zero)) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3640.1.1','0.1.2.0',theory(equality)]),
% 1.73/2.19 [pos('R.2','L')]).
% 1.73/2.19 cnf('0.3640.1.3',plain,
% 1.73/2.19 ( sat_comm(suc(zero),double(suc(zero))) = bfalse ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3640.1.2','0.7.2.0',theory(equality)]),
% 1.73/2.19 [pos('R','L')]).
% 1.73/2.19 cnf('0.3640.2.0',plain,
% 1.73/2.19 ( sat_comm(suc(zero),double(suc(zero))) = bfalse ),
% 1.73/2.19 inference(orient,[status(thm)],['0.3640.1.3',theory(equality)]),
% 1.73/2.19 [u,rule_3628]).
% 1.73/2.19 cnf('0.3641.0.0',plain,
% 1.73/2.19 ( false = eq1(btrue,eq2(bfalse,bfalse)) ),
% 1.73/2.19 inference(cp,[status(thm)],['0.33.2.0','0.3640.2.0',theory(equality)]),
% 1.73/2.19 [pos('L.2.1','L')]).
% 1.73/2.19 cnf('0.3641.0.1',plain,
% 1.73/2.19 ( false = eq1(btrue,btrue) ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3641.0.0','0.20.2.0',theory(equality)]),
% 1.73/2.19 [pos('R.2','L')]).
% 1.73/2.19 cnf('0.3641.0.2',plain,
% 1.73/2.19 ( false = true ),
% 1.73/2.19 inference(reduction,[status(thm)],['0.3641.0.1','0.32.2.0',theory(equality)]),
% 1.73/2.19 [pos('R','L')]).
% 1.73/2.19 cnf('0.3641.1.0',plain,
% 1.73/2.19 ( false = true ),
% 1.73/2.19 inference(weigh,[status(thm)],['0.3641.0.2']),
% 1.73/2.19 [weight('<5,3640,33,[0,0,0,3]>')]).
% 1.73/2.19 cnf('0.3641.2.0',plain,
% 1.73/2.19 ( true = false ),
% 1.73/2.19 inference(orient,[status(thm)],['0.3641.1.0',theory(equality)]),
% 1.73/2.19 [x,rule_3629]).
% 1.73/2.19 cnf('1.0.0.0',conjecture,
% 1.73/2.19 ( true = false ),
% 1.73/2.19 file('/tmp/WALDMEISTER_10589_n023',conjecture_1)).
% 1.73/2.19 cnf('1.0.0.1',plain,
% 1.73/2.19 ( false = false ),
% 1.73/2.19 inference(reduction,[status(thm)],['1.0.0.0','0.3641.2.0',theory(equality)]),
% 1.73/2.19 [pos('L','L')]).
% 1.73/2.19 cnf('1.0.0.2',plain,
% 1.73/2.19 ( $true ),
% 1.73/2.19 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 1.73/2.19 [conjecture_1]).
% 1.73/2.19
% 1.73/2.19 Proved Goals:
% 1.73/2.19 No. 1: true ?= false, current false ?= false
% 1.73/2.19 using narrowing to prove btrue ?= eq2(sat_comm(x2,x1),bfalse)
% 1.73/2.19
% 1.73/2.19 1 goal was specified, which was proved.
% 1.73/2.19 % SZS output end CNFRefutation
% 1.73/2.19 #END OF PROOF
% 1.73/2.19
% 1.73/2.19 Problem WALDMEISTER_10589_n023
% 1.73/2.19 CPs.gen 138007
% 1.73/2.19 CPs.reexp 0
% 1.73/2.19 Select 6784
% 1.73/2.19 R 3629
% 1.73/2.19 E 12
% 1.73/2.19 vsize 9.2M
% 1.73/2.19 rss 6.7M
% 1.73/2.19 process.time 1.174s
% 1.73/2.19 wallclock.time 1.174s
% 1.73/2.19 status S
% 1.73/2.19
% 1.73/2.19
% 1.73/2.19 Waldmeister states: Goal proved.
% 1.73/2.19 % SZS status Unsatisfiable
%------------------------------------------------------------------------------