%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HWV003-1 : TPTP v9.2.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.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 04:28:52 PM UTC 2026
% Result : Unsatisfiable 16.22s 10.05s
% Output : CNFRefutation 16.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 45
% Syntax : Number of clauses : 490 ( 490 unt; 0 nHn; 294 RR)
% Number of literals : 490 ( 477 equ; 10 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 14 con; 0-3 aty)
% Number of variables : 325 ( 57 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(and_symmetry,negated_conjecture,
and(X1,X2) = and(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_symmetry) ).
cnf(and_commutativity,negated_conjecture,
and(and(X1,X2),X3) = and(and(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_commutativity) ).
cnf(and_not_evaluation1,axiom,
and(X1,not(X1)) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_not_evaluation1) ).
cnf(circuit1,negated_conjecture,
a11 = not(and(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',circuit1) ).
cnf(and_or_subsumption2,axiom,
or(and(X1,X2),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_subsumption2) ).
cnf(or_symmetry,negated_conjecture,
or(X1,X2) = or(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_symmetry) ).
cnf(demorgan1,axiom,
not(and(X1,X2)) = or(not(X1),not(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1) ).
cnf(circuit3,negated_conjecture,
a13 = not(and(a11,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',circuit3) ).
cnf(not_involution,axiom,
not(not(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_involution) ).
cnf(demorgan2,axiom,
not(or(X1,X2)) = and(not(X1),not(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2) ).
cnf(karnaugh2,axiom,
or(and(not(X1),not(X2)),X2) = or(X2,not(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',karnaugh2) ).
cnf(not_definition1,axiom,
not(n0) = n1,
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',not_definition1) ).
cnf(circuit6,negated_conjecture,
a16 = not(and(a14,a15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',circuit6) ).
cnf(and_or_subsumption3,axiom,
or(or(and(X1,X2),X3),X2) = or(X3,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_subsumption3) ).
cnf(and_idempotency,axiom,
and(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_idempotency) ).
cnf(not_definition2,axiom,
not(n1) = n0,
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',not_definition2) ).
cnf(or_definition1,axiom,
or(X1,n0) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',or_definition1) ).
cnf(circuit5,negated_conjecture,
a15 = not(and(a14,carryin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',circuit5) ).
cnf(and_or_subsumption1,axiom,
or(and(X1,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_subsumption1) ).
cnf(circuit2,negated_conjecture,
a12 = not(and(a11,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',circuit2) ).
cnf(and_not_evaluation3,axiom,
and(and(X1,X2),not(X1)) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_not_evaluation3) ).
cnf(circuit4,negated_conjecture,
a14 = not(and(a12,a13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',circuit4) ).
cnf(and_or_simplification,negated_conjecture,
and(or(X1,X2),X3) = or(and(X1,X3),and(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_simplification) ).
cnf(circuit9,negated_conjecture,
c1 = not(and(a11,a15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',circuit9) ).
cnf(karnaugh1,axiom,
or(and(X1,not(X2)),X2) = or(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',karnaugh1) ).
cnf(and_definition2,axiom,
and(X1,n1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',and_definition2) ).
cnf(karnaugh3,axiom,
or(and(and(X1,X2),not(X3)),and(X1,X3)) = or(and(X1,X2),and(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',karnaugh3) ).
cnf(or_commutativity,negated_conjecture,
or(or(X1,X2),X3) = or(or(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_commutativity) ).
cnf(or_idempotency,axiom,
or(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_idempotency) ).
cnf(and_evaluation1,axiom,
and(and(X1,X2),X2) = and(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_evaluation1) ).
cnf(and_or_subsumption4,axiom,
or(or(X1,and(X2,X3)),X3) = or(X1,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_subsumption4) ).
cnf(or_not_evaluation1,axiom,
or(X1,not(X1)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_not_evaluation1) ).
cnf(or_definition2,axiom,
or(X1,n1) = n1,
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',or_definition2) ).
cnf(and_not_evaluation2,axiom,
and(and(X1,X2),not(X2)) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_not_evaluation2) ).
cnf(circuit7,negated_conjecture,
a17 = not(and(a15,carryin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',circuit7) ).
cnf(or_not_evaluation2,axiom,
or(or(X1,X2),not(X2)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_not_evaluation2) ).
cnf(or_evaluation1,axiom,
or(or(X1,X2),X2) = or(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_evaluation1) ).
cnf(circuit8,negated_conjecture,
s1 = not(and(a16,a17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',circuit8) ).
cnf(prove_circuit,negated_conjecture,
~ circuit(sum(a,b,carryin),carryout(a,b,carryin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_circuit) ).
cnf(sum_definition,negated_conjecture,
sum(X1,X2,X3) = xor(xor(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_definition) ).
cnf(xor_definition,axiom,
xor(X1,X2) = or(and(X1,not(X2)),and(X2,not(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_definition) ).
cnf(carryout_definition,negated_conjecture,
carryout(X1,X2,X3) = or(and(X1,or(X2,X3)),and(not(X1),and(X2,X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',carryout_definition) ).
cnf(or_not_evaluation3,axiom,
or(or(X1,X2),not(X1)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_not_evaluation3) ).
cnf(and_not_evaluation4,axiom,
and(and(and(X1,X2),X3),not(X1)) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_not_evaluation4) ).
cnf(the_output_circuit,negated_conjecture,
circuit(s1,c1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_output_circuit) ).
cnf(c_0_45,negated_conjecture,
and(X1,X2) = and(X2,X1),
and_symmetry ).
cnf(c_0_46,negated_conjecture,
and(and(X1,X2),X3) = and(and(X1,X3),X2),
and_commutativity ).
cnf(c_0_47,axiom,
and(X1,not(X1)) = n0,
and_not_evaluation1 ).
cnf(c_0_48,negated_conjecture,
a11 = not(and(a,b)),
circuit1 ).
cnf(c_0_49,negated_conjecture,
and(and(X1,X2),X3) = and(X2,and(X1,X3)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,axiom,
or(and(X1,X2),X1) = X1,
and_or_subsumption2 ).
cnf(c_0_51,negated_conjecture,
or(X1,X2) = or(X2,X1),
or_symmetry ).
cnf(c_0_52,axiom,
not(and(X1,X2)) = or(not(X1),not(X2)),
demorgan1 ).
cnf(c_0_53,negated_conjecture,
a13 = not(and(a11,b)),
circuit3 ).
cnf(c_0_54,negated_conjecture,
and(b,and(a11,a)) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_46]),c_0_45]),c_0_45]) ).
cnf(c_0_55,negated_conjecture,
and(X1,and(X2,X3)) = and(X3,and(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_49]),c_0_49]) ).
cnf(c_0_56,axiom,
not(not(X1)) = X1,
not_involution ).
cnf(c_0_57,plain,
or(X1,and(X1,X2)) = X1,
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_58,axiom,
not(or(X1,X2)) = and(not(X1),not(X2)),
demorgan2 ).
cnf(c_0_59,axiom,
or(and(not(X1),not(X2)),X2) = or(X2,not(X1)),
karnaugh2 ).
cnf(c_0_60,negated_conjecture,
not(and(X1,and(a11,b))) = or(a13,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_51]) ).
cnf(c_0_61,negated_conjecture,
and(a,and(a11,b)) = n0,
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,axiom,
not(n0) = n1,
not_definition1 ).
cnf(c_0_63,negated_conjecture,
not(a13) = and(a11,b),
inference(spm,[status(thm)],[c_0_56,c_0_53]) ).
cnf(c_0_64,negated_conjecture,
a16 = not(and(a14,a15)),
circuit6 ).
cnf(c_0_65,plain,
not(and(X1,or(X1,X2))) = not(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_52]) ).
cnf(c_0_66,axiom,
or(or(and(X1,X2),X3),X2) = or(X3,X2),
and_or_subsumption3 ).
cnf(c_0_67,axiom,
and(X1,X1) = X1,
and_idempotency ).
cnf(c_0_68,plain,
or(X1,not(or(X2,X1))) = or(X1,not(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_58]),c_0_51]) ).
cnf(c_0_69,negated_conjecture,
or(a13,not(a)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
cnf(c_0_70,axiom,
not(n1) = n0,
not_definition2 ).
cnf(c_0_71,axiom,
or(X1,n0) = X1,
or_definition1 ).
cnf(c_0_72,negated_conjecture,
or(and(a11,b),not(X1)) = not(and(X1,a13)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_63]),c_0_51]) ).
cnf(c_0_73,negated_conjecture,
not(and(a15,a14)) = a16,
inference(rw,[status(thm)],[c_0_64,c_0_45]) ).
cnf(c_0_74,negated_conjecture,
a15 = not(and(a14,carryin)),
circuit5 ).
cnf(c_0_75,plain,
and(X1,or(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_65]),c_0_56]) ).
cnf(c_0_76,plain,
or(X1,or(and(X2,X1),X3)) = or(X3,X1),
inference(rw,[status(thm)],[c_0_66,c_0_51]) ).
cnf(c_0_77,negated_conjecture,
not(and(X1,and(a,b))) = or(a11,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_48]),c_0_51]) ).
cnf(c_0_78,negated_conjecture,
and(X1,and(X1,X2)) = and(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_67]),c_0_45]) ).
cnf(c_0_79,axiom,
or(and(X1,X2),X2) = X2,
and_or_subsumption1 ).
cnf(c_0_80,negated_conjecture,
not(and(a,a13)) = not(a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_71]),c_0_63]),c_0_51]),c_0_72]) ).
cnf(c_0_81,negated_conjecture,
a12 = not(and(a11,a)),
circuit2 ).
cnf(c_0_82,negated_conjecture,
not(a16) = and(a15,a14),
inference(spm,[status(thm)],[c_0_56,c_0_73]) ).
cnf(c_0_83,negated_conjecture,
not(and(carryin,a14)) = a15,
inference(rw,[status(thm)],[c_0_74,c_0_45]) ).
cnf(c_0_84,axiom,
and(and(X1,X2),not(X1)) = n0,
and_not_evaluation3 ).
cnf(c_0_85,plain,
and(X1,or(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_86,negated_conjecture,
or(a11,not(a)) = a11,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_48]) ).
cnf(c_0_87,plain,
or(X1,and(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_79,c_0_51]) ).
cnf(c_0_88,negated_conjecture,
and(a,a13) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_80]),c_0_56]) ).
cnf(c_0_89,negated_conjecture,
not(a12) = and(a11,a),
inference(spm,[status(thm)],[c_0_56,c_0_81]) ).
cnf(c_0_90,negated_conjecture,
a14 = not(and(a12,a13)),
circuit4 ).
cnf(c_0_91,negated_conjecture,
or(and(a15,a14),not(X1)) = not(and(X1,a16)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_82]),c_0_51]) ).
cnf(c_0_92,negated_conjecture,
not(a15) = and(carryin,a14),
inference(spm,[status(thm)],[c_0_56,c_0_83]) ).
cnf(c_0_93,negated_conjecture,
and(or(X1,X2),X3) = or(and(X1,X3),and(X2,X3)),
and_or_simplification ).
cnf(c_0_94,negated_conjecture,
not(and(X1,and(carryin,a14))) = or(a15,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_83]),c_0_51]) ).
cnf(c_0_95,negated_conjecture,
and(not(X1),and(X1,X2)) = n0,
inference(spm,[status(thm)],[c_0_45,c_0_84]) ).
cnf(c_0_96,negated_conjecture,
and(a14,and(a15,carryin)) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_83]),c_0_46]),c_0_45]),c_0_45]) ).
cnf(c_0_97,negated_conjecture,
c1 = not(and(a11,a15)),
circuit9 ).
cnf(c_0_98,axiom,
or(and(X1,not(X2)),X2) = or(X1,X2),
karnaugh1 ).
cnf(c_0_99,negated_conjecture,
and(b,and(a11,not(X1))) = not(or(X1,a13)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_63]),c_0_55]) ).
cnf(c_0_100,negated_conjecture,
and(a11,not(a)) = not(a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_45]) ).
cnf(c_0_101,negated_conjecture,
or(a,a13) = a13,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_51]) ).
cnf(c_0_102,negated_conjecture,
or(and(a11,a),and(a11,b)) = a14,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_89]),c_0_90]),c_0_51]) ).
cnf(c_0_103,plain,
or(X1,and(X2,and(X3,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_87]),c_0_87]),c_0_51]) ).
cnf(c_0_104,negated_conjecture,
not(and(a15,a16)) = and(a14,or(a15,carryin)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_45]) ).
cnf(c_0_105,negated_conjecture,
or(a15,carryin) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_62]),c_0_56]) ).
cnf(c_0_106,axiom,
and(X1,n1) = X1,
and_definition2 ).
cnf(c_0_107,axiom,
or(and(and(X1,X2),not(X3)),and(X1,X3)) = or(and(X1,X2),and(X1,X3)),
karnaugh3 ).
cnf(c_0_108,negated_conjecture,
not(and(X1,and(a15,a14))) = or(a16,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_73]),c_0_51]) ).
cnf(c_0_109,negated_conjecture,
and(carryin,and(a15,a14)) = n0,
inference(rw,[status(thm)],[c_0_96,c_0_55]) ).
cnf(c_0_110,negated_conjecture,
or(or(X1,X2),X3) = or(or(X1,X3),X2),
or_commutativity ).
cnf(c_0_111,axiom,
or(X1,X1) = X1,
or_idempotency ).
cnf(c_0_112,negated_conjecture,
or(and(carryin,a14),not(X1)) = not(and(X1,a15)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_92]),c_0_51]) ).
cnf(c_0_113,negated_conjecture,
not(a14) = and(a12,a13),
inference(spm,[status(thm)],[c_0_56,c_0_90]) ).
cnf(c_0_114,negated_conjecture,
not(c1) = and(a11,a15),
inference(spm,[status(thm)],[c_0_56,c_0_97]) ).
cnf(c_0_115,plain,
or(X1,and(X2,not(X1))) = or(X2,X1),
inference(rw,[status(thm)],[c_0_98,c_0_51]) ).
cnf(c_0_116,negated_conjecture,
and(b,not(a)) = and(a11,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]),c_0_63]) ).
cnf(c_0_117,negated_conjecture,
or(a,and(a11,b)) = or(a,a14),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_102]),c_0_51]) ).
cnf(c_0_118,negated_conjecture,
or(a13,and(X1,a)) = a13,
inference(spm,[status(thm)],[c_0_103,c_0_88]) ).
cnf(c_0_119,negated_conjecture,
not(and(a15,a16)) = a14,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_105]),c_0_106]) ).
cnf(c_0_120,plain,
or(and(X1,X2),and(and(X1,X3),not(X2))) = or(and(X1,X3),and(X1,X2)),
inference(rw,[status(thm)],[c_0_107,c_0_51]) ).
cnf(c_0_121,negated_conjecture,
or(n0,X1) = X1,
inference(spm,[status(thm)],[c_0_71,c_0_51]) ).
cnf(c_0_122,axiom,
and(and(X1,X2),X2) = and(X1,X2),
and_evaluation1 ).
cnf(c_0_123,negated_conjecture,
or(a16,not(carryin)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_62]) ).
cnf(c_0_124,axiom,
or(or(X1,and(X2,X3)),X3) = or(X1,X3),
and_or_subsumption4 ).
cnf(c_0_125,axiom,
or(X1,not(X1)) = n1,
or_not_evaluation1 ).
cnf(c_0_126,negated_conjecture,
or(X1,or(X1,X2)) = or(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_51]) ).
cnf(c_0_127,negated_conjecture,
or(and(carryin,a14),and(a12,a13)) = a16,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_45]),c_0_73]) ).
cnf(c_0_128,negated_conjecture,
or(and(a11,a15),not(X1)) = not(and(X1,c1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_114]),c_0_51]) ).
cnf(c_0_129,negated_conjecture,
or(a,a14) = or(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]),c_0_51]) ).
cnf(c_0_130,negated_conjecture,
not(and(and(a,b),X1)) = or(a11,not(X1)),
inference(spm,[status(thm)],[c_0_52,c_0_48]) ).
cnf(c_0_131,negated_conjecture,
and(a,and(X1,a13)) = and(X1,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_118]),c_0_49]) ).
cnf(c_0_132,negated_conjecture,
and(a12,a13) = and(a15,a16),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_119]),c_0_113]) ).
cnf(c_0_133,negated_conjecture,
and(a12,and(b,X1)) = and(b,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_54]),c_0_81]),c_0_121]),c_0_71]),c_0_45]) ).
cnf(c_0_134,plain,
and(X1,and(X2,X1)) = and(X2,X1),
inference(rw,[status(thm)],[c_0_122,c_0_45]) ).
cnf(c_0_135,negated_conjecture,
not(and(and(a15,a14),X1)) = or(a16,not(X1)),
inference(spm,[status(thm)],[c_0_52,c_0_73]) ).
cnf(c_0_136,negated_conjecture,
or(a15,not(carryin)) = a15,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_78]),c_0_83]) ).
cnf(c_0_137,negated_conjecture,
not(and(carryin,a16)) = not(carryin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_123]),c_0_70]),c_0_71]),c_0_82]),c_0_51]),c_0_91]) ).
cnf(c_0_138,plain,
or(X1,or(X2,and(X3,X1))) = or(X2,X1),
inference(rw,[status(thm)],[c_0_124,c_0_51]) ).
cnf(c_0_139,negated_conjecture,
or(a15,and(carryin,a14)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_83]),c_0_51]) ).
cnf(c_0_140,axiom,
or(X1,n1) = n1,
or_definition2 ).
cnf(c_0_141,negated_conjecture,
or(a16,and(carryin,a14)) = a16,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_51]) ).
cnf(c_0_142,negated_conjecture,
not(and(c1,and(a,b))) = a11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_48]),c_0_45]),c_0_51]),c_0_57]) ).
cnf(c_0_143,negated_conjecture,
not(a11) = and(a,b),
inference(spm,[status(thm)],[c_0_56,c_0_48]) ).
cnf(c_0_144,axiom,
and(and(X1,X2),not(X2)) = n0,
and_not_evaluation2 ).
cnf(c_0_145,negated_conjecture,
not(or(X1,and(a11,b))) = and(a13,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_53]),c_0_45]) ).
cnf(c_0_146,negated_conjecture,
or(a,and(a11,b)) = or(a,b),
inference(rw,[status(thm)],[c_0_117,c_0_129]) ).
cnf(c_0_147,negated_conjecture,
not(and(b,and(a,X1))) = or(a11,not(X1)),
inference(rw,[status(thm)],[c_0_130,c_0_49]) ).
cnf(c_0_148,negated_conjecture,
and(a,and(a15,a16)) = and(a,a12),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_45]) ).
cnf(c_0_149,negated_conjecture,
and(b,and(X1,a12)) = and(X1,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_55]) ).
cnf(c_0_150,negated_conjecture,
not(and(a14,and(a15,X1))) = or(a16,not(X1)),
inference(rw,[status(thm)],[c_0_135,c_0_49]) ).
cnf(c_0_151,negated_conjecture,
and(a15,not(carryin)) = not(carryin),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_136]),c_0_45]) ).
cnf(c_0_152,plain,
not(and(X1,not(X2))) = or(not(X1),X2),
inference(spm,[status(thm)],[c_0_52,c_0_56]) ).
cnf(c_0_153,negated_conjecture,
and(carryin,a16) = carryin,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_137]),c_0_56]) ).
cnf(c_0_154,negated_conjecture,
or(a15,a14) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_140]) ).
cnf(c_0_155,negated_conjecture,
or(n1,X1) = n1,
inference(spm,[status(thm)],[c_0_140,c_0_51]) ).
cnf(c_0_156,negated_conjecture,
a17 = not(and(a15,carryin)),
circuit7 ).
cnf(c_0_157,negated_conjecture,
and(a16,and(carryin,a14)) = and(carryin,a14),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_141]),c_0_45]) ).
cnf(c_0_158,negated_conjecture,
and(c1,and(a,b)) = and(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_142]),c_0_143]) ).
cnf(c_0_159,plain,
and(X1,not(or(X2,X1))) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_58]),c_0_56]),c_0_45]) ).
cnf(c_0_160,negated_conjecture,
not(or(a,b)) = and(a13,not(a)),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_161,negated_conjecture,
or(and(a,b),and(carryin,a14)) = c1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_143]),c_0_97]),c_0_51]) ).
cnf(c_0_162,negated_conjecture,
not(and(and(a11,a15),X1)) = or(c1,not(X1)),
inference(spm,[status(thm)],[c_0_52,c_0_97]) ).
cnf(c_0_163,negated_conjecture,
or(a11,a14) = a11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_149]),c_0_48]),c_0_104]),c_0_105]),c_0_106]) ).
cnf(c_0_164,negated_conjecture,
or(carryin,and(a15,a16)) = or(carryin,a16),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_152]),c_0_113]),c_0_132]),c_0_51]),c_0_56]),c_0_51]) ).
cnf(c_0_165,negated_conjecture,
or(carryin,a16) = a16,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_153]),c_0_51]) ).
cnf(c_0_166,negated_conjecture,
or(and(a12,a13),not(X1)) = not(and(X1,a14)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_113]),c_0_51]) ).
cnf(c_0_167,negated_conjecture,
or(a14,or(a15,X1)) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_154]),c_0_155]),c_0_51]) ).
cnf(c_0_168,negated_conjecture,
or(or(X1,X2),X3) = or(X2,or(X1,X3)),
inference(spm,[status(thm)],[c_0_51,c_0_110]) ).
cnf(c_0_169,axiom,
or(or(X1,X2),not(X2)) = n1,
or_not_evaluation2 ).
cnf(c_0_170,negated_conjecture,
and(a17,and(a14,X1)) = and(a14,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_96]),c_0_156]),c_0_121]),c_0_71]),c_0_45]) ).
cnf(c_0_171,negated_conjecture,
and(a14,and(carryin,a16)) = and(carryin,a14),
inference(rw,[status(thm)],[c_0_157,c_0_55]) ).
cnf(c_0_172,negated_conjecture,
or(c1,and(a,b)) = c1,
inference(spm,[status(thm)],[c_0_57,c_0_158]) ).
cnf(c_0_173,plain,
or(and(X1,X2),and(X3,and(X1,not(X2)))) = or(and(X1,X3),and(X1,X2)),
inference(rw,[status(thm)],[c_0_120,c_0_49]) ).
cnf(c_0_174,negated_conjecture,
and(b,and(a13,not(a))) = n0,
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_175,negated_conjecture,
or(and(a,b),not(X1)) = not(and(X1,a11)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_143]),c_0_51]) ).
cnf(c_0_176,negated_conjecture,
or(a14,and(a,b)) = or(a14,c1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_161]),c_0_51]) ).
cnf(c_0_177,negated_conjecture,
not(and(a15,and(a11,X1))) = or(c1,not(X1)),
inference(rw,[status(thm)],[c_0_162,c_0_49]) ).
cnf(c_0_178,negated_conjecture,
and(a11,a14) = a14,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_163]),c_0_45]) ).
cnf(c_0_179,negated_conjecture,
or(carryin,and(a15,a16)) = a16,
inference(rw,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_180,negated_conjecture,
or(and(a15,a16),not(X1)) = not(and(X1,a14)),
inference(rw,[status(thm)],[c_0_166,c_0_132]) ).
cnf(c_0_181,negated_conjecture,
or(a14,or(X1,a15)) = n1,
inference(spm,[status(thm)],[c_0_167,c_0_76]) ).
cnf(c_0_182,negated_conjecture,
or(X1,or(X2,X3)) = or(X3,or(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_168]),c_0_168]) ).
cnf(c_0_183,plain,
or(X1,not(and(X2,X1))) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_52]),c_0_56]),c_0_51]) ).
cnf(c_0_184,negated_conjecture,
and(a14,and(carryin,a17)) = and(carryin,a14),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_55]) ).
cnf(c_0_185,negated_conjecture,
or(a11,c1) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_172]),c_0_48]),c_0_51]) ).
cnf(c_0_186,axiom,
or(or(X1,X2),X2) = or(X1,X2),
or_evaluation1 ).
cnf(c_0_187,negated_conjecture,
not(and(a11,a13)) = and(b,or(a11,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_143]),c_0_93]),c_0_45]) ).
cnf(c_0_188,negated_conjecture,
or(a11,a) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_95]),c_0_62]),c_0_56]) ).
cnf(c_0_189,negated_conjecture,
or(a,and(b,a13)) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_45]),c_0_88]),c_0_71]),c_0_45]),c_0_45]),c_0_88]),c_0_51]) ).
cnf(c_0_190,negated_conjecture,
not(and(a16,and(a11,a15))) = or(a14,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_119]),c_0_51]),c_0_176]),c_0_46]),c_0_45]),c_0_45]) ).
cnf(c_0_191,negated_conjecture,
or(c1,and(a15,a16)) = a16,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_73]),c_0_113]),c_0_132]) ).
cnf(c_0_192,negated_conjecture,
or(and(a15,a14),and(a15,a16)) = a15,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_179]),c_0_82]),c_0_180]),c_0_83]),c_0_51]) ).
cnf(c_0_193,negated_conjecture,
or(a15,or(X1,a14)) = n1,
inference(rw,[status(thm)],[c_0_181,c_0_182]) ).
cnf(c_0_194,negated_conjecture,
or(a15,and(carryin,a17)) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_184]),c_0_83]),c_0_51]) ).
cnf(c_0_195,negated_conjecture,
or(c1,or(a11,X1)) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_185]),c_0_155]),c_0_51]) ).
cnf(c_0_196,negated_conjecture,
or(a16,and(a15,a14)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_73]),c_0_51]) ).
cnf(c_0_197,plain,
or(X1,or(X2,X1)) = or(X2,X1),
inference(rw,[status(thm)],[c_0_186,c_0_51]) ).
cnf(c_0_198,negated_conjecture,
or(b,and(a11,a)) = or(b,a14),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_102]),c_0_51]) ).
cnf(c_0_199,negated_conjecture,
or(and(a11,a),not(X1)) = not(and(X1,a12)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_89]),c_0_51]) ).
cnf(c_0_200,negated_conjecture,
not(and(a11,a13)) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_187,c_0_188]),c_0_106]) ).
cnf(c_0_201,negated_conjecture,
not(or(X1,and(a11,a))) = and(a12,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_81]),c_0_45]) ).
cnf(c_0_202,plain,
or(not(X1),and(X2,X1)) = or(X2,not(X1)),
inference(spm,[status(thm)],[c_0_115,c_0_56]) ).
cnf(c_0_203,negated_conjecture,
and(b,and(a12,X1)) = and(X1,b),
inference(spm,[status(thm)],[c_0_149,c_0_45]) ).
cnf(c_0_204,negated_conjecture,
and(b,a13) = and(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_189]),c_0_49]),c_0_45]),c_0_55]),c_0_88]),c_0_45]) ).
cnf(c_0_205,negated_conjecture,
not(or(a14,c1)) = and(a16,and(a11,a15)),
inference(spm,[status(thm)],[c_0_56,c_0_190]) ).
cnf(c_0_206,negated_conjecture,
not(or(X1,and(a,b))) = and(a11,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_48]),c_0_45]) ).
cnf(c_0_207,negated_conjecture,
and(or(X1,X2),not(X2)) = and(X1,not(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_47]),c_0_71]) ).
cnf(c_0_208,negated_conjecture,
not(or(and(a11,a15),X1)) = and(c1,not(X1)),
inference(spm,[status(thm)],[c_0_58,c_0_97]) ).
cnf(c_0_209,negated_conjecture,
or(and(a11,a15),and(a15,a16)) = a15,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_191]),c_0_82]),c_0_51]),c_0_192]),c_0_114]),c_0_51]) ).
cnf(c_0_210,negated_conjecture,
or(a11,a15) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_163]),c_0_51]) ).
cnf(c_0_211,negated_conjecture,
not(and(and(a15,carryin),X1)) = or(a17,not(X1)),
inference(spm,[status(thm)],[c_0_52,c_0_156]) ).
cnf(c_0_212,negated_conjecture,
not(or(and(carryin,a14),X1)) = and(a15,not(X1)),
inference(spm,[status(thm)],[c_0_58,c_0_83]) ).
cnf(c_0_213,negated_conjecture,
or(and(carryin,a14),and(carryin,a17)) = and(carryin,a17),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_194]),c_0_70]),c_0_71]),c_0_92]),c_0_51]) ).
cnf(c_0_214,negated_conjecture,
or(c1,or(X1,a11)) = n1,
inference(spm,[status(thm)],[c_0_195,c_0_76]) ).
cnf(c_0_215,negated_conjecture,
not(and(and(a11,b),X1)) = or(a13,not(X1)),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_216,negated_conjecture,
not(and(b,or(a11,a))) = and(a11,a13),
inference(spm,[status(thm)],[c_0_56,c_0_187]) ).
cnf(c_0_217,negated_conjecture,
or(a14,a16) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_196]),c_0_140]),c_0_51]) ).
cnf(c_0_218,negated_conjecture,
or(and(a11,a),or(b,a14)) = or(b,a14),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_219,negated_conjecture,
or(a,or(b,a14)) = or(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_198]),c_0_51]) ).
cnf(c_0_220,negated_conjecture,
not(and(a13,and(a11,a12))) = or(b,a14),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_51]),c_0_198]),c_0_46]),c_0_45]) ).
cnf(c_0_221,negated_conjecture,
and(a,a12) = and(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_86]),c_0_143]),c_0_56]),c_0_45]) ).
cnf(c_0_222,negated_conjecture,
and(b,and(a15,a16)) = and(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_132]),c_0_45]),c_0_204]) ).
cnf(c_0_223,negated_conjecture,
not(or(a14,c1)) = and(a15,and(a11,a16)),
inference(rw,[status(thm)],[c_0_205,c_0_55]) ).
cnf(c_0_224,negated_conjecture,
and(a15,and(a11,a16)) = and(a11,and(a15,a16)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_176]),c_0_205]),c_0_55]),c_0_113]),c_0_132]) ).
cnf(c_0_225,negated_conjecture,
and(X1,and(X2,or(X3,X1))) = and(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_134]),c_0_51]),c_0_87]),c_0_55]) ).
cnf(c_0_226,negated_conjecture,
and(a11,or(a14,c1)) = a14,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_176]),c_0_48]),c_0_48]),c_0_45]),c_0_178]),c_0_45]) ).
cnf(c_0_227,negated_conjecture,
and(a14,c1) = and(carryin,a14),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_209]),c_0_92]),c_0_104]),c_0_105]),c_0_106]),c_0_45]) ).
cnf(c_0_228,negated_conjecture,
or(a15,and(a,b)) = a15,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_210]),c_0_70]),c_0_71]),c_0_143]) ).
cnf(c_0_229,negated_conjecture,
not(and(carryin,and(a15,X1))) = or(a17,not(X1)),
inference(rw,[status(thm)],[c_0_211,c_0_49]) ).
cnf(c_0_230,negated_conjecture,
and(a15,not(and(carryin,a17))) = not(and(carryin,a17)),
inference(spm,[status(thm)],[c_0_212,c_0_213]) ).
cnf(c_0_231,negated_conjecture,
or(a11,or(X1,c1)) = n1,
inference(rw,[status(thm)],[c_0_214,c_0_182]) ).
cnf(c_0_232,negated_conjecture,
not(and(a14,or(carryin,a16))) = a15,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_164]),c_0_180]),c_0_180]),c_0_83]),c_0_45]) ).
cnf(c_0_233,negated_conjecture,
not(and(X1,and(a11,a15))) = or(c1,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_97]),c_0_51]) ).
cnf(c_0_234,negated_conjecture,
not(and(b,and(a11,X1))) = or(a13,not(X1)),
inference(rw,[status(thm)],[c_0_215,c_0_49]) ).
cnf(c_0_235,negated_conjecture,
or(a13,and(carryin,a14)) = or(a13,a16),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_127]),c_0_51]) ).
cnf(c_0_236,negated_conjecture,
not(b) = and(a11,a13),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_216,c_0_188]),c_0_106]) ).
cnf(c_0_237,negated_conjecture,
or(a16,or(a14,X1)) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_217]),c_0_155]),c_0_51]) ).
cnf(c_0_238,negated_conjecture,
or(a14,or(a,b)) = or(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_218]),c_0_219]),c_0_110]),c_0_51]),c_0_51]) ).
cnf(c_0_239,negated_conjecture,
not(or(b,a14)) = and(a13,and(a11,a12)),
inference(spm,[status(thm)],[c_0_56,c_0_220]) ).
cnf(c_0_240,negated_conjecture,
and(a,and(a15,a16)) = and(a,b),
inference(rw,[status(thm)],[c_0_148,c_0_221]) ).
cnf(c_0_241,negated_conjecture,
or(a14,c1) = or(b,a14),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_222]),c_0_104]),c_0_105]),c_0_106]),c_0_176]),c_0_104]),c_0_105]),c_0_106]) ).
cnf(c_0_242,negated_conjecture,
not(or(a14,c1)) = and(a11,and(a15,a16)),
inference(rw,[status(thm)],[c_0_223,c_0_224]) ).
cnf(c_0_243,negated_conjecture,
or(a14,not(or(a,b))) = or(a14,not(a)),
inference(spm,[status(thm)],[c_0_68,c_0_129]) ).
cnf(c_0_244,negated_conjecture,
and(carryin,a14) = and(a11,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_226]),c_0_45]),c_0_227]) ).
cnf(c_0_245,negated_conjecture,
and(b,and(a,a15)) = and(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_228]),c_0_49]) ).
cnf(c_0_246,plain,
not(or(X1,not(X2))) = and(not(X1),X2),
inference(spm,[status(thm)],[c_0_58,c_0_56]) ).
cnf(c_0_247,negated_conjecture,
or(and(carryin,a17),not(carryin)) = a17,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_152]),c_0_56]),c_0_87]),c_0_51]) ).
cnf(c_0_248,negated_conjecture,
not(a17) = and(a15,carryin),
inference(spm,[status(thm)],[c_0_56,c_0_156]) ).
cnf(c_0_249,negated_conjecture,
s1 = not(and(a16,a17)),
circuit8 ).
cnf(c_0_250,negated_conjecture,
or(a11,or(c1,X1)) = n1,
inference(spm,[status(thm)],[c_0_231,c_0_51]) ).
cnf(c_0_251,negated_conjecture,
and(a14,or(carryin,a16)) = and(carryin,a14),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_232]),c_0_92]) ).
cnf(c_0_252,negated_conjecture,
or(c1,and(a11,a13)) = or(a13,a16),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_234]),c_0_92]),c_0_235]),c_0_236]) ).
cnf(c_0_253,negated_conjecture,
or(a16,or(a,b)) = n1,
inference(spm,[status(thm)],[c_0_237,c_0_238]) ).
cnf(c_0_254,negated_conjecture,
or(a,and(a11,a13)) = or(a,a13),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_100]),c_0_152]),c_0_51]),c_0_236]),c_0_56]),c_0_51]) ).
cnf(c_0_255,negated_conjecture,
not(or(b,a14)) = and(a12,and(a11,a13)),
inference(rw,[status(thm)],[c_0_239,c_0_55]) ).
cnf(c_0_256,negated_conjecture,
or(b,a14) = or(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_240]),c_0_104]),c_0_105]),c_0_106]),c_0_176]),c_0_241]),c_0_104]),c_0_105]),c_0_106]),c_0_129]) ).
cnf(c_0_257,negated_conjecture,
and(a12,and(a11,a13)) = and(a11,and(a15,a16)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_242,c_0_241]),c_0_239]),c_0_55]) ).
cnf(c_0_258,negated_conjecture,
or(a14,and(a13,not(a))) = or(a14,not(a)),
inference(rw,[status(thm)],[c_0_243,c_0_160]) ).
cnf(c_0_259,negated_conjecture,
not(a15) = and(a11,c1),
inference(rw,[status(thm)],[c_0_92,c_0_244]) ).
cnf(c_0_260,negated_conjecture,
and(a15,c1) = and(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_161]),c_0_83]),c_0_45]),c_0_83]),c_0_49]),c_0_245]) ).
cnf(c_0_261,negated_conjecture,
and(carryin,not(and(carryin,a17))) = and(a15,carryin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_247]),c_0_248]),c_0_45]) ).
cnf(c_0_262,negated_conjecture,
not(s1) = and(a16,a17),
inference(spm,[status(thm)],[c_0_56,c_0_249]) ).
cnf(c_0_263,negated_conjecture,
or(a11,a16) = n1,
inference(spm,[status(thm)],[c_0_250,c_0_191]) ).
cnf(c_0_264,negated_conjecture,
not(and(X1,and(a16,a17))) = or(s1,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_249]),c_0_51]) ).
cnf(c_0_265,negated_conjecture,
and(a14,and(X1,a17)) = and(X1,a14),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_134]),c_0_55]) ).
cnf(c_0_266,negated_conjecture,
and(a14,a16) = and(carryin,a14),
inference(rw,[status(thm)],[c_0_251,c_0_165]) ).
cnf(c_0_267,negated_conjecture,
or(a13,a16) = or(c1,a13),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_252]),c_0_126]) ).
cnf(c_0_268,negated_conjecture,
or(b,or(a,a16)) = n1,
inference(rw,[status(thm)],[c_0_253,c_0_182]) ).
cnf(c_0_269,negated_conjecture,
or(a,and(a11,a13)) = a13,
inference(rw,[status(thm)],[c_0_254,c_0_101]) ).
cnf(c_0_270,negated_conjecture,
or(c1,and(a15,a14)) = or(a14,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_190,c_0_233]),c_0_82]) ).
cnf(c_0_271,negated_conjecture,
and(a13,not(a)) = and(a11,and(a15,a16)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_255,c_0_256]),c_0_160]),c_0_257]) ).
cnf(c_0_272,negated_conjecture,
or(a14,not(a)) = or(a14,and(a11,a13)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_256]),c_0_160]),c_0_258]),c_0_236]) ).
cnf(c_0_273,negated_conjecture,
and(a14,c1) = and(a11,c1),
inference(rw,[status(thm)],[c_0_227,c_0_244]) ).
cnf(c_0_274,negated_conjecture,
or(and(a11,a15),and(a11,c1)) = a11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_259]),c_0_260]),c_0_48]) ).
cnf(c_0_275,negated_conjecture,
not(or(and(a15,carryin),X1)) = and(a17,not(X1)),
inference(spm,[status(thm)],[c_0_58,c_0_156]) ).
cnf(c_0_276,negated_conjecture,
or(and(a15,carryin),and(carryin,a17)) = carryin,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_261]),c_0_57]),c_0_51]) ).
cnf(c_0_277,negated_conjecture,
not(or(X1,and(a15,carryin))) = and(a17,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_156]),c_0_45]) ).
cnf(c_0_278,negated_conjecture,
and(a17,and(a16,not(X1))) = not(or(X1,s1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_262]),c_0_55]) ).
cnf(c_0_279,negated_conjecture,
or(a16,and(a,b)) = a16,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_263]),c_0_70]),c_0_71]),c_0_143]) ).
cnf(c_0_280,negated_conjecture,
or(s1,and(a15,a16)) = a15,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_264,c_0_265]),c_0_113]),c_0_132]),c_0_45]),c_0_266]),c_0_83]) ).
cnf(c_0_281,negated_conjecture,
or(c1,and(a11,a13)) = or(c1,a13),
inference(rw,[status(thm)],[c_0_252,c_0_267]) ).
cnf(c_0_282,negated_conjecture,
or(c1,a13) = or(a,a16),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_268]),c_0_70]),c_0_168]),c_0_71]),c_0_236]),c_0_168]),c_0_269]),c_0_51]),c_0_267]),c_0_51]) ).
cnf(c_0_283,plain,
or(X1,not(or(X2,and(X3,X1)))) = or(not(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_68]),c_0_76]),c_0_51]) ).
cnf(c_0_284,negated_conjecture,
or(c1,and(a15,a14)) = or(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_270,c_0_241]),c_0_256]) ).
cnf(c_0_285,negated_conjecture,
or(a14,and(a11,and(a15,a16))) = or(a14,and(a11,a13)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_258,c_0_271]),c_0_272]) ).
cnf(c_0_286,negated_conjecture,
or(a14,and(a11,a15)) = a11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_273]),c_0_114]),c_0_274]),c_0_114]) ).
cnf(c_0_287,negated_conjecture,
and(a14,and(a11,a)) = and(a11,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_102]),c_0_45]) ).
cnf(c_0_288,negated_conjecture,
and(a17,not(and(carryin,a17))) = not(carryin),
inference(spm,[status(thm)],[c_0_275,c_0_276]) ).
cnf(c_0_289,negated_conjecture,
and(carryin,a17) = and(a11,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_277,c_0_202]),c_0_136]),c_0_92]),c_0_244]),c_0_56]),c_0_45]) ).
cnf(c_0_290,negated_conjecture,
not(and(a11,c1)) = a15,
inference(rw,[status(thm)],[c_0_83,c_0_244]) ).
cnf(c_0_291,negated_conjecture,
not(or(a11,s1)) = and(a17,and(b,and(a,a16))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_278,c_0_143]),c_0_55]) ).
cnf(c_0_292,negated_conjecture,
and(b,and(a,a16)) = and(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_279]),c_0_49]) ).
cnf(c_0_293,negated_conjecture,
and(a15,s1) = s1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_280]),c_0_45]) ).
cnf(c_0_294,negated_conjecture,
and(or(X1,X2),not(X1)) = and(X2,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_47]),c_0_121]) ).
cnf(c_0_295,negated_conjecture,
and(a11,and(a15,a14)) = and(a15,a14),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_279]),c_0_82]),c_0_82]) ).
cnf(c_0_296,negated_conjecture,
or(c1,and(a11,a13)) = or(a,a16),
inference(rw,[status(thm)],[c_0_281,c_0_282]) ).
cnf(c_0_297,negated_conjecture,
or(a14,and(a11,a13)) = a11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_283,c_0_284]),c_0_160]),c_0_271]),c_0_285]),c_0_114]),c_0_51]),c_0_286]) ).
cnf(c_0_298,negated_conjecture,
and(a,and(a11,a14)) = and(a11,a),
inference(rw,[status(thm)],[c_0_287,c_0_55]) ).
cnf(c_0_299,negated_conjecture,
not(carryin) = and(a15,a17),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_288,c_0_289]),c_0_290]),c_0_45]) ).
cnf(c_0_300,negated_conjecture,
or(and(X1,X2),and(X2,X3)) = and(or(X1,X3),X2),
inference(spm,[status(thm)],[c_0_93,c_0_45]) ).
cnf(c_0_301,negated_conjecture,
and(a11,and(a,b)) = n0,
inference(spm,[status(thm)],[c_0_47,c_0_143]) ).
cnf(c_0_302,negated_conjecture,
not(or(a11,s1)) = and(b,and(a,a17)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_291,c_0_292]),c_0_55]) ).
cnf(c_0_303,negated_conjecture,
and(s1,and(a15,X1)) = and(s1,X1),
inference(spm,[status(thm)],[c_0_49,c_0_293]) ).
cnf(c_0_304,negated_conjecture,
not(and(and(a11,a),X1)) = or(a12,not(X1)),
inference(spm,[status(thm)],[c_0_52,c_0_81]) ).
cnf(c_0_305,negated_conjecture,
and(a14,not(a)) = and(a11,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_294,c_0_129]),c_0_294]),c_0_116]) ).
cnf(c_0_306,negated_conjecture,
or(and(a15,a14),and(X1,a16)) = or(X1,and(a15,a14)),
inference(spm,[status(thm)],[c_0_115,c_0_73]) ).
cnf(c_0_307,negated_conjecture,
or(a16,and(a11,a13)) = or(a,a16),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_295]),c_0_108]),c_0_236]),c_0_73]),c_0_267]),c_0_282]) ).
cnf(c_0_308,negated_conjecture,
and(b,or(a,a16)) = and(b,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_296]),c_0_187]),c_0_188]),c_0_106]),c_0_187]),c_0_188]),c_0_106]),c_0_45]),c_0_45]) ).
cnf(c_0_309,plain,
not(and(or(X1,X2),or(X2,not(X1)))) = not(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_68]),c_0_52]),c_0_52]),c_0_45]),c_0_85]) ).
cnf(c_0_310,negated_conjecture,
or(a14,not(a)) = a11,
inference(rw,[status(thm)],[c_0_272,c_0_297]) ).
cnf(c_0_311,negated_conjecture,
and(a,a14) = and(a11,a),
inference(rw,[status(thm)],[c_0_298,c_0_178]) ).
cnf(c_0_312,negated_conjecture,
not(and(carryin,c1)) = and(a15,or(a11,a17)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_299]),c_0_300]),c_0_45]) ).
cnf(c_0_313,negated_conjecture,
and(carryin,and(a15,not(X1))) = not(or(X1,a17)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_248]),c_0_55]) ).
cnf(c_0_314,negated_conjecture,
and(b,and(a,or(a11,X1))) = and(X1,and(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_301]),c_0_121]),c_0_55]) ).
cnf(c_0_315,negated_conjecture,
or(a11,and(a15,carryin)) = or(a11,s1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_302]),c_0_147]),c_0_248]) ).
cnf(c_0_316,negated_conjecture,
and(b,and(a,s1)) = and(s1,c1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_303,c_0_260]),c_0_55]) ).
cnf(c_0_317,negated_conjecture,
not(and(and(carryin,a14),X1)) = or(a15,not(X1)),
inference(spm,[status(thm)],[c_0_52,c_0_83]) ).
cnf(c_0_318,negated_conjecture,
or(a13,a16) = or(a,a16),
inference(rw,[status(thm)],[c_0_267,c_0_282]) ).
cnf(c_0_319,negated_conjecture,
and(a14,a17) = a14,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_106]),c_0_45]) ).
cnf(c_0_320,negated_conjecture,
or(X1,or(and(X1,X2),X3)) = or(X3,X1),
inference(spm,[status(thm)],[c_0_76,c_0_45]) ).
cnf(c_0_321,negated_conjecture,
or(and(a15,a16),and(X1,a14)) = or(X1,and(a15,a16)),
inference(spm,[status(thm)],[c_0_115,c_0_119]) ).
cnf(c_0_322,negated_conjecture,
or(X1,or(X2,and(X1,X3))) = or(X2,X1),
inference(spm,[status(thm)],[c_0_138,c_0_45]) ).
cnf(c_0_323,negated_conjecture,
or(a14,and(a11,b)) = a14,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_102]),c_0_51]) ).
cnf(c_0_324,negated_conjecture,
not(and(a,and(a11,X1))) = or(a12,not(X1)),
inference(rw,[status(thm)],[c_0_304,c_0_49]) ).
cnf(c_0_325,negated_conjecture,
and(a11,and(carryin,a14)) = and(carryin,a14),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_228]),c_0_92]),c_0_92]) ).
cnf(c_0_326,negated_conjecture,
or(a,and(a15,a16)) = a13,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_305]),c_0_53]),c_0_113]),c_0_132]),c_0_51]) ).
cnf(c_0_327,negated_conjecture,
and(b,a12) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_106]),c_0_45]) ).
cnf(c_0_328,negated_conjecture,
or(and(a11,c1),and(a,b)) = c1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_161,c_0_244]),c_0_51]) ).
cnf(c_0_329,negated_conjecture,
or(a14,and(X1,a16)) = or(X1,a14),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_306]),c_0_138]),c_0_51]) ).
cnf(c_0_330,negated_conjecture,
and(b,a16) = and(b,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_307]),c_0_187]),c_0_188]),c_0_106]),c_0_187]),c_0_188]),c_0_106]),c_0_45]),c_0_45]),c_0_308]) ).
cnf(c_0_331,negated_conjecture,
not(and(a11,a12)) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_309,c_0_310]),c_0_113]),c_0_132]),c_0_51]),c_0_180]),c_0_311]),c_0_81]),c_0_56]) ).
cnf(c_0_332,negated_conjecture,
not(and(a15,or(a11,a17))) = and(carryin,c1),
inference(spm,[status(thm)],[c_0_56,c_0_312]) ).
cnf(c_0_333,negated_conjecture,
not(or(a11,a17)) = and(carryin,and(b,and(a,a15))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_313,c_0_143]),c_0_55]) ).
cnf(c_0_334,negated_conjecture,
and(b,and(a,carryin)) = and(s1,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_314,c_0_315]),c_0_314]),c_0_55]),c_0_316]),c_0_49]),c_0_55]),c_0_245]),c_0_55]) ).
cnf(c_0_335,negated_conjecture,
not(and(a14,and(carryin,X1))) = or(a15,not(X1)),
inference(rw,[status(thm)],[c_0_317,c_0_49]) ).
cnf(c_0_336,negated_conjecture,
or(a16,not(a)) = or(a16,and(a11,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_318]),c_0_68]),c_0_63]) ).
cnf(c_0_337,negated_conjecture,
~ circuit(sum(a,b,carryin),carryout(a,b,carryin)),
prove_circuit ).
cnf(c_0_338,negated_conjecture,
sum(X1,X2,X3) = xor(xor(X1,X2),X3),
sum_definition ).
cnf(c_0_339,axiom,
xor(X1,X2) = or(and(X1,not(X2)),and(X2,not(X1))),
xor_definition ).
cnf(c_0_340,negated_conjecture,
carryout(X1,X2,X3) = or(and(X1,or(X2,X3)),and(not(X1),and(X2,X3))),
carryout_definition ).
cnf(c_0_341,axiom,
or(or(X1,X2),not(X1)) = n1,
or_not_evaluation3 ).
cnf(c_0_342,negated_conjecture,
or(a14,a17) = a17,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_319]),c_0_51]) ).
cnf(c_0_343,negated_conjecture,
or(a15,and(X1,a14)) = or(X1,a15),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_320,c_0_321]),c_0_322]),c_0_51]) ).
cnf(c_0_344,negated_conjecture,
and(a14,and(carryin,not(X1))) = not(or(X1,a15)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_92]),c_0_55]) ).
cnf(c_0_345,negated_conjecture,
or(b,or(a,a15)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_129]),c_0_182]) ).
cnf(c_0_346,negated_conjecture,
and(a14,and(a11,b)) = and(a11,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_323]),c_0_45]) ).
cnf(c_0_347,negated_conjecture,
not(and(X1,and(a11,c1))) = or(a15,not(X1)),
inference(rw,[status(thm)],[c_0_94,c_0_244]) ).
cnf(c_0_348,negated_conjecture,
or(a15,not(a)) = or(a15,a12),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_324,c_0_325]),c_0_94]),c_0_83]),c_0_51]) ).
cnf(c_0_349,negated_conjecture,
or(and(a11,b),and(a15,a16)) = a12,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_326]),c_0_63]),c_0_180]),c_0_311]),c_0_81]),c_0_51]) ).
cnf(c_0_350,negated_conjecture,
or(b,a12) = a12,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_327]),c_0_51]) ).
cnf(c_0_351,negated_conjecture,
or(and(a11,a15),and(a,b)) = a15,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_328]),c_0_114]),c_0_290]),c_0_51]),c_0_228]),c_0_51]) ).
cnf(c_0_352,negated_conjecture,
or(X1,not(or(X1,X2))) = or(X1,not(X2)),
inference(spm,[status(thm)],[c_0_68,c_0_51]) ).
cnf(c_0_353,negated_conjecture,
or(a14,and(b,c1)) = or(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_329,c_0_330]),c_0_256]) ).
cnf(c_0_354,negated_conjecture,
not(a) = and(a11,a12),
inference(spm,[status(thm)],[c_0_56,c_0_331]) ).
cnf(c_0_355,negated_conjecture,
or(and(a,b),and(carryin,c1)) = c1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_332]),c_0_49]),c_0_45]),c_0_233]),c_0_333]),c_0_245]),c_0_55]),c_0_334]),c_0_87]) ).
cnf(c_0_356,negated_conjecture,
or(a15,not(or(carryin,X1))) = a15,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_335,c_0_75]),c_0_45]),c_0_83]) ).
cnf(c_0_357,negated_conjecture,
or(a16,and(a11,b)) = or(a12,a16),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_324,c_0_295]),c_0_108]),c_0_336]),c_0_73]) ).
cnf(c_0_358,negated_conjecture,
or(a12,or(b,X1)) = or(X1,a12),
inference(spm,[status(thm)],[c_0_76,c_0_327]) ).
cnf(c_0_359,negated_conjecture,
or(b,and(carryin,a14)) = or(b,c1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_161]),c_0_51]) ).
cnf(c_0_360,negated_conjecture,
~ circuit(or(and(or(and(a,not(b)),and(b,not(a))),not(carryin)),and(carryin,not(or(and(a,not(b)),and(b,not(a)))))),or(and(a,or(b,carryin)),and(not(a),and(b,carryin)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_337,c_0_338]),c_0_339]),c_0_339]),c_0_340]) ).
cnf(c_0_361,negated_conjecture,
or(a17,and(a12,a13)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_341,c_0_342]),c_0_113]) ).
cnf(c_0_362,negated_conjecture,
or(a15,and(a14,X1)) = or(X1,a15),
inference(spm,[status(thm)],[c_0_343,c_0_45]) ).
cnf(c_0_363,negated_conjecture,
and(a14,and(a11,X1)) = and(a14,X1),
inference(spm,[status(thm)],[c_0_49,c_0_178]) ).
cnf(c_0_364,negated_conjecture,
not(or(a15,a13)) = and(a14,and(b,and(a11,carryin))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_344,c_0_63]),c_0_51]),c_0_55]) ).
cnf(c_0_365,negated_conjecture,
or(a15,a13) = or(a,a15),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_345]),c_0_70]),c_0_168]),c_0_71]),c_0_236]),c_0_168]),c_0_269]),c_0_51]) ).
cnf(c_0_366,negated_conjecture,
and(b,and(a11,a14)) = and(a11,b),
inference(rw,[status(thm)],[c_0_346,c_0_55]) ).
cnf(c_0_367,negated_conjecture,
or(a12,and(a11,a15)) = or(a15,a12),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_324,c_0_347]),c_0_348]),c_0_114]) ).
cnf(c_0_368,negated_conjecture,
or(b,and(a15,a16)) = a12,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_349]),c_0_350]),c_0_51]) ).
cnf(c_0_369,negated_conjecture,
or(b,and(a11,a15)) = or(b,a15),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_351]),c_0_51]) ).
cnf(c_0_370,negated_conjecture,
or(a14,not(and(b,c1))) = a11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_352,c_0_353]),c_0_160]),c_0_354]),c_0_55]),c_0_257]),c_0_285]),c_0_297]) ).
cnf(c_0_371,negated_conjecture,
or(a13,or(a,X1)) = or(X1,a13),
inference(spm,[status(thm)],[c_0_76,c_0_88]) ).
cnf(c_0_372,negated_conjecture,
or(a,and(carryin,c1)) = or(a,c1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_320,c_0_355]),c_0_51]) ).
cnf(c_0_373,negated_conjecture,
or(a15,and(a11,not(carryin))) = a15,
inference(spm,[status(thm)],[c_0_356,c_0_206]) ).
cnf(c_0_374,negated_conjecture,
and(a15,and(a11,not(X1))) = not(or(X1,c1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_114]),c_0_55]) ).
cnf(c_0_375,negated_conjecture,
or(a14,c1) = or(a,b),
inference(rw,[status(thm)],[c_0_241,c_0_256]) ).
cnf(c_0_376,negated_conjecture,
or(b,or(a12,a16)) = or(b,a16),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_357]),c_0_51]) ).
cnf(c_0_377,negated_conjecture,
or(a12,and(carryin,a14)) = or(c1,a12),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_358,c_0_359]),c_0_358]),c_0_51]) ).
cnf(c_0_378,negated_conjecture,
and(c1,a16) = c1,
inference(spm,[status(thm)],[c_0_75,c_0_191]) ).
cnf(c_0_379,negated_conjecture,
~ circuit(or(and(carryin,not(or(and(a,not(b)),and(b,not(a))))),and(not(carryin),or(and(a,not(b)),and(b,not(a))))),or(and(a,or(b,carryin)),and(and(b,carryin),not(a)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_360,c_0_45]),c_0_45]),c_0_51]) ).
cnf(c_0_380,negated_conjecture,
or(and(a11,a),and(a11,a13)) = and(a11,a13),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_236]),c_0_327]),c_0_236]) ).
cnf(c_0_381,negated_conjecture,
or(and(a15,carryin),and(a12,a13)) = and(a12,a13),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_361]),c_0_70]),c_0_71]),c_0_248]),c_0_51]) ).
cnf(c_0_382,negated_conjecture,
or(a15,and(a11,X1)) = or(X1,a15),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_362,c_0_363]),c_0_362]),c_0_51]) ).
cnf(c_0_383,negated_conjecture,
not(or(a,a15)) = and(a14,and(b,and(a11,carryin))),
inference(rw,[status(thm)],[c_0_364,c_0_365]) ).
cnf(c_0_384,negated_conjecture,
and(b,a14) = and(a11,b),
inference(rw,[status(thm)],[c_0_366,c_0_178]) ).
cnf(c_0_385,negated_conjecture,
or(and(a,b),and(X1,a11)) = or(X1,and(a,b)),
inference(spm,[status(thm)],[c_0_115,c_0_48]) ).
cnf(c_0_386,negated_conjecture,
or(and(a11,a),and(X1,a12)) = or(X1,and(a11,a)),
inference(spm,[status(thm)],[c_0_115,c_0_81]) ).
cnf(c_0_387,negated_conjecture,
and(c1,or(a15,a12)) = and(c1,a12),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_367]),c_0_97]),c_0_97]),c_0_45]),c_0_45]) ).
cnf(c_0_388,negated_conjecture,
or(a15,a12) = or(b,a15),
inference(spm,[status(thm)],[c_0_322,c_0_368]) ).
cnf(c_0_389,negated_conjecture,
and(c1,or(b,a15)) = and(b,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_369]),c_0_97]),c_0_97]),c_0_45]) ).
cnf(c_0_390,negated_conjecture,
and(a14,and(b,c1)) = and(a11,and(b,c1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_370]),c_0_56]),c_0_56]) ).
cnf(c_0_391,axiom,
and(and(and(X1,X2),X3),not(X1)) = n0,
and_not_evaluation4 ).
cnf(c_0_392,negated_conjecture,
or(a16,and(X1,carryin)) = a16,
inference(spm,[status(thm)],[c_0_103,c_0_153]) ).
cnf(c_0_393,negated_conjecture,
or(a13,and(carryin,c1)) = or(a,a16),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_371,c_0_372]),c_0_371]),c_0_282]),c_0_51]) ).
cnf(c_0_394,negated_conjecture,
or(carryin,or(X1,a16)) = or(X1,a16),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_153]),c_0_182]) ).
cnf(c_0_395,plain,
or(X1,and(X2,not(and(X3,X1)))) = or(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_115]),c_0_138]),c_0_51]) ).
cnf(c_0_396,negated_conjecture,
not(or(carryin,c1)) = and(a11,not(carryin)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_373]),c_0_49]),c_0_55]),c_0_374]) ).
cnf(c_0_397,negated_conjecture,
or(c1,and(a13,not(a))) = a16,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_375]),c_0_160]),c_0_113]),c_0_132]),c_0_191]) ).
cnf(c_0_398,negated_conjecture,
or(a12,a16) = or(b,a16),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_376]),c_0_168]),c_0_358]),c_0_51]),c_0_197]) ).
cnf(c_0_399,negated_conjecture,
or(c1,not(a)) = or(a12,and(carryin,a14)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_324]),c_0_92]) ).
cnf(c_0_400,negated_conjecture,
or(a12,and(a11,c1)) = or(c1,a12),
inference(rw,[status(thm)],[c_0_377,c_0_244]) ).
cnf(c_0_401,negated_conjecture,
and(a14,and(a15,not(X1))) = not(or(X1,a16)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_82]),c_0_55]) ).
cnf(c_0_402,negated_conjecture,
and(a16,or(a14,c1)) = c1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_270]),c_0_73]),c_0_73]),c_0_378]),c_0_45]) ).
cnf(c_0_403,negated_conjecture,
~ circuit(or(and(carryin,not(or(and(a,and(a11,a13)),and(b,not(a))))),and(not(carryin),or(and(a,and(a11,a13)),and(b,not(a))))),or(and(a,or(b,carryin)),and(and(b,carryin),not(a)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_379,c_0_236]),c_0_236]) ).
cnf(c_0_404,negated_conjecture,
and(and(a11,a),and(a11,a13)) = and(a11,a),
inference(spm,[status(thm)],[c_0_75,c_0_380]) ).
cnf(c_0_405,negated_conjecture,
or(and(a15,carryin),and(a15,a16)) = and(a15,a16),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_381,c_0_132]),c_0_132]) ).
cnf(c_0_406,negated_conjecture,
and(a14,and(b,and(a11,carryin))) = and(b,and(a11,carryin)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_344,c_0_200]),c_0_51]),c_0_382]),c_0_51]),c_0_365]),c_0_383]),c_0_45]),c_0_55]),c_0_384]),c_0_55]) ).
cnf(c_0_407,negated_conjecture,
or(a,and(X1,a11)) = or(X1,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_320,c_0_385]),c_0_322]),c_0_51]) ).
cnf(c_0_408,negated_conjecture,
or(a,and(X1,a12)) = or(X1,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_386]),c_0_138]),c_0_51]) ).
cnf(c_0_409,negated_conjecture,
and(c1,a12) = and(b,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_387,c_0_388]),c_0_389]) ).
cnf(c_0_410,negated_conjecture,
or(a14,and(a11,and(b,c1))) = a14,
inference(spm,[status(thm)],[c_0_57,c_0_390]) ).
cnf(c_0_411,plain,
and(not(X1),and(and(X1,X2),X3)) = n0,
inference(rw,[status(thm)],[c_0_391,c_0_45]) ).
cnf(c_0_412,negated_conjecture,
and(carryin,and(X1,a16)) = and(X1,carryin),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_392]),c_0_49]) ).
cnf(c_0_413,negated_conjecture,
or(carryin,a13) = or(a,a16),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_322,c_0_393]),c_0_394]),c_0_51]) ).
cnf(c_0_414,negated_conjecture,
not(or(a,a16)) = and(b,and(a11,a15)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_374,c_0_63]),c_0_78]),c_0_51]),c_0_282]),c_0_55]) ).
cnf(c_0_415,negated_conjecture,
or(a13,and(X1,a11)) = or(X1,a13),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_395,c_0_204]),c_0_48]) ).
cnf(c_0_416,negated_conjecture,
not(or(carryin,c1)) = and(a11,and(a15,a17)),
inference(rw,[status(thm)],[c_0_396,c_0_299]) ).
cnf(c_0_417,negated_conjecture,
or(b,and(carryin,c1)) = or(b,c1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_355]),c_0_51]) ).
cnf(c_0_418,negated_conjecture,
or(c1,a12) = or(b,a16),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_397]),c_0_51]),c_0_336]),c_0_357]),c_0_398]),c_0_399]),c_0_244]),c_0_400]) ).
cnf(c_0_419,negated_conjecture,
or(c1,not(a)) = or(c1,a12),
inference(rw,[status(thm)],[c_0_399,c_0_377]) ).
cnf(c_0_420,negated_conjecture,
not(or(a12,a16)) = and(a14,and(a,and(a11,a15))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_401,c_0_89]),c_0_55]) ).
cnf(c_0_421,negated_conjecture,
not(or(b,a16)) = and(a14,and(a15,and(a11,a13))),
inference(spm,[status(thm)],[c_0_401,c_0_236]) ).
cnf(c_0_422,negated_conjecture,
or(a16,not(a)) = or(a12,a16),
inference(rw,[status(thm)],[c_0_336,c_0_357]) ).
cnf(c_0_423,negated_conjecture,
and(a16,or(b,a14)) = c1,
inference(rw,[status(thm)],[c_0_402,c_0_241]) ).
cnf(c_0_424,negated_conjecture,
or(a15,and(a11,a13)) = or(a,a15),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_325]),c_0_94]),c_0_236]),c_0_83]),c_0_51]),c_0_365]) ).
cnf(c_0_425,negated_conjecture,
~ circuit(or(and(carryin,not(or(and(a,and(a11,a13)),and(b,not(a))))),and(not(carryin),or(and(a,and(a11,a13)),and(b,not(a))))),or(and(a,or(b,carryin)),and(carryin,and(b,not(a))))),
inference(rw,[status(thm)],[c_0_403,c_0_49]) ).
cnf(c_0_426,negated_conjecture,
and(a,and(a11,a13)) = and(a11,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_404,c_0_49]),c_0_78]) ).
cnf(c_0_427,negated_conjecture,
and(and(a15,carryin),and(a15,a16)) = and(a15,carryin),
inference(spm,[status(thm)],[c_0_75,c_0_405]) ).
cnf(c_0_428,negated_conjecture,
or(and(a15,carryin),not(X1)) = not(and(X1,a17)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_248]),c_0_51]) ).
cnf(c_0_429,negated_conjecture,
not(or(a,a15)) = and(b,and(a11,carryin)),
inference(rw,[status(thm)],[c_0_383,c_0_406]) ).
cnf(c_0_430,negated_conjecture,
or(a,and(a11,X1)) = or(X1,a),
inference(spm,[status(thm)],[c_0_407,c_0_45]) ).
cnf(c_0_431,negated_conjecture,
or(a,and(b,c1)) = or(a,c1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_408,c_0_409]),c_0_51]) ).
cnf(c_0_432,negated_conjecture,
and(b,and(a11,c1)) = and(a11,and(b,c1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_410]),c_0_49]),c_0_178]),c_0_49]),c_0_384]),c_0_55]) ).
cnf(c_0_433,negated_conjecture,
or(a14,and(X1,a13)) = or(X1,a14),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_395,c_0_384]),c_0_53]) ).
cnf(c_0_434,plain,
and(not(X1),and(X2,and(X1,X3))) = n0,
inference(rw,[status(thm)],[c_0_411,c_0_49]) ).
cnf(c_0_435,negated_conjecture,
and(carryin,and(b,c1)) = and(b,carryin),
inference(spm,[status(thm)],[c_0_412,c_0_330]) ).
cnf(c_0_436,negated_conjecture,
and(X1,not(and(X1,X2))) = and(not(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_294,c_0_52]),c_0_56]),c_0_56]),c_0_45]) ).
cnf(c_0_437,negated_conjecture,
and(b,and(a11,and(a15,a17))) = and(b,and(a11,a15)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_299]),c_0_413]),c_0_414]) ).
cnf(c_0_438,negated_conjecture,
or(a13,and(a11,X1)) = or(X1,a13),
inference(spm,[status(thm)],[c_0_415,c_0_45]) ).
cnf(c_0_439,negated_conjecture,
not(and(a11,and(a15,a17))) = or(carryin,c1),
inference(spm,[status(thm)],[c_0_56,c_0_416]) ).
cnf(c_0_440,negated_conjecture,
or(and(X1,c1),not(X1)) = or(c1,not(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_128]),c_0_56]),c_0_97]),c_0_51]),c_0_51]) ).
cnf(c_0_441,negated_conjecture,
or(a12,and(carryin,c1)) = or(b,a16),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_358,c_0_417]),c_0_358]),c_0_418]),c_0_51]) ).
cnf(c_0_442,negated_conjecture,
not(or(c1,a12)) = and(a,and(a11,a15)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_419]),c_0_114]),c_0_49]),c_0_55]) ).
cnf(c_0_443,negated_conjecture,
and(a14,and(a15,and(a11,a13))) = and(a14,and(a,and(a11,a15))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_420,c_0_398]),c_0_421]) ).
cnf(c_0_444,negated_conjecture,
or(a16,not(a)) = or(b,a16),
inference(rw,[status(thm)],[c_0_422,c_0_398]) ).
cnf(c_0_445,negated_conjecture,
and(X1,and(X2,or(X1,X3))) = and(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_134]),c_0_87]),c_0_55]) ).
cnf(c_0_446,negated_conjecture,
and(a16,or(a,b)) = c1,
inference(rw,[status(thm)],[c_0_423,c_0_256]) ).
cnf(c_0_447,negated_conjecture,
or(a13,and(a11,a15)) = or(a,a15),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_347]),c_0_236]),c_0_424]),c_0_114]) ).
cnf(c_0_448,negated_conjecture,
~ circuit(or(and(carryin,not(or(and(a11,a),and(b,not(a))))),and(not(carryin),or(and(a11,a),and(b,not(a))))),or(and(a,or(b,carryin)),and(carryin,and(b,not(a))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_425,c_0_426]),c_0_426]) ).
cnf(c_0_449,negated_conjecture,
and(carryin,and(a15,a16)) = and(a15,carryin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_427,c_0_49]),c_0_78]) ).
cnf(c_0_450,negated_conjecture,
and(a14,not(carryin)) = and(a15,a14),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_401,c_0_151]),c_0_165]),c_0_82]) ).
cnf(c_0_451,negated_conjecture,
or(and(a15,carryin),and(a15,a14)) = s1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_428,c_0_82]),c_0_249]) ).
cnf(c_0_452,negated_conjecture,
or(a,and(b,and(a11,carryin))) = or(a,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_352,c_0_429]),c_0_92]),c_0_244]),c_0_430]),c_0_51]) ).
cnf(c_0_453,negated_conjecture,
and(c1,and(a11,a12)) = and(a11,and(b,c1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_294,c_0_431]),c_0_294]),c_0_354]),c_0_354]),c_0_49]),c_0_149]),c_0_55]),c_0_432]) ).
cnf(c_0_454,negated_conjecture,
or(a14,and(a13,X1)) = or(X1,a14),
inference(spm,[status(thm)],[c_0_433,c_0_45]) ).
cnf(c_0_455,negated_conjecture,
and(a13,and(a11,and(b,carryin))) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_434,c_0_435]),c_0_236]),c_0_49]) ).
cnf(c_0_456,negated_conjecture,
or(carryin,and(a,b)) = or(carryin,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_396]),c_0_152]),c_0_143]),c_0_51]) ).
cnf(c_0_457,negated_conjecture,
or(not(X1),and(X1,X2)) = or(X2,not(X1)),
inference(spm,[status(thm)],[c_0_202,c_0_45]) ).
cnf(c_0_458,negated_conjecture,
and(b,or(carryin,c1)) = and(b,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_436,c_0_437]),c_0_234]),c_0_92]),c_0_244]),c_0_438]),c_0_282]),c_0_308]),c_0_439]),c_0_45]) ).
cnf(c_0_459,negated_conjecture,
or(and(a11,a13),and(b,c1)) = or(a,a16),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_440,c_0_236]),c_0_281]),c_0_282]),c_0_51]) ).
cnf(c_0_460,negated_conjecture,
and(a,and(a11,not(X1))) = not(or(X1,a12)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_89]),c_0_55]) ).
cnf(c_0_461,negated_conjecture,
or(carryin,a12) = or(b,a16),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_322,c_0_441]),c_0_394]),c_0_51]) ).
cnf(c_0_462,negated_conjecture,
and(a14,and(a,and(a11,a15))) = and(a,and(a11,a15)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_442,c_0_418]),c_0_421]),c_0_443]) ).
cnf(c_0_463,negated_conjecture,
or(a12,and(X1,a11)) = or(X1,a12),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_395,c_0_221]),c_0_48]) ).
cnf(c_0_464,negated_conjecture,
and(a,or(b,a16)) = and(a,a16),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_444]),c_0_56]),c_0_56]),c_0_45]),c_0_45]) ).
cnf(c_0_465,negated_conjecture,
and(a,a16) = and(a,c1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_445,c_0_446]),c_0_45]) ).
cnf(c_0_466,negated_conjecture,
or(a,and(a11,a15)) = or(a,a15),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_322,c_0_351]),c_0_51]) ).
cnf(c_0_467,negated_conjecture,
and(c1,or(a,a15)) = and(c1,a13),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_447]),c_0_97]),c_0_97]),c_0_45]),c_0_45]) ).
cnf(c_0_468,negated_conjecture,
~ circuit(s1,or(and(b,and(a11,carryin)),and(a,or(b,carryin)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_448,c_0_116]),c_0_102]),c_0_113]),c_0_132]),c_0_449]),c_0_116]),c_0_102]),c_0_45]),c_0_450]),c_0_451]),c_0_116]),c_0_55]),c_0_51]) ).
cnf(c_0_469,negated_conjecture,
and(b,and(a11,carryin)) = and(a11,and(b,c1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_294,c_0_452]),c_0_294]),c_0_354]),c_0_453]),c_0_354]),c_0_49]),c_0_149]),c_0_49]),c_0_78]),c_0_55]) ).
cnf(c_0_470,negated_conjecture,
or(a14,and(a11,and(b,carryin))) = a14,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_454,c_0_455]),c_0_71]),c_0_51]) ).
cnf(c_0_471,negated_conjecture,
and(or(X1,X2),or(X2,not(X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_68]),c_0_56]),c_0_56]),c_0_85]),c_0_45]) ).
cnf(c_0_472,negated_conjecture,
or(b,or(carryin,c1)) = or(b,carryin),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_456]),c_0_51]) ).
cnf(c_0_473,negated_conjecture,
or(c1,or(carryin,and(a11,a13))) = or(a,a16),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_457,c_0_458]),c_0_236]),c_0_459]),c_0_236]),c_0_168]) ).
cnf(c_0_474,negated_conjecture,
and(a,and(a11,and(a15,a17))) = and(a,and(a11,a15)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_460,c_0_299]),c_0_461]),c_0_421]),c_0_443]),c_0_462]) ).
cnf(c_0_475,negated_conjecture,
or(a12,and(a11,X1)) = or(X1,a12),
inference(spm,[status(thm)],[c_0_463,c_0_45]) ).
cnf(c_0_476,negated_conjecture,
and(a,or(b,a16)) = and(a,c1),
inference(rw,[status(thm)],[c_0_464,c_0_465]) ).
cnf(c_0_477,negated_conjecture,
and(c1,a13) = and(a,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_466]),c_0_97]),c_0_45]),c_0_467]),c_0_97]) ).
cnf(c_0_478,negated_conjecture,
~ circuit(s1,or(and(a11,and(b,c1)),and(a,or(b,carryin)))),
inference(rw,[status(thm)],[c_0_468,c_0_469]) ).
cnf(c_0_479,negated_conjecture,
and(a11,and(b,c1)) = and(a11,and(b,carryin)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_470]),c_0_49]),c_0_178]),c_0_49]),c_0_384]),c_0_55]),c_0_469]) ).
cnf(c_0_480,negated_conjecture,
and(X1,and(or(X1,X2),X3)) = and(X3,X1),
inference(spm,[status(thm)],[c_0_445,c_0_45]) ).
cnf(c_0_481,negated_conjecture,
and(or(a,a16),or(b,carryin)) = or(carryin,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_471,c_0_472]),c_0_236]),c_0_168]),c_0_473]),c_0_45]) ).
cnf(c_0_482,negated_conjecture,
and(a,or(carryin,c1)) = and(a,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_436,c_0_474]),c_0_324]),c_0_92]),c_0_244]),c_0_475]),c_0_418]),c_0_476]),c_0_439]),c_0_45]) ).
cnf(c_0_483,negated_conjecture,
or(and(X1,X2),not(X2)) = or(X1,not(X2)),
inference(spm,[status(thm)],[c_0_51,c_0_202]) ).
cnf(c_0_484,negated_conjecture,
and(c1,or(a,a15)) = and(a,c1),
inference(rw,[status(thm)],[c_0_467,c_0_477]) ).
cnf(c_0_485,negated_conjecture,
~ circuit(s1,or(and(a11,and(b,carryin)),and(a,or(b,carryin)))),
inference(rw,[status(thm)],[c_0_478,c_0_479]) ).
cnf(c_0_486,negated_conjecture,
and(a,or(b,carryin)) = and(a,c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_480,c_0_481]),c_0_482]),c_0_45]) ).
cnf(c_0_487,negated_conjecture,
or(and(a,c1),and(a11,and(b,carryin))) = c1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_483,c_0_484]),c_0_383]),c_0_469]),c_0_363]),c_0_390]),c_0_383]),c_0_469]),c_0_363]),c_0_390]),c_0_103]),c_0_479]) ).
cnf(c_0_488,negated_conjecture,
circuit(s1,c1),
the_output_circuit ).
cnf(c_0_489,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_485,c_0_486]),c_0_51]),c_0_487]),c_0_488])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HWV003-1 : TPTP v9.2.1. Released v1.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.33 % Computer : n010.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Mon May 4 19:10:06 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 16.22/10.05 % Version : CSE_E---1.7
% 16.22/10.05 % Problem : theBenchmark.p
% 16.22/10.05 % SZS status Unsatisfiable for theBenchmark.p
% 16.22/10.05 % SZS output start CNFRefutation
% See solution above
% 16.22/10.11 % Total time : 7.384s
%------------------------------------------------------------------------------